test_torch.py

import sys
import io
import inspect
import math
import random
import re
import copy
import torch
import torch.cuda
import torch.backends.cuda
import tempfile
import unittest
import warnings
import types
import pickle
import textwrap
from torch.utils.dlpack import from_dlpack, to_dlpack
from torch._six import inf, nan, string_classes, istuple
from itertools import product, combinations, combinations_with_replacement, permutations
from functools import reduce
from random import randrange
from torch import multiprocessing as mp
from torch.testing._internal.common_methods_invocations import tri_tests_args, run_additional_tri_tests, \
    _compare_trilu_indices
from torch.testing._internal.common_utils import TestCase, iter_indices, TEST_NUMPY, TEST_SCIPY, TEST_MKL, \
    TEST_LIBROSA, TEST_WITH_ROCM, run_tests, skipIfNoLapack, suppress_warnings, \
    IS_WINDOWS, NO_MULTIPROCESSING_SPAWN, do_test_dtypes, do_test_empty_full, \
    IS_SANDCASTLE, load_tests, slowTest, skipCUDANonDefaultStreamIf, skipCUDAMemoryLeakCheckIf, \
    BytesIOContext, skipIfRocm, torch_to_numpy_dtype_dict
from multiprocessing.reduction import ForkingPickler
from torch.testing._internal.common_device_type import instantiate_device_type_tests, \
    skipCPUIfNoLapack, skipCPUIfNoMkl, skipCUDAIfNoMagma, skipCUDAIfRocm, skipCUDAIfNotRocm, onlyCUDA, onlyCPU, \
    dtypes, dtypesIfCUDA, dtypesIfCPU, deviceCountAtLeast, skipCUDAIf, precisionOverride, \
    PYTORCH_CUDA_MEMCHECK, largeCUDATensorTest, onlyOnCPUAndCUDA
import torch.backends.quantized
import torch.testing._internal.data


# load_tests from torch.testing._internal.common_utils is used to automatically filter tests for
# sharding on sandcastle. This line silences flake warnings
load_tests = load_tests

if TEST_NUMPY:
    import numpy as np

if TEST_SCIPY:
    import scipy
    from scipy import signal

if TEST_LIBROSA:
    import librosa

SIZE = 100

# This is intentionally prefixed by an underscore. Otherwise pytest will try to
# run its methods as test cases.
class _TestTorchMixin(object):
    def _make_tensors(self, shape, val_range=(-100, 100), use_floating=True, use_integral=True):
        float_types = [torch.double,
                       torch.float]
        int_types = [torch.int64,
                     torch.int32,
                     torch.int16]

        def make_contiguous(shape, dtype):
            if dtype in float_types:
                val = torch.randn(shape, dtype=dtype)
                val = val * ((val_range[1] - val_range[0]) / (math.pi * 2.0))
                val = val + ((val_range[1] - val_range[0]) / 2.0)
                val = torch.clamp(val, min=val_range[0], max=val_range[1])
                return val
            result = torch.zeros(shape, dtype=dtype)
            result.apply_(lambda x: random.randint(val_range[0], val_range[1]))
            return result

        def make_non_contiguous(shape, dtype):
            contig = make_contiguous(shape, dtype)
            non_contig = torch.empty(shape + (2, 2), dtype=dtype)[..., 0]
            non_contig = non_contig.select(-1, -1)
            non_contig.copy_(contig)
            self.assertFalse(non_contig.is_contiguous())
            return non_contig

        def make_contiguous_slice(size, dtype):
            contig = make_contiguous((1, size), dtype)
            non_contig = contig[:1, 1:size - 1]
            self.assertTrue(non_contig.is_contiguous())
            return contig

        types = []
        if use_floating:
            types += float_types
        if use_integral:
            types += int_types
        tensors = {"cont": [], "noncont": [], "slice": []}
        for dtype in types:
            tensors["cont"].append(make_contiguous(shape, dtype))
            tensors["noncont"].append(make_non_contiguous(shape, dtype))
            tensors["slice"].append(make_contiguous_slice(sum(list(shape)), dtype))

        return tensors

    def test_dir(self):
        dir(torch)

    def test_type_conversion_via_dtype_name(self):
        x = torch.tensor([1])
        self.assertEqual(x.byte().dtype, torch.uint8)
        self.assertEqual(x.bool().dtype, torch.bool)
        self.assertEqual(x.char().dtype, torch.int8)
        self.assertEqual(x.double().dtype, torch.float64)
        self.assertEqual(x.float().dtype, torch.float32)
        self.assertEqual(x.half().dtype, torch.float16)
        self.assertEqual(x.int().dtype, torch.int32)
        self.assertEqual(x.bfloat16().dtype, torch.bfloat16)

    def test_doc_template(self):
        from torch._torch_docs import __file__ as doc_file
        from torch._torch_docs import multi_dim_common, single_dim_common, factory_common_args, factory_like_common_args

        with open(doc_file, "r") as f:
            doc_strs = f.read()

        for doc_str in re.findall(r'add_docstr\((.*?),.*?("""|\'\'\')(.*?)("""|\'\'\')\)', doc_strs, re.MULTILINE | re.DOTALL):
            for common_args in [multi_dim_common, single_dim_common, factory_common_args, factory_like_common_args]:
                for k, v in common_args.items():
                    self.assertNotIn(v, doc_str[2], 'The argument description "{}" in {} can be '
                                                    'replaced by {{{}}}'.format(v, doc_str[0], k))

    def test_doc(self):
        checked_types = (types.MethodType, types.FunctionType,
                         types.BuiltinFunctionType, types.BuiltinMethodType)

        def test_namespace(ns, *skips):
            if isinstance(ns, object):
                ns_name = ns.__class__.__name__
            else:
                ns_name = ns.__name__
            skip_regexes = []
            for r in skips:
                if isinstance(r, string_classes):
                    skip_regexes.append(re.compile('^{}$'.format(re.escape(r))))
                else:
                    skip_regexes.append(r)
            skipnames = ['copy_real', 'copy_imag']
            for name in dir(ns):
                if name.startswith('_') or name in skipnames:
                    continue
                var = getattr(ns, name)
                if not isinstance(var, checked_types):
                    continue
                doc = var.__doc__
                has_doc = doc is not None and len(doc.strip()) > 0
                full_name = ns_name + '.' + name
                if any(r.match(name) for r in skip_regexes):
                    self.assertFalse(has_doc,
                                     'New docs have been added for {}, please remove '
                                     'it from the skipped list in TestTorch.test_doc'.format(full_name))
                else:
                    self.assertTrue(has_doc, '{} is missing documentation'.format(full_name))

        # FIXME: All of the following should be marked as expected failures
        # so that it is easier to tell when missing has been added.
        # FIXME: fix all the skipped ones below!
        test_namespace(torch.randn(1),
                       'as_strided_',
                       re.compile('^clamp_(min|max)_?$'),
                       'coalesce',
                       'is_coalesced',
                       'is_distributed',
                       'is_nonzero',
                       'is_same_size',
                       'log_softmax',
                       'map2_',
                       'new',
                       'reinforce',
                       'relu',
                       'relu_',
                       'prelu',
                       'resize',
                       'resize_as',
                       'smm',
                       'softmax',
                       'split_with_sizes',
                       'sspaddmm',
                       'to_dense',
                       'sparse_resize_',
                       'sparse_resize_and_clear_',
                       )
        test_namespace(torch.nn)
        test_namespace(torch.nn.functional, 'assert_int_or_pair')
        # TODO: add torch.* tests when we have proper namespacing on ATen functions
        # test_namespace(torch)

    def test_linear_algebra_scalar_raises(self):
        m = torch.randn(5, 5)
        v = torch.randn(5)
        s = torch.tensor(7)
        self.assertRaises(RuntimeError, lambda: torch.mv(m, s))
        self.assertRaises(RuntimeError, lambda: torch.addmv(v, m, s))
        self.assertRaises(RuntimeError, lambda: torch.ger(v, s))
        self.assertRaises(RuntimeError, lambda: torch.ger(s, v))
        self.assertRaises(RuntimeError, lambda: torch.addr(m, v, s))
        self.assertRaises(RuntimeError, lambda: torch.addr(m, s, v))

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_mvlgamma(self):
        from scipy.special import multigammaln
        for d in range(1, 5):
            input = torch.empty(10).uniform_(d, 10)
            res_torch = torch.mvlgamma(input, d)
            res_scipy = multigammaln(input.numpy(), d)
            self.assertEqual(res_torch.numpy(), res_scipy, atol=1e-5)

    def test_mvlgamma_argcheck(self):
        def run_test(d):
            input = torch.linspace((d - 2) / 2, 10, 10)
            torch.mvlgamma(input, d)

        with self.assertRaisesRegex(RuntimeError, r"All elements must be greater than \(p-1\)/2"):
            run_test(3)

    def test_msnpu_error(self):
        with self.assertRaisesRegex(RuntimeError, "support for msnpu"):
            torch.zeros(1, device=torch.device('msnpu'))

    def test_polygamma_neg(self):
        with self.assertRaisesRegex(RuntimeError, r'polygamma\(n, x\) does not support negative n\.'):
            torch.polygamma(-1, torch.tensor([1.0, 2.0]))


    def test_has_storage(self):
        self.assertIsNotNone(torch.Tensor().storage())
        self.assertIsNotNone(torch.Tensor(0).storage())
        self.assertIsNotNone(torch.Tensor([]).storage())
        self.assertIsNotNone(torch.Tensor().clone().storage())
        self.assertIsNotNone(torch.Tensor([0, 0, 0]).nonzero().storage())
        self.assertIsNotNone(torch.Tensor().new().storage())

    def _testSelection(self, torchfn, mathfn):
        # contiguous
        m1 = torch.randn(100, 100)
        res1 = torchfn(m1)
        res2 = m1[0, 0]
        for i, j in iter_indices(m1):
            res2 = mathfn(res2, m1[i, j])
        self.assertEqual(res1, res2)

        # non-contiguous
        m1 = torch.randn(10, 10, 10)
        m2 = m1[:, 4]
        res1 = torchfn(m2)
        res2 = m2[0, 0]
        for i, j in iter_indices(m2):
            res2 = mathfn(res2, m2[i][j])
        self.assertEqual(res1, res2)

        # with indices
        m1 = torch.randn(100, 100)
        res1val, res1ind = torchfn(m1, 1, False)
        res2val = m1[:, 0:1].clone().squeeze()
        res2ind = res1ind.clone().fill_(0)
        for i, j in iter_indices(m1):
            if mathfn(res2val[i], m1[i, j]) != res2val[i]:
                res2val[i] = m1[i, j]
                res2ind[i] = j

        maxerr = 0
        for i in range(res1val.size(0)):
            maxerr = max(maxerr, abs(res1val[i] - res2val[i]))
            self.assertEqual(res1ind[i], res2ind[i])
        self.assertLessEqual(abs(maxerr), 1e-5)

        # NaNs
        for index in (0, 4, 99):
            m1 = torch.randn(100)
            m1[index] = nan
            res1val, res1ind = torch.max(m1, 0)
            self.assertTrue(math.isnan(res1val))
            self.assertEqual(res1ind, index)
            res1val = torchfn(m1)
            self.assertTrue(math.isnan(res1val))

        # Bool
        m1 = torch.tensor([True, False, True], dtype=torch.bool)
        res1 = torchfn(m1)
        res2 = m1[0]
        for i in iter_indices(m1):
            res2 = mathfn(res2, m1[i])
        self.assertEqual(res1, res2)

    def test_max(self):
        self._testSelection(torch.max, max)

    def test_min(self):
        self._testSelection(torch.min, min)

    def test_dim_reduction_uint8_overflow(self):
        example = [[-1, 2, 1], [5, 3, 6]]
        x = torch.tensor(example, dtype=torch.uint8)
        self.assertEqual(x.sum(dtype=torch.uint8).item(), 16)
        self.assertEqual(x.sum(0, dtype=torch.uint8), torch.tensor([4, 5, 7], dtype=torch.uint8))
        self.assertEqual(x.sum(1, dtype=torch.uint8), torch.tensor([2, 14], dtype=torch.uint8))
        y = torch.tensor(example, dtype=torch.uint8)
        torch.sum(x, 0, out=y)
        self.assertEqual(x.sum(0, dtype=torch.uint8), y)

    def test_dim_reduction_less_than_64(self):
        sizes = [1] * 65
        x = torch.randn(sizes)
        with self.assertRaisesRegex(RuntimeError, "PyTorch doesn't support reduction operations for dim>=64"):
            torch.sum(x, 64)
        with self.assertRaisesRegex(RuntimeError, "PyTorch doesn't support reduction operations for dim>=64"):
            torch.sum(x, -1)

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_logsumexp(self):
        from scipy.special import logsumexp
        a = torch.randn(5, 4)
        a[0, 0] = inf
        a[1, :] = -inf
        actual = a.logsumexp(1)
        expected = logsumexp(a.numpy(), 1)
        self.assertEqual(expected.shape, actual.shape)
        self.assertTrue(np.allclose(expected, actual.numpy()))
        # check that out is actually inplace
        b = torch.zeros(5, 2)
        c = b[:, 0]
        torch.logsumexp(a, 1, out=c)
        self.assertTrue(np.allclose(expected, b[:, 0].numpy()))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_cpu_parallel(self):
        # To use parallel branches we'll need to compare on tensors
        # that are relatively large. Even if this is run on a single
        # core machine these tests will still give you signal on
        # the correctness

        def _run_test(size):
            for dim in range(len(size) + 1):
                nv = np.round(np.random.rand(*size))  # 0s and 1s
                tv = torch.from_numpy(nv)
                # Parallelisim is only used if numel is
                # larger than grainsize defined in Parallel.h
                self.assertTrue(tv.numel() > 32768)
                if dim == len(size):
                    nvs = nv.sum()
                    tvs = tv.sum()
                else:
                    nvs = nv.sum(dim)
                    tvs = tv.sum(dim)
                diff = np.abs(nvs - tvs.numpy()).sum()
                self.assertEqual(diff, 0)

        _run_test([2, 3, 3, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3])
        _run_test([4, 4, 4, 4, 4, 4, 4, 4, 4, 4])
        _run_test([1, 32 * 8 * 32 * 8])
        _run_test([1, 32770])

    def _testCSelection(self, torchfn, mathfn):
        # Two tensors
        size = (100, 100)
        a = torch.rand(*size)
        b = torch.rand(*size)
        c = torchfn(a, b)
        expected_c = torch.zeros(*size)
        expected_c.map2_(a, b, lambda _, a, b: mathfn(a, b))
        self.assertEqual(expected_c, c, 0)

    def test_max_elementwise(self):
        self._testCSelection(torch.max, max)

    def test_min_elementwise(self):
        self._testCSelection(torch.min, min)

    def test_all_any(self):
        def test(size):
            x = torch.ones(*size).byte()
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x[3] = 0
            self.assertFalse(x.all())
            self.assertTrue(x.any())

            x.zero_()
            self.assertFalse(x.all())
            self.assertFalse(x.any())

            x.fill_(2)
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x = torch.ones(*size).bool()
            self.assertTrue(x.all())
            self.assertTrue(x.any())

            x[3] = False
            self.assertFalse(x.all())
            self.assertTrue(x.any())

        test((10,))
        test((5, 5))

    def test_where_invalid_device(self):
        if torch.cuda.is_available():
            for devices in [('cpu', 'cuda', 'cuda'), ('cuda', 'cpu', 'cpu'),
                            ('cuda', 'cpu', 'cuda'), ('cpu', 'cuda', 'cpu')]:
                condition = torch.rand(16, device=devices[0])
                x = torch.rand(16, device=devices[1])
                y = torch.rand(16, device=devices[2])
                with self.assertRaisesRegex(RuntimeError,
                                            "Expected condition, x and y to be on the same device"):
                    torch.where(condition, x, y)

    def test_where_bool_tensor(self):
        for d in torch.testing.get_all_device_types():
            a = torch.tensor([True, False], device=d)
            res = torch.where(a > 0)
            self.assertEqual(1, len(res))

    def test_where_tensor(self):
        def rand_tensor(size, dtype, device):
            if dtype.is_floating_point or dtype.is_complex:
                return torch.rand(size=size, dtype=dtype, device=device)
            elif dtype == torch.uint8:
                return torch.randint(1, 5, size=size, dtype=dtype, device=device)
            elif dtype == torch.bool:
                return torch.randint(0, 1, size=size, dtype=dtype, device=device).bool()
            else:
                return torch.randint(-5, 5, size=size, dtype=dtype, device=device)

        def get_tensor(size, dtype, device, contiguous):
            if not contiguous and len(size) < 2:
                raise RuntimeError("Unable to generate non contiguous tensor with size < 2")
            t = rand_tensor(size, dtype, device)
            if contiguous:
                return t
            else:
                return t.transpose(0, 1)

        height = 5
        width = 5
        for device in torch.testing.get_all_device_types():
            for dt1 in torch.testing.get_all_math_dtypes(device):
                for dt2 in torch.testing.get_all_math_dtypes(device):
                    for contiguous in [True, False]:
                        x1 = get_tensor((height, width), dt1, device, contiguous)
                        x2 = get_tensor((height, width), dt2, device, contiguous)
                        if dt1 != dt2:
                            self.assertRaisesRegex(RuntimeError, "expected scalar type", lambda: torch.where(x1 == 1, x1, x2))
                        else:
                            if x1.is_floating_point():
                                condition = (x1 < 0.5)
                            elif x1.is_complex():
                                condition = (x1.abs() < 0.5)
                            else:
                                condition = (x1 == 1)
                            expected = condition.to(x1.dtype) * x1 + (~condition).to(x2.dtype) * x2
                            result = torch.where(condition, x1, x2)
                            self.assertEqual(expected, result)

    def test_all_any_with_dim(self):
        def test(x):
            r1 = x.prod(dim=0, keepdim=False).byte()
            r2 = x.all(dim=0, keepdim=False)
            self.assertEqual(r1.shape, r2.shape)
            self.assertTrue((r1 == r2).all())

            r3 = x.sum(dim=1, keepdim=True).clamp(0, 1).byte()
            r4 = x.any(dim=1, keepdim=True)
            self.assertEqual(r3.shape, r4.shape)
            self.assertTrue((r3 == r4).all())

        test(torch.ByteTensor([[0, 0, 0],
                               [0, 0, 1],
                               [0, 1, 1],
                               [1, 1, 1]]))

    @slowTest
    def test_mv(self):
        def _test_mv(m1, v1):
            res1 = torch.mv(m1, v1)
            res2 = res1.clone().zero_()
            for i, j in iter_indices(m1):
                res2[i] += m1[i][j] * v1[j]

            self.assertEqual(res1, res2, atol=1e-5)

        _test_mv(torch.randn(100, 100, dtype=torch.float32), torch.randn(100, dtype=torch.float32))
        _test_mv(torch.randn(100, 100, dtype=torch.float64), torch.randn(100, dtype=torch.float64))
        _test_mv(torch.randint(0, 100, (100, 100), dtype=torch.int32), torch.randint(0, 100, (100, ), dtype=torch.int32))
        _test_mv(torch.randint(0, 100, (100, 100), dtype=torch.int64), torch.randint(0, 100, (100, ), dtype=torch.int64))
        _test_mv(torch.randn(100, 100, dtype=torch.float32).bfloat16(), torch.randn(100, dtype=torch.float32).bfloat16())

    def test_numpy_args(self):
        x1 = torch.randn(10)
        x2 = torch.randn(10)
        res1 = torch.add(input=x1, other=x2)
        res2 = torch.add(x1=x1, x2=x2)
        self.assertEqual(res1, res2)

        x1 = torch.randn(10, 10, 10)
        res1 = x1.sum(dim=(0, 2), keepdim=True)
        res2 = x1.sum(axis=(0, 2), keepdims=True)
        self.assertEqual(res1, res2)

    def _assert_matches_numpy(self, t, n):
        self.assertEqual(n.shape, t.shape)
        if t.dtype == torch.float:
            self.assertTrue(np.allclose(n, t.numpy(), rtol=1e-03, atol=1e-05,
                                        equal_nan=True))
        else:
            self.assertTrue(np.allclose(n, t.numpy(), equal_nan=True))

    def _test_dim_ops(self, pytorch_op, numpy_op,
                      use_floating=True, use_integral=True):
        def do_one(tensors_dict, dim):
            for category, tensors in tensors_dict.items():
                if category == "slice":
                    dim = 0
                for tensor in tensors:
                    # we have no control over NumPy warnings...
                    with warnings.catch_warnings():
                        warnings.simplefilter("ignore")
                        expected = numpy_op(tensor.numpy(), dim)
                    actual = pytorch_op(tensor, dim)
                    self._assert_matches_numpy(actual, expected)
                    if torch.cuda.is_available():
                        self._assert_matches_numpy(pytorch_op(tensor.cuda(),
                                                              dim).cpu(),
                                                   expected)
        do_one(self._make_tensors((5, 400000), use_floating=use_floating,
                                  use_integral=use_integral), 1)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
                                  use_integral=use_integral), 0)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
                                  use_integral=use_integral), 1)
        do_one(self._make_tensors((3, 5, 7), use_floating=use_floating,
                                  use_integral=use_integral), 2)
        do_one(self._make_tensors((100000, ), use_floating=use_floating,
                                  use_integral=use_integral), -1)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), 0)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), 1)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), 2)
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), (1, 2))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), (1, -1))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), (0, 2))
        do_one(self._make_tensors((50, 50, 50), use_floating=use_floating,
                                  use_integral=use_integral), (0, 2, 1))

    @slowTest
    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_sum_dim(self):
        self._test_dim_ops(
            lambda t, d: t.sum(d),
            lambda n, d: n.sum(d))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_mean_dim(self):
        self._test_dim_ops(
            lambda t, d: t.mean(d),
            lambda n, d: n.mean(d),
            use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_std_dim(self):
        for unbiased in [False, True]:
            self._test_dim_ops(
                lambda t, d: t.std(d, unbiased=unbiased),
                lambda n, d: n.std(d, ddof=1 if unbiased else 0),
                use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_var_dim(self):
        for unbiased in [False, True]:
            self._test_dim_ops(
                lambda t, d: t.var(d, unbiased=unbiased),
                lambda n, d: n.var(d, ddof=1 if unbiased else 0),
                use_integral=False)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    @unittest.skipIf(not TEST_SCIPY, 'Scipy not found')
    def test_logsumexp_dim(self):
        from scipy.special import logsumexp
        self._test_dim_ops(
            lambda t, d: t.logsumexp(d),
            lambda n, d: logsumexp(n, d),
            use_integral=False)

    def _test_reduce_integer_upcast(self, fn, has_out=True, test_complex=True):
        shape = (3, 4, 5)
        reduced_shape = fn(torch.ones(shape)).shape

        def _test_out(dtype, other_dtype):
            out = torch.ones(reduced_shape, dtype=dtype)
            result = fn(x, out=out)
            self.assertIs(out.dtype, result.dtype)
            self.assertEqual(fn(x.to(dtype)), result, exact_dtype=False)
            result = fn(x, out=out, dtype=dtype)
            self.assertIs(out.dtype, result.dtype)
            self.assertEqual(fn(x.to(dtype)), result, exact_dtype=False)
            # 'out' is favored over dtype, check error
            self.assertRaises(RuntimeError, lambda: fn(x, out=out, dtype=other_dtype))

        for dtype in [dtype for dtype in torch.testing.get_all_math_dtypes('cpu') if dtype != torch.float16]:
            x = torch.ones(shape, dtype=dtype)
            expected_dtype = dtype if dtype.is_floating_point or dtype.is_complex else torch.int64
            self.assertIs(expected_dtype, fn(x).dtype)
            self.assertEqual(fn(x.to(expected_dtype)), fn(x))

            if dtype.is_floating_point:
                other_dtype = torch.float32 if dtype == torch.float64 else torch.float64
            elif dtype.is_complex:
                other_dtype = torch.complex64 if dtype == torch.complex128 else torch.complex128
            else:
                other_dtype = torch.int32 if dtype != torch.int32 else torch.int16
            self.assertIs(other_dtype, fn(x, dtype=other_dtype).dtype)
            self.assertEqual(fn(x.to(other_dtype)), fn(x, dtype=other_dtype), exact_dtype=False)

            # test mixed int/float/complex
            if dtype.is_floating_point:
                mixed_dtypes = [torch.int32, torch.complex64]
            elif dtype.is_complex:
                mixed_dtypes = [torch.int32, torch.float32]
            else:
                mixed_dtypes = [torch.float32, torch.complex64]

            for mixed_dtype in mixed_dtypes:
                self.assertIs(mixed_dtype, fn(x, dtype=mixed_dtype).dtype)
                self.assertEqual(fn(x.to(mixed_dtype)), fn(x, dtype=mixed_dtype), exact_dtype=False)

                if has_out:
                    _test_out(dtype, other_dtype)
                    _test_out(dtype, mixed_dtype)

    def test_sum_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.sum(x, **kwargs), False)
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.sum(x, 0, **kwargs))

    def test_prod_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.prod(x, **kwargs), False)
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.prod(x, 0, **kwargs))

    def test_cumsum_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.cumsum(x, 0, **kwargs))

    def test_cumprod_integer_upcast(self):
        self._test_reduce_integer_upcast(lambda x, **kwargs: torch.cumprod(x, 0, **kwargs))

    def test_cross_validation(self):
        self.assertRaisesRegex(
            RuntimeError, "inconsistent tensors dimensions",
            lambda: torch.cross(torch.rand(100, 3), torch.rand(100, 3, 10)))
        self.assertRaisesRegex(
            RuntimeError, "inconsistent tensors sizes",
            lambda: torch.cross(torch.rand(5, 3), torch.rand(3, 5)))
        self.assertRaisesRegex(
            RuntimeError, "no dimension of size 3 in input",
            lambda: torch.cross(torch.rand(5, 4), torch.rand(5, 4)))
        self.assertRaisesRegex(
            RuntimeError, "dimension 0 does not have size 3",
            lambda: torch.cross(torch.rand(5, 4, 3), torch.rand(5, 4, 3), dim=0))
        self.assertRaisesRegex(
            RuntimeError, "dimension -1 does not have size 3",
            lambda: torch.cross(torch.rand(5, 3, 4), torch.rand(5, 3, 4), dim=-1))
        self.assertRaisesRegex(
            IndexError, "Dimension out of range",
            lambda: torch.cross(torch.rand(5, 3, 4), torch.rand(5, 3, 4), dim=-5))

    def test_zeros(self):
        res1 = torch.zeros(100, 100)
        res2 = torch.Tensor()
        torch.zeros(100, 100, out=res2)
        self.assertEqual(res1, res2)

        boolTensor = torch.zeros(2, 2, dtype=torch.bool)
        expected = torch.tensor([[False, False], [False, False]], dtype=torch.bool)
        self.assertEqual(boolTensor, expected)

        halfTensor = torch.zeros(1, 1, dtype=torch.half)
        expected = torch.tensor([[0.]], dtype=torch.float16)
        self.assertEqual(halfTensor, expected)

        bfloat16Tensor = torch.zeros(1, 1, dtype=torch.bfloat16)
        expected = torch.tensor([[0.]], dtype=torch.bfloat16)
        self.assertEqual(bfloat16Tensor, expected)

        complexTensor = torch.zeros(2, 2, dtype=torch.complex64)
        expected = torch.tensor([[0., 0.], [0., 0.]], dtype=torch.complex64)
        self.assertEqual(complexTensor, expected)

    def test_zeros_out(self):
        shape = (3, 4)
        out = torch.zeros(shape)
        torch.zeros(shape, out=out)

        # change the dtype, layout, device
        self.assertRaises(RuntimeError, lambda: torch.zeros(shape, dtype=torch.int64, out=out))
        self.assertRaises(RuntimeError, lambda: torch.zeros(shape, layout=torch.sparse_coo, out=out))
        if torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: torch.zeros(shape, device='cuda', out=out))

        # leave them the same
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, dtype=out.dtype, out=out))
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, layout=torch.strided, out=out))
        self.assertEqual(torch.zeros(shape), torch.zeros(shape, device='cpu', out=out))

    def test_ones(self):
        res1 = torch.ones(100, 100)
        res2 = torch.Tensor()
        torch.ones(100, 100, out=res2)
        self.assertEqual(res1, res2)

        # test boolean tensor
        res1 = torch.ones(1, 2, dtype=torch.bool)
        expected = torch.tensor([[True, True]], dtype=torch.bool)
        self.assertEqual(res1, expected)

    def test_ones_like(self):
        expected = torch.ones(100, 100)

        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

        # test boolean tensor
        expected = torch.tensor([True, True], dtype=torch.bool)
        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

    def test_dtypes(self):
        all_dtypes = torch.testing.get_all_dtypes()
        do_test_dtypes(self, all_dtypes, torch.strided, torch.device('cpu'))
        if torch.cuda.is_available():
            all_dtypes.remove(torch.bfloat16)  # Remove once _th_zero_ is enabled on cuda for bfloat16
            do_test_dtypes(self, all_dtypes, torch.strided, torch.device('cuda:0'))

    def test_copy_dtypes(self):
        all_dtypes = torch.testing.get_all_dtypes()
        for dtype in all_dtypes:
            copied_dtype = copy.deepcopy(dtype)
            self.assertIs(dtype, copied_dtype)

    def test_copy_transpose(self):
        x = torch.arange(100 * 100, dtype=torch.float).reshape(100, 100).t()
        y = torch.empty(100, 100, dtype=torch.float)
        y.copy_(x)
        self.assertEqual(y[:, 0], range(100))
        self.assertEqual(y[:, 40], range(4000, 4100))

        y = torch.empty(100, 100, dtype=torch.double)
        y.copy_(x)
        self.assertEqual(y[:, 0], range(100))
        self.assertEqual(y[:, 40], range(4000, 4100))

    def test_device(self):
        cpu = torch.device('cpu')
        self.assertEqual('cpu', str(cpu))
        self.assertEqual('cpu', cpu.type)
        self.assertEqual(None, cpu.index)

        cpu0 = torch.device('cpu:0')
        self.assertEqual('cpu:0', str(cpu0))
        self.assertEqual('cpu', cpu0.type)
        self.assertEqual(0, cpu0.index)

        cpu0 = torch.device('cpu', 0)
        self.assertEqual('cpu:0', str(cpu0))
        self.assertEqual('cpu', cpu0.type)
        self.assertEqual(0, cpu0.index)

        cuda = torch.device('cuda')
        self.assertEqual('cuda', str(cuda))
        self.assertEqual('cuda', cuda.type)
        self.assertEqual(None, cuda.index)

        cuda1 = torch.device('cuda:1')
        self.assertEqual('cuda:1', str(cuda1))
        self.assertEqual('cuda', cuda1.type)
        self.assertEqual(1, cuda1.index)

        cuda1 = torch.device('cuda', 1)
        self.assertEqual('cuda:1', str(cuda1))
        self.assertEqual('cuda', cuda1.type)
        self.assertEqual(1, cuda1.index)

        self.assertRaises(RuntimeError, lambda: torch.device('cpu:-1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu:1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu', -1))
        self.assertRaises(RuntimeError, lambda: torch.device('cpu', 1))
        self.assertRaises(RuntimeError, lambda: torch.device('cuda:-1'))
        self.assertRaises(RuntimeError, lambda: torch.device('cuda', -1))
        self.assertRaises(RuntimeError, lambda: torch.device(-1))

        self.assertRaises(RuntimeError, lambda: torch.device('other'))
        self.assertRaises(RuntimeError, lambda: torch.device('other:0'))

        device_set = {'cpu', 'cpu:0', 'cuda', 'cuda:0', 'cuda:1', 'cuda:10', 'cuda:100'}
        device_hash_set = set()
        for device in list(device_set):
            device_hash_set.add(hash(torch.device(device)))
        self.assertEqual(len(device_set), len(device_hash_set))

    def test_tensor_device(self):
        def assertEqual(device_str, fn):
            self.assertEqual(torch.device(device_str), fn().device)
            self.assertEqual(device_str, str(fn().device))

        assertEqual('cpu', lambda: torch.tensor(5))
        assertEqual('cpu', lambda: torch.ones((2, 3), dtype=torch.float32, device='cpu'))
        # NOTE: 'cpu' is the canonical representation of 'cpu:0', but 'cuda:X' is the canonical
        # representation of cuda devices.
        assertEqual('cpu', lambda: torch.ones((2, 3), dtype=torch.float32, device='cpu:0'))
        assertEqual('cpu', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cpu:0'))
        if TEST_NUMPY:
            assertEqual('cpu', lambda: torch.tensor(np.random.randn(2, 3), device='cpu'))

        if torch.cuda.is_available():
            assertEqual('cuda:0', lambda: torch.tensor(5).cuda(0))
            assertEqual('cuda:0', lambda: torch.tensor(5).cuda('cuda:0'))
            self.assertRaises(RuntimeError, lambda: torch.tensor(5).cuda('cpu'))
            self.assertRaises(RuntimeError, lambda: torch.tensor(5).cuda('cpu:0'))
            assertEqual('cuda:0', lambda: torch.tensor(5, dtype=torch.int64, device=0))
            assertEqual('cuda:0', lambda: torch.tensor(5, dtype=torch.int64, device='cuda:0'))
            assertEqual('cuda:' + str(torch.cuda.current_device()),
                        lambda: torch.tensor(5, dtype=torch.int64, device='cuda'))
            assertEqual('cuda:0', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cuda:0'))
            if TEST_NUMPY:
                assertEqual('cuda:0', lambda: torch.tensor(np.random.randn(2, 3), device='cuda:0'))

            if torch.cuda.device_count() > 1:
                assertEqual('cuda:1', lambda: torch.tensor(5).cuda(1))
                assertEqual('cuda:1', lambda: torch.tensor(5).cuda('cuda:1'))
                assertEqual('cuda:1', lambda: torch.tensor(5, dtype=torch.int64, device=1))
                assertEqual('cuda:1', lambda: torch.tensor(5, dtype=torch.int64, device='cuda:1'))
                assertEqual('cuda:1', lambda: torch.tensor(torch.ones((2, 3), dtype=torch.float32), device='cuda:1'))
                if TEST_NUMPY:
                    assertEqual('cuda:1', lambda: torch.tensor(np.random.randn(2, 3), device='cuda:1'))

    def test_to(self):
        def test_copy_behavior(t, non_blocking=False):
            self.assertIs(t, t.to(t, non_blocking=non_blocking))
            self.assertIs(t, t.to(t.dtype, non_blocking=non_blocking))
            self.assertIs(t, t.to(torch.empty_like(t), non_blocking=non_blocking))
            self.assertIsNot(t, t.to(t, non_blocking=non_blocking, copy=True))
            self.assertIsNot(t, t.to(t.dtype, non_blocking=non_blocking, copy=True))
            self.assertIsNot(t, t.to(torch.empty_like(t), non_blocking=non_blocking, copy=True))

            devices = [t.device]
            if t.device.type == 'cuda':
                if t.device.index == -1:
                    devices.append('cuda:{}'.format(torch.cuda.current_device()))
                elif t.device.index == torch.cuda.current_device():
                    devices.append('cuda')
            for device in devices:
                self.assertIs(t, t.to(device, non_blocking=non_blocking))
                self.assertIs(t, t.to(device, t.dtype, non_blocking=non_blocking))
                self.assertIsNot(t, t.to(device, non_blocking=non_blocking, copy=True))
                self.assertIsNot(t, t.to(device, t.dtype, non_blocking=non_blocking, copy=True))

        a = torch.tensor(5)
        test_copy_behavior(a)
        self.assertEqual(a.device, a.to('cpu').device)
        self.assertEqual(a.device, a.to('cpu', dtype=torch.float32).device)
        self.assertIs(torch.float32, a.to('cpu', dtype=torch.float32).dtype)
        self.assertEqual(a.device, a.to(torch.float32).device)
        self.assertIs(torch.float32, a.to(dtype=torch.float32).dtype)
        self.assertEqual(a.data_ptr(), a.to('cpu').data_ptr())
        self.assertEqual(a.data_ptr(), a.to(dtype=a.dtype, device=a.device, copy=False).data_ptr())
        self.assertEqual(a.data_ptr(), a.to('cpu', copy=False).data_ptr())
        self.assertNotEqual(a.data_ptr(), a.to('cpu', copy=True).data_ptr())

        if torch.cuda.is_available():
            for non_blocking in [True, False]:
                for cuda in ['cuda', 'cuda:0' if torch.cuda.device_count() == 1 else 'cuda:1']:
                    b = torch.tensor(5., device=cuda)
                    test_copy_behavior(b, non_blocking)
                    self.assertEqual(b.device, b.to(cuda, non_blocking=non_blocking).device)
                    self.assertEqual(a.device, b.to('cpu', non_blocking=non_blocking).device)
                    self.assertEqual(b.device, a.to(cuda, non_blocking=non_blocking).device)
                    self.assertIs(torch.int32, b.to('cpu', dtype=torch.int32, non_blocking=non_blocking).dtype)
                    self.assertEqual(a.device, b.to('cpu', dtype=torch.int32, non_blocking=non_blocking).device)
                    self.assertIs(torch.int32, b.to(dtype=torch.int32).dtype)
                    self.assertEqual(b.device, b.to(dtype=torch.int32).device)

    def test_to_with_tensor(self):
        a = torch.tensor(5)
        self.assertEqual(a.device, a.to(a).device)

        if torch.cuda.is_available():
            for non_blocking in [True, False]:
                for cuda in ['cuda', 'cuda:0' if torch.cuda.device_count() == 1 else 'cuda:1']:
                    b = torch.tensor(5., device=cuda)
                    self.assertEqual(b.device, b.to(b, non_blocking=non_blocking).device)
                    self.assertEqual(a.device, b.to(a, non_blocking=non_blocking).device)
                    self.assertEqual(b.device, a.to(b, non_blocking=non_blocking).device)

    def test_empty_full(self):
        do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, torch.device('cpu'))
        if torch.cuda.device_count() > 0:
            do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, None)
            do_test_empty_full(self, torch.testing.get_all_math_dtypes('cpu'), torch.strided, torch.device('cuda:0'))

    def test_dtype_out_match(self):
        d = torch.autograd.Variable(torch.DoubleTensor(2, 3))
        self.assertRaises(RuntimeError, lambda: torch.zeros((2, 3), out=d, dtype=torch.float32))

    def test_as_subclass(self):
        class SubTensor(torch.Tensor):
            member_var = object()

        t0 = torch.tensor(0)
        t1 = torch.tensor([1, 2])
        t2 = torch.tensor([[3, 4], [5, 6]])

        s0 = t0.as_subclass(SubTensor)
        s1 = t1.as_subclass(SubTensor)
        s2 = t2.as_subclass(SubTensor)

        # Check that the correct type is returned.
        self.assertTrue(type(s0) is SubTensor)
        self.assertTrue(type(s1) is SubTensor)
        self.assertTrue(type(s2) is SubTensor)

        # Check that the data is equal.
        self.assertEqual(t0, s0)
        self.assertEqual(t1, s1)
        self.assertEqual(t2, s2)

        t0[()] = 1
        t1[1] = 3
        t2[1, 1] = 7

        # Check that the data is equal even after modification.
        self.assertEqual(t0, s0)
        self.assertEqual(t1, s1)
        self.assertEqual(t2, s2)

        # Check that member variables are passed through.
        self.assertTrue(s0.member_var is SubTensor.member_var)
        self.assertTrue(s1.member_var is SubTensor.member_var)
        self.assertTrue(s2.member_var is SubTensor.member_var)

        # Test that autograd is propagated.
        t = torch.tensor(5, dtype=torch.float32, requires_grad=True)

        # Run a calculation on the tensor.
        exp_t = torch.exp(t)

        # Cast exp_t to a subclass.
        exp_s = exp_t.as_subclass(SubTensor)

        # Make sure that t.grad was initially None
        self.assertTrue(t.grad is None)

        # Run the autograd calculation.
        exp_s.backward()

        # Make sure autograd was propagated to the original tensor
        # declared with requires_grad.
        self.assertTrue(t.grad is not None)

    def test_constructor_dtypes(self):
        default_type = torch.Tensor().type()
        self.assertIs(torch.Tensor().dtype, torch.get_default_dtype())

        self.assertIs(torch.uint8, torch.ByteTensor.dtype)
        self.assertIs(torch.float32, torch.FloatTensor.dtype)
        self.assertIs(torch.float64, torch.DoubleTensor.dtype)

        torch.set_default_tensor_type('torch.FloatTensor')
        self.assertIs(torch.float32, torch.get_default_dtype())
        self.assertIs(torch.FloatStorage, torch.Storage)

        torch.set_default_dtype(torch.float64)
        self.assertIs(torch.float64, torch.get_default_dtype())
        self.assertIs(torch.DoubleStorage, torch.Storage)

        torch.set_default_tensor_type(torch.FloatTensor)
        self.assertIs(torch.float32, torch.get_default_dtype())
        self.assertIs(torch.FloatStorage, torch.Storage)

        if torch.cuda.is_available():
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertIs(torch.float32, torch.get_default_dtype())
            self.assertIs(torch.float32, torch.cuda.FloatTensor.dtype)
            self.assertIs(torch.cuda.FloatStorage, torch.Storage)

            torch.set_default_dtype(torch.float64)
            self.assertIs(torch.float64, torch.get_default_dtype())
            self.assertIs(torch.cuda.DoubleStorage, torch.Storage)

        # don't support integral or sparse default types.
        self.assertRaises(TypeError, lambda: torch.set_default_tensor_type('torch.IntTensor'))
        self.assertRaises(TypeError, lambda: torch.set_default_dtype(torch.int64))

        # don't allow passing dtype to set_default_tensor_type
        self.assertRaises(TypeError, lambda: torch.set_default_tensor_type(torch.float32))

        torch.set_default_tensor_type(default_type)

    def test_constructor_device_legacy(self):
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor(device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.FloatTensor((2.0, 3.0), device='cuda'))

        self.assertRaises(RuntimeError, lambda: torch.Tensor(device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.Tensor(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: torch.Tensor((2.0, 3.0), device='cuda'))

        x = torch.randn((3,), device='cpu')
        self.assertRaises(RuntimeError, lambda: x.new(device='cuda'))
        self.assertRaises(RuntimeError, lambda: x.new(torch.Size([2, 3, 4]), device='cuda'))
        self.assertRaises(RuntimeError, lambda: x.new((2.0, 3.0), device='cuda'))

        if torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor(device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.cuda.FloatTensor((2.0, 3.0), device='cpu'))

            default_type = torch.Tensor().type()
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertRaises(RuntimeError, lambda: torch.Tensor(device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.Tensor(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: torch.Tensor((2.0, 3.0), device='cpu'))
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            torch.set_default_tensor_type(default_type)

            x = torch.randn((3,), device='cuda')
            self.assertRaises(RuntimeError, lambda: x.new(device='cpu'))
            self.assertRaises(RuntimeError, lambda: x.new(torch.Size([2, 3, 4]), device='cpu'))
            self.assertRaises(RuntimeError, lambda: x.new((2.0, 3.0), device='cpu'))

    def test_type(self):
        x = torch.randn(3, 3).double()
        self.assertEqual(x.type('torch.FloatTensor').dtype, torch.float32)
        self.assertEqual(x.type(torch.FloatTensor).dtype, torch.float32)
        self.assertEqual(x.int().type(torch.Tensor).dtype, torch.get_default_dtype())
        self.assertEqual(x.type(torch.int32).dtype, torch.int32)

    def test_tensor_factory(self):
        # TODO: This test probably doesn't make too much sense now that
        # torch.tensor has been established for a while; it makes more
        # sense to test the legacy behavior in terms of the new behavior
        expected = torch.Tensor([1, 1])
        # test data
        res1 = torch.tensor([1, 1])
        self.assertEqual(res1, expected, exact_dtype=False)

        res1 = torch.tensor([1, 1], dtype=torch.int)
        self.assertEqual(res1, expected, exact_dtype=False)
        self.assertIs(torch.int, res1.dtype)

        # test copy
        res2 = torch.tensor(expected)
        self.assertEqual(res2, expected)
        res2[1] = 2
        self.assertEqual(expected, torch.ones_like(expected))

        res2 = torch.tensor(expected, dtype=torch.int)
        self.assertEqual(res1, expected, exact_dtype=False)
        self.assertIs(torch.int, res1.dtype)

        # test copy with numpy
        if TEST_NUMPY:
            for dtype in [np.float64, np.int64, np.int8, np.uint8]:
                a = np.array([5.]).astype(dtype)
                res1 = torch.tensor(a)
                self.assertEqual(5., res1[0].item())
                a[0] = 7.
                self.assertEqual(5., res1[0].item())

        # test boolean tensor
        a = torch.tensor([True, True, False, True, True], dtype=torch.bool)
        b = torch.tensor([-1, -1.1, 0, 1, 1.1], dtype=torch.bool)
        self.assertEqual(a, b)

    def test_tensor_factory_copy_var(self):

        def check_copy(copy, is_leaf, requires_grad, data_ptr=None):
            if data_ptr is None:
                data_ptr = copy.data_ptr
            self.assertEqual(copy, source, exact_dtype=False)
            self.assertTrue(copy.is_leaf == is_leaf)
            self.assertTrue(copy.requires_grad == requires_grad)
            self.assertTrue(copy.data_ptr == data_ptr)

        source = torch.randn(5, 5, dtype=torch.double, requires_grad=True)
        # test torch.tensor()
        check_copy(torch.tensor(source), True, False)
        check_copy(torch.tensor(source, requires_grad=False), True, False)
        check_copy(torch.tensor(source, requires_grad=True), True, True)

        # test tensor.new_tensor()
        copy = torch.randn(1)
        check_copy(copy.new_tensor(source), True, False)
        check_copy(copy.new_tensor(source, requires_grad=False), True, False)
        check_copy(copy.new_tensor(source, requires_grad=True), True, True)

        # test torch.as_tensor()
        check_copy(torch.as_tensor(source), source.is_leaf, source.requires_grad, source.data_ptr)  # not copy
        check_copy(torch.as_tensor(source, dtype=torch.float), False, True)  # copy and keep the graph

    def test_tensor_factory_type_inference(self):
        def test_inference(default_dtype):
            saved_dtype = torch.get_default_dtype()
            torch.set_default_dtype(default_dtype)
            default_complex_dtype = torch.complex64 if default_dtype == torch.float32 else torch.complex128
            self.assertIs(default_dtype, torch.tensor(()).dtype)
            self.assertIs(default_dtype, torch.tensor(5.).dtype)
            self.assertIs(torch.int64, torch.tensor(5).dtype)
            self.assertIs(torch.bool, torch.tensor(True).dtype)
            self.assertIs(torch.int32, torch.tensor(5, dtype=torch.int32).dtype)
            self.assertIs(default_dtype, torch.tensor(((7, 5), (9, 5.))).dtype)
            self.assertIs(default_dtype, torch.tensor(((5., 5), (3, 5))).dtype)
            self.assertIs(torch.int64, torch.tensor(((5, 3), (3, 5))).dtype)
            self.assertIs(default_complex_dtype, torch.tensor(((5, 3 + 2j), (3, 5 + 4j))).dtype)

            if TEST_NUMPY:
                self.assertIs(torch.float64, torch.tensor(np.array(())).dtype)
                self.assertIs(torch.float64, torch.tensor(np.array(5.)).dtype)
                if np.array(5).dtype == np.int64:  # np long, which can be 4 bytes (e.g. on windows)
                    self.assertIs(torch.int64, torch.tensor(np.array(5)).dtype)
                else:
                    self.assertIs(torch.int32, torch.tensor(np.array(5)).dtype)
                self.assertIs(torch.uint8, torch.tensor(np.array(3, dtype=np.uint8)).dtype)
                self.assertIs(default_dtype, torch.tensor(((7, np.array(5)), (np.array(9), 5.))).dtype)
                self.assertIs(torch.float64, torch.tensor(((7, 5), (9, np.array(5.)))).dtype)
                self.assertIs(torch.int64, torch.tensor(((5, np.array(3)), (np.array(3), 5))).dtype)
            torch.set_default_dtype(saved_dtype)

        test_inference(torch.float64)
        test_inference(torch.float32)

    def test_qengine(self):
        qengines = torch.backends.quantized.supported_engines
        original_qe = torch.backends.quantized.engine
        for qe in qengines:
            torch.backends.quantized.engine = qe
            assert torch.backends.quantized.engine == qe, 'qengine not set successfully'
        torch.backends.quantized.engine = original_qe

    def test_new_tensor(self):
        expected = torch.autograd.Variable(torch.ByteTensor([1, 1]))
        # test data
        res1 = expected.new_tensor([1, 1])
        self.assertEqual(res1, expected)
        res1 = expected.new_tensor([1, 1], dtype=torch.int)
        self.assertEqual(res1, expected, exact_dtype=False)
        self.assertIs(torch.int, res1.dtype)

        # test copy
        res2 = expected.new_tensor(expected)
        self.assertEqual(res2, expected)
        res2[1] = 2
        self.assertEqual(expected, torch.ones_like(expected))
        res2 = expected.new_tensor(expected, dtype=torch.int)
        self.assertEqual(res2, expected, exact_dtype=False)
        self.assertIs(torch.int, res2.dtype)

        # test copy with numpy
        if TEST_NUMPY:
            a = np.array([5.])
            res1 = torch.tensor(a)
            res1 = res1.new_tensor(a)
            self.assertEqual(5., res1[0].item())
            a[0] = 7.
            self.assertEqual(5., res1[0].item())

        if torch.cuda.device_count() >= 2:
            expected = expected.cuda(1)
            res1 = expected.new_tensor([1, 1])
            self.assertEqual(res1.get_device(), expected.get_device())
            res1 = expected.new_tensor([1, 1], dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res1.get_device(), expected.get_device())

            res2 = expected.new_tensor(expected)
            self.assertEqual(res2.get_device(), expected.get_device())
            res2 = expected.new_tensor(expected, dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res2.get_device(), expected.get_device())
            res2 = expected.new_tensor(expected, dtype=torch.int, device=0)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res2.get_device(), 0)

            res1 = expected.new_tensor(1)
            self.assertEqual(res1.get_device(), expected.get_device())
            res1 = expected.new_tensor(1, dtype=torch.int)
            self.assertIs(torch.int, res1.dtype)
            self.assertEqual(res1.get_device(), expected.get_device())

    def test_as_tensor(self):
        # from python data
        x = [[0, 1], [2, 3]]
        self.assertEqual(torch.tensor(x), torch.as_tensor(x))
        self.assertEqual(torch.tensor(x, dtype=torch.float32), torch.as_tensor(x, dtype=torch.float32))

        # python data with heterogeneous types
        z = [0, 'torch']
        with self.assertRaisesRegex(TypeError, "invalid data type"):
            torch.tensor(z)
            torch.as_tensor(z)

        # python data with self-referential lists
        z = [0]
        z += [z]
        with self.assertRaisesRegex(TypeError, "self-referential lists are incompatible"):
            torch.tensor(z)
            torch.as_tensor(z)

        z = [[1, 2], z]
        with self.assertRaisesRegex(TypeError, "self-referential lists are incompatible"):
            torch.tensor(z)
            torch.as_tensor(z)

        # from tensor (doesn't copy unless type is different)
        y = torch.tensor(x)
        self.assertIs(y, torch.as_tensor(y))
        self.assertIsNot(y, torch.as_tensor(y, dtype=torch.float32))
        if torch.cuda.is_available():
            self.assertIsNot(y, torch.as_tensor(y, device='cuda'))
            y_cuda = y.to('cuda')
            self.assertIs(y_cuda, torch.as_tensor(y_cuda))
            self.assertIs(y_cuda, torch.as_tensor(y_cuda, device='cuda'))

        if TEST_NUMPY:
            # doesn't copy
            for dtype in [np.float64, np.int64, np.int8, np.uint8]:
                n = np.random.rand(5, 6).astype(dtype)
                n_astensor = torch.as_tensor(n)
                self.assertEqual(torch.tensor(n), n_astensor)
                n_astensor[0][0] = 25.7
                self.assertEqual(torch.tensor(n), n_astensor)

            # changing dtype causes copy
            n = np.random.rand(5, 6).astype(np.float32)
            n_astensor = torch.as_tensor(n, dtype=torch.float64)
            self.assertEqual(torch.tensor(n, dtype=torch.float64), n_astensor)
            n_astensor[0][1] = 250.8
            self.assertNotEqual(torch.tensor(n, dtype=torch.float64), n_astensor)

            # changing device causes copy
            if torch.cuda.is_available():
                n = np.random.randn(5, 6)
                n_astensor = torch.as_tensor(n, device='cuda')
                self.assertEqual(torch.tensor(n, device='cuda'), n_astensor)
                n_astensor[0][2] = 250.9
                self.assertNotEqual(torch.tensor(n, device='cuda'), n_astensor)

    def test_renorm(self):
        m1 = torch.randn(10, 5)
        res1 = torch.Tensor()

        def renorm(matrix, value, dim, max_norm):
            m1 = matrix.transpose(dim, 0).contiguous()
            # collapse non-dim dimensions.
            m2 = m1.clone().resize_(m1.size(0), int(math.floor(m1.nelement() / m1.size(0))))
            norms = m2.norm(value, 1, True)
            # clip
            new_norms = norms.clone()
            new_norms[torch.gt(norms, max_norm)] = max_norm
            new_norms.div_(norms.add_(1e-7))
            # renormalize
            m1.mul_(new_norms.expand_as(m1))
            return m1.transpose(dim, 0)

        # note that the axis fed to torch.renorm is different (2~=1)
        maxnorm = m1.norm(2, 1).mean()
        m2 = renorm(m1, 2, 1, maxnorm)
        m1.renorm_(2, 1, maxnorm)
        self.assertEqual(m1, m2, 1e-5)
        self.assertEqual(m1.norm(2, 0), m2.norm(2, 0), 1e-5)

        m1 = torch.randn(3, 4, 5)
        m2 = m1.transpose(1, 2).contiguous().clone().resize_(15, 4)
        maxnorm = m2.norm(2, 0).mean()
        m2 = renorm(m2, 2, 1, maxnorm)
        m1.renorm_(2, 1, maxnorm)
        m3 = m1.transpose(1, 2).contiguous().clone().resize_(15, 4)
        self.assertEqual(m3, m2)
        self.assertEqual(m3.norm(2, 0), m2.norm(2, 0))

    def _spawn_method(self, method, arg):
        try:
            mp.set_start_method('spawn')
        except RuntimeError:
            pass
        with mp.Pool(1) as pool:
            self.assertTrue(pool.map(method, [arg]))

    @staticmethod
    def _test_multinomial_invalid_probs(probs):
        try:
            # n_sample = 1 is a special case, test n_sample=2 which is more general
            torch.multinomial(probs.to('cpu'), 2)
            return False  # Should not be reached
        except RuntimeError as e:
            return 'invalid multinomial distribution' in str(e)

    @slowTest
    @unittest.skipIf(NO_MULTIPROCESSING_SPAWN, "Disabled for environments that \
                     don't support multiprocessing with spawn start method")
    @unittest.skipIf(IS_WINDOWS, 'FIXME: CUDA OOM error on Windows')
    def test_multinomial_invalid_probs(self):
        test_method = _TestTorchMixin._test_multinomial_invalid_probs
        self._spawn_method(test_method, torch.Tensor([1, -1, 1]))
        self._spawn_method(test_method, torch.Tensor([1, inf, 1]))
        self._spawn_method(test_method, torch.Tensor([1, -inf, 1]))
        self._spawn_method(test_method, torch.Tensor([1, 1, nan]))
        self._spawn_method(test_method, torch.Tensor([0, 1, 0]))

    @suppress_warnings
    def test_range(self):
        res1 = torch.range(0, 1)
        res2 = torch.Tensor()
        torch.range(0, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Check range for non-contiguous tensors.
        x = torch.zeros(2, 3)
        torch.range(0, 3, out=x.narrow(1, 1, 2))
        res2 = torch.Tensor(((0, 0, 1), (0, 2, 3)))
        self.assertEqual(x, res2, 1e-16)

        # Check negative
        res1 = torch.Tensor((1, 0))
        res2 = torch.Tensor()
        torch.range(1, 0, -1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Equal bounds
        res1 = torch.ones(1)
        res2 = torch.Tensor()
        torch.range(1, 1, -1, out=res2)
        self.assertEqual(res1, res2, 0)
        torch.range(1, 1, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # FloatTensor
        res1 = torch.range(0.6, 0.9, 0.1, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 4)
        res1 = torch.range(1, 10, 0.3, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 31)

        # DoubleTensor
        res1 = torch.range(0.6, 0.9, 0.1, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 4)
        res1 = torch.range(1, 10, 0.3, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 31)

    def test_range_warning(self):
        with warnings.catch_warnings(record=True) as w:
            torch.range(0, 10)
            self.assertEqual(len(w), 1)

    def test_arange(self):
        res1 = torch.arange(0, 1)
        res2 = torch.tensor([], dtype=torch.int64)
        torch.arange(0, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Check arange with only one argument
        res1 = torch.arange(10)
        res2 = torch.arange(0, 10)
        self.assertEqual(res1, res2, 0)

        # Check arange for non-contiguous tensors.
        x = torch.zeros(2, 3)
        torch.arange(0, 4, out=x.narrow(1, 1, 2))
        res2 = torch.Tensor(((0, 0, 1), (0, 2, 3)))
        self.assertEqual(x, res2, 1e-16)

        # Check negative
        res1 = torch.Tensor((1, 0))
        res2 = torch.Tensor()
        torch.arange(1, -1, -1, out=res2)
        self.assertEqual(res1, res2, 0)

        # Equal bounds
        res1 = torch.ones(1)
        res2 = torch.Tensor()
        torch.arange(1, 0, -1, out=res2)
        self.assertEqual(res1, res2, 0)
        torch.arange(1, 2, 1, out=res2)
        self.assertEqual(res1, res2, 0)

        # FloatTensor
        res1 = torch.arange(0.6, 0.89, 0.1, out=torch.FloatTensor())
        self.assertEqual(res1, [0.6, 0.7, 0.8])
        res1 = torch.arange(1, 10, 0.3, out=torch.FloatTensor())
        self.assertEqual(res1.size(0), 30)
        self.assertEqual(res1[0], 1)
        self.assertEqual(res1[29], 9.7)

        # DoubleTensor
        res1 = torch.arange(0.6, 0.89, 0.1, out=torch.DoubleTensor())
        self.assertEqual(res1, [0.6, 0.7, 0.8])
        res1 = torch.arange(1, 10, 0.3, out=torch.DoubleTensor())
        self.assertEqual(res1.size(0), 30)
        self.assertEqual(res1[0], 1)
        self.assertEqual(res1[29], 9.7)

        # Bool Input matching numpy semantics
        r = torch.arange(True)
        self.assertEqual(r[0], 0)
        r2 = torch.arange(False)
        self.assertEqual(len(r2), 0)
        self.assertEqual(r.dtype, torch.int64)
        self.assertEqual(r2.dtype, torch.int64)

        # Check that it's exclusive
        r = torch.arange(0, 5)
        self.assertEqual(r.min(), 0)
        self.assertEqual(r.max(), 4)
        self.assertEqual(r.numel(), 5)

        r = torch.arange(0, 5, 2)
        self.assertEqual(r.min(), 0)
        self.assertEqual(r.max(), 4)
        self.assertEqual(r.numel(), 3)

        r1 = torch.arange(0, 5 + 1e-6)
        # NB: without the dtype, we'll infer output type to be int64
        r2 = torch.arange(0, 5, dtype=torch.float32)
        r3 = torch.arange(0, 5 - 1e-6)
        self.assertEqual(r1[:-1], r2, 0)
        self.assertEqual(r2, r3, 0)

        r1 = torch.arange(10, -1 + 1e-6, -1)
        # NB: without the dtype, we'll infer output type to be int64
        r2 = torch.arange(10, -1, -1, dtype=torch.float32)
        r3 = torch.arange(10, -1 - 1e-6, -1)
        self.assertEqual(r1, r2, 0)
        self.assertEqual(r2, r3[:-1], 0)

        # Test Rounding Errors
        line = torch.zeros(size=(1, 49))
        self.assertWarnsRegex(UserWarning, 'The out tensor will be resized',
                              lambda: torch.arange(-1, 1, 2. / 49, dtype=torch.float32, out=line))
        self.assertEqual(line.shape, [50])

        x = torch.empty(1).expand(10)
        self.assertRaises(RuntimeError, lambda: torch.arange(10, out=x))
        msg = "unsupported range"
        self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('inf')))
        self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('inf')))

        for device in torch.testing.get_all_device_types():
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(-5, float('nan'), device=device))
            # check with step size
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('-inf'), -1, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(0, float('inf'), device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('-inf'), 10, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('nan'), 10, device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('inf'), device=device))
            self.assertRaisesRegex(RuntimeError, msg, lambda: torch.arange(float('nan'), device=device))

            self.assertRaisesRegex(
                RuntimeError, "overflow",
                lambda: torch.arange(1.175494351e-38, 3.402823466e+38, device=device))

            # check that it holds a consistent output shape on precision-cornered step sizes
            d = torch.arange(-4.0, 4.0, 0.01, dtype=torch.float32, device=device)
            self.assertEqual(d.shape[0], 800)

    def test_arange_inference(self):
        saved_dtype = torch.get_default_dtype()
        torch.set_default_dtype(torch.float32)
        # end only
        self.assertIs(torch.float32, torch.arange(1.).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1.)).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1., dtype=torch.float64)).dtype)

        self.assertIs(torch.int64, torch.arange(1).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1)).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1, dtype=torch.int16)).dtype)

        # start, end, [step]
        self.assertIs(torch.float32, torch.arange(1., 3).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1., dtype=torch.float64), 3).dtype)
        self.assertIs(torch.float32, torch.arange(1, 3.).dtype)
        self.assertIs(torch.float32, torch.arange(torch.tensor(1, dtype=torch.int16), torch.tensor(3.)).dtype)
        self.assertIs(torch.float32, torch.arange(1, 3, 1.).dtype)
        self.assertIs(torch.float32,
                      torch.arange(torch.tensor(1),
                                   torch.tensor(3, dtype=torch.int16),
                                   torch.tensor(1., dtype=torch.float64)).dtype)

        self.assertIs(torch.int64, torch.arange(1, 3).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1), 3).dtype)
        self.assertIs(torch.int64, torch.arange(torch.tensor(1), torch.tensor(3, dtype=torch.int16)).dtype)
        self.assertIs(torch.int64, torch.arange(1, 3, 1).dtype)
        self.assertIs(torch.int64,
                      torch.arange(torch.tensor(1),
                                   torch.tensor(3),
                                   torch.tensor(1, dtype=torch.int16)).dtype)
        torch.set_default_dtype(saved_dtype)

    def test_randint_inference(self):
        size = (2, 1)
        for args in [(3,), (1, 3)]:  # (low,) and (low, high)
            self.assertIs(torch.int64, torch.randint(*args, size=size).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, layout=torch.strided).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, generator=torch.default_generator).dtype)
            self.assertIs(torch.float32, torch.randint(*args, size=size, dtype=torch.float32).dtype)
            out = torch.empty(size, dtype=torch.float32)
            self.assertIs(torch.float32, torch.randint(*args, size=size, out=out).dtype)
            self.assertIs(torch.float32, torch.randint(*args, size=size, out=out, dtype=torch.float32).dtype)
            out = torch.empty(size, dtype=torch.int64)
            self.assertIs(torch.int64, torch.randint(*args, size=size, out=out).dtype)
            self.assertIs(torch.int64, torch.randint(*args, size=size, out=out, dtype=torch.int64).dtype)

    def test_broadcast_empty(self):
        # empty + empty
        self.assertRaises(RuntimeError, lambda: torch.randn(5, 0) + torch.randn(0, 5))
        self.assertEqual(torch.randn(5, 0), torch.randn(0) + torch.randn(5, 0))
        self.assertEqual(torch.randn(5, 0, 0), torch.randn(0) + torch.randn(5, 0, 1))

        # scalar + empty
        self.assertEqual(torch.randn(5, 0, 6), torch.randn(()) + torch.randn(5, 0, 6))

        # non-empty, empty
        self.assertEqual(torch.randn(0), torch.randn(0) + torch.randn(1))
        self.assertEqual(torch.randn(0, 7, 0, 6, 5, 0, 7),
                         torch.randn(0, 7, 0, 6, 5, 0, 1) + torch.randn(1, 1, 5, 1, 7))
        self.assertRaises(RuntimeError, lambda: torch.randn(7, 0) + torch.randn(2, 1))

    def test_scalars_as_floats(self):
        "zero-dim variables that don't require grad should bind to scalar arguments"
        x = torch.tensor(2.)
        y = torch.tensor(3.)
        # 3 + (3 * 3) * 2
        self.assertEqual(y.addcmul(y, y, value=x), 21)

        x = torch.tensor(2., requires_grad=True)
        self.assertRaises(Exception, lambda: y.addcmul(y, y, value=x))

    def test_copy_broadcast(self):
        torch.zeros(5, 6).copy_(torch.zeros(6))
        self.assertRaises(RuntimeError, lambda: torch.zeros(5, 6).copy_(torch.zeros(30)))

    def test_copy_many_to_one(self):
        # Testing in-place copy where it attempt to write from many memory
        # storage to a single storage would cause RuntimeError to be thrown
        self.assertRaises(RuntimeError, lambda: torch.zeros(1, 6).expand(5, 6).copy_(torch.zeros(5, 6)))

    def test_not_equal(self):
        ones = torch.ones(10, dtype=torch.int)
        self.assertRaisesRegex(AssertionError, "0 not greater than",
                               lambda: self.assertNotEqual(ones, ones))

    def assertIsOrdered(self, order, x, mxx, ixx, task):
        SIZE = 4
        if order == 'descending':
            def check_order(a, b):
                # `a != a` because we put NaNs
                # at the end of ascending sorted lists,
                # and the beginning of descending ones.
                return a != a or a >= b
        elif order == 'ascending':
            def check_order(a, b):
                # see above
                return b != b or a <= b
        else:
            error('unknown order "{}", must be "ascending" or "descending"'.format(order))

        are_ordered = True
        for j, k in product(range(SIZE), range(1, SIZE)):
            self.assertTrue(check_order(mxx[j][k - 1], mxx[j][k]),
                            'torch.sort ({}) values unordered for {}'.format(order, task))

        seen = set()
        indicesCorrect = True
        size = x.size(x.dim() - 1)
        for k in range(size):
            seen.clear()
            for j in range(size):
                self.assertEqual(x[k][ixx[k][j]], mxx[k][j],
                                 'torch.sort ({}) indices wrong for {}'.format(order, task))
                seen.add(ixx[k][j])
            self.assertEqual(len(seen), size)

    def test_sort(self):
        SIZE = 4
        x = torch.rand(SIZE, SIZE)
        res1val, res1ind = torch.sort(x)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.sort(x, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)
        self.assertEqual(torch.argsort(x), res1ind)
        self.assertEqual(x.argsort(), res1ind)

        # Test sorting of random numbers
        self.assertIsOrdered('ascending', x, res2val, res2ind, 'random')

        # Test simple sort
        self.assertEqual(
            torch.sort(torch.Tensor((50, 40, 30, 20, 10)))[0],
            torch.Tensor((10, 20, 30, 40, 50)),
            0
        )

        # Test that we still have proper sorting with duplicate keys
        x = torch.floor(torch.rand(SIZE, SIZE) * 10)
        torch.sort(x, out=(res2val, res2ind))
        self.assertIsOrdered('ascending', x, res2val, res2ind, 'random with duplicate keys')

        # DESCENDING SORT
        x = torch.rand(SIZE, SIZE)
        res1val, res1ind = torch.sort(x, x.dim() - 1, True)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.sort(x, x.dim() - 1, True, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)
        self.assertEqual(torch.argsort(x, x.dim() - 1, True), res1ind)
        self.assertEqual(x.argsort(x.dim() - 1, True), res1ind)

        # Test sorting of random numbers
        self.assertIsOrdered('descending', x, res2val, res2ind, 'random')

        # Test simple sort task
        self.assertEqual(
            torch.sort(torch.Tensor((10, 20, 30, 40, 50)), 0, True)[0],
            torch.Tensor((50, 40, 30, 20, 10)),
            0
        )

        # Test that we still have proper sorting with duplicate keys
        self.assertIsOrdered('descending', x, res2val, res2ind, 'random with duplicate keys')

        # Test sorting with NaNs
        x = torch.rand(SIZE, SIZE)
        x[1][2] = float('NaN')
        x[3][0] = float('NaN')
        torch.sort(x, out=(res2val, res2ind))
        self.assertIsOrdered('ascending', x, res2val, res2ind,
                             'random with NaNs')
        torch.sort(x, out=(res2val, res2ind), descending=True)
        self.assertIsOrdered('descending', x, res2val, res2ind,
                             'random with NaNs')

    def test_topk(self):
        def topKViaSort(t, k, dim, dir):
            sorted, indices = t.sort(dim, dir)
            return sorted.narrow(dim, 0, k), indices.narrow(dim, 0, k)

        def compareTensors(t, res1, ind1, res2, ind2, dim):
            # Values should be exactly equivalent
            self.assertEqual(res1, res2, 0)

            # Indices might differ based on the implementation, since there is
            # no guarantee of the relative order of selection
            if not ind1.eq(ind2).all():
                # To verify that the indices represent equivalent elements,
                # gather from the input using the topk indices and compare against
                # the sort indices
                vals = t.gather(dim, ind2)
                self.assertEqual(res1, vals, 0)

        def compare(t, k, dim, dir):
            topKVal, topKInd = t.topk(k, dim, dir, True)
            sortKVal, sortKInd = topKViaSort(t, k, dim, dir)
            compareTensors(t, sortKVal, sortKInd, topKVal, topKInd, dim)

        t = torch.rand(random.randint(1, SIZE),
                       random.randint(1, SIZE),
                       random.randint(1, SIZE))

        for _kTries in range(3):
            for _dimTries in range(3):
                for transpose in (True, False):
                    for dir in (True, False):
                        testTensor = t
                        if transpose:
                            dim1 = random.randrange(t.ndimension())
                            dim2 = dim1
                            while dim1 == dim2:
                                dim2 = random.randrange(t.ndimension())

                            testTensor = t.transpose(dim1, dim2)

                        dim = random.randrange(testTensor.ndimension())
                        k = random.randint(1, testTensor.size(dim))
                        compare(testTensor, k, dim, dir)

    def test_topk_arguments(self):
        q = torch.randn(10, 2, 10)
        # Make sure True isn't mistakenly taken as the 2nd dimension (interpreted as 1)
        self.assertRaises(TypeError, lambda: q.topk(4, True))

    def test_median(self):
        for size in (155, 156):
            x = torch.rand(size, size)
            x0 = x.clone()

            nelem = x.nelement()
            res1val = torch.median(x)
            res2val, _ = torch.sort(x.view(nelem))
            ind = int(math.floor((nelem + 1) / 2) - 1)

            self.assertEqual(res2val[ind], res1val, 0)

            res1val, res1ind = torch.median(x, dim=1, keepdim=False)
            res2val, res2ind = torch.sort(x)
            ind = int(math.floor((size + 1) / 2) - 1)

            self.assertEqual(res2val.select(1, ind), res1val, 0)
            self.assertEqual(res2val.select(1, ind), res1val, 0)

            # Test use of result tensor
            res2val = torch.Tensor()
            res2ind = torch.LongTensor()
            torch.median(x, dim=-1, keepdim=False, out=(res2val, res2ind))
            self.assertEqual(res2val, res1val, 0)
            self.assertEqual(res2ind, res1ind, 0)

            # Test non-default dim
            res1val, res1ind = torch.median(x, 0, keepdim=False)
            res2val, res2ind = torch.sort(x, 0)
            self.assertEqual(res1val, res2val[ind], 0)
            self.assertEqual(res1ind, res2ind[ind], 0)

            # input unchanged
            self.assertEqual(x, x0, 0)

    def test_mode(self):
        x = torch.arange(1., SIZE * SIZE + 1).clone().resize_(SIZE, SIZE)
        x[:2] = 1
        x[:, :2] = 1
        x0 = x.clone()

        # Pre-calculated results.
        res1val = torch.Tensor(SIZE).fill_(1)
        # The indices are the position of the last appearance of the mode element.
        res1ind = torch.LongTensor(SIZE).fill_(1)
        res1ind[0] = SIZE - 1
        res1ind[1] = SIZE - 1

        res2val, res2ind = torch.mode(x, keepdim=False)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # Test use of result tensor
        res2val = torch.Tensor()
        res2ind = torch.LongTensor()
        torch.mode(x, keepdim=False, out=(res2val, res2ind))
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # Test non-default dim
        res2val, res2ind = torch.mode(x, 0, False)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # input unchanged
        self.assertEqual(x, x0, 0)

    def test_trilu_indices(self):
        for test_args in tri_tests_args:
            _compare_trilu_indices(self, *test_args)
        run_additional_tri_tests(self, 'cpu')

        # test default options
        x = torch.ones(
            3, 3, dtype=torch.long, device='cpu', layout=torch.strided)
        self.assertEqual(
            x.tril(0).nonzero().transpose(0, 1), torch.tril_indices(3, 3))
        self.assertEqual(
            x.triu(0).nonzero().transpose(0, 1), torch.triu_indices(3, 3))

        # test stride 0 cases
        x = torch.ones(
            3, 1, 3, 3, dtype=torch.long, device='cpu', layout=torch.strided)
        output = x.triu(2).expand(3, 3, 3, 3)
        b = x.clone().expand(3, 3, 3, 3)
        self.assertEqual(b.triu(2), output)
        self.assertRaises(RuntimeError, lambda: b.triu_(2))

    def test_narrow(self):
        x = torch.Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
        self.assertEqual(x.narrow(0, 0, 1), torch.Tensor([[0, 1, 2]]))
        self.assertEqual(x.narrow(0, 0, 2), torch.Tensor([[0, 1, 2], [3, 4, 5]]))
        self.assertEqual(x.narrow(0, 1, 1), torch.Tensor([[3, 4, 5]]))
        self.assertEqual(x.narrow(0, -1, 1), torch.Tensor([[6, 7, 8]]))
        self.assertEqual(x.narrow(0, -2, 2), torch.Tensor([[3, 4, 5], [6, 7, 8]]))
        self.assertEqual(x.narrow(0, -3, 3), torch.Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]]))
        self.assertEqual(x.narrow(-1, -1, 1), torch.Tensor([[2], [5], [8]]))
        self.assertEqual(x.narrow(-2, -1, 1), torch.Tensor([[6, 7, 8]]))

    def test_narrow_tensor(self):
        x = torch.Tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
        self.assertEqual(x.narrow(0, torch.tensor(0), 1), torch.Tensor([[0, 1, 2]]))
        with self.assertRaises(Exception):
            x.narrow(0, torch.tensor(0.), 1)
        with self.assertRaises(Exception):
            x.narrow(0, torch.tensor([0]), 1)
        with self.assertRaises(Exception):
            x.narrow(0, torch.tensor([0, 1]), 1)

    def test_stack(self):
        for dtype in (torch.half, torch.double, torch.int):
            x = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            y = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            z = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            for dim in range(4):
                res = torch.stack((x, y, z), dim)
                res_neg = torch.stack((x, y, z), dim - 4)
                expected_size = x.size()[:dim] + (3,) + x.size()[dim:]
                self.assertEqual(res, res_neg)
                self.assertEqual(res.size(), expected_size)
                self.assertEqual(res.select(dim, 0), x, 0)
                self.assertEqual(res.select(dim, 1), y, 0)
                self.assertEqual(res.select(dim, 2), z, 0)

    def test_stack_out(self):
        for dtype in (torch.half, torch.double, torch.int):
            x = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            y = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            z = torch.randint(low=-100, high=100, size=(2, 3, 4)).to(dtype)
            for dim in range(4):
                expected_size = x.size()[:dim] + (3,) + x.size()[dim:]
                res_out = x.new(expected_size)
                res_neg_out = x.new(expected_size)
                res_out_dp = res_out.data_ptr()
                res_out_neg_dp = res_neg_out.data_ptr()
                torch.stack((x, y, z), dim, out=res_out)
                torch.stack((x, y, z), dim - 4, out=res_neg_out)
                self.assertEqual(res_out, res_neg_out)
                self.assertEqual(res_out.size(), expected_size)
                self.assertEqual(res_out_dp, res_out.data_ptr())
                self.assertEqual(res_out_neg_dp, res_neg_out.data_ptr())
                self.assertEqual(res_out.select(dim, 0), x, 0)
                self.assertEqual(res_out.select(dim, 1), y, 0)
                self.assertEqual(res_out.select(dim, 2), z, 0)

    def test_unbind(self):
        x = torch.rand(2, 3, 4, 5)
        for dim in range(4):
            res = torch.unbind(x, dim)
            res2 = x.unbind(dim)
            self.assertEqual(x.size(dim), len(res))
            self.assertEqual(x.size(dim), len(res2))
            for i in range(dim):
                self.assertEqual(x.select(dim, i), res[i])
                self.assertEqual(x.select(dim, i), res2[i])

    def test_randint(self):
        def seed(generator):
            if generator is None:
                torch.manual_seed(123456)
            else:
                generator.manual_seed(123456)
            return generator

        for generator in (None, torch.Generator()):
            generator = seed(generator)
            res1 = torch.randint(0, 6, (SIZE, SIZE), generator=generator)
            res2 = torch.empty((), dtype=torch.int64)
            generator = seed(generator)
            torch.randint(0, 6, (SIZE, SIZE), generator=generator, out=res2)
            generator = seed(generator)
            res3 = torch.randint(6, (SIZE, SIZE), generator=generator)
            res4 = torch.empty((), dtype=torch.int64)
            generator = seed(generator)
            torch.randint(6, (SIZE, SIZE), out=res4, generator=generator)
            self.assertEqual(res1, res2)
            self.assertEqual(res1, res3)
            self.assertEqual(res1, res4)
            self.assertEqual(res2, res3)
            self.assertEqual(res2, res4)
            self.assertEqual(res3, res4)
            self.assertTrue((res1 < 6).all().item())
            self.assertTrue((res1 >= 0).all().item())

    def test_slice(self):
        empty = torch.empty(0, 4)
        x = torch.arange(0., 16).view(4, 4)
        self.assertEqual(x[:], x)
        self.assertEqual(x[:4], x)
        # start and stop are clamped to the size of dim
        self.assertEqual(x[:5], x)
        # if start >= stop then the result is empty
        self.assertEqual(x[2:1], empty)
        self.assertEqual(x[2:2], empty)
        # out of bounds is also empty
        self.assertEqual(x[10:12], empty)
        # additional correctness checks
        self.assertEqual(x[:1].tolist(), [[0, 1, 2, 3]])
        self.assertEqual(x[:-3].tolist(), [[0, 1, 2, 3]])
        self.assertEqual(x[:, -2:3].tolist(), [[2], [6], [10], [14]])
        self.assertEqual(x[0:-1:2].tolist(), [[0, 1, 2, 3], [8, 9, 10, 11]])

    @skipIfNoLapack
    def test_ormqr(self):
        mat1 = torch.randn(7, 7)
        mat2 = torch.randn(7, 7)
        q, r = torch.qr(mat1)
        m, tau = torch.geqrf(mat1)
        out_holder = torch.empty_like(mat1)

        res1 = torch.mm(q, mat2)
        res2 = torch.ormqr(m, tau, mat2, left=True, transpose=False)
        torch.ormqr(m, tau, mat2, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(mat2, q)
        res2 = torch.ormqr(m, tau, mat2, left=False, transpose=False)
        torch.ormqr(m, tau, mat2, left=False, transpose=False, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(q.t(), mat2)
        res2 = torch.ormqr(m, tau, mat2, left=True, transpose=True)
        torch.ormqr(m, tau, mat2, left=True, transpose=True, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

        res1 = torch.mm(mat2, q.t())
        res2 = torch.ormqr(m, tau, mat2, left=False, transpose=True)
        torch.ormqr(m, tau, mat2, left=False, transpose=True, out=out_holder)
        self.assertEqual(res1, res2)
        self.assertEqual(res2, out_holder)

    @staticmethod
    def _test_fft_ifft_rfft_irfft(self, device='cpu', dtype=torch.double):
        def _test_complex(sizes, signal_ndim, prepro_fn=lambda x: x):
            x = prepro_fn(torch.randn(*sizes, dtype=dtype, device=device))
            for normalized in (True, False):
                res = x.fft(signal_ndim, normalized=normalized)
                rec = res.ifft(signal_ndim, normalized=normalized)
                self.assertEqual(x, rec, atol=1e-8, message='fft and ifft')
                res = x.ifft(signal_ndim, normalized=normalized)
                rec = res.fft(signal_ndim, normalized=normalized)
                self.assertEqual(x, rec, atol=1e-8, message='ifft and fft')

        def _test_real(sizes, signal_ndim, prepro_fn=lambda x: x):
            x = prepro_fn(torch.randn(*sizes, dtype=dtype, device=device))
            signal_numel = 1
            signal_sizes = x.size()[-signal_ndim:]
            for normalized, onesided in product((True, False), repeat=2):
                res = x.rfft(signal_ndim, normalized=normalized, onesided=onesided)
                if not onesided:  # check Hermitian symmetry
                    def test_one_sample(res, test_num=10):
                        idxs_per_dim = [torch.LongTensor(test_num).random_(s).tolist() for s in signal_sizes]
                        for idx in zip(*idxs_per_dim):
                            reflected_idx = tuple((s - i) % s for i, s in zip(idx, res.size()))
                            idx_val = res.__getitem__(idx)
                            reflected_val = res.__getitem__(reflected_idx)
                            self.assertEqual(idx_val[0], reflected_val[0], 'rfft hermitian symmetry on real part')
                            self.assertEqual(idx_val[1], -reflected_val[1], 'rfft hermitian symmetry on imaginary part')
                    if len(sizes) == signal_ndim:
                        test_one_sample(res)
                    else:
                        output_non_batch_shape = res.size()[-(signal_ndim + 1):]
                        flatten_batch_res = res.view(-1, *output_non_batch_shape)
                        nb = flatten_batch_res.size(0)
                        test_idxs = torch.LongTensor(min(nb, 4)).random_(nb)
                        for test_idx in test_idxs.tolist():
                            test_one_sample(flatten_batch_res[test_idx])
                    # compare with C2C
                    xc = torch.stack([x, torch.zeros_like(x)], -1)
                    xc_res = xc.fft(signal_ndim, normalized=normalized)
                    self.assertEqual(res, xc_res)
                test_input_signal_sizes = [signal_sizes]
                rec = res.irfft(signal_ndim, normalized=normalized,
                                onesided=onesided, signal_sizes=signal_sizes)
                self.assertEqual(x, rec, atol=1e-8, message='rfft and irfft')
                if not onesided:  # check that we can use C2C ifft
                    rec = res.ifft(signal_ndim, normalized=normalized)
                    self.assertEqual(x, rec.select(-1, 0), atol=1e-8, message='twosided rfft and ifft real')
                    self.assertEqual(rec.select(-1, 1).abs().mean(), 0, atol=1e-8, message='twosided rfft and ifft imaginary')

        # contiguous case
        _test_real((100,), 1)
        _test_real((10, 1, 10, 100), 1)
        _test_real((100, 100), 2)
        _test_real((2, 2, 5, 80, 60), 2)
        _test_real((50, 40, 70), 3)
        _test_real((30, 1, 50, 25, 20), 3)

        _test_complex((100, 2), 1)
        _test_complex((100, 100, 2), 1)
        _test_complex((100, 100, 2), 2)
        _test_complex((1, 20, 80, 60, 2), 2)
        _test_complex((50, 40, 70, 2), 3)
        _test_complex((6, 5, 50, 25, 20, 2), 3)

        # non-contiguous case
        _test_real((165,), 1, lambda x: x.narrow(0, 25, 100))  # input is not aligned to complex type
        _test_real((100, 100, 3), 1, lambda x: x[:, :, 0])
        _test_real((100, 100), 2, lambda x: x.t())
        _test_real((20, 100, 10, 10), 2, lambda x: x.view(20, 100, 100)[:, :60])
        _test_real((65, 80, 115), 3, lambda x: x[10:60, 13:53, 10:80])
        _test_real((30, 20, 50, 25), 3, lambda x: x.transpose(1, 2).transpose(2, 3))

        _test_complex((2, 100), 1, lambda x: x.t())
        _test_complex((100, 2), 1, lambda x: x.expand(100, 100, 2))
        _test_complex((300, 200, 3), 2, lambda x: x[:100, :100, 1:])  # input is not aligned to complex type
        _test_complex((20, 90, 110, 2), 2, lambda x: x[:, 5:85].narrow(2, 5, 100))
        _test_complex((40, 60, 3, 80, 2), 3, lambda x: x.transpose(2, 0).select(0, 2)[5:55, :, 10:])
        _test_complex((30, 55, 50, 22, 2), 3, lambda x: x[:, 3:53, 15:40, 1:21])

        # non-contiguous with strides not representable as aligned with complex type
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [3, 2, 1]))
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [4, 2, 2]))
        _test_complex((50,), 1, lambda x: x.as_strided([5, 5, 2], [4, 3, 1]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [3, 3, 1]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [4, 2, 2]))
        _test_complex((50,), 2, lambda x: x.as_strided([5, 5, 2], [4, 3, 1]))

    @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
    def test_fft_ifft_rfft_irfft(self):
        self._test_fft_ifft_rfft_irfft(self)

    @unittest.skip("Not implemented yet")
    def test_conv2(self):
        x = torch.rand(math.floor(torch.uniform(50, 100)), math.floor(torch.uniform(50, 100)))
        k = torch.rand(math.floor(torch.uniform(10, 20)), math.floor(torch.uniform(10, 20)))
        imvc = torch.conv2(x, k)
        imvc2 = torch.conv2(x, k, 'V')
        imfc = torch.conv2(x, k, 'F')

        ki = k.clone()
        ks = k.storage()
        kis = ki.storage()
        for i in range(ks.size() - 1, 0, -1):
            kis[ks.size() - i + 1] = ks[i]
        # for i=ks.size(), 1, -1 do kis[ks.size()-i+1]=ks[i] end
        imvx = torch.xcorr2(x, ki)
        imvx2 = torch.xcorr2(x, ki, 'V')
        imfx = torch.xcorr2(x, ki, 'F')

        self.assertEqual(imvc, imvc2, atol=0, message='torch.conv2')
        self.assertEqual(imvc, imvx, atol=0, message='torch.conv2')
        self.assertEqual(imvc, imvx2, atol=0, message='torch.conv2')
        self.assertEqual(imfc, imfx, atol=0, message='torch.conv2')
        self.assertLessEqual(math.abs(x.dot(x) - torch.xcorr2(x, x)[0][0]), 1e-10, 'torch.conv2')

        xx = torch.Tensor(2, x.size(1), x.size(2))
        xx[1].copy_(x)
        xx[2].copy_(x)
        kk = torch.Tensor(2, k.size(1), k.size(2))
        kk[1].copy_(k)
        kk[2].copy_(k)

        immvc = torch.conv2(xx, kk)
        immvc2 = torch.conv2(xx, kk, 'V')
        immfc = torch.conv2(xx, kk, 'F')

        self.assertEqual(immvc[0], immvc[1], atol=0, message='torch.conv2')
        self.assertEqual(immvc[0], imvc, atol=0, message='torch.conv2')
        self.assertEqual(immvc2[0], imvc2, atol=0, message='torch.conv2')
        self.assertEqual(immfc[0], immfc[1], atol=0, message='torch.conv2')
        self.assertEqual(immfc[0], imfc, atol=0, message='torch.conv2')

    @unittest.skip("Not implemented yet")
    def test_conv3(self):
        x = torch.rand(math.floor(torch.uniform(20, 40)),
                       math.floor(torch.uniform(20, 40)),
                       math.floor(torch.uniform(20, 40)))
        k = torch.rand(math.floor(torch.uniform(5, 10)),
                       math.floor(torch.uniform(5, 10)),
                       math.floor(torch.uniform(5, 10)))
        imvc = torch.conv3(x, k)
        imvc2 = torch.conv3(x, k, 'V')
        imfc = torch.conv3(x, k, 'F')

        ki = k.clone()
        ks = k.storage()
        kis = ki.storage()
        for i in range(ks.size() - 1, 0, -1):
            kis[ks.size() - i + 1] = ks[i]
        imvx = torch.xcorr3(x, ki)
        imvx2 = torch.xcorr3(x, ki, 'V')
        imfx = torch.xcorr3(x, ki, 'F')

        self.assertEqual(imvc, imvc2, atol=0, message='torch.conv3')
        self.assertEqual(imvc, imvx, atol=0, message='torch.conv3')
        self.assertEqual(imvc, imvx2, atol=0, message='torch.conv3')
        self.assertEqual(imfc, imfx, atol=0, message='torch.conv3')
        self.assertLessEqual(math.abs(x.dot(x) - torch.xcorr3(x, x)[0][0][0]), 4e-10, 'torch.conv3')

        xx = torch.Tensor(2, x.size(1), x.size(2), x.size(3))
        xx[1].copy_(x)
        xx[2].copy_(x)
        kk = torch.Tensor(2, k.size(1), k.size(2), k.size(3))
        kk[1].copy_(k)
        kk[2].copy_(k)

        immvc = torch.conv3(xx, kk)
        immvc2 = torch.conv3(xx, kk, 'V')
        immfc = torch.conv3(xx, kk, 'F')

        self.assertEqual(immvc[0], immvc[1], atol=0, message='torch.conv3')
        self.assertEqual(immvc[0], imvc, atol=0, message='torch.conv3')
        self.assertEqual(immvc2[0], imvc2, atol=0, message='torch.conv3')
        self.assertEqual(immfc[0], immfc[1], atol=0, message='torch.conv3')
        self.assertEqual(immfc[0], imfc, atol=0, message='torch.conv3')

    @unittest.skip("Not implemented yet")
    def _test_conv_corr_eq(self, fn, fn_2_to_3):
        ix = math.floor(random.randint(20, 40))
        iy = math.floor(random.randint(20, 40))
        iz = math.floor(random.randint(20, 40))
        kx = math.floor(random.randint(5, 10))
        ky = math.floor(random.randint(5, 10))
        kz = math.floor(random.randint(5, 10))

        x = torch.rand(ix, iy, iz)
        k = torch.rand(kx, ky, kz)

        o3 = fn(x, k)
        o32 = torch.zeros(o3.size())
        fn_2_to_3(x, k, o3, o32)
        self.assertEqual(o3, o32)

    @unittest.skip("Not implemented yet")
    def test_xcorr3_xcorr2_eq(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.xcorr2(x[i + j - 1], k[j]))
        self._test_conv_corr_eq(torch.xcorr3, reference)

    @unittest.skip("Not implemented yet")
    def test_xcorr3_xcorr2_eq_full(self):
        def reference(x, k, o3, o32):
            for i in range(x.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.xcorr2(x[i], k[k.size(1) - j + 1], 'F'))
        self._test_conv_corr_eq(lambda x, k: torch.xcorr3(x, k, 'F'), reference)

    @unittest.skip("Not implemented yet")
    def test_conv3_conv2_eq_valid(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i].add(torch.conv2(x[i + j - 1], k[k.size(1) - j + 1]))
        self._test_conv_corr_eq(torch.conv3, reference)

    @unittest.skip("Not implemented yet")
    def test_fconv3_fconv2_eq(self):
        def reference(x, k, o3, o32):
            for i in range(o3.size(1)):
                for j in range(k.size(1)):
                    o32[i + j - 1].add(torch.conv2(x[i], k[j], 'F'))
        self._test_conv_corr_eq(lambda x, k: torch.conv3(x, k, 'F'), reference)

    def test_dtype_is_signed(self):
        for dtype in torch.testing.get_all_dtypes():
            self.assertEqual(dtype.is_signed, torch.is_signed(torch.tensor(0, dtype=dtype)))

        self.assertRaisesRegex(RuntimeError, 'not supported for quantized', lambda: torch.quint8.is_signed)
        self.assertRaisesRegex(RuntimeError, 'not supported for quantized', lambda: torch.qint8.is_signed)
        self.assertRaisesRegex(RuntimeError, 'not supported for quantized', lambda: torch.qint32.is_signed)

    def test_RNGState(self):
        state = torch.get_rng_state()
        stateCloned = state.clone()
        before = torch.rand(1000)

        self.assertEqual(state.ne(stateCloned).long().sum(), 0, 0)

        torch.set_rng_state(state)
        after = torch.rand(1000)
        self.assertEqual(before, after, 0)

    def test_RNGStateAliasing(self):
        # Fork the random number stream at this point
        gen = torch.Generator()
        gen.set_state(torch.get_rng_state())
        self.assertEqual(gen.get_state(), torch.get_rng_state())

        target_value = torch.rand(1000)
        # Dramatically alter the internal state of the main generator
        _ = torch.rand(100000)
        forked_value = torch.rand(1000, generator=gen)
        self.assertEqual(target_value, forked_value, atol=0, message="RNG has not forked correctly.")

    def test_RNG_after_pickle(self):
        torch.random.manual_seed(100)
        before = torch.rand(10)

        torch.random.manual_seed(100)
        buf = io.BytesIO()
        tensor = torch.Tensor([1, 2, 3])
        ForkingPickler(buf, pickle.HIGHEST_PROTOCOL).dump(tensor)
        after = torch.rand(10)

        self.assertEqual(before, after, 0)

    def test_boxMullerState(self):
        torch.manual_seed(123)
        odd_number = 101
        seeded = torch.randn(odd_number)
        state = torch.get_rng_state()
        midstream = torch.randn(odd_number)
        torch.set_rng_state(state)
        repeat_midstream = torch.randn(odd_number)
        torch.manual_seed(123)
        reseeded = torch.randn(odd_number)
        self.assertEqual(midstream, repeat_midstream, atol=0,
                         message='get_rng_state/set_rng_state not generating same sequence of normally distributed numbers')
        self.assertEqual(seeded, reseeded, atol=0,
                         message='repeated calls to manual_seed not generating same sequence of normally distributed numbers')

    def test_manual_seed(self):
        rng_state = torch.get_rng_state()
        torch.manual_seed(2)
        x = torch.randn(100)
        self.assertEqual(torch.initial_seed(), 2)
        torch.manual_seed(2)
        y = torch.randn(100)
        self.assertEqual(x, y)
        torch.set_rng_state(rng_state)

    def test_numel(self):
        b = torch.ByteTensor(3, 100, 100)
        self.assertEqual(b.nelement(), 3 * 100 * 100)
        self.assertEqual(b.numel(), 3 * 100 * 100)

    # Note: the warning this tests for only appears once per program, so
    # other instances of this warning should be addressed to avoid
    # the tests depending on the order in which they're run.
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_non_writeable(self):
        arr = np.zeros(5)
        arr.flags['WRITEABLE'] = False
        self.assertWarns(UserWarning, lambda: torch.from_numpy(arr))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_empty_storage_view(self):
        # we should be able to "modify" slices of a 0-element
        # array without an error being raised due to
        # trying to resize its storage
        t = torch.from_numpy(np.empty((0, 4)))
        t[:, 1::2] *= 1

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_newaxis_numpy_comparison(self):
        def run_test(tensor, *idx):
            npt = tensor.numpy()
            self.assertEqual(tensor[idx], npt[idx])

        # 1D Tensor Tests
        x = torch.arange(0, 10)
        cases = [
            [None],
            [None, None],
            [Ellipsis, None],
            [None, Ellipsis],
            [2, None],
            [None, 2],
            [Ellipsis, None, 2],
            [Ellipsis, 2, None],
            [2, Ellipsis, None],
            [2, None, Ellipsis],
            [None, 2, Ellipsis],
            [None, Ellipsis, 2],
        ]

        for case in cases:
            run_test(x, *case)

        # 2D Tensor Tests
        x = torch.arange(0, 12).view(3, 4)
        cases = [
            [None],
            [None, None],
            [None, None, None],
            [Ellipsis, None],
            [Ellipsis, None, None],
            [None, Ellipsis],
            [None, Ellipsis, None],
            [None, None, Ellipsis],
            [2, None],
            [2, None, Ellipsis],
            [2, Ellipsis, None],
            [None, 2, Ellipsis],
            [Ellipsis, 2, None],
            [Ellipsis, None, 2],
            [None, Ellipsis, 2],
            [1, 2, None],
            [1, 2, Ellipsis, None],
            [1, Ellipsis, 2, None],
            [Ellipsis, 1, None, 2],
            [Ellipsis, 1, 2, None],
            [1, None, 2, Ellipsis],
            [None, 1, Ellipsis, 2],
            [None, 1, 2, Ellipsis],
        ]

        for case in cases:
            run_test(x, *case)

    def _consecutive(self, size, start=1):
        sequence = torch.ones(int(torch.Tensor(size).prod(0))).cumsum(0)
        sequence.add_(start - 1)
        return sequence.resize_(*size)

    def test_newindex(self):
        reference = self._consecutive((3, 3, 3))
        # This relies on __index__() being correct - but we have separate tests for that

        def checkPartialAssign(index):
            reference = torch.zeros(3, 3, 3)
            reference[index] = self._consecutive((3, 3, 3))[index]
            self.assertEqual(reference[index], self._consecutive((3, 3, 3))[index], 0)
            reference[index] = 0
            self.assertEqual(reference, torch.zeros(3, 3, 3), 0)

        checkPartialAssign(0)
        checkPartialAssign(1)
        checkPartialAssign(2)
        checkPartialAssign((0, 1))
        checkPartialAssign((1, 2))
        checkPartialAssign((0, 2))
        checkPartialAssign(torch.LongTensor((0, 2)))

        with self.assertRaises(IndexError):
            reference[1, 1, 1, 1] = 1
        with self.assertRaises(IndexError):
            reference[1, 1, 1, (1, 1)] = 1
        with self.assertRaises(IndexError):
            reference[3, 3, 3, 3, 3, 3, 3, 3] = 1
        with self.assertRaises(IndexError):
            reference[0.0] = 1
        with self.assertRaises(TypeError):
            reference[0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, :, 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, ..., 0.0:2.0] = 1
        with self.assertRaises(IndexError):
            reference[0.0, :, 0.0] = 1

    def test_index_add(self):
        for dest_contig, src_contig, index_contig in product([True, False], repeat=3):
            for other_sizes in ((), (4, 5)):
                num_copy, num_dest = 3, 3
                dest = torch.randn(num_dest, *other_sizes)
                if not dest_contig:
                    dest = torch.testing.make_non_contiguous(dest)
                src = torch.randn(num_copy, *other_sizes)
                if not src_contig:
                    src = torch.testing.make_non_contiguous(src)
                idx = torch.randperm(num_dest).narrow(0, 0, num_copy)
                if not index_contig:
                    idx = torch.testing.make_non_contiguous(idx)
                dest2 = dest.clone()
                dest.index_add_(0, idx, src)
                for i in range(idx.size(0)):
                    dest2[idx[i]] += src[i]
                self.assertEqual(dest, dest2)

    # add coverage for issue with atomic add that appeared only for
    # specific dtypes on cuda:
    # https://github.com/pytorch/pytorch/issues/29153
    def test_index_add_all_dtypes(self):
        for device in torch.testing.get_all_device_types():
            for dtype in torch.testing.get_all_math_dtypes(device):
                size = [5, 5]
                if dtype.is_floating_point or dtype.is_complex:
                    tensor = torch.rand(size, dtype=dtype, device=device)
                elif dtype.is_signed:
                    tensor = torch.randint(-5, 15, size, dtype=dtype, device=device)
                else:
                    tensor = torch.randint(0, 10, size, dtype=dtype, device=device)

                # index_add calls atomicAdd on cuda.
                zeros = torch.zeros(size, dtype=dtype, device=device)

                # index_add is not supported for complex dtypes on cuda yet
                if device.startswith('cuda') and dtype.is_complex:
                    continue

                added = zeros.index_add(0, torch.arange(0, size[0], dtype=torch.long, device=device), tensor)
                self.assertEqual(added, tensor)

    def test_t(self):
        # Test 0D tensors
        x = torch.randn(())
        self.assertEqual(x, x.t())
        x = x.to_sparse()
        self.assertEqual(x, x.t())

        # Test 1D tensors
        x = torch.arange(4)
        self.assertEqual(x, x.t())
        x = x.to_sparse()
        self.assertEqual(x, x.t())

        # Test 2D tensors
        x = torch.rand((2, 2))
        self.assertEqual(x.t(), x.transpose(0, 1))
        x = x.to_sparse()
        self.assertEqual(x.t(), x.transpose(0, 1))

        # Test 3D tensor
        x = torch.rand((2, 2, 2))
        with self.assertRaisesRegex(RuntimeError, 'expects a tensor with <= 2 dimensions, but self is 3D'):
            x.t()
        x = x.to_sparse()
        with self.assertRaisesRegex(RuntimeError, 'expects a tensor with <= 2 sparse and 0 dense dimensions'):
            x.t()

    def test_take(self):
        def check(src, idx):
            expected = src.contiguous().view(-1).index_select(
                0, idx.contiguous().view(-1)).view_as(idx)
            actual = src.take(idx)
            self.assertEqual(actual.size(), idx.size())
            self.assertEqual(expected, actual)

        src = torch.randn(2, 3, 5)
        idx = torch.LongTensor([[0, 2], [3, 4]])
        check(src, idx)
        check(src.transpose(1, 2), idx)
        check(src.bool(), idx)

    def test_put_(self):
        def check(dst, idx, value):
            expected = dst.clone(memory_format=torch.contiguous_format).view(-1).index_copy_(
                0, idx.contiguous().view(-1), value.contiguous().view(-1))
            expected = expected.view_as(dst)
            dst.put_(idx, value)
            self.assertEqual(expected, dst)

        dst = torch.randn(2, 3, 5)
        idx = torch.LongTensor([[0, 2], [3, 4]])
        values = torch.randn(2, 2)
        check(dst, idx, values)
        check(dst.transpose(1, 2), idx, values)

        values = torch.tensor([[False, False], [False, False]])
        check(dst.bool(), idx, values)

    def test_put_accumulate(self):
        dst = torch.ones(2, 2)
        idx = torch.LongTensor([[0, 1], [0, 1]])
        src = torch.Tensor([1, 2, 3, 4])
        dst.put_(idx, src, accumulate=True)
        self.assertEqual(dst.tolist(), [[5, 7], [1, 1]])

    # Fill idx with valid indices.
    @staticmethod
    def _fill_indices(self, idx, dim, dim_size, elems_per_row, m, n, o):
        for i in range(1 if dim == 0 else m):
            for j in range(1 if dim == 1 else n):
                for k in range(1 if dim == 2 else o):
                    ii = [i, j, k]
                    ii[dim] = slice(0, idx.size(dim) + 1)
                    idx[tuple(ii)] = torch.randperm(dim_size)[0:elems_per_row]

    def test_flatten(self):
        # Test that flatten returns 1-dim tensor when given a 0-dim tensor
        zero_dim_tensor = torch.tensor(123)
        flat0 = zero_dim_tensor.flatten()
        one_dim_tensor = torch.tensor([123])
        flat1 = zero_dim_tensor.flatten()

        self.assertEqual(zero_dim_tensor.shape, torch.Size([]))
        self.assertEqual(flat0.shape, torch.Size([1]))
        self.assertEqual(one_dim_tensor.shape, torch.Size([1]))
        self.assertEqual(flat1.shape, torch.Size([1]))
        self.assertEqual(flat0, one_dim_tensor)
        self.assertEqual(flat0, flat1)
        self.assertEqual(flat0.shape, flat1.shape)

        # Test both float tensor and quantized tensor
        tensors = [torch.randn(5, 5, 5, 5),
                   torch._empty_affine_quantized([5, 5, 5, 5],
                                                 scale=2,
                                                 zero_point=3,
                                                 dtype=torch.quint8)]
        for src in tensors:
            flat = src.flatten(0, -1)
            self.assertEqual(flat.shape, torch.Size([625]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(0, 2)
            self.assertEqual(flat.shape, torch.Size([125, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(0, 1)
            self.assertEqual(flat.shape, torch.Size([25, 5, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(1, 2)
            self.assertEqual(flat.shape, torch.Size([5, 25, 5]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(2, 3)
            self.assertEqual(flat.shape, torch.Size([5, 5, 25]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(-2, -1)
            self.assertEqual(flat.shape, torch.Size([5, 5, 25]))
            self.assertEqual(src.view(-1), flat.view(-1))

            flat = src.flatten(2, 2)
            self.assertEqual(flat, src)

            # out of bounds index
            with self.assertRaisesRegex(IndexError, 'Dimension out of range'):
                src.flatten(5, 10)

            # invalid start and end
            with self.assertRaisesRegex(RuntimeError, 'start_dim cannot come after end_dim'):
                src.flatten(2, 0)

    @staticmethod
    def _test_gather(self, cast, test_bounds=True):
        m, n, o = random.randint(10, 20), random.randint(10, 20), random.randint(10, 20)
        elems_per_row = random.randint(1, 10)
        dim = random.randrange(3)

        src = torch.randn(m, n, o)
        idx_size = [m, n, o]
        idx_size[dim] = elems_per_row
        idx = torch.LongTensor().resize_(*idx_size)
        _TestTorchMixin._fill_indices(self, idx, dim, src.size(dim), elems_per_row, m, n, o)

        src = cast(src)
        idx = cast(idx)

        actual = torch.gather(src, dim, idx)
        expected = cast(torch.Tensor().resize_(*idx_size))
        for i in range(idx_size[0]):
            for j in range(idx_size[1]):
                for k in range(idx_size[2]):
                    ii = [i, j, k]
                    ii[dim] = idx[i, j, k]
                    expected[i, j, k] = src[tuple(ii)]
        self.assertEqual(actual, expected, 0)

        bad_src = torch.randn(*[i - 1 for i in idx_size])
        self.assertRaises(RuntimeError, lambda: torch.gather(bad_src, dim, idx))

        if test_bounds:
            idx[0][0][0] = 23
            self.assertRaises(RuntimeError, lambda: torch.gather(src, dim, idx))

        src = cast(torch.randn(3, 4, 5))
        expected, idx = src.max(2, True)
        expected = cast(expected)
        idx = cast(idx)
        actual = torch.gather(src, 2, idx)
        self.assertEqual(actual, expected, 0)

        # Bool test case
        t = torch.tensor([[False, True], [True, True]])
        self.assertEqual(torch.gather(t, 1, torch.tensor([[0, 0], [1, 0]])), torch.tensor([[False, False], [True, True]]))

    def test_gather(self):
        self._test_gather(self, lambda t: t)

    @staticmethod
    def _test_scatter_base(self, cast, method, is_scalar=False, test_bounds=True):
        m, n, o = random.randint(10, 20), random.randint(10, 20), random.randint(10, 20)
        elems_per_row = random.randint(1, 10)
        dim = random.randrange(3)

        idx_size = [m, n, o]
        idx_size[dim] = elems_per_row
        idx = cast(torch.LongTensor().resize_(*idx_size))
        _TestTorchMixin._fill_indices(self, idx, dim, ([m, n, o])[dim], elems_per_row, m, n, o)

        src_size = [random.randint(1, 5) + s for s in idx_size]
        if is_scalar:
            src = random.random()
        else:
            src = cast(torch.Tensor(*src_size).normal_())

        base = cast(torch.randn(m, n, o))
        actual = getattr(base.clone(), method)(dim, idx, src)
        expected = base.clone()
        for i in range(idx_size[0]):
            for j in range(idx_size[1]):
                for k in range(idx_size[2]):
                    ii = [i, j, k]
                    ii[dim] = idx[i, j, k]
                    if method == 'scatter_' and not is_scalar:
                        expected[tuple(ii)] = src[i, j, k]
                    elif method == 'scatter_add_':
                        expected[tuple(ii)] += src[i, j, k]
                    else:
                        expected[tuple(ii)] = src
        self.assertEqual(actual, expected, 0)

        if test_bounds:
            idx[0][0][0] = 34
            with self.assertRaises(RuntimeError):
                getattr(base.clone(), method)(dim, idx, src)

        # test for empty index, should be a no-op
        idx = cast(torch.LongTensor())
        actual = getattr(base.clone(), method)(dim, idx, src)
        self.assertEqual(actual, base, 0)

    def test_scatter(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_')

    def test_scatterAdd(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_add_')

    def test_scatterFill(self):
        self._test_scatter_base(self, lambda t: t, 'scatter_', True)

    def test_masked_scatter(self):
        with warnings.catch_warnings(record=True) as w:
            warnings.simplefilter("always")
            for maskType in [torch.uint8, torch.bool]:
                for dt in torch.testing.get_all_dtypes():
                    num_copy, num_dest = 3, 10
                    dest = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype=dt)
                    dest2 = dest.clone()
                    src = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dt)
                    mask = torch.tensor((0, 0, 0, 0, 1, 0, 1, 0, 1, 0), dtype=maskType)

                    if dt == torch.bool:
                        # torch.bool is a special case and is being tested
                        # in a separate test
                        continue

                    # TODO: update test when masked scatter is supported for complex
                    if dt == torch.half or dt.is_complex:
                        self.assertRaises(RuntimeError, lambda: dest.masked_scatter_(mask, src))
                        continue

                    dest.masked_scatter_(mask, src)
                    j = 0
                    for i in range(num_dest):
                        if mask[i]:
                            dest2[i] = src[j]
                            j += 1
                    self.assertEqual(dest, dest2, 0)

                    # make source bigger than number of 1s in mask
                    src = torch.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=dt)
                    dest.masked_scatter_(mask, src)

                    # make src smaller. this should fail
                    src = torch.randn(num_copy - 1)
                    with self.assertRaises(RuntimeError):
                        dest.masked_scatter_(mask, src)
        # Only 16 (not 25) here as the warnings in the assertRaises are not caught on the python side
        self.assertEqual(len(w), 16)

        warn = 'masked_scatter_ received a mask with dtype torch.uint8,'
        for wi in w:
            self.assertEqual(str(wi.message)[0:55], str(warn))

    def test_masked_fill(self):
        with warnings.catch_warnings(record=True) as w:
            warnings.simplefilter("always")
            for dt in torch.testing.get_all_dtypes():
                for dtype in [torch.uint8, torch.bool]:
                    num_dest = 10
                    dst = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dt)
                    mask = torch.rand(num_dest).mul(2).floor().to(dtype)
                    val = random.random()
                    dst2 = dst.clone()

                    if dt == torch.half:
                        self.assertRaises(RuntimeError, lambda: dst.masked_fill_(mask, val))
                        continue

                    dst.masked_fill_(mask, val)
                    for i in range(num_dest):
                        if mask[i]:
                            dst2[i] = val
                    self.assertEqual(dst, dst2, 0)

                    # test non-contiguous case
                    dst = torch.randn(num_dest, num_dest, num_dest).permute((2, 0, 1))
                    dst2 = dst.clone()
                    dst.masked_fill_((dst > 0).to(dtype), val)
                    dst2.masked_fill_((dst2 > 0).to(dtype), val)
                    self.assertEqual(dst, dst2, 0)
            # Only 33 (not 32) here as the warning in the assertRaises are not caught on the python side
            self.assertEqual(len(w), 33)

            warn = 'masked_fill_ received a mask with dtype torch.uint8,'
            for wi in w:
                self.assertEqual(str(wi.message)[0:52], str(warn))


    def test_unbiased(self):
        tensor = torch.randn(100)
        self.assertEqual(tensor.var(0), tensor.var(0, unbiased=True))
        self.assertEqual(tensor.var(), tensor.var(unbiased=True))
        self.assertEqual(tensor.var(unbiased=False), tensor.var(0, unbiased=False))

        tensor = torch.FloatTensor([1.0, 2.0])
        self.assertEqual(tensor.var(unbiased=True), 0.5)
        self.assertEqual(tensor.var(unbiased=False), 0.25)

        tensor = torch.FloatTensor([1.0, 2.0, 3.0])
        self.assertEqual(tensor.var(unbiased=True), 1.0)
        self.assertEqual(tensor.var(unbiased=False), 2.0 / 3.0)

        tensor = torch.randn(100)
        self.assertEqual(tensor.std(0), tensor.std(0, unbiased=True))
        self.assertEqual(tensor.std(), tensor.std(unbiased=True))
        self.assertEqual(tensor.std(unbiased=False), tensor.std(0, unbiased=False))

    def test_structseq_repr(self):
        a = torch.arange(250).reshape(5, 5, 10)
        expected = """
        torch.return_types.max(
        values=tensor([[ 40,  41,  42,  43,  44,  45,  46,  47,  48,  49],
                [ 90,  91,  92,  93,  94,  95,  96,  97,  98,  99],
                [140, 141, 142, 143, 144, 145, 146, 147, 148, 149],
                [190, 191, 192, 193, 194, 195, 196, 197, 198, 199],
                [240, 241, 242, 243, 244, 245, 246, 247, 248, 249]]),
        indices=tensor([[4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],
                [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]]))"""
        self.assertEqual(repr(a.max(1)), textwrap.dedent(expected).strip())

    def test_var_stability(self):
        tensor = torch.FloatTensor([2281.5, 2281.25])
        self.assertEqual(tensor.var(dim=0), 0.03125)
        self.assertEqual(tensor.var(), 0.03125)

    def test_view_empty(self):
        x = torch.randn(0, 6)
        self.assertEqual((1, 0, 6, 1, 1), x.view(1, 0, 6, 1, 1).shape)

    def test_reshape(self):
        x = torch.randn(3, 3)
        self.assertEqual(x.data_ptr(), x.reshape(-1).data_ptr())
        self.assertEqual(x.data_ptr(), x.reshape(1, 9, 1).data_ptr())
        self.assertEqual(torch.reshape(x, (9,)), x.reshape(9))
        self.assertRaises(RuntimeError, lambda: x.reshape(-1, -1))

        y = torch.randn(4, 4, 4)[:, 0, :]
        self.assertNotEqual(y.data_ptr(), y.reshape(-1).data_ptr())
        self.assertEqual(y.contiguous().view(-1), y.reshape(-1))
        self.assertEqual(y.reshape(2, 2, 4).data_ptr(), y.data_ptr())

        s = torch.randn(())
        self.assertEqual(s.data_ptr(), s.reshape(()).data_ptr())
        self.assertEqual(s.reshape(-1).shape, (1,))
        self.assertRaises(RuntimeError, lambda: s.reshape(2))

        empty = torch.tensor([])
        self.assertEqual(empty, empty.reshape(-1))
        self.assertEqual(empty, empty.reshape([0]))
        # TODO: fix these once we have multi-dimensional empty tensors
        self.assertEqual(empty.reshape([0, 1]).shape, (0, 1))
        self.assertEqual(empty.reshape([1, -1]).shape, (1, 0))
        self.assertRaises(RuntimeError, lambda: empty.reshape(1))

        x = torch.randn(3, 3)
        self.assertEqual(x.data_ptr(), x.reshape_as(torch.rand(9)).data_ptr())
        self.assertEqual(x.data_ptr(), x.reshape_as(torch.rand(1, 9, 1)).data_ptr())
        self.assertRaises(RuntimeError, lambda: x.reshape_as(torch.rand(10)))

    def test_empty_reshape(self):
        x = torch.randn(0, 6)
        self.assertEqual((1, 0, 6, 1, 1), x.reshape(1, 0, 6, 1, 1).shape)
        # should be viewable -- i.e. data_ptr is the same.
        self.assertEqual(x.data_ptr(), x.reshape(1, 0, 6, 1, 1).data_ptr())

        # match NumPy semantics -- don't infer the size of dimension with a degree of freedom
        self.assertRaises(RuntimeError, lambda: x.reshape(0, -1))

    def check_single_matmul(self, x, y, shape):
        a = np.array(x, copy=False)
        b = np.array(y, copy=False)
        expected = np.matmul(a, b)

        ans = torch.matmul(x, y)
        self.assertTrue(ans.is_contiguous())
        self.assertTrue(np.array_equal(ans, expected))

        out = torch.zeros(*shape, dtype=torch.int64)
        ans = torch.matmul(x, y, out=out)
        self.assertIs(ans, out)
        self.assertTrue(ans.is_contiguous())
        self.assertTrue(np.array_equal(ans, expected))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_matmul_small_brute_force_1d_Nd(self):
        # Issue #20452: range(0, 10) does not work.
        n = 1
        for m in range(1, 8):
            for p in range(1, 8):
                for o in range(1, 5):
                    # 1d, 3d, inner dimensions C
                    x = torch.arange(m)
                    y = torch.arange(o * m * p).reshape(o, m, p)
                    self.check_single_matmul(x, y, (o, n, p))

                    # 1d, 3d, inner dimensions Fortran
                    x = torch.arange(m)
                    y = torch.arange(o * p * m).reshape(o, p, m).transpose(-1, -2)
                    self.check_single_matmul(x, y, (o, n, p))

                    # 1d, 3d, inner dimensions non-contiguous
                    x = torch.arange(2 * m)[::2]
                    y = torch.arange(o * m * 2 * p).reshape(o, m, 2 * p)[:, :, ::2]
                    self.check_single_matmul(x, y, (o, n, p))

                    for r in range(1, 5):
                        # 1d, 4d, inner dimensions C
                        x = torch.arange(m)
                        y = torch.arange(r * o * m * p).reshape(r, o, m, p)
                        self.check_single_matmul(x, y, (r, o, n, p))

                        # 1d, 4d, inner dimensions Fortran
                        x = torch.arange(m)
                        y = torch.arange(r * o * p * m).reshape(r, o, p, m).transpose(-1, -2)
                        self.check_single_matmul(x, y, (r, o, n, p))

                        # 1d, 4d, inner dimensions non-contiguous
                        x = torch.arange(2 * m)[::2]
                        y = torch.arange(r * o * m * 2 * p).reshape(r, o, m, 2 * p)[:, :, :, ::2]
                        self.check_single_matmul(x, y, (r, o, n, p))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_matmul_small_brute_force_2d_Nd(self):
        # Issue #20452: range(0, 10) does not work.
        for n in range(1, 5):
            for m in range(1, 5):
                for p in range(1, 5):
                    for o in range(1, 3):
                        # 2d, 3d, inner dimensions C
                        x = torch.arange(n * m).reshape(n, m)
                        y = torch.arange(o * m * p).reshape(o, m, p)
                        self.check_single_matmul(x, y, (o, n, p))

                        # 2d, 3d, inner dimensions Fortran
                        x = torch.arange(m * n).reshape(m, n).transpose(-1, -2)
                        y = torch.arange(o * p * m).reshape(o, p, m).transpose(-1, -2)
                        self.check_single_matmul(x, y, (o, n, p))

                        # 2d, 3d, inner dimensions non-contiguous
                        x = torch.arange(n * 2 * m).reshape(n, 2 * m)[:, ::2]
                        y = torch.arange(o * m * 2 * p).reshape(o, m, 2 * p)[:, :, ::2]
                        self.check_single_matmul(x, y, (o, n, p))

                        for r in range(1, 2):
                            # 2d, 4d, inner dimensions C
                            x = torch.arange(n * m).reshape(n, m)
                            y = torch.arange(r * o * m * p).reshape(r, o, m, p)
                            self.check_single_matmul(x, y, (r, o, n, p))

                            # 2d, 4d, inner dimensions Fortran
                            x = torch.arange(m * n).reshape(m, n).transpose(-1, -2)
                            y = torch.arange(r * o * p * m).reshape(r, o, p, m).transpose(-1, -2)
                            self.check_single_matmul(x, y, (r, o, n, p))

                            # 2d, 4d, inner dimensions non-contiguous
                            x = torch.arange(n * 2 * m).reshape(n, 2 * m)[:, ::2]
                            y = torch.arange(r * o * m * 2 * p).reshape(r, o, m, 2 * p)[:, :, :, ::2]
                            self.check_single_matmul(x, y, (r, o, n, p))

    def test_expand(self):
        tensor = torch.rand(1, 8, 1)
        tensor2 = torch.rand(5)
        template = torch.rand(4, 8, 5)
        target = template.size()
        self.assertEqual(tensor.expand_as(template).size(), target)
        self.assertEqual(tensor.expand(4, 8, 5).size(), target)
        self.assertEqual(tensor.expand(target).size(), target)
        self.assertEqual(tensor2.expand_as(template).size(), target)
        self.assertEqual(tensor2.expand(4, 8, 5).size(), target)
        self.assertEqual(tensor2.expand(target).size(), target)

        # test double expand
        self.assertEqual(tensor2.expand(1, 5).expand(2, 2, 5), tensor2.repeat(2, 2, 1))

        # test non-contiguous
        noncontig = torch.randn(5, 2, 1, 3)[:, 0]
        self.assertFalse(noncontig.is_contiguous())
        self.assertEqual(noncontig.expand(2, 5, 4, 3), noncontig.contiguous().repeat(2, 1, 4, 1))

        # make sure it's compatible with unsqueeze
        expanded = tensor2.expand(1, 1, 5)
        unsqueezed = tensor2.unsqueeze(0).unsqueeze(1)
        self.assertEqual(expanded, unsqueezed)
        self.assertEqual(expanded.stride(), unsqueezed.stride())

        # test -1 as target size
        self.assertEqual(tensor.expand(4, -1, 5), tensor.expand(4, 8, 5))
        self.assertRaises(RuntimeError, lambda: tensor2.expand(-1, -1))

        # test expanding empty to empty
        self.assertEqual(torch.zeros(0).expand((0,)), torch.zeros(0))

    def test_repeat(self):
        initial_shape = (8, 4)
        tensor = torch.rand(*initial_shape)

        size = (3, 1, 1)
        torchSize = torch.Size(size)
        target = [3, 8, 4]
        self.assertEqual(tensor.repeat(*size).size(), target, 'Error in repeat')
        self.assertEqual(tensor.repeat(torchSize).size(), target,
                         'Error in repeat using LongStorage')
        result = tensor.repeat(*size)
        self.assertEqual(result.size(), target, 'Error in repeat using result')
        result = tensor.repeat(torchSize)
        self.assertEqual(result.size(), target, 'Error in repeat using result and LongStorage')
        self.assertEqual(result.mean(0).view(8, 4), tensor, 'Error in repeat (not equal)')

        zeroDimTarget = torch.Size([24, 0])
        self.assertEqual(tensor.repeat((3, 0)).size(), zeroDimTarget, "Error when calling with 0 repeats")

    def test_repeat_interleave(self):
        x = torch.tensor([0, 1, 2, 3])
        expected = torch.tensor([1, 2, 2, 3, 3, 3])
        self.assertEqual(torch.repeat_interleave(x), expected)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.arange(4).reshape(2, 2))

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.arange(4.0))

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(torch.tensor([1, 2, -1, 3, 4]))

        y = torch.tensor([[1, 2], [3, 4]])

        y1_v1 = torch.repeat_interleave(y, 2)
        y1_v2 = torch.repeat_interleave(y, torch.tensor(2))
        y1_v3 = torch.repeat_interleave(y, torch.tensor([2]))
        y1_expect = torch.tensor([1, 1, 2, 2, 3, 3, 4, 4])
        self.assertEqual(y1_v1, y1_expect)
        self.assertEqual(y1_v2, y1_expect)
        self.assertEqual(y1_v3, y1_expect)

        y2 = torch.repeat_interleave(y, 3, dim=1)
        y2_expect = torch.tensor([[1, 1, 1, 2, 2, 2],
                                  [3, 3, 3, 4, 4, 4]])
        self.assertEqual(y2, y2_expect)

        y3 = torch.repeat_interleave(y, torch.tensor([1, 2]), dim=0)
        y3_expect = torch.tensor([[1, 2],
                                  [3, 4],
                                  [3, 4]])
        self.assertEqual(y3, y3_expect)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(y, torch.tensor([1, 2, 3]), dim=0)

        with self.assertRaises(RuntimeError):
            torch.repeat_interleave(y, torch.arange(9).reshape(3, 3), dim=0)

        # test zero sized dimension
        x = torch.zeros((5, 0))
        y = torch.repeat_interleave(x, repeats=3, dim=1)
        self.assertEqual(y, x.new_zeros(5, 0))

        x = torch.tensor([], dtype=torch.int64)
        y = torch.repeat_interleave(x, x)
        self.assertEqual(y, x)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_repeat_tile(self):

        initial_shape = (8, 4)

        repeats = ((3, 1, 1),
                   (3, 3, 3),
                   (1, 2, 1),
                   (2, 2, 2, 2))

        def _generate_noncontiguous_input():

            out = np.broadcast_to(np.random.random((1, 4)),
                                  initial_shape)
            # Note: non-writeable NumPy arrays will warn if converted to tensors
            out.setflags(write=True)

            assert not (out.flags.c_contiguous or out.flags.f_contiguous)

            return out

        for repeat in repeats:
            for tensor in (torch.from_numpy(np.random.random(initial_shape)),
                           torch.from_numpy(_generate_noncontiguous_input()),):

                self.assertEqual(tensor.repeat(*repeat).numpy(),
                                 np.tile(tensor.numpy(), repeat))

    def test_is_same_size(self):
        t1 = torch.Tensor(3, 4, 9, 10)
        t2 = torch.Tensor(3, 4)
        t3 = torch.Tensor(1, 9, 3, 3)
        t4 = torch.Tensor(3, 4, 9, 10)

        self.assertFalse(t1.is_same_size(t2))
        self.assertFalse(t1.is_same_size(t3))
        self.assertTrue(t1.is_same_size(t4))

    def test_tensor_set(self):
        t1 = torch.Tensor()
        t2 = torch.Tensor(3, 4, 9, 10).uniform_()
        t1.set_(t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        size = torch.Size([9, 3, 4, 10])
        t1.set_(t2.storage(), 0, size)
        self.assertEqual(t1.size(), size)
        t1.set_(t2.storage(), 0, tuple(size))
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), (120, 40, 10, 1))
        stride = (10, 360, 90, 1)
        t1.set_(t2.storage(), 0, size, stride)
        self.assertEqual(t1.stride(), stride)
        t1.set_(t2.storage(), 0, size=size, stride=stride)
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), stride)

        # test argument names
        t1 = torch.Tensor()
        # 1. case when source is tensor
        t1.set_(source=t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        # 2. case when source is storage
        t1.set_(source=t2.storage())
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)
        # 3. case when source is storage, and other args also specified
        t1.set_(source=t2.storage(), storage_offset=0, size=size, stride=stride)
        self.assertEqual(t1.size(), size)
        self.assertEqual(t1.stride(), stride)

        t1 = torch.tensor([True, True], dtype=torch.bool)
        t2 = torch.tensor([False, False], dtype=torch.bool)
        t1.set_(t2)
        self.assertEqual(t1.storage()._cdata, t2.storage()._cdata)

    def test_tensor_set_errors(self):
        f_cpu = torch.randn((2, 3), dtype=torch.float32)
        d_cpu = torch.randn((2, 3), dtype=torch.float64)

        # change dtype
        self.assertRaises(RuntimeError, lambda: f_cpu.set_(d_cpu.storage()))
        self.assertRaises(RuntimeError,
                          lambda: f_cpu.set_(d_cpu.storage(), 0, d_cpu.size(), d_cpu.stride()))
        self.assertRaises(RuntimeError, lambda: f_cpu.set_(d_cpu))

        # change device
        if torch.cuda.is_available():
            f_cuda = torch.randn((2, 3), dtype=torch.float32, device='cuda')

            # cpu -> cuda
            self.assertRaises(RuntimeError, lambda: f_cpu.set_(f_cuda.storage()))
            self.assertRaises(RuntimeError,
                              lambda: f_cpu.set_(f_cuda.storage(), 0, f_cuda.size(), f_cuda.stride()))
            self.assertRaises(RuntimeError, lambda: f_cpu.set_(f_cuda))

            # cuda -> cpu
            self.assertRaises(RuntimeError, lambda: f_cuda.set_(f_cpu.storage()))
            self.assertRaises(RuntimeError,
                              lambda: f_cuda.set_(f_cpu.storage(), 0, f_cpu.size(), f_cpu.stride()))
            self.assertRaises(RuntimeError, lambda: f_cuda.set_(f_cpu))

    def test_equal(self):
        # Contiguous, 1D
        t1 = torch.Tensor((3, 4, 9, 10))
        t2 = t1.contiguous()
        t3 = torch.Tensor((1, 9, 3, 10))
        t4 = torch.Tensor((3, 4, 9))
        t5 = torch.Tensor()
        self.assertTrue(t1.equal(t2))
        self.assertFalse(t1.equal(t3))
        self.assertFalse(t1.equal(t4))
        self.assertFalse(t1.equal(t5))
        self.assertTrue(torch.equal(t1, t2))
        self.assertFalse(torch.equal(t1, t3))
        self.assertFalse(torch.equal(t1, t4))
        self.assertFalse(torch.equal(t1, t5))

        # Non contiguous, 2D
        s = torch.Tensor(((1, 2, 3, 4), (5, 6, 7, 8)))
        s1 = s[:, 1:3]
        s2 = s1.clone()
        s3 = torch.Tensor(((2, 3), (6, 7)))
        s4 = torch.Tensor(((0, 0), (0, 0)))

        self.assertFalse(s1.is_contiguous())
        self.assertTrue(s1.equal(s2))
        self.assertTrue(s1.equal(s3))
        self.assertFalse(s1.equal(s4))
        self.assertTrue(torch.equal(s1, s2))
        self.assertTrue(torch.equal(s1, s3))
        self.assertFalse(torch.equal(s1, s4))

    def test_element_size(self):
        byte = torch.ByteStorage().element_size()
        char = torch.CharStorage().element_size()
        short = torch.ShortStorage().element_size()
        int = torch.IntStorage().element_size()
        long = torch.LongStorage().element_size()
        float = torch.FloatStorage().element_size()
        double = torch.DoubleStorage().element_size()
        bool = torch.BoolStorage().element_size()
        bfloat16 = torch.BFloat16Storage().element_size()
        complexfloat = torch.ComplexFloatStorage().element_size()
        complexdouble = torch.ComplexDoubleStorage().element_size()

        self.assertEqual(byte, torch.ByteTensor().element_size())
        self.assertEqual(char, torch.CharTensor().element_size())
        self.assertEqual(short, torch.ShortTensor().element_size())
        self.assertEqual(int, torch.IntTensor().element_size())
        self.assertEqual(long, torch.LongTensor().element_size())
        self.assertEqual(float, torch.FloatTensor().element_size())
        self.assertEqual(double, torch.DoubleTensor().element_size())
        self.assertEqual(bool, torch.BoolTensor().element_size())
        self.assertEqual(bfloat16, torch.tensor([], dtype=torch.bfloat16).element_size())
        self.assertEqual(complexfloat, torch.tensor([], dtype=torch.complex64).element_size())
        self.assertEqual(complexdouble, torch.tensor([], dtype=torch.complex128).element_size())

        self.assertGreater(byte, 0)
        self.assertGreater(char, 0)
        self.assertGreater(short, 0)
        self.assertGreater(int, 0)
        self.assertGreater(long, 0)
        self.assertGreater(float, 0)
        self.assertGreater(double, 0)
        self.assertGreater(bool, 0)
        self.assertGreater(bfloat16, 0)
        self.assertGreater(complexfloat, 0)
        self.assertGreater(complexdouble, 0)

        # These tests are portable, not necessarily strict for your system.
        self.assertEqual(byte, 1)
        self.assertEqual(char, 1)
        self.assertEqual(bool, 1)
        self.assertGreaterEqual(short, 2)
        self.assertGreaterEqual(int, 2)
        self.assertGreaterEqual(int, short)
        self.assertGreaterEqual(long, 4)
        self.assertGreaterEqual(long, int)
        self.assertGreaterEqual(double, float)

    def test_split(self):
        tensor = torch.rand(7, 4)
        split_size = 3
        dim = 0
        target_sizes = ([3, 4], [3, 4], [1, 4])
        splits = tensor.split(split_size, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        # Variable sections split
        tensor = torch.randn(20, 10)
        dim = 0
        split_sizes = [5, 5, 10]
        target_sizes = ([[5, 10], [5, 10], [10, 10]])
        splits = tensor.split(split_sizes, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        split_sizes = [2, 2, 6]
        target_sizes = ([20, 2], [20, 2], [20, 6])
        dim = 1
        splits = tensor.split(split_sizes, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

    def test_chunk(self):
        tensor = torch.rand(4, 7)
        num_chunks = 3
        dim = 1
        target_sizes = ([4, 3], [4, 3], [4, 1])
        splits = tensor.chunk(num_chunks, dim)
        start = 0
        for target_size, split in zip(target_sizes, splits):
            self.assertEqual(split.size(), target_size)
            self.assertEqual(tensor.narrow(dim, start, target_size[dim]), split, 0)
            start = start + target_size[dim]

        # Invalid chunk sizes
        error_regex = 'chunk expects.*greater than 0'
        with self.assertRaisesRegex(RuntimeError, error_regex):
            tensor.chunk(0)
        with self.assertRaisesRegex(RuntimeError, error_regex):
            tensor.chunk(-2)

    def test_tolist(self):
        list0D = []
        tensor0D = torch.Tensor(list0D)
        self.assertEqual(tensor0D.tolist(), list0D)

        table1D = [1, 2, 3]
        tensor1D = torch.Tensor(table1D)
        storage = torch.Storage(table1D)
        self.assertEqual(tensor1D.tolist(), table1D)
        self.assertEqual(storage.tolist(), table1D)
        self.assertEqual(tensor1D.tolist(), table1D)
        self.assertEqual(storage.tolist(), table1D)

        table2D = [[1, 2], [3, 4]]
        tensor2D = torch.Tensor(table2D)
        self.assertEqual(tensor2D.tolist(), table2D)

        tensor3D = torch.Tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
        tensorNonContig = tensor3D.select(1, 1)
        self.assertFalse(tensorNonContig.is_contiguous())
        self.assertEqual(tensorNonContig.tolist(), [[3, 4], [7, 8]])

    def test_permute(self):
        orig = [1, 2, 3, 4, 5, 6, 7]
        perm = torch.randperm(7).tolist()
        x = torch.Tensor(*orig).fill_(0)
        new = list(map(lambda x: x - 1, x.permute(*perm).size()))
        self.assertEqual(perm, new)
        self.assertEqual(x.size(), orig)

    def test_reversed(self):
        val = torch.arange(0, 10)
        self.assertEqual(reversed(val), torch.arange(9, -1, -1))

        val = torch.arange(1, 10).view(3, 3)
        self.assertEqual(reversed(val), torch.tensor([[7, 8, 9], [4, 5, 6], [1, 2, 3]]))

        val = torch.tensor(42)
        self.assertEqual(reversed(val), torch.tensor(42))

    def test_contains(self):
        x = torch.arange(0, 10)
        self.assertEqual(4 in x, True)
        self.assertEqual(12 in x, False)

        x = torch.arange(1, 10).view(3, 3)
        val = torch.arange(1, 4)
        self.assertEqual(val in x, True)
        val += 10
        self.assertEqual(val in x, False)

        self.assertRaisesRegex(
            RuntimeError,
            "Tensor.__contains__ only supports Tensor or scalar, but you passed in a {}.".format(type("foo")),
            lambda: "foo" in x)
        self.assertRaisesRegex(
            RuntimeError,
            "Tensor.__contains__ only supports Tensor or scalar, but you passed in a {}.".format(type([1, 2])),
            lambda: [1, 2] in x)

    def test_deepcopy_parameter(self):
        from copy import deepcopy
        l = torch.nn.Linear(10, 1)
        s = l.state_dict(keep_vars=True)
        self.assertEqual(torch.nn.Parameter, type(s['weight']))
        self.assertEqual(torch.nn.Parameter, type(s['bias']))

        s2 = deepcopy(s)
        self.assertEqual(torch.nn.Parameter, type(s2['weight']))
        self.assertEqual(torch.nn.Parameter, type(s2['bias']))

    def test_pickle(self):
        import pickle
        a = torch.randn(5, 5)
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertEqual(a, b)

    def test_pickle_parameter(self):
        import pickle
        a = torch.nn.Parameter(torch.randn(5, 5))
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.nn.Parameter))
        self.assertEqual(a.requires_grad, b.requires_grad)
        self.assertEqual(a, b)

    def test_pickle_parameter_no_requires_grad(self):
        import pickle
        a = torch.nn.Parameter(torch.randn(5, 5), requires_grad=False)
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.nn.Parameter))
        self.assertEqual(a.requires_grad, b.requires_grad)
        self.assertEqual(a, b)

    def test_pickle_dtype(self):
        t = torch.float32
        serialized = pickle.dumps(t)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.dtype))
        self.assertEqual(id(b), id(t))

    def test_pickle_size(self):
        a = torch.rand(10).size()
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertTrue(isinstance(b, torch.Size))
        self.assertEqual(a, b)

    def test_pickle_function(self):
        # https://github.com/pytorch/pytorch/issues/37703
        a = torch.tanh
        serialized = pickle.dumps(a)
        b = pickle.loads(serialized)
        self.assertEqual(a, b)

    def test_norm_fastpaths(self):
        x = torch.randn(3, 5)

        # slow path
        result = torch.norm(x, 4.5, 1)
        expected = torch.pow(x.abs().pow(4.5).sum(1), 1.0 / 4.5)
        self.assertEqual(result, expected)

        # fast 0-norm
        result = torch.norm(x, 0, 1)
        expected = (x != 0).type_as(x).sum(1)
        self.assertEqual(result, expected)

        # fast 1-norm
        result = torch.norm(x, 1, 1)
        expected = x.abs().sum(1)
        self.assertEqual(result, expected)

        # fast 2-norm
        result = torch.norm(x, 2, 1)
        expected = torch.sqrt(x.pow(2).sum(1))
        self.assertEqual(result, expected)

        # fast 3-norm
        result = torch.norm(x, 3, 1)
        expected = torch.pow(x.pow(3).abs().sum(1), 1.0 / 3.0)
        self.assertEqual(result, expected)

    @staticmethod
    def _test_bernoulli(self, t_dtype, p_dtype, device):
        for trivial_p in ([0, 1], [1, 0, 1, 1, 0, 1]):
            x = torch.tensor(trivial_p, dtype=p_dtype, device=device)
            self.assertEqual(x.bernoulli().tolist(), trivial_p)

        def isBinary(t):
            return torch.ne(t, 0).mul_(torch.ne(t, 1)).sum().item() == 0

        p = torch.rand(5, 5, dtype=p_dtype, device=device)
        self.assertTrue(isBinary(p.bernoulli()))

        p = torch.rand(5, dtype=p_dtype, device=device).expand(5, 5)
        self.assertTrue(isBinary(p.bernoulli()))

        p = torch.rand(5, 5, dtype=p_dtype, device=device)
        torch.bernoulli(torch.rand_like(p), out=p)
        self.assertTrue(isBinary(p))

        p = torch.rand(5, dtype=p_dtype, device=device).expand(5, 5)
        torch.bernoulli(torch.rand_like(p), out=p)
        self.assertTrue(isBinary(p))

        t = torch.empty(10, 10, dtype=t_dtype, device=device)

        t.fill_(2)
        t.bernoulli_(0.5)
        self.assertTrue(isBinary(t))

        p = torch.rand(10, dtype=p_dtype, device=device).expand(10, 10)
        t.fill_(2)
        t.bernoulli_(p)
        self.assertTrue(isBinary(t))

        t.fill_(2)
        torch.bernoulli(torch.rand_like(t, dtype=p_dtype), out=t)
        self.assertTrue(isBinary(t))

        t.fill_(2)
        t.bernoulli_(torch.rand_like(t, dtype=p_dtype))
        self.assertTrue(isBinary(t))

    def test_bernoulli(self):
        self._test_bernoulli(self, torch.float32, torch.float64, 'cpu')
        # test that it works with integral tensors
        self._test_bernoulli(self, torch.uint8, torch.float64, 'cpu')
        # test that it works with bool tensors
        self._test_bernoulli(self, torch.bool, torch.float32, 'cpu')

    @slowTest
    def test_bernoulli_edge_cases(self):
        # Need to draw a lot of samples to cover every random floating point number.
        a = torch.zeros(10000, 10000, dtype=torch.float32)  # probability of drawing "1" is 0
        num_ones = (torch.bernoulli(a) == 1).sum()
        self.assertEqual(num_ones, 0)

        b = torch.ones(10000, 10000, dtype=torch.float32)  # probability of drawing "1" is 1
        num_zeros = (torch.bernoulli(b) == 0).sum()
        self.assertEqual(num_zeros, 0)

    def test_generator_cpu(self):
        # test default generators are equal
        self.assertEqual(torch.default_generator, torch.default_generator)

        # tests Generator API
        # manual_seed, seed, initial_seed, get_state, set_state
        g1 = torch.Generator()
        g2 = torch.Generator()
        g1.manual_seed(12345)
        g2.manual_seed(12345)
        self.assertEqual(g1.initial_seed(), g2.initial_seed())

        g1.seed()
        g2.seed()
        self.assertNotEqual(g1.initial_seed(), g2.initial_seed())

        g1 = torch.Generator()
        g2_state = g2.get_state()
        g2_randn = torch.randn(1, generator=g2)
        g1.set_state(g2_state)
        g1_randn = torch.randn(1, generator=g1)
        self.assertEqual(g1_randn, g2_randn)

        default_state = torch.default_generator.get_state()
        q = torch.Tensor(100)
        g1_normal = q.normal_()
        g2 = torch.Generator()
        g2.set_state(default_state)
        g2_normal = q.normal_(generator=g2)
        self.assertEqual(g1_normal, g2_normal)

    def test_sobolengine_unscrambled_lowdim(self):
        engine_1d = torch.quasirandom.SobolEngine(1)
        expected_1d = torch.tensor([0.5, 0.75, 0.25, 0.375, 0.875, 0.625, 0.125, 0.1875, 0.6875, 0.9375])
        actual_1d = engine_1d.draw(10)
        self.assertEqual(actual_1d.view(-1), expected_1d)
        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))

        # Test out kwarg
        engine_1d.reset()
        actual_1d_out = torch.Tensor().float()
        engine_1d.draw(10, out=actual_1d_out)
        self.assertEqual(actual_1d.view(-1), expected_1d)

        engine_3d = torch.quasirandom.SobolEngine(3)
        expected_3d = torch.tensor([0.5, 0.75, 0.25, 0.625, 0.125, 0.375, 0.875, 0.3125, 0.8125, 0.5625])
        actual_3d = engine_3d.draw(10)
        self.assertEqual(actual_3d[:, 2], expected_3d)
        self.assertEqual(actual_3d[:, 0], expected_1d)
        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))

        engine_3d = torch.quasirandom.SobolEngine(3)
        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
        self.assertEqual(draws, actual_3d)

        engine_3d = torch.quasirandom.SobolEngine(3).fast_forward(5)
        draws = engine_3d.draw(5)
        self.assertEqual(draws, actual_3d[5:])
        engine_3d.reset()
        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
        engine_3d.fast_forward(2)
        self.assertEqual(engine_3d.draw(5), actual_3d[5:])

    def test_sobolengine_unscrambled_highdim(self):
        from collections import Counter
        engine = torch.quasirandom.SobolEngine(1111)
        count1 = dict(Counter(engine.draw().view(-1).tolist()))
        count2 = dict(Counter(engine.draw().view(-1).tolist()))
        count3 = dict(Counter(engine.draw().view(-1).tolist()))
        self.assertTrue(count1 == {0.5: 1111})
        self.assertTrue(count2 == {0.25: 580, 0.75: 531})
        self.assertTrue(count3 == {0.25: 531, 0.75: 580})

        engine = torch.quasirandom.SobolEngine(1111)
        draws = engine.draw(1000)
        self.assertTrue(torch.all(draws <= 1))
        self.assertTrue(torch.all(draws >= 0))

    def test_sobolengine_scrambled_lowdim(self):
        engine_1d = torch.quasirandom.SobolEngine(1, scramble=True, seed=1729)
        expected_1d = [0.16478512, 0.43221009, 0.84261382, 0.99750268, 0.27460563,
                       0.01084163, 0.73373985, 0.65039611, 0.12329865, 0.35587373]
        actual_1d = engine_1d.draw(10)
        self.assertEqual(actual_1d.flatten(), torch.tensor(expected_1d), atol=1e-5)
        self.assertEqual(actual_1d.size(), torch.Size([10, 1]))
        # make sure random seed if chosen if none is provided
        engine_1d_a = torch.quasirandom.SobolEngine(1, scramble=True)
        engine_1d_b = torch.quasirandom.SobolEngine(1, scramble=True)
        self.assertNotEqual(engine_1d_a.draw(2), engine_1d_b.draw(2))

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        expected_3d = [0.32642800, 0.17881306, 0.68837059, 0.46492538, 0.91789097,
                       0.58075899, 0.03642474, 0.68229187, 0.20051685, 0.30083340]
        actual_3d = engine_3d.draw(10)
        self.assertEqual(actual_3d[:, 2], torch.tensor(expected_3d))
        self.assertEqual(actual_3d.size(), torch.Size([10, 3]))

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        draws = torch.cat([engine_3d.draw() for _ in range(0, 10)])
        self.assertEqual(draws, actual_3d)

        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True, seed=1729)
        engine_3d.fast_forward(5)
        draws = engine_3d.draw(5)
        self.assertEqual(draws, actual_3d[5:])
        engine_3d.reset()
        self.assertEqual(engine_3d.draw(3), actual_3d[:3])
        engine_3d.fast_forward(2)
        self.assertEqual(engine_3d.draw(5), actual_3d[5:])

    def test_sobolengine_scrambled_lowdim_default_rng(self):
        expected_1d = [0.039826, 0.484409, 0.953192, 0.799275, 0.267996]
        torch.manual_seed(123456)
        engine_1d = torch.quasirandom.SobolEngine(1, scramble=True)
        actual_1d = engine_1d.draw(5)
        self.assertEqual(actual_1d[:, 0], expected_1d)
        torch.manual_seed(123456)
        expected_3d = [0.133490, 0.480183, 0.855304, 0.970967, 0.345844]
        engine_3d = torch.quasirandom.SobolEngine(3, scramble=True)
        actual_3d = engine_3d.draw(5)
        self.assertEqual(actual_3d[:, 0], expected_3d)

    def test_sobolengine_scrambled_highdim(self):
        engine = torch.quasirandom.SobolEngine(1111, scramble=True)
        draws = engine.draw(1000)
        self.assertTrue(torch.all(draws <= 1))
        self.assertTrue(torch.all(draws >= 0))

    def test_parsing_int64(self):
        # accepts integer arguments
        x = torch.cumsum(torch.ones(5, 5), 0)
        self.assertEqual(x, torch.cumsum(torch.ones(5, 5), torch.tensor(0)))
        # doesn't accept floating point variables
        self.assertRaises(TypeError, lambda: torch.cumsum(torch.ones(5, 5), torch.tensor(0.)))

    def test_parsing_double(self):
        # accepts floating point and integer arguments
        x = torch.randn(2, 3)
        torch.isclose(x, x, 1, 1)
        self.assertTrue(torch.isclose(x, x, 1, 1).all())
        self.assertTrue(torch.isclose(x, x, 1.5, 1.).all())
        # accepts floating point and integer tensors
        self.assertTrue(torch.isclose(x, x, torch.tensor(1), torch.tensor(1)).all())
        self.assertTrue(torch.isclose(x, x, torch.tensor(1.5), torch.tensor(1.)).all())
        # doesn't accept variables with requires_grad
        self.assertRaises(TypeError,
                          lambda: torch.isclose(x, x, torch.tensor(1.5), torch.tensor(1., requires_grad=True)).all())

    def test_parsing_intlist(self):
        #  parse with integer variables
        self.assertEqual(torch.Size([3, 4]), torch.ones((torch.tensor(3), torch.tensor(4))).shape)
        self.assertEqual(torch.Size([3, 4]), torch.ones(torch.tensor(3), torch.tensor(4)).shape)
        # parse with numpy integers
        if TEST_NUMPY:
            self.assertEqual(torch.Size([3, 4]), torch.ones((np.array(3), np.int64(4))).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones(np.array(3), np.int64(4)).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones((np.int64(3), np.array(4))).shape)
            self.assertEqual(torch.Size([3, 4]), torch.ones(np.int64(3), np.array(4)).shape)

        # fail parse with float variables
        self.assertRaises(TypeError, lambda: torch.ones((torch.tensor(3.), torch.tensor(4))))
        # fail parse with numpy floats
        if TEST_NUMPY:
            self.assertRaises(TypeError, lambda: torch.ones((np.float(3.), torch.tensor(4))))
            self.assertRaises(TypeError, lambda: torch.ones((np.array(3.), torch.tensor(4))))

        # fail parse with > 1 element variables
        self.assertRaises(TypeError, lambda: torch.ones(torch.tensor(3, 3)))
        self.assertRaises(TypeError, lambda: torch.ones((torch.tensor(3, 3))))
        if TEST_NUMPY:
            self.assertRaises(TypeError, lambda: torch.ones(np.array(3, 3)))
            self.assertRaises(TypeError, lambda: torch.ones((np.array(3, 3))))

        # fail parse with additional positional args after intlist arg
        self.assertRaisesRegex(TypeError,
                               "received an invalid combination of arguments",
                               lambda: torch.LongTensor((6, 0), 1, 1, 0))
        self.assertRaisesRegex(TypeError,
                               "missing 1 required positional arguments",
                               lambda: torch.tensor().new_zeros((5, 5), 0))

    def test_half_tensor(self):
        x = torch.randn(5, 5).float()
        y = torch.randn(5, 5).float()
        xh, yh = x.half(), y.half()

        self.assertEqual(x.half().float(), x, 1e-3)

        z = torch.Tensor(5, 5)
        self.assertEqual(z.copy_(xh), x, 1e-3)

        with tempfile.NamedTemporaryFile() as f:
            torch.save(xh, f)
            f.seek(0)
            xh2 = torch.load(f)
            self.assertEqual(xh.float(), xh2.float())

    def test_from_buffer(self):
        a = bytearray([1, 2, 3, 4])
        self.assertEqual(torch.ByteStorage.from_buffer(a).tolist(), [1, 2, 3, 4])
        shorts = torch.ShortStorage.from_buffer(a, 'big')
        self.assertEqual(shorts.size(), 2)
        self.assertEqual(shorts.tolist(), [258, 772])
        ints = torch.IntStorage.from_buffer(a, 'little')
        self.assertEqual(ints.size(), 1)
        self.assertEqual(ints[0], 67305985)
        f = bytearray([0x40, 0x10, 0x00, 0x00])
        floats = torch.FloatStorage.from_buffer(f, 'big')
        self.assertEqual(floats.size(), 1)
        self.assertEqual(floats[0], 2.25)

        f = bytearray([0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x10, 0x40])
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 8)
        self.assertEqual(bools.tolist(), [False, True, True, True, True, True, True, True])
        self.assertEqual(bools.type(), 'torch.BoolStorage')

        f = bytearray(b'\x80\x02\x8a\nl\xfc\x9cF\xf9 j\xa8P\x19.\x80\x02M\xe9')
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 19)

        f = bytearray(b'\0x4A')
        bools = torch.BoolStorage.from_buffer(f, 'big')
        self.assertEqual(bools.size(), 4)
        self.assertEqual(bools.tolist(), [False, True, True, True])

    def test_storage_casts(self):
        storage = torch.IntStorage([-1, 0, 1, 2, 3, 4])
        self.assertEqual(storage.size(), 6)
        self.assertEqual(storage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(storage.type(), 'torch.IntStorage')
        self.assertIs(storage.dtype, torch.int32)

        floatStorage = storage.float()
        self.assertEqual(floatStorage.size(), 6)
        self.assertEqual(floatStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(floatStorage.type(), 'torch.FloatStorage')
        self.assertEqual(floatStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(floatStorage.dtype, torch.float32)

        halfStorage = storage.half()
        self.assertEqual(halfStorage.size(), 6)
        self.assertEqual(halfStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(halfStorage.type(), 'torch.HalfStorage')
        self.assertEqual(halfStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(halfStorage.dtype, torch.float16)

        bfloat16Storage = storage.bfloat16()
        self.assertEqual(bfloat16Storage.size(), 6)
        self.assertEqual(bfloat16Storage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(bfloat16Storage.type(), 'torch.BFloat16Storage')
        self.assertEqual(bfloat16Storage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(bfloat16Storage.dtype, torch.bfloat16)

        longStorage = storage.long()
        self.assertEqual(longStorage.size(), 6)
        self.assertEqual(longStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(longStorage.type(), 'torch.LongStorage')
        self.assertEqual(longStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(longStorage.dtype, torch.int64)

        shortStorage = storage.short()
        self.assertEqual(shortStorage.size(), 6)
        self.assertEqual(shortStorage.tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertEqual(shortStorage.type(), 'torch.ShortStorage')
        self.assertEqual(shortStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(shortStorage.dtype, torch.int16)

        doubleStorage = storage.double()
        self.assertEqual(doubleStorage.size(), 6)
        self.assertEqual(doubleStorage.tolist(), [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
        self.assertEqual(doubleStorage.type(), 'torch.DoubleStorage')
        self.assertEqual(doubleStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(doubleStorage.dtype, torch.float64)

        charStorage = storage.char()
        self.assertEqual(charStorage.size(), 6)
        self.assertEqual(charStorage.tolist(), [-1.0, 0.0, 1.0, 2.0, 3.0, 4.0])
        self.assertEqual(charStorage.type(), 'torch.CharStorage')
        self.assertEqual(charStorage.int().tolist(), [-1, 0, 1, 2, 3, 4])
        self.assertIs(charStorage.dtype, torch.int8)

        byteStorage = storage.byte()
        self.assertEqual(byteStorage.size(), 6)
        self.assertEqual(byteStorage.tolist(), [255, 0, 1, 2, 3, 4])
        self.assertEqual(byteStorage.type(), 'torch.ByteStorage')
        self.assertEqual(byteStorage.int().tolist(), [255, 0, 1, 2, 3, 4])
        self.assertIs(byteStorage.dtype, torch.uint8)

        boolStorage = storage.bool()
        self.assertEqual(boolStorage.size(), 6)
        self.assertEqual(boolStorage.tolist(), [True, False, True, True, True, True])
        self.assertEqual(boolStorage.type(), 'torch.BoolStorage')
        self.assertEqual(boolStorage.int().tolist(), [1, 0, 1, 1, 1, 1])
        self.assertIs(boolStorage.dtype, torch.bool)

        complexfloat_storage = torch.ComplexFloatStorage([-1, 0, 1 + 2j, 2.5j, 3.5, 4 - 2j])
        self.assertEqual(complexfloat_storage.size(), 6)
        self.assertEqual(complexfloat_storage.tolist(), [-1, 0, 1 + 2j, 2.5j, 3.5, 4 - 2j])
        self.assertEqual(complexfloat_storage.type(), 'torch.ComplexFloatStorage')
        self.assertIs(complexfloat_storage.dtype, torch.complex64)

        complexdouble_storage = complexfloat_storage.complex_double()
        self.assertEqual(complexdouble_storage.size(), 6)
        self.assertEqual(complexdouble_storage.tolist(), [-1, 0, 1 + 2j, 2.5j, 3.5, 4 - 2j])
        self.assertEqual(complexdouble_storage.type(), 'torch.ComplexDoubleStorage')
        self.assertIs(complexdouble_storage.dtype, torch.complex128)

    @unittest.skipIf(IS_WINDOWS, "TODO: need to fix this test case for Windows")
    def test_from_file(self):
        size = 10000
        with tempfile.NamedTemporaryFile() as f:
            s1 = torch.FloatStorage.from_file(f.name, True, size)
            t1 = torch.FloatTensor(s1).copy_(torch.randn(size))

            # check mapping
            s2 = torch.FloatStorage.from_file(f.name, True, size)
            t2 = torch.FloatTensor(s2)
            self.assertEqual(t1, t2, 0)

            # check changes to t1 from t2
            rnum = random.uniform(-1, 1)
            t1.fill_(rnum)
            self.assertEqual(t1, t2, 0)

            # check changes to t2 from t1
            rnum = random.uniform(-1, 1)
            t2.fill_(rnum)
            self.assertEqual(t1, t2, 0)

    @unittest.skipIf(IS_WINDOWS, "TODO: need to fix this test case for Windows")
    def test_torch_from_file(self):
        size = 10000
        with tempfile.NamedTemporaryFile() as f:
            s1 = torch.from_file(f.name, True, size, dtype=torch.float)
            t1 = torch.FloatTensor(s1).copy_(torch.randn(size))

            # check mapping
            s2 = torch.from_file(f.name, True, size, dtype=torch.float)
            t2 = torch.FloatTensor(s2)
            self.assertEqual(t1, t2, 0)

            # check changes to t1 from t2
            rnum = random.uniform(-1, 1)
            t1.fill_(rnum)
            self.assertEqual(t1, t2, 0)

            # check changes to t2 from t1
            rnum = random.uniform(-1, 1)
            t2.fill_(rnum)
            self.assertEqual(t1, t2, 0)

    def test_print(self):
        default_type = torch.Tensor().type()
        for t in torch._tensor_classes:
            if t == torch.HalfTensor:
                continue  # HalfTensor does not support fill
            if t.is_sparse:
                continue
            if t.is_cuda and not torch.cuda.is_available():
                continue
            obj = t(100, 100).fill_(1)
            obj.__repr__()
            str(obj)
        # test half tensor
        obj = torch.rand(100, 100, device='cpu').half()
        obj.__repr__()
        str(obj)
        for t in torch._storage_classes:
            if t == torch.BFloat16Storage:
                continue  # Fix once fill is enabled for bfloat16
            if t.is_cuda and not torch.cuda.is_available():
                continue
            if t == torch.BoolStorage or t == torch.cuda.BoolStorage:
                obj = t(100).fill_(True)
            else:
                obj = t(100).fill_(1)
            obj.__repr__()
            str(obj)

        # test complex tensor
        x = torch.tensor([2.3 + 4j, 7 + 6j])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([(2.3000+4.0000j), (7.0000+6.0000j)])''')

        # test big integer
        x = torch.tensor(2341234123412341)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(2341234123412341)''')

        # test scientific notation
        x = torch.tensor([1e28, 1e-28])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+28, 1.0000e-28])''')

        # test scientific notation using set_printoptions
        x = torch.tensor([1e2, 1e-2])
        torch.set_printoptions(sci_mode=True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+02, 1.0000e-02])''')
        torch.set_printoptions(sci_mode=False)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([  100.0000,     0.0100])''')
        torch.set_printoptions(sci_mode=None)  # reset to the default value

        # test no leading space if all elements positive
        x = torch.tensor([1, 2])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1, 2])''')

        # test for leading space if there are negative elements
        x = torch.tensor([1, -2])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([ 1, -2])''')

        # test inf and nan
        x = torch.tensor([4, inf, 1.5, -inf, 0, nan, 1])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([4.0000,    inf, 1.5000,   -inf, 0.0000,    nan, 1.0000])''')

        # test dtype
        torch.set_default_dtype(torch.float)
        x = torch.tensor([1e-324, 1e-323, 1e-322, 1e307, 1e308, 1e309], dtype=torch.float64)
        self.assertEqual(x.__repr__(), str(x))
        expected_str = '''\
tensor([ 0.0000e+00, 9.8813e-324, 9.8813e-323, 1.0000e+307, 1.0000e+308,
                inf], dtype=torch.float64)'''
        self.assertExpectedInline(str(x), expected_str)

        # test changing default dtype
        torch.set_default_dtype(torch.float64)
        self.assertEqual(x.__repr__(), str(x))
        expected_str = '''\
tensor([ 0.0000e+00, 9.8813e-324, 9.8813e-323, 1.0000e+307, 1.0000e+308,
                inf])'''
        self.assertExpectedInline(str(x), expected_str)

        # test summary
        x = torch.zeros(10000)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([0., 0., 0.,  ..., 0., 0., 0.])''')

        # test internal summary function
        x = torch.rand(1, 20, 5, 30)
        summary = torch._tensor_str.get_summarized_data(x)
        self.assertEqual(summary.shape, (1, 6, 5, 6))
        first_and_last = [0, 1, 2, -3, -2, -1]
        self.assertEqual(summary, x[:, first_and_last][..., first_and_last])

        # test device
        if torch.cuda.is_available():
            x = torch.tensor([123], device='cuda:0')
            self.assertEqual(x.__repr__(), str(x))
            self.assertExpectedInline(str(x), '''tensor([123], device='cuda:0')''')

            # test changing default to cuda
            torch.set_default_tensor_type(torch.cuda.FloatTensor)
            self.assertEqual(x.__repr__(), str(x))
            self.assertExpectedInline(str(x), '''tensor([123])''')

            # test printing a tensor on a different gpu than current one.
            if torch.cuda.device_count() >= 2:
                with torch.cuda.device(1):
                    self.assertEqual(x.__repr__(), str(x))
                    self.assertExpectedInline(str(x), '''tensor([123], device='cuda:0')''')

            # test printing cpu tensor when default device is cuda
            y = torch.tensor([123], device='cpu')
            self.assertEqual(y.__repr__(), str(y))
            self.assertExpectedInline(str(y), '''tensor([123], device='cpu')''')
        torch.set_default_tensor_type(default_type)


        # test integral floats and requires_grad
        x = torch.tensor([123.], requires_grad=True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([123.], requires_grad=True)''')

        # test non-contiguous print
        # sliced tensor should have > PRINT_OPTS.threshold elements
        x = torch.ones(100, 2, 2, 10)
        y = x.as_strided(size=(100, 2, 10), stride=(2 * 2 * 10, 2 * 10, 1))
        self.assertEqual(str(y), y.__repr__())
        expected_str = '''\
tensor([[[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        ...,

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]],

        [[1., 1., 1.,  ..., 1., 1., 1.],
         [1., 1., 1.,  ..., 1., 1., 1.]]])\
'''

        self.assertExpectedInline(str(y), expected_str)

        # test print 0-dim tensor: there's no 0-dim in Numpy, we match arrayprint style
        x = torch.tensor(0.00002)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(2.0000e-05)''')

        # test print boolean tensor
        x = torch.tensor([True])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([True])''')

        x = torch.tensor(True)
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor(True)''')

        # [Numpy] test print float in sci_mode when min < 0.0001.
        x = torch.tensor([0.00002])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([2.0000e-05])''')

        # [Numpy] test print float in sci_mode when max > 1e8.
        # TODO: Pytorch uses fixed precision to print, while Numpy uses dragon4_scientific
        # to do automatic trimming and padding.
        x = torch.tensor([123456789.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.2346e+08])''')

        # [Numpy] test print float in sci_mode when max / min > 1000.
        x = torch.tensor([0.01, 11])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e-02, 1.1000e+01])''')

        # [Numpy] test print int max / min > 1000, no sci_mode
        x = torch.tensor([1, 1010])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([   1, 1010])''')

        # [Numpy] test print int > 1e8, no sci_mode
        x = torch.tensor([1000000000])  # 1e9
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1000000000])''')

        # [Numpy] test printing float in int_mode
        x = torch.tensor([1., 1000.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([   1., 1000.])''')

        # [Numpy] test printing float in int_mode in sci format when max / min > 1000.
        x = torch.tensor([1., 1010.])
        self.assertEqual(x.__repr__(), str(x))
        self.assertExpectedInline(str(x), '''tensor([1.0000e+00, 1.0100e+03])''')

    def test_sizeof(self):
        sizeof_empty = torch.randn(0).storage().__sizeof__()
        sizeof_10 = torch.randn(10).storage().__sizeof__()
        sizeof_100 = torch.randn(100).storage().__sizeof__()
        self.assertEqual((sizeof_100 - sizeof_empty) // (sizeof_10 - sizeof_empty), 10)
        self.assertEqual((sizeof_100 - sizeof_empty) % (sizeof_10 - sizeof_empty), 0)

        sizeof_empty = torch.randn(0).to(torch.uint8).storage().__sizeof__()
        sizeof_10 = torch.randn(10).to(torch.uint8).storage().__sizeof__()
        sizeof_100 = torch.randn(100).to(torch.uint8).storage().__sizeof__()
        self.assertEqual((sizeof_100 - sizeof_empty) // (sizeof_10 - sizeof_empty), 10)
        self.assertEqual((sizeof_100 - sizeof_empty) % (sizeof_10 - sizeof_empty), 0)

    def test_unsqueeze(self):
        x = torch.randn(2, 3, 4)
        y = x.unsqueeze(1)
        self.assertEqual(y, x.view(2, 1, 3, 4))
        y = x.clone().unsqueeze_(2)
        self.assertEqual(y, x.view(2, 3, 1, 4))

        x = x[:, 1]
        self.assertFalse(x.is_contiguous())
        y = x.unsqueeze(1)
        self.assertEqual(y, x.contiguous().view(2, 1, 4))
        y = x.clone().unsqueeze_(2)
        self.assertEqual(y, x.contiguous().view(2, 4, 1))

    def test_iter(self):
        x = torch.randn(5, 5)
        for i, sub in enumerate(x):
            self.assertEqual(sub, x[i])

        x = torch.Tensor()
        self.assertEqual(list(x), [])

    def test_accreal_type(self):
        x = torch.ones(2, 3, 4)
        self.assertIsInstance(x.double().sum().item(), float)
        self.assertIsInstance(x.float().sum().item(), float)
        self.assertIsInstance(x.long().sum().item(), int)
        self.assertIsInstance(x.int().sum().item(), int)
        self.assertIsInstance(x.short().sum().item(), int)
        self.assertIsInstance(x.char().sum().item(), int)
        self.assertIsInstance(x.byte().sum().item(), int)

    def test_assertEqual(self):
        x = torch.FloatTensor([0])
        self.assertEqual(x, 0)
        xv = torch.autograd.Variable(x)
        self.assertEqual(xv, 0)
        self.assertEqual(x, xv)
        self.assertEqual(xv, x)

        self.assertRaisesRegex(AssertionError, "don't combine",
                               lambda: self.assertEqual(x, xv, 1.0, atol=4))

        self.assertRaisesRegex(TypeError, "takes from 3 to 4 positional arguments",
                               lambda: self.assertEqual(x, xv, 1.0, ""))

    def test_new(self):
        x = torch.autograd.Variable(torch.Tensor())
        y = torch.autograd.Variable(torch.randn(4, 4))
        z = torch.autograd.Variable(torch.IntTensor([1, 2, 3]))
        self.assertEqual(x.new().shape, [0])
        self.assertEqual(x.new(), x)
        self.assertEqual(x.new(1, 2).shape, [1, 2])
        self.assertEqual(x.new(torch.Size([3, 4])).shape, [3, 4])
        self.assertEqual(x.new([3, 4]).shape, [2])
        self.assertEqual(x.new([3, 4]).tolist(), [3, 4])
        self.assertEqual(x.new((3, 4)).tolist(), [3, 4])
        if TEST_NUMPY:
            self.assertEqual(x.new([np.int32(3), np.float64(4)]).tolist(), [3, 4])
            self.assertEqual(x.new(np.array((3, 4))).tolist(), [3, 4])
        self.assertEqual(x.new([z[2], z[0] + 3]).tolist(), [3, 4])
        self.assertEqual(x.new(size=(3, 4)).shape, [3, 4])
        self.assertEqual(x.new(()).shape, [0])
        self.assertEqual(x.new(y.storage()).data_ptr(), y.data_ptr())
        self.assertEqual(x.new(y).data_ptr(), y.data_ptr())
        self.assertIsNot(x.new(y), y)

        self.assertRaises(TypeError, lambda: x.new(z))
        # TypeError would be better
        self.assertRaises(RuntimeError, lambda: x.new(z.storage()))

    def test_empty_like(self):
        x = torch.autograd.Variable(torch.Tensor())
        y = torch.autograd.Variable(torch.randn(4, 4))
        z = torch.autograd.Variable(torch.IntTensor([1, 2, 3]))
        for a in (x, y, z):
            self.assertEqual(torch.empty_like(a).shape, a.shape)
            self.assertEqualTypeString(torch.empty_like(a), a)

    @unittest.skipIf(PYTORCH_CUDA_MEMCHECK, "is_pinned uses failure to detect pointer property")
    def test_pin_memory(self):
        x = torch.randn(3, 5)
        self.assertFalse(x.is_pinned())
        if not torch.cuda.is_available():
            self.assertRaises(RuntimeError, lambda: x.pin_memory())
        else:
            pinned = x.pin_memory()
            self.assertTrue(pinned.is_pinned())
            self.assertEqual(pinned, x)
            self.assertNotEqual(pinned.data_ptr(), x.data_ptr())
            # test that pin_memory on already pinned tensor has no effect
            self.assertIs(pinned, pinned.pin_memory())
            self.assertEqual(pinned.data_ptr(), pinned.pin_memory().data_ptr())

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_unresizable(self):
        x = np.zeros((2, 2))
        y = torch.from_numpy(x)
        with self.assertRaises(ValueError):
            x.resize((5, 5))

        z = torch.randn(5, 5)
        w = z.numpy()
        with self.assertRaises(RuntimeError):
            z.resize_(10, 10)
        with self.assertRaises(ValueError):
            w.resize((10, 10))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_to_numpy(self):
        def get_castable_tensor(shape, dtype):
            if dtype.is_floating_point:
                dtype_info = torch.finfo(dtype)
                # can't directly use min and max, because for double, max - min
                # is greater than double range and sampling always gives inf.
                low = max(dtype_info.min, -1e10)
                high = min(dtype_info.max, 1e10)
                t = torch.empty(shape, dtype=torch.float64).uniform_(low, high)
            else:
                # can't directly use min and max, because for int64_t, max - min
                # is greater than int64_t range and triggers UB.
                dtype_info = torch.iinfo(dtype)
                low = max(dtype_info.min, int(-1e10))
                high = min(dtype_info.max, int(1e10))
                dtype_info = torch.iinfo(dtype)
                t = torch.empty(shape, dtype=torch.int64).random_(low, high)
            return t.to(dtype)

        dtypes = [
            torch.uint8,
            torch.int8,
            torch.short,
            torch.int,
            torch.half,
            torch.float,
            torch.double,
            torch.long,
        ]
        for dtp in dtypes:
            # 1D
            sz = 10
            x = get_castable_tensor(sz, dtp)
            y = x.numpy()
            for i in range(sz):
                self.assertEqual(x[i], y[i])

            # 1D > 0 storage offset
            xm = get_castable_tensor(sz * 2, dtp)
            x = xm.narrow(0, sz - 1, sz)
            self.assertTrue(x.storage_offset() > 0)
            y = x.numpy()
            for i in range(sz):
                self.assertEqual(x[i], y[i])

            def check2d(x, y):
                for i in range(sz1):
                    for j in range(sz2):
                        self.assertEqual(x[i][j], y[i][j])

            # empty
            x = torch.Tensor().to(dtp)
            y = x.numpy()
            self.assertEqual(y.size, 0)

            # contiguous 2D
            sz1 = 3
            sz2 = 5
            x = get_castable_tensor((sz1, sz2), dtp)
            y = x.numpy()
            check2d(x, y)
            self.assertTrue(y.flags['C_CONTIGUOUS'])

            # with storage offset
            xm = get_castable_tensor((sz1 * 2, sz2), dtp)
            x = xm.narrow(0, sz1 - 1, sz1)
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)
            self.assertTrue(y.flags['C_CONTIGUOUS'])

            # non-contiguous 2D
            x = get_castable_tensor((sz2, sz1), dtp).t()
            y = x.numpy()
            check2d(x, y)
            self.assertFalse(y.flags['C_CONTIGUOUS'])

            # with storage offset
            xm = get_castable_tensor((sz2 * 2, sz1), dtp)
            x = xm.narrow(0, sz2 - 1, sz2).t()
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)

            # non-contiguous 2D with holes
            xm = get_castable_tensor((sz2 * 2, sz1 * 2), dtp)
            x = xm.narrow(0, sz2 - 1, sz2).narrow(1, sz1 - 1, sz1).t()
            y = x.numpy()
            self.assertTrue(x.storage_offset() > 0)
            check2d(x, y)

            if dtp != torch.half:
                # check writeable
                x = get_castable_tensor((3, 4), dtp)
                y = x.numpy()
                self.assertTrue(y.flags.writeable)
                y[0][1] = 3
                self.assertTrue(x[0][1] == 3)
                y = x.t().numpy()
                self.assertTrue(y.flags.writeable)
                y[0][1] = 3
                self.assertTrue(x[0][1] == 3)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_to_numpy_bool(self):
        x = torch.tensor([True, False], dtype=torch.bool)
        self.assertEqual(x.dtype, torch.bool)

        y = x.numpy()
        self.assertEqual(y.dtype, np.bool)
        for i in range(len(x)):
            self.assertEqual(x[i], y[i])

        x = torch.tensor([True], dtype=torch.bool)
        self.assertEqual(x.dtype, torch.bool)

        y = x.numpy()
        self.assertEqual(y.dtype, np.bool)
        self.assertEqual(x[0], y[0])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_from_numpy(self):
        dtypes = [
            np.double,
            np.float,
            np.float16,
            np.complex64,
            np.complex128,
            np.int64,
            np.int32,
            np.int16,
            np.int8,
            np.uint8,
            np.longlong,
            np.bool,
        ]
        complex_dtypes = [
            np.complex64,
            np.complex128,
        ]

        for dtype in dtypes:
            array = np.array([1, 2, 3, 4], dtype=dtype)
            tensor_from_array = torch.from_numpy(array)
            # TODO: change to tensor equality check once HalfTensor
            # implements `==`
            for i in range(len(array)):
                self.assertEqual(tensor_from_array[i], array[i])
            # ufunc 'remainder' not supported for complex dtypes
            if dtype not in complex_dtypes:
                # This is a special test case for Windows
                # https://github.com/pytorch/pytorch/issues/22615
                array2 = array % 2
                tensor_from_array2 = torch.from_numpy(array2)
                for i in range(len(array2)):
                    self.assertEqual(tensor_from_array2[i], array2[i])

        # Test unsupported type
        array = np.array([1, 2, 3, 4], dtype=np.uint16)
        with self.assertRaises(TypeError):
            tensor_from_array = torch.from_numpy(array)

        # check storage offset
        x = np.linspace(1, 125, 125)
        x.shape = (5, 5, 5)
        x = x[1]
        expected = torch.arange(1, 126, dtype=torch.float64).view(5, 5, 5)[1]
        self.assertEqual(torch.from_numpy(x), expected)

        # check noncontiguous
        x = np.linspace(1, 25, 25)
        x.shape = (5, 5)
        expected = torch.arange(1, 26, dtype=torch.float64).view(5, 5).t()
        self.assertEqual(torch.from_numpy(x.T), expected)

        # check noncontiguous with holes
        x = np.linspace(1, 125, 125)
        x.shape = (5, 5, 5)
        x = x[:, 1]
        expected = torch.arange(1, 126, dtype=torch.float64).view(5, 5, 5)[:, 1]
        self.assertEqual(torch.from_numpy(x), expected)

        # check zero dimensional
        x = np.zeros((0, 2))
        self.assertEqual(torch.from_numpy(x).shape, (0, 2))
        x = np.zeros((2, 0))
        self.assertEqual(torch.from_numpy(x).shape, (2, 0))

        # check ill-sized strides raise exception
        x = np.array([3., 5., 8.])
        x.strides = (3,)
        self.assertRaises(ValueError, lambda: torch.from_numpy(x))

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_ctor_with_numpy_scalar_ctor(self):
        dtypes = [
            np.double,
            np.float,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.uint8,
            np.bool,
        ]
        for dtype in dtypes:
            self.assertEqual(dtype(42), torch.tensor(dtype(42)).item())

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_index(self):
        i = np.int32([0, 1, 2])
        x = torch.randn(5, 5)
        for idx in i:
            self.assertFalse(isinstance(idx, int))
            self.assertEqual(x[idx], x[int(idx)])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_numpy_array_interface(self):
        types = [
            torch.DoubleTensor,
            torch.FloatTensor,
            torch.HalfTensor,
            torch.LongTensor,
            torch.IntTensor,
            torch.ShortTensor,
            torch.ByteTensor,
        ]
        dtypes = [
            np.float64,
            np.float32,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.uint8,
        ]
        for tp, dtype in zip(types, dtypes):
            if np.dtype(dtype).kind == 'u':
                x = torch.Tensor([1, 2, 3, 4]).type(tp)
                array = np.array([1, 2, 3, 4], dtype=dtype)
            else:
                x = torch.Tensor([1, -2, 3, -4]).type(tp)
                array = np.array([1, -2, 3, -4], dtype=dtype)

            # Test __array__ w/o dtype argument
            asarray = np.asarray(x)
            self.assertIsInstance(asarray, np.ndarray)
            self.assertEqual(asarray.dtype, dtype)
            for i in range(len(x)):
                self.assertEqual(asarray[i], x[i])

            # Test __array_wrap__, same dtype
            abs_x = np.abs(x)
            abs_array = np.abs(array)
            self.assertIsInstance(abs_x, tp)
            for i in range(len(x)):
                self.assertEqual(abs_x[i], abs_array[i])

        # Test __array__ with dtype argument
        for dtype in dtypes:
            x = torch.IntTensor([1, -2, 3, -4])
            asarray = np.asarray(x, dtype=dtype)
            self.assertEqual(asarray.dtype, dtype)
            if np.dtype(dtype).kind == 'u':
                wrapped_x = np.array([1, -2, 3, -4], dtype=dtype)
                for i in range(len(x)):
                    self.assertEqual(asarray[i], wrapped_x[i])
            else:
                for i in range(len(x)):
                    self.assertEqual(asarray[i], x[i])

        # Test some math functions with float types
        float_types = [torch.DoubleTensor, torch.FloatTensor]
        float_dtypes = [np.float64, np.float32]
        for tp, dtype in zip(float_types, float_dtypes):
            x = torch.Tensor([1, 2, 3, 4]).type(tp)
            array = np.array([1, 2, 3, 4], dtype=dtype)
            for func in ['sin', 'sqrt', 'ceil']:
                ufunc = getattr(np, func)
                res_x = ufunc(x)
                res_array = ufunc(array)
                self.assertIsInstance(res_x, tp)
                for i in range(len(x)):
                    self.assertEqual(res_x[i], res_array[i])

        # Test functions with boolean return value
        for tp, dtype in zip(types, dtypes):
            x = torch.Tensor([1, 2, 3, 4]).type(tp)
            array = np.array([1, 2, 3, 4], dtype=dtype)
            geq2_x = np.greater_equal(x, 2)
            geq2_array = np.greater_equal(array, 2).astype('uint8')
            self.assertIsInstance(geq2_x, torch.ByteTensor)
            for i in range(len(x)):
                self.assertEqual(geq2_x[i], geq2_array[i])

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_multiplication_numpy_scalar(self):
        for np_dtype in [np.float32, np.float64, np.int32, np.int64, np.int16, np.uint8]:
            for t_dtype in [torch.float, torch.double]:
                np_sc = np_dtype(2.0)
                t = torch.ones(2, requires_grad=True, dtype=t_dtype)
                r1 = t * np_sc
                self.assertIsInstance(r1, torch.Tensor)
                self.assertTrue(r1.dtype == t_dtype)
                self.assertTrue(r1.requires_grad)
                r2 = np_sc * t
                self.assertIsInstance(r2, torch.Tensor)
                self.assertTrue(r2.dtype == t_dtype)
                self.assertTrue(r2.requires_grad)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_parse_numpy_int(self):
        self.assertRaisesRegex(RuntimeError, "Overflow",
                               lambda: torch.mean(torch.randn(1, 1), np.uint64(-1)))
        # https://github.com/pytorch/pytorch/issues/29252
        for nptype in [np.int16, np.int8, np.uint8, np.int32, np.int64]:
            scalar = 3
            np_arr = np.array([scalar], dtype=nptype)
            np_val = np_arr[0]

            # np integral type can be treated as a python int in native functions with
            # int parameters:
            self.assertEqual(torch.ones(5).diag(scalar), torch.ones(5).diag(np_val))
            self.assertEqual(torch.ones([2, 2, 2, 2]).mean(scalar), torch.ones([2, 2, 2, 2]).mean(np_val))

            # numpy integral type parses like a python int in custom python bindings:
            self.assertEqual(torch.Storage(np_val).size(), scalar)

            tensor = torch.tensor([2], dtype=torch.int)
            tensor[0] = np_val
            self.assertEqual(tensor[0], np_val)

            # Original reported issue, np integral type parses to the correct
            # PyTorch integral type when passed for a `Scalar` parameter in
            # arithmetic operations:
            t = torch.from_numpy(np_arr)
            self.assertEqual((t + np_val).dtype, t.dtype)
            self.assertEqual((np_val + t).dtype, t.dtype)

    def test_error_msg_type_translation(self):
        with self.assertRaisesRegex(
                RuntimeError,
                # message includes both Double and Long
                '(?=.*Double)(?=.*Long)'):

            # Calls model with a LongTensor input but DoubleTensor weights
            input = torch.zeros(1, 1, 1, 6, dtype=torch.long)
            weight = torch.nn.Parameter(torch.zeros(1, 1, 1, 3, dtype=torch.double))
            model = torch.nn.Conv2d(1, 1, (1, 3), stride=1, padding=0, bias=False)
            model.weight = weight
            out = model(input)

    def test_tensor_from_sequence(self):
        class MockSequence(object):
            def __init__(self, lst):
                self.lst = lst

            def __len__(self):
                return len(self.lst)

            def __getitem__(self, item):
                raise TypeError

        class GoodMockSequence(MockSequence):
            def __getitem__(self, item):
                return self.lst[item]

        bad_mock_seq = MockSequence([1.0, 2.0, 3.0])
        good_mock_seq = GoodMockSequence([1.0, 2.0, 3.0])
        with self.assertRaisesRegex(ValueError, 'could not determine the shape'):
            torch.Tensor(bad_mock_seq)
        self.assertEqual(torch.Tensor([1.0, 2.0, 3.0]), torch.Tensor(good_mock_seq))

    def test_comparison_ops(self):
        x = torch.randn(5, 5)
        y = torch.randn(5, 5)

        eq = x == y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] == y[idx], eq[idx] == 1)

        ne = x != y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] != y[idx], ne[idx] == 1)

        lt = x < y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] < y[idx], lt[idx] == 1)

        le = x <= y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] <= y[idx], le[idx] == 1)

        gt = x > y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] > y[idx], gt[idx] == 1)

        ge = x >= y
        for idx in iter_indices(x):
            self.assertEqual(x[idx] >= y[idx], ge[idx] == 1)

    def test_comparison_ops_must_take_bool_output(self):
        for op in [torch.lt, torch.le, torch.gt, torch.ge, torch.eq, torch.ne,
                   torch.logical_and, torch.logical_or, torch.logical_xor]:
            self.assertEqual(op(torch.tensor([True]), torch.tensor([False])).dtype, torch.bool)

    def test_inplace_comparison_ops_require_inputs_have_same_dtype(self):
        with self.assertRaisesRegex(RuntimeError, 'Expected object of scalar type'):
            for op in ['lt_', 'le_', 'gt_', 'ge_', 'eq_', 'ne_', 'logical_xor_', 'logical_and_', 'logical_or_']:
                x = torch.tensor([1], dtype=torch.int)
                y = torch.tensor([2], dtype=torch.long)
                in_place_method = getattr(x, op)
                in_place_method(y)

    def test_comparison_ops_check_for_scalar_overflow(self):
        with self.assertRaisesRegex(RuntimeError, 'value cannot be converted to type'):
            torch.tensor([1 << 5], dtype=torch.uint8) < (1 << 20)
            (1 << 20) < torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) <= (1 << 20)
            (1 << 20) <= torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) > (1 << 20)
            (1 << 20) > torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) >= (1 << 20)
            (1 << 20) >= torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) == (1 << 20)
            (1 << 20) == torch.tensor([1 << 5], dtype=torch.uint8)
            torch.tensor([1 << 5], dtype=torch.uint8) != (1 << 20)
            (1 << 20) != torch.tensor([1 << 5], dtype=torch.uint8)

    def test_comparison_ops_check_for_zerodim_tensor_overflow(self):
        with self.assertRaisesRegex(RuntimeError, 'value cannot be converted to type'):
            torch.tensor([1 << 5], dtype=torch.uint8) < torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) < torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) <= torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) <= torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) > torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) > torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) >= torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) >= torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) == torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) == torch.tensor([1 << 30], dtype=torch.int32)
            torch.tensor([1 << 5], dtype=torch.uint8) != torch.tensor(1 << 20, dtype=torch.int32)
            torch.tensor(1 << 40, dtype=torch.int64) != torch.tensor([1 << 30], dtype=torch.int32)

    def test_bitwise_ops(self):
        x = torch.randn(5, 5).gt(0)
        y = torch.randn(5, 5).gt(0)

        and_result = x & y
        for idx in iter_indices(x):
            if and_result[idx]:
                self.assertTrue(x[idx] and y[idx])
            else:
                self.assertFalse(x[idx] and y[idx])

        or_result = x | y
        for idx in iter_indices(x):
            if or_result[idx]:
                self.assertTrue(x[idx] or y[idx])
            else:
                self.assertFalse(x[idx] or y[idx])

        xor_result = x ^ y
        for idx in iter_indices(x):
            if xor_result[idx]:
                self.assertTrue(x[idx] ^ y[idx])
            else:
                self.assertFalse(x[idx] ^ y[idx])

        x_clone = x.clone()
        x_clone &= y
        self.assertEqual(x_clone, and_result)

        x_clone = x.clone()
        x_clone |= y
        self.assertEqual(x_clone, or_result)

        x_clone = x.clone()
        x_clone ^= y
        self.assertEqual(x_clone, xor_result)

    def test_op_invert(self):
        res = 0xffff - torch.arange(127, dtype=torch.int8)
        for dtype in (torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            a = torch.arange(127, dtype=dtype)
            self.assertEqual(res.to(dtype), ~a)

        self.assertEqual(torch.tensor([True, False]),
                         ~torch.tensor([False, True]))

        # test exceptions
        for dtype in(torch.half, torch.float, torch.double):
            a = torch.zeros(10, dtype=dtype)
            with self.assertRaises(TypeError):
                b = ~a

    def test_apply(self):
        x = torch.arange(1, 6)
        res = x.clone().apply_(lambda k: k + k)
        self.assertEqual(res, x * 2)
        self.assertRaises(TypeError, lambda: x.apply_(lambda k: "str"))

    def test_map(self):
        x = torch.autograd.Variable(torch.randn(3, 3))
        y = torch.autograd.Variable(torch.randn(3))
        res = x.clone()
        res.map_(y, lambda a, b: a + b)
        self.assertEqual(res, x + y)
        self.assertRaisesRegex(TypeError, "not callable", lambda: res.map_(y, "str"))

    def test_map2(self):
        x = torch.autograd.Variable(torch.randn(3, 3))
        y = torch.autograd.Variable(torch.randn(3))
        z = torch.autograd.Variable(torch.randn(1, 3))
        res = x.clone()
        res.map2_(y, z, lambda a, b, c: a + b * c)
        self.assertEqual(res, x + y * z)
        z.requires_grad = True
        self.assertRaisesRegex(
            RuntimeError, "requires grad",
            lambda: res.map2_(y, z, lambda a, b, c: a + b * c))

    def test_Size(self):
        x = torch.Size([1, 2, 3])
        self.assertIsInstance(x, tuple)
        self.assertEqual(x[0], 1)
        self.assertEqual(x[1], 2)
        self.assertEqual(x[2], 3)
        self.assertEqual(len(x), 3)
        self.assertRaises(TypeError, lambda: torch.Size(torch.ones(3)))

        self.assertIsInstance(x * 2, torch.Size)
        self.assertIsInstance(x[:-1], torch.Size)
        self.assertIsInstance(x + x, torch.Size)

    def test_Size_scalar(self):
        three = torch.tensor(3)
        two = torch.tensor(2)
        x = torch.Size([0, 1, two, three, 4])
        for i in range(1, 5):
            self.assertEqual(x[i], i)

    def test_Size_iter(self):
        for sizes in [iter([1, 2, 3, 4, 5]), range(1, 6)]:
            x = torch.Size(sizes)
            for i in range(0, 5):
                self.assertEqual(x[i], i + 1)

    def test_t_not_2d_error(self):
        self.assertRaises(RuntimeError, lambda: torch.randn(2, 3, 4).t())
        self.assertRaises(RuntimeError, lambda: torch.randn(2, 3, 4).t_())

    # unit test for special case transposed copy (see ATen/native/Copy.cpp for details)
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_big_transpose(self):
        t = torch.rand(456, 789)
        t1 = t.t().contiguous()
        t2 = torch.from_numpy(t.numpy().transpose())
        self.assertEqual(t1, t2)

    def test_inplace_division(self):
        t = torch.rand(5, 5)
        id_before = id(t)
        t /= 2
        id_after = id(t)
        self.assertEqual(id_before, id_after)

    def test_simple_scalar_cast(self):
        ok = [torch.Tensor([1.5]), torch.zeros(1, 1, 1, 1)]
        ok_values = [1.5, 0]

        not_ok = map(torch.Tensor, [[], [1, 2], [[1, 2], [3, 4]]])

        for tensor, value in zip(ok, ok_values):
            self.assertEqual(int(tensor), int(value))
            self.assertEqual(float(tensor), float(value))

        for tensor in not_ok:
            self.assertRaises(ValueError, lambda: int(tensor))
            self.assertRaises(ValueError, lambda: float(tensor))

    def test_offset_scalar_cast(self):
        x = torch.Tensor([1, 2, 3])
        y = x[2:]
        self.assertEqual(int(y), 3)

    # skip this test for now as it affects all tests
    @unittest.skipIf(True, "flush_denormal not supported")
    def test_set_flush_denormal(self):
        tiny_float = 1e-42
        tiny_double = 1e-320
        float_tensor = torch.FloatTensor([1.0, tiny_float])
        double_tensor = torch.DoubleTensor([1.0, tiny_float, tiny_double])

        self.assertEqual(float_tensor[0], 1.0, atol=0.0)
        self.assertEqual(float_tensor[1], tiny_float, atol=tiny_float / 16)
        self.assertEqual(double_tensor[0], 1.0, atol=0.0)
        self.assertEqual(double_tensor[1], tiny_float, atol=0.0)
        self.assertEqual(double_tensor[2], tiny_double, atol=0.0)

        torch.set_flush_denormal(True)
        self.assertEqual(float_tensor[0], 1.0, atol=0.0)
        self.assertEqual(float_tensor[1], 0.0, atol=0.0)  # tiny_float to zero
        self.assertEqual(double_tensor[0], 1.0, atol=0.0)
        # tiny_float is not converted to zero in double type
        self.assertEqual(double_tensor[1], tiny_float, atol=0.0)
        self.assertEqual(double_tensor[2], 0.0, atol=0.0)  # tiny_double to zero
        torch.set_flush_denormal(False)

    def test_show_config(self):
        # We can't usefully test the output; just make sure this doesn't crash
        torch.__config__.show()

    def test_parallel_info(self):
        torch.__config__.parallel_info()

    @slowTest
    def test_slow_test(self):
        # Just a smoketest to make sure our slowTest decorator works.
        pass

    def test_is_nonzero(self):
        self.assertExpectedRaisesInline(
            RuntimeError,
            lambda: torch.tensor([]).is_nonzero(),
            "Boolean value of Tensor with no values is ambiguous",
        )
        self.assertExpectedRaisesInline(
            RuntimeError,
            lambda: torch.tensor([0, 0]).is_nonzero(),
            "Boolean value of Tensor with more than one value is ambiguous",
        )
        self.assertFalse(torch.tensor(0).is_nonzero())
        self.assertTrue(torch.tensor(1).is_nonzero())
        self.assertFalse(torch.tensor([0]).is_nonzero())
        self.assertTrue(torch.tensor([1]).is_nonzero())
        self.assertFalse(torch.tensor([[0]]).is_nonzero())
        self.assertTrue(torch.tensor([[1]]).is_nonzero())

    def test_meshgrid(self):
        a = torch.tensor(1)
        b = torch.tensor([1, 2, 3])
        c = torch.tensor([1, 2])
        grid_a, grid_b, grid_c = torch.meshgrid([a, b, c])
        self.assertEqual(grid_a.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_b.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_c.shape, torch.Size([1, 3, 2]))
        grid_a2, grid_b2, grid_c2 = torch.meshgrid(a, b, c)
        self.assertEqual(grid_a2.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_b2.shape, torch.Size([1, 3, 2]))
        self.assertEqual(grid_c2.shape, torch.Size([1, 3, 2]))
        expected_grid_a = torch.ones(1, 3, 2, dtype=torch.int64)
        expected_grid_b = torch.tensor([[[1, 1],
                                         [2, 2],
                                         [3, 3]]])
        expected_grid_c = torch.tensor([[[1, 2],
                                         [1, 2],
                                         [1, 2]]])
        self.assertTrue(grid_a.equal(expected_grid_a))
        self.assertTrue(grid_b.equal(expected_grid_b))
        self.assertTrue(grid_c.equal(expected_grid_c))
        self.assertTrue(grid_a2.equal(expected_grid_a))
        self.assertTrue(grid_b2.equal(expected_grid_b))
        self.assertTrue(grid_c2.equal(expected_grid_c))

    # NB: we must not be built with CUDA; if we are built with CUDA but no CUDA
    # is available, we get a different error.
    @unittest.skipIf(torch.backends.cuda.is_built() or IS_SANDCASTLE, "CUDA is built, can't test CUDA not built error")
    def test_cuda_not_built(self):
        msg = "Torch not compiled with CUDA enabled"
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.cuda.current_device())
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1], device="cuda"))
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1]).cuda())
        self.assertRaisesRegex(TypeError, msg, lambda: torch.cuda.FloatTensor())
        self.assertRaisesRegex(TypeError, msg, lambda: torch.set_default_tensor_type(torch.cuda.FloatTensor))
        self.assertRaisesRegex(AssertionError, msg, lambda: torch.tensor([1]).to(device="cuda"))

    def test_cast_binary_op(self):
        # Scalar
        a = torch.tensor(2)
        b = torch.tensor(3)
        a_copy = a.clone()
        b_copy = b.clone()

        self.assertEqual(torch.tensor(6, dtype=torch.float), a.float() * b)

        self.assertEqualTypeString(a, a_copy)
        self.assertEqualTypeString(b, b_copy)

    def test_cartesian_prod(self):
        a = torch.tensor([1])
        b = torch.tensor([1, 2, 3])
        c = torch.tensor([1, 2])
        prod = torch.cartesian_prod(a, b, c)
        expected = torch.tensor(list(product([a], b, c)))
        self.assertEqual(expected, prod)

        # test 0 size input
        d = torch.empty(0, dtype=b.dtype)
        prod = torch.cartesian_prod(a, b, c, d)
        expected = torch.empty(0, 4, dtype=b.dtype)
        self.assertEqual(expected, prod)

        # test single input
        prod = torch.cartesian_prod(b)
        self.assertEqual(b, prod)

    def test_combinations(self):
        a = torch.tensor([1, 2, 3])

        c = torch.combinations(a, r=1)
        expected = torch.tensor(list(combinations(a, r=1)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=1, with_replacement=True)
        expected = torch.tensor(list(combinations_with_replacement(a, r=1)))
        self.assertEqual(c, expected)

        c = torch.combinations(a)
        expected = torch.tensor(list(combinations(a, r=2)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, with_replacement=True)
        expected = torch.tensor(list(combinations_with_replacement(a, r=2)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=3)
        expected = torch.tensor(list(combinations(a, r=3)))
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=4)
        expected = torch.empty(0, 4, dtype=a.dtype)
        self.assertEqual(c, expected)

        c = torch.combinations(a, r=5)
        expected = torch.empty(0, 5, dtype=a.dtype)
        self.assertEqual(c, expected)

        # test empty imput
        a = torch.empty(0)
        c1 = torch.combinations(a)
        c2 = torch.combinations(a, with_replacement=True)
        expected = torch.empty(0, 2, dtype=a.dtype)
        self.assertEqual(c1, expected)
        self.assertEqual(c2, expected)

    def test_has_internal_overlap(self):
        OVERLAP_NO = 0
        OVERLAP_YES = 1
        OVERLAP_TOO_HARD = 2

        # Check for contiguous tensors
        a = torch.randn(3, 3)
        self.assertEqual(torch._debug_has_internal_overlap(a), OVERLAP_NO)

        # Checks for zero strides
        b = torch.randn(1, 3)
        b_expanded = b.expand(4, 3)
        self.assertEqual(torch._debug_has_internal_overlap(b_expanded), OVERLAP_YES)

        # Check for zero strided, size 1 axis, in non-contiguous storage (gh-33812)
        c = torch.randn(10).as_strided([2, 1, 5], [1, 0, 2])
        self.assertEqual(torch._debug_has_internal_overlap(c), OVERLAP_TOO_HARD)

    def test_allow_tensor_metadata_change(self):
        def do_test(t):
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_sizes_contiguous is not allowed on a Tensor created from .data or .detach()"):
                t.resize_((2, 1))
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_storage is not allowed on a Tensor created from .data or .detach()"):
                t.set_()
            with self.assertRaisesRegex(
                    RuntimeError,
                    "set_storage_offset is not allowed on a Tensor created from .data or .detach()"):
                t.set_(t.storage(), 0, t.size(), list(t.stride()))

        do_test(torch.tensor([[1, 2]]).data)
        do_test(torch.tensor([[1, 2]]).detach())

    def test_c10_layer_norm(self):
        # test that we can call c10 ops and they return a reasonable result
        X = torch.rand(5, 5, dtype=torch.float)
        weight = torch.rand(*X.size()[1:], dtype=torch.float)
        bias = torch.rand(*X.size()[1:], dtype=torch.float)
        epsilon = 1e-4

        expected_norm = torch.nn.functional.layer_norm(
            X, X.size()[1:], weight=weight, bias=bias, eps=epsilon)
        actual_norm, actual_mean, actual_stdev = \
            torch.ops._caffe2.LayerNorm(torch.tensor(X), torch.tensor(
                weight), torch.tensor(bias), 1, epsilon, True)
        torch.testing.assert_allclose(expected_norm, actual_norm)

    def test_memory_format(self):
        def test_helper(x, memory_format):
            y = x.contiguous(memory_format=memory_format)
            self.assertFalse(y.is_contiguous())
            self.assertTrue(y.is_contiguous(memory_format=memory_format))
            self.assertEqual(y, x)

        test_helper(torch.randn(4, 3, 8, 8), torch.channels_last)
        test_helper(torch.randn(4, 3, 8, 8, 8), torch.channels_last_3d)

    def test_memory_format_contiguous_returns_same_tensor_if_already_satisfies(self):
        def test_helper(x, memory_format):
            alias = x.contiguous(memory_format=memory_format)
            alias.fill_(7)
            self.assertEqual(x, alias)

        test_helper(torch.randn(4, 8, 8, 3).permute(0, 3, 1, 2), torch.channels_last)
        test_helper(torch.randn(4, 8, 8, 8, 3).permute(0, 4, 1, 2, 3), torch.channels_last_3d)

    def test_memory_format_empty(self):
        def test_helper(dim1, dim2, memory_format):
            with self.assertRaises(RuntimeError):
                x = torch.empty(dim1, memory_format=memory_format)
            x = torch.empty(dim2, memory_format=memory_format)
            self.assertTrue(x.is_contiguous(memory_format=memory_format))

        test_helper((3, 3), (3, 3, 3, 3), torch.channels_last)
        test_helper((3, 3, 3), (3, 3, 3, 3, 3), torch.channels_last_3d)

    def test_subclass_tensors(self):
        # raise an error when trying to subclass FloatTensor
        with self.assertRaisesRegex(TypeError, "type 'torch.FloatTensor' is not an acceptable base type"):
            class Foo1(torch.FloatTensor):
                pass

        # but allow subclassing Tensor:
        class Foo2(torch.Tensor):
            def foo(self):
                return 5
        f = Foo2()
        self.assertEqual(f.foo(), 5)

    def test_ndim(self):
        a = torch.randn(1, 2, 3)
        self.assertEqual(3, a.ndim)
        b = torch.randn(())
        self.assertEqual(0, b.ndim)
        c = torch.randn(1, 0)
        self.assertEqual(2, c.ndim)

    def test_T(self):
        a = torch.randn(2, 3, 4)
        t1 = a.T
        t2 = a.permute(2, 1, 0)
        self.assertEqual(t2, t1)
        b = torch.randn(10)
        self.assertEqual(b, b.T)
        scalar = torch.tensor(5)
        self.assertEqual(scalar, scalar.T)

    def test_python_types(self):
        a1 = torch.randn((1, 2), dtype=torch.float64)
        a2 = torch.randn((1, 2), dtype=float)
        self.assertEqual(a1.dtype, a2.dtype)

        b1 = torch.arange(10, 20, dtype=torch.int64)
        b2 = torch.arange(10, 20, dtype=int)
        self.assertEqual(b1.dtype, b2.dtype)

        c1 = torch.tensor([True, False], dtype=torch.bool)
        c2 = torch.tensor([True, False], dtype=bool)
        self.assertEqual(c1.dtype, c2.dtype)

    def test_fill_diagonal(self):
        a1 = torch.randn(7, 3)
        a2 = a1.clone()
        v = 1
        for i in range(3):
            a2[i][i] = v
        a1.fill_diagonal_(v)
        self.assertEqual(a1, a2)

        b1 = torch.randn(7, 3)
        b2 = b1.clone()
        for i in range(3):
            b2[i][i] = v
            b2[i + 4][i] = v
        b1.fill_diagonal_(v, wrap=True)
        self.assertEqual(b1, b2)

        c1 = torch.rand(3, 3, 3)
        c2 = c1.clone()
        for i in range(3):
            c2[i][i][i] = v
        c1.fill_diagonal_(v)
        self.assertEqual(c1, c2)

        # non-contiguous tensor
        d1 = torch.rand(3, 3, 3)[:, 1, ...]
        d2 = d1.clone()
        for i in range(3):
            d2[i][i] = v
        d1.fill_diagonal_(v)
        self.assertEqual(d1, d2)

        e1 = torch.rand(7, 3, 3)[:, 1, ...]
        e2 = e1.clone()
        for i in range(3):
            e2[i][i] = v
            e2[i + 4][i] = v
        e1.fill_diagonal_(v, wrap=True)
        self.assertEqual(e1, e2)

    def test_batch_norm_cpu_inference(self):
        # input nchw in (2,1,1,1), (2,2,2,2)
        inputs = [
            torch.tensor([[[[-0.5000]]], [[[0.5000]]]]),
            torch.tensor([
                [
                    [[-0.5000, 0.5000], [-1.0000, 1.0000]],
                    [[-0.2500, -0.5000], [0.2500, 0.5000]]
                ],
                [
                    [[0.1000, 1.0000], [1.0000, 0.1000]],
                    [[1.0000, 0.5000], [1.5000, -1.5000]]
                ]])]
        # output nchw in (2,1,1,1), (2,2,2,2)
        outputs = [
            torch.tensor([
                [[[-0.499997496604919433593750000]]],
                [[[0.499997496604919433593750000]]]]),
            torch.tensor([
                [[[-0.499997496604919433593750000, 0.499997496604919433593750000],
                  [-0.999994993209838867187500000, 0.999994993209838867187500000]],
                 [[-0.249998748302459716796875000, -0.499997496604919433593750000],
                  [0.249998748302459716796875000, 0.499997496604919433593750000]]],
                [[[0.099999502301216125488281250, 0.999994993209838867187500000],
                  [0.999994993209838867187500000, 0.099999502301216125488281250]],
                 [[0.999994993209838867187500000, 0.499997496604919433593750000],
                  [1.499992489814758300781250000, -1.499992489814758300781250000]]]])]


        for i in range(len(inputs)):
            for affine in [False, True]:
                m = torch.nn.BatchNorm2d(inputs[i].size()[1], 1e-05, 0.1, affine=affine)
                m.eval()
                # contiguous case
                input1 = inputs[i].contiguous()
                output1 = m(input1)
                # non-contiguous case
                input2 = input1.permute(0, 1, 3, 2)
                output2 = m(input2).permute(0, 1, 3, 2)
                # channels last case
                input3 = input1.contiguous(memory_format=torch.channels_last)
                output3 = m(input3)
                self.assertEqual(output3, outputs[i])
                self.assertEqual(output3, output1)
                self.assertEqual(output3, output2)

    def test_tensor_grad_warnings(self):
        dummy = torch.empty(1)

        with warnings.catch_warnings(record=True) as w:
            # Accessing .grad on leaf
            dummy.requires_grad_()
            foo = dummy.grad
            self.assertEqual(len(w), 0)

            # Accessing .grad on non-leaf
            dummy = dummy.clone()
            foo = dummy.grad
            self.assertEqual(len(w), 1)

            # Accessing .grad on non-leaf that retains gradients
            dummy.retain_grad()
            foo = dummy.grad
            self.assertEqual(len(w), 1)

    def test_normal_shape(self):
        warned = False
        for device in torch.testing.get_all_device_types():
            tensor1 = torch.rand(1, device=device)
            tensor4 = torch.rand(4, device=device)
            tensor120 = torch.rand(120, device=device)
            tensor2145 = torch.rand(2, 1, 4, 5, device=device)
            tensor2345 = torch.rand(2, 3, 4, 5, device=device)
            tensor2345_non_contiguous = torch.rand(2, 4, 3, 5, device=device).permute(0, 2, 1, 3)
            tensor2345_channels_last = tensor2345.contiguous(memory_format=torch.channels_last)
            output2345 = torch.zeros(2, 3, 4, 5, device=device)
            output345 = torch.zeros(3, 4, 5, device=device)

            # inputs have same size
            self.assertEqual(torch.normal(tensor2345, tensor2345).size(), (2, 3, 4, 5))
            self.assertEqual(torch.normal(tensor2345_non_contiguous, tensor2345).size(), (2, 3, 4, 5))
            self.assertEqual(torch.normal(tensor2345, tensor2345_channels_last).size(), (2, 3, 4, 5))
            self.assertEqual(torch.normal(tensor2345_non_contiguous, tensor2345_channels_last).size(), (2, 3, 4, 5))

            # scalar case
            self.assertEqual(torch.normal(tensor2345, 2).size(), (2, 3, 4, 5))
            self.assertEqual(torch.normal(2, tensor2345).size(), (2, 3, 4, 5))

            # inputs are expandable tensors
            self.assertEqual(torch.normal(tensor2345, tensor1).size(), (2, 3, 4, 5))
            self.assertEqual(torch.normal(tensor2145, tensor2345).size(), (2, 3, 4, 5))

            # inputs are non-expandable tensors, but they have same number of elements
            # TORCH_WARN_ONCE is used in torch.normal, only 1st assertEqual will show warn msg
            if not warned:
                self.assertWarnsRegex(UserWarning, "deprecated and the support will be removed",
                                      lambda: self.assertEqual(torch.normal(tensor120, tensor2345).size(), (120,)))
                warned = True
            else:
                self.assertEqual(torch.normal(tensor120, tensor2345).size(), (120,))
            self.assertEqual(torch.normal(tensor2345, tensor120).size(), (2, 3, 4, 5))

            # inputs are non-expandable tensors and they don't have same number of elements
            with self.assertRaisesRegex(RuntimeError, "inconsistent tensor"):
                torch.normal(tensor2345, tensor4)

            # output and inputs are size compatible
            self.assertEqual(torch.normal(tensor2345, tensor2345, out=output2345).size(), (2, 3, 4, 5))

            # output and inputs are not size compatible
            with self.assertRaisesRegex(RuntimeError, "inconsistent tensor"):
                # inputs are expandable but have different broadcasted size than output
                torch.normal(tensor2345, tensor2145, out=output345)
            with self.assertRaisesRegex(RuntimeError, "inconsistent tensor"):
                # inputs are not expandable but reshapeable, output size is not the same as mean
                torch.normal(tensor2345, tensor120, out=output345)

    def test_tensoriterator_output_setup(self):
        # Test whether the output's memory layout is correct
        def test_memory_layout(x, y, scale, zero_point, out):
            self.assertEqual(x.dim(), 4)
            self.assertEqual(x.size(), y.size())
            self.assertEqual(y.size(), out.size())

            shape = x.size()
            for n in range(shape[0]):
                for c in range(shape[1]):
                    for h in range(shape[2]):
                        for w in range(shape[3]):
                            if scale is not None and zero_point is not None:
                                self.assertEqual(
                                    out[n][c][h][w],
                                    torch.ops.quantized.add(x[n][c][h][w], y[n][c][h][w], scale, zero_point))
                            else:
                                self.assertEqual(out[n][c][h][w], x[n][c][h][w] + y[n][c][h][w])

        xraw = torch.rand(2, 3, 4, 4)
        yraw = torch.rand(2, 3, 4, 4)
        qxraw = torch.quantize_per_tensor(xraw, 0.1, 5, torch.quint8)
        qyraw = torch.quantize_per_tensor(yraw, 0.1, 5, torch.quint8)

        # contiguous case fast setup
        test_memory_layout(xraw, yraw, None, None, xraw + yraw)
        test_memory_layout(qxraw, qyraw, 0.1, 5, torch.ops.quantized.add(qxraw, qyraw, 0.1, 5))

        # channels last case fast setup
        x = xraw.contiguous(memory_format=torch.channels_last)
        y = yraw.contiguous(memory_format=torch.channels_last)
        test_memory_layout(x, y, None, None, x + y)
        qx = qxraw.contiguous(memory_format=torch.channels_last)
        qy = qyraw.contiguous(memory_format=torch.channels_last)
        test_memory_layout(qx, qy, 0.1, 5, torch.ops.quantized.add(qx, qy, 0.1, 5))

        # non contiguous case fast setup (dense, non-overlapping, same shape and sizes)
        x = xraw.permute(0, 2, 3, 1)
        y = yraw.permute(0, 2, 3, 1)
        test_memory_layout(x, y, None, None, x + y)
        qx = qxraw.permute(0, 2, 3, 1)
        qy = qyraw.permute(0, 2, 3, 1)
        test_memory_layout(qx, qy, 0.1, 5, torch.ops.quantized.add(qx, qy, 0.1, 5))

        # non contiguous case non fast setup
        x = xraw.permute(0, 2, 3, 1)
        y = yraw.permute(0, 3, 2, 1)
        test_memory_layout(x, y, None, None, x + y)
        qx = qxraw.permute(0, 2, 3, 1)
        qy = qyraw.permute(0, 3, 2, 1)
        test_memory_layout(qx, qy, 0.1, 5, torch.ops.quantized.add(qx, qy, 0.1, 5))

    # Tests to make sure we still handle .data properly until it is removed
    def test_dot_data_use(self):
        # .data allows to change the Tensors types inplace, check that we still
        # raise a nice error.
        with self.assertRaisesRegex(
                RuntimeError,
                # message includes both Double and Long
                '(?=.*Double)(?=.*Long)'):

            # Calls model with a LongTensor input but DoubleTensor weights
            input = torch.randn(1, 1, 1, 6, dtype=torch.double)
            weight = torch.zeros(1, 1, 1, 3, dtype=torch.long)
            model = torch.nn.Conv2d(1, 1, (1, 3), stride=1, padding=0, bias=False)
            model.weight.data = weight
            out = model(input)


# Functions to test negative dimension wrapping
METHOD = 1
INPLACE_METHOD = 2
FUNCTIONAL = 4
DIM_ARG = None

def make_neg_dim_test(name, tensor_arg, arg_constr, types, extra_dim=0):
    def neg_dim_test(self):
        if isinstance(tensor_arg, list):
            assert METHOD not in types and INPLACE_METHOD not in types
            x = [torch.randn(arg) for arg in tensor_arg]
            ndim = len(tensor_arg[-1])
        else:
            x = torch.randn(*tensor_arg)
            ndim = len(tensor_arg)
        ndim += extra_dim

        n_dim_to_test = sum(map(lambda e: e is DIM_ARG, arg_constr()))

        for dims_val in combinations(range(ndim), n_dim_to_test):
            arg = arg_constr()
            arg_neg = copy.deepcopy(arg)
            idx = 0
            for i, v in enumerate(arg):
                if v is DIM_ARG:
                    arg[i] = dims_val[idx]
                    arg_neg[i] = dims_val[idx] - ndim
                    idx += 1

            if METHOD in types:
                a = getattr(x, name)(*arg)
                b = getattr(x, name)(*arg_neg)
                self.assertEqual(a, b)

            if INPLACE_METHOD in types:
                a = x.clone()
                getattr(a, name + '_')(*arg)
                b = x.clone()
                getattr(b, name + '_')(*arg_neg)
                self.assertEqual(a, b)

            if FUNCTIONAL in types:
                a = getattr(torch, name)(x, *arg)
                b = getattr(torch, name)(x, *arg_neg)
                self.assertEqual(a, b)

    return neg_dim_test


def idx_tensor(size, max_val):
    return torch.LongTensor(*size).random_(0, max_val - 1)


def add_neg_dim_tests():
    neg_dim_tests = [
        ('narrow', (10, 20, 30), lambda: [DIM_ARG, 0, 5], [METHOD]),
        ('transpose', (10, 20, 30), lambda: [DIM_ARG, DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('size', (10, 20, 30), lambda: [DIM_ARG], [METHOD]),
        ('cat', [(2, 3, 4), (2, 3, 4)], lambda: [DIM_ARG], [FUNCTIONAL]),
        ('chunk', (10, 20, 30), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('gather', (10, 20), lambda: [DIM_ARG, idx_tensor((10, 20), 10)], [METHOD, FUNCTIONAL]),
        ('index_select', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10)], [METHOD, FUNCTIONAL]),
        ('split', (10, 20), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('squeeze', (10, 1, 20, 1), lambda: [DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('unbind', (2, 3, 4), lambda: [DIM_ARG], [FUNCTIONAL]),
        ('unsqueeze', (10, 20), lambda: [DIM_ARG], [METHOD, INPLACE_METHOD, FUNCTIONAL], 1),
        ('cumprod', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('cumsum', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('cummax', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('cummin', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('mean', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('median', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('mode', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('norm', (10, 20), lambda: [2, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('prod', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('std', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('sum', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('var', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('kthvalue', (10, 20), lambda: [3, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('max', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('min', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('sort', (10, 20), lambda: [DIM_ARG], [METHOD, FUNCTIONAL]),
        ('topk', (10, 20), lambda: [5, DIM_ARG], [METHOD, FUNCTIONAL]),
        ('renorm', (10, 20), lambda: [2, DIM_ARG, 1], [METHOD, INPLACE_METHOD, FUNCTIONAL]),
        ('index_add', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('index_copy', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('index_fill', (10, 10), lambda: [DIM_ARG, idx_tensor((10,), 10), 12], [INPLACE_METHOD]),
        ('scatter', (10, 10), lambda: [DIM_ARG, idx_tensor((10, 10), 10), torch.randn(10, 10)], [INPLACE_METHOD]),
        ('select', (10, 20), lambda: [DIM_ARG, 3], [METHOD]),
        ('unfold', (10, 20), lambda: [DIM_ARG, 5, 2], [METHOD]),
    ]

    for decl in neg_dim_tests:
        if len(decl) == 4:
            name, tensor_arg, arg_constr, types = decl
            extra_dim = 0
        elif len(decl) == 5:
            name, tensor_arg, arg_constr, types, extra_dim = decl

        test_name = 'test_' + name + '_neg_dim'

        assert not hasattr(_TestTorchMixin, test_name), "Duplicated test name: " + test_name
        setattr(_TestTorchMixin, test_name, make_neg_dim_test(name, tensor_arg, arg_constr, types, extra_dim))


# Device-generic tests. Instantiated below and not run directly.
class TestTorchDeviceType(TestCase):
    exact_dtype = True

    @dtypes(torch.float32, torch.complex64)
    def test_storage(self, device, dtype):
        v = torch.randn(3, 5, dtype=dtype, device=device)
        self.assertEqual(v.storage()[0], v[0][0])
        self.assertEqual(v.storage()[14], v[2][4])

    @dtypes(torch.float32, torch.complex64)
    def test_deepcopy(self, device, dtype):
        from copy import deepcopy
        a = torch.randn(5, 5, dtype=dtype, device=device)
        b = torch.randn(5, 5, dtype=dtype, device=device)
        c = a.view(25)
        q = [a, [a.storage(), b.storage()], b, c]
        w = deepcopy(q)
        self.assertEqual(w[0], q[0], 0)
        self.assertEqual(w[1][0], q[1][0], 0)
        self.assertEqual(w[1][1], q[1][1], 0)
        self.assertEqual(w[1], q[1], 0)
        self.assertEqual(w[2], q[2], 0)

        # Check that deepcopy preserves sharing
        w[0].add_(1)
        for i in range(a.numel()):
            self.assertEqual(w[1][0][i], q[1][0][i] + 1)
        self.assertEqual(w[3], c + 1)
        w[2].sub_(1)
        for i in range(a.numel()):
            self.assertEqual(w[1][1][i], q[1][1][i] - 1)

    @dtypes(torch.float32, torch.complex64)
    def test_deepcopy_scalar(self, device, dtype):
        from copy import deepcopy
        a = torch.tensor(5, dtype=dtype, device=device)
        self.assertEqual(a.size(), deepcopy(a).size())
        self.assertEqual(a, deepcopy(a))

    def _isclose_helper(self, tests, device, dtype, equal_nan, atol=1e-08, rtol=1e-05):
        for test in tests:
            a = torch.tensor((test[0],), device=device, dtype=dtype)
            b = torch.tensor((test[1],), device=device, dtype=dtype)

            actual = torch.isclose(a, b, equal_nan=equal_nan, atol=atol, rtol=rtol)
            expected = test[2]
            self.assertEqual(actual.item(), expected)

    # torch.close is not implemented for bool tensors
    # see https://github.com/pytorch/pytorch/issues/33048
    def test_isclose_bool(self, device):
        tests = (
            (True, True, True),
            (False, False, True),
            (True, False, False),
            (False, True, False),
        )

        with self.assertRaises(RuntimeError):
            self._isclose_helper(tests, device, torch.bool, False)

    @dtypes(torch.uint8,
            torch.int8, torch.int16, torch.int32, torch.int64)
    def test_isclose_integer(self, device, dtype):
        tests = (
            (0, 0, True),
            (0, 1, False),
            (1, 0, False),
        )

        self._isclose_helper(tests, device, dtype, False)

        # atol and rtol tests
        tests = [
            (0, 1, True),
            (1, 0, False),
            (1, 3, True),
        ]

        self._isclose_helper(tests, device, dtype, False, atol=.5, rtol=.5)

        if dtype is torch.uint8:
            tests = [
                (-1, 1, False),
                (1, -1, False)
            ]
        else:
            tests = [
                (-1, 1, True),
                (1, -1, True)
            ]

        self._isclose_helper(tests, device, dtype, False, atol=1.5, rtol=.5)

    @dtypes(torch.float16, torch.float32, torch.float64)
    def test_isclose_float(self, device, dtype):
        tests = (
            (0, 0, True),
            (0, -1, False),
            (float('inf'), float('inf'), True),
            (-float('inf'), float('inf'), False),
            (float('inf'), float('nan'), False),
            (float('nan'), float('nan'), False),
            (0, float('nan'), False),
            (1, 1, True),
        )

        self._isclose_helper(tests, device, dtype, False)

        # atol and rtol tests
        eps = 1e-2 if dtype is torch.half else 1e-6
        tests = (
            (0, 1, True),
            (0, 1 + eps, False),
            (1, 0, False),
            (1, 3, True),
            (1 - eps, 3, False),
            (-.25, .5, True),
            (-.25 - eps, .5, False),
            (.25, -.5, True),
            (.25 + eps, -.5, False),
        )

        self._isclose_helper(tests, device, dtype, False, atol=.5, rtol=.5)

        # equal_nan = True tests
        tests = (
            (0, float('nan'), False),
            (float('inf'), float('nan'), False),
            (float('nan'), float('nan'), True),
        )

        self._isclose_helper(tests, device, dtype, True)

    # torch.close with equal_nan=True is not implemented for complex inputs
    # see https://github.com/numpy/numpy/issues/15959
    @dtypes(torch.complex64, torch.complex128)
    def test_isclose_complex(self, device, dtype):
        tests = (
            (complex(1, 1), complex(1, 1 + 1e-8), True),
            (complex(0, 1), complex(1, 1), False),
            (complex(1, 1), complex(1, 0), False),
            (complex(1, 1), complex(1, float('nan')), False),
            (complex(1, float('nan')), complex(1, float('nan')), False),
            (complex(1, 1), complex(1, float('inf')), False),
            (complex(float('inf'), 1), complex(1, float('inf')), False),
            (complex(-float('inf'), 1), complex(1, float('inf')), False),
            (complex(-float('inf'), 1), complex(float('inf'), 1), False),
            (complex(float('inf'), 1), complex(float('inf'), 1), True),
            (complex(float('inf'), 1), complex(float('inf'), 1 + 1e-4), False),
        )

        self._isclose_helper(tests, device, dtype, False)

        # atol and rtol tests

        # atol and rtol tests
        eps = 1e-6
        tests = (
            # Complex versions of float tests (real part)
            (complex(0, 0), complex(1, 0), True),
            (complex(0, 0), complex(1 + eps, 0), False),
            (complex(1, 0), complex(0, 0), False),
            (complex(1, 0), complex(3, 0), True),
            (complex(1 - eps, 0), complex(3, 0), False),
            (complex(-.25, 0), complex(.5, 0), True),
            (complex(-.25 - eps, 0), complex(.5, 0), False),
            (complex(.25, 0), complex(-.5, 0), True),
            (complex(.25 + eps, 0), complex(-.5, 0), False),
            # Complex versions of float tests (imaginary part)
            (complex(0, 0), complex(0, 1), True),
            (complex(0, 0), complex(0, 1 + eps), False),
            (complex(0, 1), complex(0, 0), False),
            (complex(0, 1), complex(0, 3), True),
            (complex(0, 1 - eps), complex(0, 3), False),
            (complex(0, -.25), complex(0, .5), True),
            (complex(0, -.25 - eps), complex(0, .5), False),
            (complex(0, .25), complex(0, -.5), True),
            (complex(0, .25 + eps), complex(0, -.5), False),
            # Complex-specific tests
            (complex(1, -1), complex(-1, 1), False),
            (complex(1, -1), complex(2, -2), True),
            (complex(-math.sqrt(2), math.sqrt(2)),
             complex(-math.sqrt(.5), math.sqrt(.5)), True),
            (complex(-math.sqrt(2), math.sqrt(2)),
             complex(-math.sqrt(.501), math.sqrt(.499)), False),
            (complex(2, 4), complex(1., 8.8523607), True),
            (complex(2, 4), complex(1., 8.8523607 + eps), False),
        )

        self._isclose_helper(tests, device, dtype, False, atol=.5, rtol=.5)

        # equal_nan = True tests
        tests = (
            (complex(1, 1), complex(1, float('nan')), False),
            (complex(float('nan'), 1), complex(1, float('nan')), False),
            (complex(float('nan'), 1), complex(float('nan'), 1), True),
        )

        with self.assertRaises(RuntimeError):
            self._isclose_helper(tests, device, dtype, True)

    # Tests that rtol or atol values less than zero thow RuntimeErrors
    @dtypes(torch.bool, torch.uint8,
            torch.int8, torch.int16, torch.int32, torch.int64,
            torch.float16, torch.float32, torch.float64)
    def test_isclose_atol_rtol_greater_than_zero(self, device, dtype):
        t = torch.tensor((1,), device=device, dtype=dtype)

        with self.assertRaises(RuntimeError):
            torch.isclose(t, t, atol=-1, rtol=1)
        with self.assertRaises(RuntimeError):
            torch.isclose(t, t, atol=1, rtol=-1)
        with self.assertRaises(RuntimeError):
            torch.isclose(t, t, atol=-1, rtol=-1)

    # XLA tests fail for self.assertRaises for complex dtypes
    @onlyOnCPUAndCUDA
    def test_complex_assert_raises(self, device):
        for dtype in [torch.complex64, torch.complex128]:
            size = [5, 5]
            tensor = torch.rand(size, dtype=dtype, device=device)

            # index_add calls atomicAdd on cuda.
            zeros = torch.zeros(size, dtype=dtype, device=device)

            # index_add is not supported for complex dtypes on cuda yet
            if device.startswith('cuda') and dtype.is_complex:
                self.assertRaises(RuntimeError,
                                  lambda: zeros.index_add(0, torch.arange(0, size[0], dtype=torch.long, device=device), tensor))

            self.assertRaises(RuntimeError, lambda: torch.sign(torch.tensor([4j], device=device, dtype=dtype)))

            a = torch.rand((2, 2), dtype=dtype, device=device)
            b = torch.rand((2, 2), dtype=dtype, device=device)
            c = torch.rand((2, 2), dtype=dtype, device=device)
            alpha = 3

            # addcmul is not supported for complex dtypes on cuda yet
            if device.startswith('cuda') and dtype.is_complex:
                self.assertRaises(RuntimeError, lambda: torch.addcmul(a, b, c, value=alpha))

    def check_internal_mem_overlap(self, inplace_op, num_inputs,
                                   dtype, device,
                                   expected_failure=False):
        if isinstance(inplace_op, str):
            inplace_op = getattr(torch.Tensor, inplace_op)
        input = torch.randn(1, dtype=dtype, device=device).expand(3, 3)
        inputs = [input] + [torch.randn_like(input)
                            for i in range(num_inputs - 1)]
        if not expected_failure:
            with self.assertRaisesRegex(RuntimeError, 'single memory location'):
                inplace_op(*inputs)
        else:
            with self.assertRaises(AssertionError):
                with self.assertRaisesRegex(RuntimeError, 'single memory location'):
                    inplace_op(*inputs)

    def unary_check_input_output_mem_overlap(self, data, sz, op,
                                             expected_failure=False):

        def _test(op, output, input):
            output_exp = torch.empty_like(output)
            op(input, out=output_exp)
            self.assertEqual(op(input, out=output), output_exp, op.__name__)

        # output is identical to input:
        _test(op, output=data[0:sz], input=data[0:sz])
        # output and input are independent:
        _test(op, output=data[0:sz], input=data[sz:2 * sz])
        # output partially overlaps with input:
        if not expected_failure:
            with self.assertRaisesRegex(RuntimeError, 'unsupported operation'):
                _test(op, data[0:sz], data[1:sz + 1])
        else:
            with self.assertRaises(AssertionError):
                with self.assertRaisesRegex(RuntimeError, 'unsupported operation'):
                    _test(op, data[0:sz], data[1:sz + 1])

    def binary_check_input_output_mem_overlap(self, op, device,
                                              expected_failure=False):
        sz = 3
        data = torch.randn(2 * sz, device=device)
        other = torch.randn(sz, device=device)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other, input, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(input, other, out=out),
            expected_failure=expected_failure)

    def ternary_check_input_output_mem_overlap(self, op, device,
                                               expected_failure=False):
        sz = 3
        data = torch.randn(2 * sz, device=device)
        other1 = torch.randn(sz, device=device)
        other2 = torch.randn(sz, device=device)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(input, other1, other2, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other1, input, other2, out=out),
            expected_failure=expected_failure)

        self.unary_check_input_output_mem_overlap(
            data, sz, lambda input, out: op(other1, other2, input, out=out),
            expected_failure=expected_failure)

    def _test_pow(self, base, exponent, np_exponent=None):
        if np_exponent is None:
            np_exponent = exponent

        def to_np(value):
            if isinstance(value, torch.Tensor):
                return value.cpu().numpy()
            return value

        try:
            expected = torch.from_numpy(
                np.power(to_np(base), to_np(np_exponent)))
        except ValueError as e:
            err_msg = "Integers to negative integer powers are not allowed."
            self.assertEqual(str(e), err_msg)
            out = torch.empty_like(base)
            test_cases = [
                lambda: base.pow(exponent),
                lambda: base.pow_(exponent),
                lambda: torch.pow(base, exponent),
                lambda: torch.pow(base, exponent, out=out)
            ]
            for test_case in test_cases:
                self.assertRaisesRegex(RuntimeError, err_msg, test_case)
        else:
            if isinstance(base, torch.Tensor):
                actual = base.pow(exponent)
                self.assertEqual(actual, expected.to(actual), allow_inf=True)

                actual = base.clone()
                actual2 = actual.pow_(exponent)
                self.assertEqual(actual, expected.to(actual), allow_inf=True)
                self.assertEqual(actual2, expected.to(actual), allow_inf=True)

            actual = torch.pow(base, exponent)
            self.assertEqual(actual, expected.to(actual), allow_inf=True)

            actual2 = torch.pow(base, exponent, out=actual)
            self.assertEqual(actual, expected.to(actual), allow_inf=True)
            self.assertEqual(actual2, expected.to(actual), allow_inf=True)

    def _select_broadcastable_dims(self, dims_full=None):
        # select full dimensionality
        if dims_full is None:
            dims_full = []
            ndims = random.randint(1, 4)
            dims_full = [random.randint(1, 8) for _ in range(ndims)]
        else:
            ndims = len(dims_full)

        # select actual dimensions for ops:
        # larger: full ndims, individual sizes may be reduced
        # smaller: possibly reduced ndims, sizes may be reduced
        smaller_ndims = random.randint(1, ndims)
        dims_small = []
        dims_large = []
        for i in range(ndims - 1, -1, -1):
            j = random.randint(1, 3)
            if j == 1:  # no reduced singleton dimension
                ds = dims_full[i]
                dl = dims_full[i]
            elif j == 2:  # larger may have reduced singleton dimension
                ds = dims_full[i]
                dl = 1 if len(dims_small) < smaller_ndims else dims_full[i]
            elif j == 3:  # smaller may have reduced singleton dimension
                ds = 1
                dl = dims_full[i]
            dims_large = [dl] + dims_large
            if len(dims_small) < smaller_ndims:
                dims_small = [ds] + dims_small
        return (dims_small, dims_large, dims_full)

    # collected tests of ops that used scalar_check in Declarations.cwrap for
    # correctness
    def test_scalar_check(self, device):
        zero_d = torch.randn((), device=device)
        one_d = torch.randn((1,), device=device)

        # _multinomial_alias_setup
        self.assertRaises(RuntimeError, lambda: torch._multinomial_alias_setup(zero_d))

        # remainder
        self.assertEqual((), torch.remainder(zero_d, zero_d).shape)
        self.assertEqual((), torch.remainder(zero_d, 2).shape)
        self.assertEqual((1,), torch.remainder(zero_d, one_d).shape)
        self.assertEqual((1,), torch.remainder(one_d, zero_d).shape)

        # fmod
        self.assertEqual((), torch.fmod(zero_d, zero_d).shape)
        self.assertEqual((), torch.fmod(zero_d, 2).shape)
        self.assertEqual((1,), torch.fmod(zero_d, one_d).shape)
        self.assertEqual((1,), torch.fmod(one_d, zero_d).shape)

        # exp, cos, cosh, tan, atan, tanh, erf, erfc, reciprocal
        self.assertEqual((), torch.exp(zero_d).shape)
        self.assertEqual((), torch.cos(zero_d).shape)
        self.assertEqual((), torch.cosh(zero_d).shape)
        self.assertEqual((), torch.tan(zero_d).shape)
        self.assertEqual((), torch.atan(zero_d).shape)
        self.assertEqual((), torch.tanh(zero_d).shape)
        self.assertEqual((), torch.erf(zero_d).shape)
        self.assertEqual((), torch.erfc(zero_d).shape)
        self.assertEqual((), torch.reciprocal(zero_d).shape)
        self.assertEqual((1,), torch.exp(one_d).shape)
        self.assertEqual((1,), torch.cos(one_d).shape)
        self.assertEqual((1,), torch.cosh(one_d).shape)
        self.assertEqual((1,), torch.tan(one_d).shape)
        self.assertEqual((1,), torch.atan(one_d).shape)
        self.assertEqual((1,), torch.tanh(one_d).shape)
        self.assertEqual((1,), torch.erf(one_d).shape)
        self.assertEqual((1,), torch.erfc(one_d).shape)
        self.assertEqual((1,), torch.reciprocal(one_d).shape)

        # clamp
        self.assertEqual((), torch.clamp(zero_d, min=0, max=1).shape)
        self.assertEqual((), torch.clamp(zero_d, min=0).shape)
        self.assertEqual((), torch.clamp(zero_d, max=1).shape)
        self.assertEqual((1,), torch.clamp(one_d, min=0, max=1).shape)
        self.assertEqual((1,), torch.clamp(one_d, min=0).shape)
        self.assertEqual((1,), torch.clamp(one_d, max=1).shape)

        # cumsum, cumprod, cummax, cummin
        self.assertEqual((), torch.cumsum(zero_d, 0).shape)
        self.assertEqual((), torch.cumprod(zero_d, 0).shape)
        self.assertEqual((), torch.cummax(zero_d, 0)[0].shape)
        self.assertEqual((), torch.cummin(zero_d, 0)[0].shape)

        # renorm
        self.assertRaises(RuntimeError, lambda: torch.renorm(zero_d, 0.5, 0, 1.0))

        # sort, topk
        self.assertEqual([(), ()], [x.shape for x in torch.sort(zero_d, 0, False)])
        self.assertEqual([(), ()], [x.shape for x in torch.sort(zero_d, 0, True)])
        self.assertEqual([(), ()], [x.shape for x in torch.topk(zero_d, 1, 0, False)])
        self.assertEqual([(), ()], [x.shape for x in torch.topk(zero_d, 1, 0, True)])

        # lstsq (gels)
        self.assertRaises(RuntimeError, lambda: torch.lstsq(zero_d, zero_d))

        # eig
        self.assertRaises(RuntimeError, lambda: torch.eig(zero_d, False))
        self.assertRaises(RuntimeError, lambda: torch.eig(zero_d, True))

        # this is only implemented on cpu
        if (torch.device(device).type == 'cpu'):
            self.assertRaises(RuntimeError, lambda: torch.ormqr(zero_d, zero_d, zero_d))

        # max, min
        self.assertEqual((), torch.max(zero_d, zero_d).shape)
        self.assertEqual((1,), torch.max(one_d, zero_d).shape)
        self.assertEqual((1,), torch.max(zero_d, one_d).shape)
        self.assertEqual((), torch.min(zero_d, zero_d).shape)
        self.assertEqual((1,), torch.min(one_d, zero_d).shape)
        self.assertEqual((1,), torch.min(zero_d, one_d).shape)

        # diag
        self.assertRaises(RuntimeError, lambda: torch.diag(zero_d))

        zero_d_int = torch.tensor(1, device=device)
        one_d_int = torch.tensor([1], device=device)

        # lshift, rshift
        self.assertEqual((), (zero_d_int >> zero_d_int).shape)
        self.assertEqual((), (zero_d_int >> 1).shape)
        self.assertEqual((1,), (one_d_int >> zero_d_int).shape)
        self.assertEqual((1,), (zero_d_int >> one_d_int).shape)
        self.assertEqual((1,), (one_d_int >> 1).shape)

        self.assertEqual((), (zero_d_int << zero_d_int).shape)
        self.assertEqual((), (zero_d_int << 1).shape)
        self.assertEqual((1,), (one_d_int << zero_d_int).shape)
        self.assertEqual((1,), (zero_d_int << one_d_int).shape)
        self.assertEqual((1,), (one_d_int << 1).shape)

        # or
        self.assertEqual((), (zero_d_int | zero_d_int).shape)
        self.assertEqual((), (zero_d_int | 1).shape)
        self.assertEqual((1,), (one_d_int | zero_d_int).shape)
        self.assertEqual((1,), (zero_d_int | one_d_int).shape)
        self.assertEqual((1,), (one_d_int | 1).shape)

        # and
        self.assertEqual((), (zero_d_int & zero_d_int).shape)
        self.assertEqual((), (zero_d_int & 1).shape)
        self.assertEqual((1,), (one_d_int & zero_d_int).shape)
        self.assertEqual((1,), (zero_d_int & one_d_int).shape)
        self.assertEqual((1,), (one_d_int & 1).shape)

        # _multinomial_alias_draw
        self.assertRaises(RuntimeError, lambda: torch._multinomial_alias_draw(zero_d, zero_d_int, 10))

        # clone
        self.assertEqual((), zero_d.clone().shape)

        zero_d_bool = torch.tensor(True, device=device)
        one_d_bool = torch.tensor([True], device=device)

        # masked_select
        self.assertEqual((1,), torch.masked_select(zero_d_bool, zero_d_bool).shape)
        self.assertEqual((1,), torch.masked_select(zero_d_bool, one_d_bool).shape)
        self.assertEqual((1,), torch.masked_select(one_d_bool, zero_d_bool).shape)

        zero_d_uint8 = torch.tensor(1, dtype=torch.uint8, device=device)
        one_d_uint8 = torch.tensor([1], dtype=torch.uint8, device=device)

        with warnings.catch_warnings():
            warnings.simplefilter("ignore")
            self.assertEqual((1,), torch.masked_select(zero_d_uint8, zero_d_uint8).shape)
            self.assertEqual((1,), torch.masked_select(zero_d_uint8, one_d_uint8).shape)
            self.assertEqual((1,), torch.masked_select(one_d_uint8, zero_d_uint8).shape)

        # mode
        self.assertEqual([(), ()], [x.shape for x in torch.mode(zero_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.mode(zero_d, dim=0, keepdim=False)])
        self.assertEqual([(1,), (1,)], [x.shape for x in torch.mode(one_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.mode(one_d, dim=0, keepdim=False)])

        # max
        self.assertEqual([(), ()], [x.shape for x in torch.max(zero_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.max(zero_d, dim=0, keepdim=False)])
        self.assertEqual([(1,), (1,)], [x.shape for x in torch.max(one_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.max(one_d, dim=0, keepdim=False)])

        # min
        self.assertEqual([(), ()], [x.shape for x in torch.min(zero_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.min(zero_d, dim=0, keepdim=False)])
        self.assertEqual([(1,), (1,)], [x.shape for x in torch.min(one_d, dim=0, keepdim=True)])
        self.assertEqual([(), ()], [x.shape for x in torch.min(one_d, dim=0, keepdim=False)])

        # set_
        zero_d_clone = zero_d.clone()
        one_d_clone = one_d.clone()
        self.assertEqual((), zero_d_clone.set_(one_d.storage(), 0, (), ()).shape)
        self.assertEqual((1,), zero_d_clone.set_(one_d.storage(), 0, (1,), (1,)).shape)
        self.assertEqual((), one_d_clone.set_(one_d.storage(), 0, (), ()).shape)
        self.assertEqual((1,), one_d_clone.set_(one_d.storage(), 0, (1,), (1,)).shape)

        self.assertEqual((), zero_d.clone().set_(zero_d).shape)
        self.assertEqual((), one_d.clone().set_(zero_d).shape)
        self.assertEqual((1,), zero_d.clone().set_(one_d).shape)
        self.assertEqual((1,), one_d.clone().set_(one_d).shape)

        # take
        self.assertEqual((), torch.randn((2, 3), device=device).take(zero_d_int).shape)
        self.assertEqual((1,), torch.randn((2, 3), device=device).take(one_d_int).shape)

        # gather
        self.assertEqual((), torch.gather(zero_d, 0, torch.zeros((), dtype=torch.int64, device=device)).shape)
        self.assertEqual((1,), torch.gather(zero_d, 0, torch.zeros((1,), dtype=torch.int64, device=device)).shape)
        self.assertEqual((), torch.gather(one_d, 0, torch.zeros((), dtype=torch.int64, device=device)).shape)
        self.assertEqual((1,), torch.gather(one_d, 0, torch.zeros((1,), dtype=torch.int64, device=device)).shape)

        # normal
        # documentation says out shape matches shape of mean
        self.assertEqual((), torch.normal(zero_d, zero_d).shape)
        self.assertEqual((1,), torch.normal(one_d, zero_d).shape)
        self.assertEqual((), torch.normal(1, zero_d).shape)
        self.assertEqual((), torch.normal(zero_d, 1).shape)
        self.assertEqual((1,), torch.normal(one_d, 1).shape)
        # TODO: this behavior differs on CPU and GPU, see https://github.com/pytorch/pytorch/issues/30480.
        # self.assertEqual((), torch.normal(zero_d, one_d).shape)
        # self.assertEqual((), torch.normal(1, one_d).shape)

        # convolutions.  Yes, we are testing nn.functional here; seems justified
        # given its similar to the other tests
        w = torch.randn(2, 1, 3, 3, device=device).div_(2).requires_grad_()
        self.assertRaises(RuntimeError, lambda: torch.nn.functional.conv2d(zero_d, w, groups=1))
        self.assertRaises(RuntimeError, lambda: torch.nn.functional.conv2d(zero_d, w, groups=2))

        # nll_loss -- verify input can't be 0-dimensional.
        self.assertRaises(ValueError, lambda: torch.nn.functional.nll_loss(zero_d, zero_d, reduction='none'))
        self.assertRaises(ValueError, lambda: torch.nn.functional.nll_loss(zero_d, one_d, reduction='none'))
        # verify output is 0-dimensional when reduction != 'none'
        for (input, target) in ((torch.randn(1, 1, device=device), torch.tensor([0], device=device)),
                                (torch.randn(1, 1, 1, 1, device=device), torch.tensor([[[0]]], device=device))):
            self.assertEqual((), torch.nn.functional.nll_loss(input, target, reduction='mean').shape)
            self.assertEqual((), torch.nn.functional.nll_loss(input, target, reduction='sum').shape)

        # multilabel_margin_loss
        for input in (zero_d, one_d, torch.randn(1, 1, device=device)):
            for target in (torch.tensor(0, device=device), torch.tensor([0], device=device), torch.tensor([[0]], device=device)):
                if (input.dim() <= 1 and target.dim() <= 1) or (input.dim() == 2 and target.dim() == 2):
                    output_shape = (target.shape[0],) if target.dim() == 2 else ()
                    self.assertEqual(output_shape,
                                     torch.nn.functional.multilabel_margin_loss(input, target, reduction='none').shape)
                    self.assertEqual((), torch.nn.functional.multilabel_margin_loss(input, target, reduction='mean').shape)
                    self.assertEqual((), torch.nn.functional.multilabel_margin_loss(input, target, reduction='sum').shape)
                else:
                    self.assertRaises(RuntimeError,
                                      lambda: torch.nn.functional.multilabel_margin_loss(input, target, reduction='none'))
                    self.assertRaises(RuntimeError,
                                      lambda: torch.nn.functional.multilabel_margin_loss(input, target, reduction='mean'))
                    self.assertRaises(RuntimeError,
                                      lambda: torch.nn.functional.multilabel_margin_loss(input, target, reduction='sum'))

        # multi_margin_loss
        for input in (zero_d, one_d, torch.randn(1, 1, device=device)):
            for target in (torch.tensor(0, device=device), torch.tensor([0], device=device)):
                self.assertEqual(target.shape, torch.nn.functional.multi_margin_loss(input, target, reduction='none').shape)
                self.assertEqual((), torch.nn.functional.multi_margin_loss(input, target, reduction='mean').shape)
                self.assertEqual((), torch.nn.functional.multi_margin_loss(input, target, reduction='sum').shape)

    # Uses mismatched arange out size to trigger a warning
    def test_cpp_warnings_have_python_context(self, device):
        import inspect
        # Creates long string in advance to avoid a too-long Python line
        s = ".+Triggered internally at.+RangeFactories.+"

        def cpp_warn_fn():
            out = torch.empty((5,))
            torch.arange(0, 3, out=out)
            return out

        # Checks eager-mode cpp warning
        with warnings.catch_warnings(record=True) as w:
            cpp_warn_fn()
            frameinfo = inspect.getframeinfo(inspect.currentframe())
            warning = w[0]

            # Checks for cpp context in the warning message
            self.assertTrue(re.search(s, str(warning.message)) is not None)

            # Checks the Python features of the warning
            # Note: the eager mode warning refers to the line in the function
            # that throws the warning.
            self.assertEqual(frameinfo.lineno - 6, warning.lineno)
            self.assertEqual(len(w), 1)

        # Checks jitted cpp warning
        with warnings.catch_warnings(record=True) as w:
            scripted_cpp_warn_fn = torch.jit.script(cpp_warn_fn)
            scripted_cpp_warn_fn()
            warning = w[0]

            # Checks for cpp context in the warning message
            self.assertTrue(re.search(s, str(warning.message)) is not None)

            # Checks the Python features of the warning
            # Note: the jitted warning's lineno refers to the call to the jitted
            # function, which in our test suite has a layer of indirection
            # that makes checking the Python lineno fragile
            self.assertEqual(len(w), 1)

        # Checks jitted Python warning
        def warn_fn():
            warnings.warn("Warning!")

        # The jit mimics an eager-mode Python warning in this case
        with warnings.catch_warnings(record=True) as w:
            scripted_warn_fn = torch.jit.script(warn_fn)
            scripted_warn_fn()
            frameinfo = inspect.getframeinfo(inspect.currentframe())
            warning = w[0]

            self.assertTrue(re.search('Warning!', str(warning.message)) is not None)

            # Checks the Python features of the warning
            self.assertEqual(frameinfo.lineno - 6, warning.lineno)
            self.assertEqual(len(w), 1)

    def _np_compare(self, fn_name, vals, device, dtype):
        assert TEST_NUMPY

        torch_fn = getattr(torch, fn_name)
        np_fn = getattr(np, fn_name)

        a = np.array(vals, dtype=torch_to_numpy_dtype_dict[dtype])
        np_result = torch.from_numpy(np_fn(a))

        t = torch.tensor(vals, device=device, dtype=dtype)
        torch_result = torch_fn(t).cpu()
        self.assertEqual(np_result, torch_result)

    @unittest.skipIf(not TEST_NUMPY, 'NumPy not found')
    @dtypes(torch.float)
    def test_isfinite_isinf_isnan(self, device, dtype):
        vals = (-float('inf'), float('inf'), float('nan'), -1, 0, 1)

        self._np_compare('isfinite', vals, device, dtype)
        self._np_compare('isinf', vals, device, dtype)
        self._np_compare('isnan', vals, device, dtype)

    @unittest.skipIf(not TEST_NUMPY, 'NumPy not found')
    @dtypes(torch.long)
    def test_isfinite_isinf_isnan_int(self, device, dtype):
        vals = (-1, 0, 1)

        self._np_compare('isfinite', vals, device, dtype)
        self._np_compare('isinf', vals, device, dtype)
        self._np_compare('isnan', vals, device, dtype)

    @unittest.skipIf(not TEST_NUMPY, 'NumPy not found')
    @dtypes(torch.complex64)
    def test_isfinite_isinf_isnan_complex(self, device, dtype):
        vals = (
            complex(-float('inf'), float('inf')),
            complex(-float('inf'), 0),
            complex(0, float('inf')),
            complex(float('inf'), float('nan')),
            complex(float('nan'), 0),
            complex(-1, 0),
            complex(0, 1)
        )

        self._np_compare('isfinite', vals, device, dtype)
        self._np_compare('isinf', vals, device, dtype)
        self._np_compare('isnan', vals, device, dtype)

    @onlyCPU
    def test_isfinite_type(self, device):
        with self.assertRaises(TypeError):
            torch.isfinite(1)  # Parameter must be a tensor

    @onlyCPU
    def test_isinf_type(self, device):
        with self.assertRaises(TypeError):
            torch.isinf(1)  # Parameter must be a tensor

    @onlyCPU
    @dtypes(torch.float)
    def test_diag(self, device, dtype):
        x = torch.rand(100, 100, dtype=dtype, device=device)
        res1 = torch.diag(x)
        res2 = torch.tensor((), dtype=dtype, device=device)
        torch.diag(x, out=res2)
        self.assertEqual(res1, res2)

    def test_diagonal(self, device):
        x = torch.randn((100, 100), device=device)
        result = torch.diagonal(x)
        expected = torch.diag(x)
        self.assertEqual(result, expected)

        x = torch.randn((100, 100), device=device)
        result = torch.diagonal(x, 17)
        expected = torch.diag(x, 17)
        self.assertEqual(result, expected)

    def test_conv_transposed_backward_agnostic_to_memory_format(self, device):
        in_channels = 64
        out_channels = 128
        scale_factor = 8
        batch_size = 8
        length = 16

        conv = torch.nn.ConvTranspose1d(
            in_channels, out_channels, kernel_size=scale_factor * 2, stride=scale_factor).to(device)
        layer_norm = torch.nn.LayerNorm(out_channels).to(device)

        input_ = torch.randn(batch_size, in_channels, length).to(device).contiguous()
        input_ = conv(input_).contiguous()
        input_ = layer_norm(input_.transpose(1, 2).contiguous()).contiguous()
        input_.sum().backward()

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    @onlyCPU
    @dtypes(torch.float)
    def test_diagonal_multidim(self, device, dtype):
        x = torch.randn(10, 11, 12, 13, dtype=dtype, device=device)
        xn = x.numpy()
        for args in [(2, 2, 3),
                     (2,),
                     (-2, 1, 2),
                     (0, -2, -1)]:
            result = torch.diagonal(x, *args)
            expected = xn.diagonal(*args)
            self.assertEqual(expected.shape, result.shape)
            self.assertTrue(np.allclose(expected, result.numpy()))
        # test non-continguous
        xp = x.permute(1, 2, 3, 0)
        result = torch.diagonal(xp, 0, -2, -1)
        expected = xp.numpy().diagonal(0, -2, -1)
        self.assertEqual(expected.shape, result.shape)
        self.assertTrue(np.allclose(expected, result.numpy()))

    @onlyCPU
    @dtypes(torch.float)
    def test_broadcast_tensors(self, device, dtype):
        x0 = torch.randn(2, 1, 3, dtype=dtype, device=device)
        x1 = torch.randn(3, dtype=dtype, device=device)
        x2 = torch.randn(3, 1, dtype=dtype, device=device)
        expected_size = (2, 3, 3)

        y0, y1, y2 = torch.broadcast_tensors(x0, x1, x2)
        self.assertTrue(y0.size() == expected_size)
        self.assertTrue(y1.size() == expected_size)
        self.assertTrue(y2.size() == expected_size)

    def _do_pow_for_exponents(self, m1, exponents, pow_fn, atol):
        for num in exponents:
            if isinstance(num, int) and num < 0 and not m1.is_floating_point() and not m1.is_complex():
                with self.assertRaisesRegex(RuntimeError,
                                            r'Integers to negative integer powers are not allowed\.'):
                    torch.pow(m1[4], num)
            else:
                # base - tensor, exponent - number
                # contiguous
                res1 = torch.pow(m1[4], num)
                res2 = res1.clone().zero_()
                # `math.pow` has issues with complex exponentiation so we need to resort to normal `pow`.
                for i in range(res2.size(0)):
                    res2[i] = pow_fn(m1[4][i], num)
                self.assertEqual(res1, res2, {'atol': atol})

                # non-contiguous
                res1 = torch.pow(m1[:, 4], num)
                res2 = res1.clone().zero_()
                for i in range(res2.size(0)):
                    res2[i] = pow_fn(m1[i, 4], num)
                self.assertEqual(res1, res2, {'atol': atol})

    def test_pow(self, device):
        # [res] torch.pow([res,] x)

        # pow has dedicated implementation for different exponents
        for dtype in torch.testing.get_all_math_dtypes(device):

            # This test won't work on torch.half because math.pow will generate a much more accurate result. We skip it
            # for now.
            if dtype == torch.half:
                continue

            # deferring to https://github.com/pytorch/pytorch/pull/36793
            if dtype.is_complex:
                continue

            m1 = torch.empty(0, dtype=dtype, device=device)
            if m1.is_floating_point() or m1.is_complex():
                m1 = torch.rand(100, 100, dtype=dtype, device=device) + 0.5
            else:
                # math.pow will overflow and throw exceptions for large integers
                range_high = 4 if dtype in (torch.int8, torch.uint8) else 10
                m1 = torch.randint(1, range_high, (100, 100), dtype=dtype, device=device)

            exponents = [-2.8, -2, -1, -0.5, 0, 0.5, 1, 2, 3, 4, 3.3]
            complex_exponents = [-2.5j, -1.0j, 0j, 1.0j, 2.5j, 1.0 + 1.0j, -1.0 - 1.5j, 3.3j]
            if m1.is_complex():
                self._do_pow_for_exponents(m1, exponents + complex_exponents, pow, 10e-4)
            else:
                self._do_pow_for_exponents(m1, exponents, math.pow, {})
                self._do_pow_for_exponents(m1, complex_exponents, pow, 10e-4)

            # base - number, exponent - tensor
            # contiguous
            res1 = torch.pow(3, m1[4])
            res2 = res1.clone().zero_()
            for i in range(res2.size(0)):
                res2[i] = math.pow(3, m1[4, i])
            self.assertEqual(res1, res2)

            # non-contiguous
            res1 = torch.pow(3, m1[:, 4])
            res2 = res1.clone().zero_()
            for i in range(res2.size(0)):
                res2[i] = math.pow(3, m1[i][4])
            self.assertEqual(res1, res2)

            # resize behavior for exp == 1
            out = torch.zeros(1, dtype=dtype, device=device)
            torch.pow(m1, 1, out=out)
            self.assertEqual(out, m1)

    def test_neg(self, device):
        int_types = [torch.int, torch.short, torch.int8, torch.uint8]
        float_types = [torch.float, torch.double, torch.long]

        # Tests bool tensor negation raises the correct error
        self.assertRaisesRegex(
            RuntimeError,
            r"Negation, the `\-` operator, on a bool tensor is not supported. "
            r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
            lambda: - torch.tensor([False, True], device=device))

        for dtype in float_types + int_types:
            if dtype in float_types:
                a = torch.randn(100, 90).to(device=device, dtype=dtype)
            if dtype == torch.uint8:
                a = torch.randint(0, 256, (100, 90), dtype=dtype, device=device)
            else:
                a = torch.randint(-128, 128, (100, 90), dtype=dtype, device=device)
            zeros = torch.zeros_like(a, device=device, dtype=dtype)

            if dtype == torch.uint8:
                res_add = torch.add(zeros, a, alpha=255)
            else:
                res_add = torch.add(zeros, a, alpha=-1)

            res_neg = a.clone()
            res_neg.neg_()
            self.assertEqual(res_neg, res_add)

            # test out of place as well
            res_neg_out_place = a.clone().neg()
            self.assertEqual(res_neg_out_place, res_add)

            # test via __neg__ operator
            res_neg_op = -a.clone()
            self.assertEqual(res_neg_op, res_add)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_inverse(self, device):
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        # no batches: 2-D tensors
        matrix = random_fullrank_matrix_distinct_singular_value(5).to(device)
        matrix_inverse = torch.inverse(matrix)

        identity = torch.eye(5, dtype=torch.float64, device=device)
        self.assertEqual(identity, torch.mm(matrix, matrix_inverse), atol=1e-8, message='inverse value')
        self.assertEqual(identity, torch.mm(matrix_inverse, matrix), atol=1e-8, message='inverse value')

        matrix_inverse_out = torch.empty(5, 5, dtype=torch.float64, device=device)
        torch.inverse(matrix, out=matrix_inverse_out)
        self.assertEqual(matrix_inverse_out, matrix_inverse, atol=0, message='inverse value in-place')
        # second call, now that matrix_inverse_out is transposed
        torch.inverse(matrix, out=matrix_inverse_out)
        self.assertEqual(matrix_inverse_out, matrix_inverse, atol=0, message='inverse value in-place')

        # one batch
        matrix = random_fullrank_matrix_distinct_singular_value(5, 1).to(device)
        matrix_inverse = torch.inverse(matrix)
        expected_inv = matrix.squeeze(0).inverse()
        self.assertEqual(matrix_inverse, expected_inv.unsqueeze(0))

        # four batches
        matrices = random_fullrank_matrix_distinct_singular_value(5, 4).to(device)
        expected_inv_list = []
        for i in range(0, 4):
            expected_inv_list.append(torch.inverse(matrices[i]))
        expected_inv = torch.stack(expected_inv_list)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(matrices_inverse, expected_inv)

        # six batches (2 x 3)
        matrices = random_fullrank_matrix_distinct_singular_value(5, 2, 3).to(device)
        expected_inv_list = []
        for mat in matrices.view(-1, 5, 5):
            expected_inv_list.append(torch.inverse(mat))
        expected_inv = torch.stack(expected_inv_list).view(2, 3, 5, 5)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(matrices_inverse, expected_inv)

        # incorrect input test
        with self.assertRaisesRegex(RuntimeError, "must be batches of square matrices"):
            torch.inverse(torch.randn(2, 3, 4, 3))

        # correctness test
        matrices = random_fullrank_matrix_distinct_singular_value(5, 3).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices, matrices_inverse), identity.expand_as(matrices))
        self.assertEqual(torch.matmul(matrices_inverse, matrices), identity.expand_as(matrices))

        # torch.inverse with out and batches
        matrices = random_fullrank_matrix_distinct_singular_value(5, 3).to(device)
        matrices_inverse = torch.empty(3, 5, 5, dtype=torch.float64, device=device)
        torch.inverse(matrices, out=matrices_inverse)
        self.assertEqual(torch.inverse(matrices), matrices_inverse)

        # non-contiguous inputs
        if not TEST_NUMPY:
            return

        from numpy.linalg import inv
        matrices = random_fullrank_matrix_distinct_singular_value(3, 2).to(device).permute(0, 2, 1)
        assert not matrices.is_contiguous()
        matrices_inverse = torch.inverse(matrices)
        expected_inv = torch.as_tensor(inv(matrices.cpu().numpy()))
        self.assertEqual(matrices_inverse, expected_inv.to(device))

    @dtypes(torch.int8, torch.int16, torch.int32, torch.int64)
    def test_signed_shift(self, device, dtype):
        "Ensure that signed integer bit shifting works as expected."
        a = torch.tensor([-10, 10], device=device, dtype=dtype)  # [11...1110110, 1010]
        expected_l = torch.tensor([-40, 40], device=device, dtype=dtype)  # [11...11011000, 101000]
        self.assertEqual(a << 2, expected_l)
        expected_r = torch.tensor([torch.iinfo(dtype).max - 4, 5], device=device, dtype=dtype)  # [1111...111011, 101]
        self.assertEqual(a >> 1, expected_r)

    def test_bitwise_not(self, device):
        res = 0xffff - torch.arange(127, dtype=torch.int8, device=device)
        for dtype in (torch.bool, torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            if dtype == torch.bool:
                a = torch.tensor([True, False], device=device)
                expected_res = torch.tensor([False, True], device=device)
            else:
                a = torch.arange(127, dtype=dtype, device=device)
                expected_res = res.to(dtype)
            # new tensor
            self.assertEqual(expected_res, a.bitwise_not())
            # out
            b = torch.empty(0, dtype=dtype, device=device)
            torch.bitwise_not(a, out=b)
            self.assertEqual(expected_res, b)
            # in-place
            a.bitwise_not_()
            self.assertEqual(expected_res, a)

        # test exceptions
        for dtype in(torch.half, torch.float, torch.double):
            a = torch.zeros(10, dtype=dtype, device=device)
            # new tensor
            with self.assertRaises(RuntimeError):
                a.bitwise_not()
            # out
            b = torch.empty(0, dtype=dtype, device=device)
            with self.assertRaises(RuntimeError):
                torch.bitwise_not(a, out=b)
            # in-place
            with self.assertRaises(RuntimeError):
                a.bitwise_not_()

    def test_bitwise_and(self, device):
        for dtype in (torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            a = torch.tensor([1, -2, 3], dtype=dtype, device=device)
            b = torch.tensor([2, 1, 3], dtype=dtype, device=device)
            expected_res = torch.tensor([0, 0, 3], dtype=dtype, device=device)
            b_scalar = 2
            expected_res_scalar = torch.tensor([0, 2, 2], dtype=dtype, device=device)

            # standard version
            self.assertEqual(torch.bitwise_and(a, b), expected_res)
            self.assertEqual(torch.bitwise_and(a, b_scalar), expected_res_scalar)

            # out
            c = torch.empty(0, dtype=dtype, device=device)
            torch.bitwise_and(a, b, out=c)
            self.assertEqual(c, expected_res)
            torch.bitwise_and(a, b_scalar, out=c)
            self.assertEqual(c, expected_res_scalar)

            # in-place
            a1 = a.clone()
            a1.bitwise_and_(b)
            self.assertEqual(a1, expected_res)
            a.bitwise_and_(b_scalar)
            self.assertEqual(a, expected_res_scalar)

        self.assertEqual(torch.tensor([False, True, False], device=device),
                         torch.bitwise_and(torch.tensor([True, True, False], device=device),
                                           torch.tensor([False, True, False], device=device)))

    def test_bitwise_or(self, device):
        for dtype in (torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            a = torch.tensor([1, -2, 3], dtype=dtype, device=device)
            b = torch.tensor([2, 1, 3], dtype=dtype, device=device)
            expected_res = torch.tensor([3, -1, 3], dtype=dtype, device=device)
            b_scalar = 2
            expected_res_scalar = torch.tensor([3, -2, 3], dtype=dtype, device=device)

            # standard version
            self.assertEqual(torch.bitwise_or(a, b), expected_res)
            self.assertEqual(torch.bitwise_or(a, b_scalar), expected_res_scalar)

            # out
            c = torch.empty(0, dtype=dtype, device=device)
            torch.bitwise_or(a, b, out=c)
            self.assertEqual(c, expected_res)
            torch.bitwise_or(a, b_scalar, out=c)
            self.assertEqual(c, expected_res_scalar)

            # in-place
            a1 = a.clone()
            a1.bitwise_or_(b)
            self.assertEqual(a1, expected_res)
            a.bitwise_or_(b_scalar)
            self.assertEqual(a, expected_res_scalar)

        self.assertEqual(torch.tensor([True, True, False], device=device),
                         torch.bitwise_or(torch.tensor([True, True, False], device=device),
                                          torch.tensor([False, True, False], device=device)))

    def test_bitwise_xor(self, device):
        for dtype in (torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64):
            a = torch.tensor([1, -2, 3], dtype=dtype, device=device)
            b = torch.tensor([2, 1, 3], dtype=dtype, device=device)
            expected_res = torch.tensor([3, -1, 0], dtype=dtype, device=device)
            b_scalar = 2
            expected_res_scalar = torch.tensor([3, -4, 1], dtype=dtype, device=device)

            # standard version
            self.assertEqual(torch.bitwise_xor(a, b), expected_res)
            self.assertEqual(torch.bitwise_xor(a, b_scalar), expected_res_scalar)

            # out
            c = torch.empty(0, dtype=dtype, device=device)
            torch.bitwise_xor(a, b, out=c)
            self.assertEqual(c, expected_res)
            torch.bitwise_xor(a, b_scalar, out=c)
            self.assertEqual(c, expected_res_scalar)

            # in-place
            a1 = a.clone()
            a1.bitwise_xor_(b)
            self.assertEqual(a1, expected_res)
            a.bitwise_xor_(b_scalar)
            self.assertEqual(a, expected_res_scalar)

        self.assertEqual(torch.tensor([True, False, False], device=device),
                         torch.bitwise_xor(torch.tensor([True, True, False], device=device),
                                           torch.tensor([False, True, False], device=device)))

    def test_logical_not(self, device):
        for dtype in torch.testing.get_all_dtypes():
            a = torch.tensor([10, 1, 0], dtype=dtype, device=device)
            if dtype == torch.bfloat16 or dtype.is_complex:
                self.assertRaises(RuntimeError, lambda: a.logical_not())
                continue
            expected_res = torch.tensor([0, 0, 1], dtype=dtype, device=device)
            # new tensor
            self.assertEqual(expected_res.bool(), a.logical_not())
            # out
            for out_dtype in torch.testing.get_all_dtypes():
                b = torch.empty(0, dtype=out_dtype, device=device)
                if out_dtype == torch.bfloat16 or out_dtype.is_complex:
                    self.assertRaises(RuntimeError, lambda: torch.logical_not(a, out=b))
                    continue
                torch.logical_not(a, out=b)
                self.assertEqual(expected_res.bool(), b.bool())
            # in-place
            a.logical_not_()
            self.assertEqual(expected_res, a)

    def _test_logical(self, device, op, a_, b_, expected_res_):
        for dtype in torch.testing.get_all_dtypes():
            expected_res = torch.tensor(expected_res_, dtype=dtype, device=device)
            a = torch.tensor(a_, dtype=dtype, device=device)
            for other_dtype in torch.testing.get_all_dtypes():
                b = torch.tensor(b_, dtype=other_dtype, device=device)

                # Skip bfloat16 on CUDA. Remove this after bfloat16 is supported on CUDA.
                if device.startswith('cuda') and torch.bfloat16 in (dtype, other_dtype):
                    with self.assertRaises(RuntimeError):
                        getattr(a, op)(b)
                    continue
                # TODO Remove this skipping after bfloat16 can be handled nicely with other dtypes.
                # Skip only if either dtype or other_dtype is bfloat16.
                if (dtype == torch.bfloat16) != (other_dtype == torch.bfloat16):
                    with self.assertRaises(RuntimeError):
                        getattr(a, op)(b)
                    continue

                if dtype.is_complex or other_dtype.is_complex:
                    with self.assertRaises(RuntimeError):
                        getattr(a, op)(b)
                    continue

                # new tensor
                self.assertEqual(expected_res.bool(), getattr(a, op)(b))
                # out
                c = torch.empty(0, dtype=torch.bool, device=device)
                getattr(torch, op)(a, b, out=c)
                self.assertEqual(expected_res.bool(), c.bool())

            # in-place
            b = torch.tensor(b_, dtype=dtype, device=device)
            # Skip bfloat16 on CUDA. Remove this after bfloat16 is supported on CUDA.
            if device.startswith('cuda') and dtype == torch.bfloat16:
                with self.assertRaises(RuntimeError):
                    getattr(a, op + '_')(b)
                continue
            if dtype.is_complex:
                with self.assertRaises(RuntimeError):
                    getattr(a, op + '_')(b)
                continue
            getattr(a, op + '_')(b)
            self.assertEqual(expected_res, a)

    def test_logical_xor(self, device):
        self._test_logical(device, 'logical_xor', [10, 0, 1, 0], [1, 0, 0, 10], [0, 0, 1, 1])

    def test_logical_and(self, device):
        self._test_logical(device, 'logical_and', [10, 0, 1, 0], [1, 0, 0, 10], [1, 0, 0, 0])

    def test_logical_or(self, device):
        self._test_logical(device, 'logical_or', [10, 0, 1, 0], [1, 0, 0, 10], [1, 0, 1, 1])

    def test_clamp(self, device):
        m1 = torch.rand(100, device=device).mul(5).add(-2.5)  # uniform in [-2.5, 2.5]
        # just in case we're extremely lucky.
        min_val = -1
        max_val = 1
        m1[1] = min_val
        m1[2] = max_val

        res1 = m1.clone()
        res1.clamp_(min_val, max_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = max(min_val, min(max_val, res2[i]))
        self.assertEqual(res1, res2)

        out = m1.clone()
        torch.clamp(m1, min=min_val, max=max_val, out=out)
        self.assertEqual(out, res1)

        res1 = torch.clamp(m1, min=min_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = max(min_val, res2[i])
        self.assertEqual(res1, res2)

        torch.clamp(m1, min=min_val, out=out)
        self.assertEqual(out, res1)

        res1 = torch.clamp(m1, max=max_val)
        res2 = m1.clone()
        for i in iter_indices(res2):
            res2[i] = min(max_val, res2[i])
        self.assertEqual(res1, res2)

        torch.clamp(m1, max=max_val, out=out)
        self.assertEqual(out, res1)

        # if the tensor contains nan case
        test_tens = torch.tensor([nan], device=device)

        res1 = test_tens.clone()
        res1.clamp_(min_val, max_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = max(min(res2[i], max_val), min_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        out = test_tens.clone()
        torch.clamp(test_tens, min=min_val, max=max_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        res1 = torch.clamp(test_tens, min=min_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = max(res2[i], min_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        torch.clamp(test_tens, min=min_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        res1 = torch.clamp(test_tens, max=max_val)
        res2 = test_tens.clone()
        for i in iter_indices(res2):
            res2[i] = min(res2[i], max_val)
        self.assertEqual(torch.isnan(res1), torch.isnan(res2))

        torch.clamp(test_tens, max=max_val, out=out)
        self.assertEqual(torch.isnan(out), torch.isnan(res1))

        error_msg = 'At least one of \'min\' or \'max\' must not be None'
        with self.assertRaisesRegex(RuntimeError, error_msg):
            m1.clamp()
        with self.assertRaisesRegex(RuntimeError, error_msg):
            m1.clamp_()

    def test_cat_empty_legacy(self, device):
        # FIXME: this is legacy behavior and should be removed
        # when we support empty tensors with arbitrary sizes
        dtype = torch.float32

        x = torch.randn((4, 3, 32, 32), dtype=dtype, device=device)
        empty = torch.randn((0,), dtype=dtype, device=device)

        res1 = torch.cat([x, empty], dim=1)
        res2 = torch.cat([empty, x], dim=1)
        self.assertEqual(res1, res2)

        res1 = torch.cat([empty, empty], dim=1)
        self.assertEqual(res1, empty)

        with self.assertRaisesRegex(RuntimeError,
                                    'non-empty list of Tensors'):
            torch.cat([], dim=1)

    def test_cat_empty(self, device):
        dtype = torch.float32

        x = torch.randn((4, 3, 32, 32), dtype=dtype, device=device)
        empty = torch.randn((4, 0, 32, 32), dtype=dtype, device=device)

        res1 = torch.cat([x, empty], dim=1)
        res2 = torch.cat([empty, x], dim=1)
        self.assertEqual(res1, res2)

        res1 = torch.cat([empty, empty], dim=1)
        self.assertEqual(res1, empty)

        # check non-legacy-behavior (sizes don't match)
        empty = torch.randn((4, 0, 31, 32), dtype=dtype, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, empty], dim=1))
        self.assertRaises(RuntimeError, lambda: torch.cat([empty, x], dim=1))

        # check non-legacy-behavior (dimensions don't match)
        empty = torch.randn((4, 0), dtype=dtype, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, empty], dim=1))
        self.assertRaises(RuntimeError, lambda: torch.cat([empty, x], dim=1))

    def test_cat_out(self, device):
        x = torch.zeros((0), device=device)
        y = torch.randn((4, 6), device=device)

        with self.assertRaisesRegex(
                RuntimeError, r"unsupported operation:.* input tensor 0"):
            torch.cat([x, y], dim=0, out=x)

        with self.assertRaisesRegex(
                RuntimeError, r"unsupported operation:.* input tensor 1"):
            torch.cat([x, y], dim=0, out=y)

        z = torch.zeros((4, 6), device=device)
        with self.assertRaisesRegex(
                RuntimeError, r"unsupported operation:.* input tensor 1"):
            torch.cat([y, z], out=z[:2, :])

        w = y.view(-1).clone()
        a = torch.cat([w[:2], w[4:6]])
        b = torch.cat([w[:2], w[4:6]], out=w[6:10])
        self.assertEqual(a, b)
        self.assertEqual(w[:6], y.view(-1)[:6])

    def test_cat_out_channels_last(self, device):
        x = torch.randn((4, 3, 8, 8))
        y = torch.randn(x.shape)
        res1 = torch.cat((x, y))
        z = res1.clone().contiguous(memory_format=torch.channels_last)
        res2 = torch.cat((x, y), out=z)
        self.assertEqual(res1, res2)

    @onlyCUDA
    def test_cat_preserve_channels_last(self, device):
        x = torch.randn((4, 3, 8, 8), device=device)
        y = torch.randn(x.shape, device=device)
        res1 = torch.cat((x, y))
        res2 = torch.cat((x.contiguous(memory_format=torch.channels_last), y.contiguous(memory_format=torch.channels_last)))
        self.assertEqual(res1, res2)
        self.assertTrue(res2.is_contiguous(memory_format=torch.channels_last))

    @onlyCUDA
    @deviceCountAtLeast(2)
    def test_cat_different_devices(self, devices):
        cuda0 = torch.randn((3, 3), device=devices[0])
        cuda1 = torch.randn((3, 3), device=devices[1])
        with self.assertRaisesRegex(RuntimeError,
                                    "input tensors must be on the same device"):
            torch.cat((cuda0, cuda1))
        cpu = torch.randn(3, 3)
        with self.assertRaisesRegex(RuntimeError,
                                    "input tensors must be on the same device"):
            torch.cat((cuda0, cpu))
        with self.assertRaisesRegex(RuntimeError,
                                    "input tensors must be on the same device"):
            torch.cat((cpu, cuda0))

    def test_block_diag(self, device):
        def block_diag_workaround(*arrs):
            arrs_expanded = []
            for a in arrs:
                if a.dim() == 2:
                    arrs_expanded.append(a)
                elif a.dim() == 1:
                    arrs_expanded.append(a.expand(1, a.size(0)))
                elif a.dim() == 0:
                    arrs_expanded.append(a.expand(1, 1))
            shapes = torch.tensor([a.shape for a in arrs_expanded], device=device)
            out = torch.zeros(
                torch.sum(shapes, dim=0).tolist(),
                dtype=arrs_expanded[0].dtype,
                device=device
            )
            r, c = 0, 0
            for i, (rr, cc) in enumerate(shapes):
                out[r:r + rr, c:c + cc] = arrs_expanded[i]
                r += rr
                c += cc
            return out

        tensors = [
            torch.rand((2, 2), device=device),
            torch.rand((2, 3), device=device),
            torch.rand(10, device=device),
            torch.rand((8, 1), device=device),
            torch.rand(1, device=device)[0]
        ]
        result = torch.block_diag(*tensors)
        result_check = block_diag_workaround(*tensors)
        self.assertEqual(result, result_check)

        tensor = torch.rand(1, device=device)[0]
        result = torch.block_diag(tensor)
        result_check = tensor.expand(1, 1)
        self.assertEqual(result, result_check)

        tensor = torch.rand(10, device=device)
        result = torch.block_diag(tensor)
        result_check = tensor.expand(1, tensor.size(0))
        self.assertEqual(result, result_check)

        result = torch.block_diag()
        result_check = torch.empty(1, 0, device=device)
        self.assertEqual(result, result_check)
        self.assertEqual(result.device.type, 'cpu')

        test_dtypes = [
            torch.uint8,
            torch.int8,
            torch.int16,
            torch.int32,
            torch.int64,
            torch.float32,
            torch.float64,
            torch.complex64,
            torch.complex128
        ]
        # Test pairs of different dtypes
        for dtype1 in test_dtypes:
            for dtype2 in test_dtypes:
                a = torch.tensor(1, device=device, dtype=dtype1)
                b = torch.tensor(2, device=device, dtype=dtype2)
                result = torch.block_diag(a, b)
                result_dtype = torch.result_type(a, b)
                result_check = torch.tensor([[1, 0], [0, 2]], device=device, dtype=result_dtype)
                self.assertEqual(result, result_check)

        with self.assertRaisesRegex(
            RuntimeError,
            "torch.block_diag: Input tensors must have 2 or fewer dimensions. Input 1 has 3 dimensions"
        ):
            torch.block_diag(torch.tensor(5), torch.tensor([[[6]]]))

        with self.assertRaisesRegex(
            RuntimeError,
            "torch.block_diag: Input tensors must have 2 or fewer dimensions. Input 0 has 4 dimensions"
        ):
            torch.block_diag(torch.tensor([[[[6]]]]))

        if device != 'cpu':
            with self.assertRaisesRegex(
                RuntimeError,
                (
                    "torch.block_diag: input tensors must all be on the same device."
                    " Input 0 is on device cpu and input 1 is on device "
                )
            ):
                torch.block_diag(torch.ones(2, 2).cpu(), torch.ones(2, 2, device=device))

    @unittest.skipIf(not TEST_SCIPY, "Scipy not found")
    def test_block_diag_scipy(self, device):
        import scipy.linalg
        scipy_tensors_list = [
            [
                1,
                [2],
                [],
                [3, 4, 5],
                [[], []],
                [[6], [7.3]]
            ],
            [
                [[1, 2], [3, 4]],
                [1]
            ],
            [
                [[4, 9], [7, 10]],
                [4.6, 9.12],
                [1j + 3]
            ],
            []
        ]

        expected_torch_types = [
            torch.float32,
            torch.int64,
            torch.complex64,
            torch.float32
        ]

        expected_scipy_types = [
            torch.float64,
            # windows scipy block_diag returns int32 types
            torch.int32 if IS_WINDOWS else torch.int64,
            torch.complex128,
            torch.float64
        ]

        for scipy_tensors, torch_type, scipy_type in zip(scipy_tensors_list, expected_torch_types, expected_scipy_types):
            torch_tensors = [torch.tensor(t, device=device) for t in scipy_tensors]
            torch_result = torch.block_diag(*torch_tensors)
            self.assertEqual(torch_result.dtype, torch_type)

            scipy_result = torch.tensor(
                scipy.linalg.block_diag(*scipy_tensors),
                device=device
            )
            self.assertEqual(scipy_result.dtype, scipy_type)
            scipy_result = scipy_result.to(torch_type)

            self.assertEqual(torch_result, scipy_result)

    def test_is_set_to(self, device):
        t1 = torch.empty(3, 4, 9, 10, device=device)
        t2 = torch.empty(3, 4, 9, 10, device=device)
        t3 = torch.tensor([], device=device).set_(t1)
        t4 = t3.clone().resize_(12, 90)
        self.assertFalse(t1.is_set_to(t2))
        self.assertTrue(t1.is_set_to(t3))
        self.assertTrue(t3.is_set_to(t1), "is_set_to should be symmetric")
        self.assertFalse(t1.is_set_to(t4))
        self.assertFalse(torch.Tensor().is_set_to(torch.Tensor()),
                         "Tensors with no storages should not appear to be set "
                         "to each other")

        t1 = torch.tensor([True, True], dtype=torch.bool, device=device)
        t2 = torch.tensor([0], dtype=torch.bool, device=device).set_(t1)
        self.assertTrue(t1.is_set_to(t2))

        # test that sizes must match
        t1 = torch.empty([2, 3, 4], device=device)
        t2 = t1.view(4, 3, 2)
        self.assertFalse(t1.is_set_to(t2))
        self.assertFalse(t2.is_set_to(t1))

        # test that legacy empty size behavior used to be respected (i.e. all
        # empty tensors were logically collapsed to size [0]).
        t1 = torch.empty([2, 5, 0], device=device)
        t2 = t1.view([0])
        self.assertFalse(t1.is_set_to(t2))
        self.assertFalse(t2.is_set_to(t1))

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_inverse_many_batches(self, device):
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        matrices = random_fullrank_matrix_distinct_singular_value(5, 256, 256).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices_inverse, matrices),
                         torch.eye(5, dtype=torch.float64).to(device).expand_as(matrices))

        matrices = random_fullrank_matrix_distinct_singular_value(3, 512, 512).to(device)
        matrices_inverse = torch.inverse(matrices)
        self.assertEqual(torch.matmul(matrices, matrices_inverse),
                         torch.eye(3, dtype=torch.float64).to(device).expand_as(matrices))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_pinverse(self, device, dtype):
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value as fullrank

        def run_test(M):
            # Testing against definition for pseudo-inverses
            MPI = torch.pinverse(M)
            if M.numel() > 0:
                self.assertEqual(M, M.matmul(MPI).matmul(M), atol=1e-8, message='pseudo-inverse condition 1')
                self.assertEqual(MPI, MPI.matmul(M).matmul(MPI), atol=1e-8, message='pseudo-inverse condition 2')
                self.assertEqual(M.matmul(MPI), (M.matmul(MPI)).transpose(-2, -1), atol=1e-8, message='pseudo-inverse condition 3')
                self.assertEqual(MPI.matmul(M), (MPI.matmul(M)).transpose(-2, -1), atol=1e-8, message='pseudo-inverse condition 4')
            else:
                self.assertEqual(M.shape, MPI.shape[:-2] + (MPI.shape[-1], MPI.shape[-2]))
        for sizes in [(5, 5), (3, 5, 5), (3, 7, 5, 5),  # square matrices
                      (3, 2), (5, 3, 2), (7, 5, 3, 2),  # fat matrices
                      (2, 3), (5, 2, 3), (7, 5, 2, 3),  # thin matrices
                      (0, 0), (0, 2), (2, 0), (3, 0, 0), (0, 3, 0), (0, 0, 3)]:  # zero numel matrices
            M = torch.randn(*sizes, dtype=dtype, device=device)
            run_test(M)

        # Test inverse and pseudo-inverse for invertible matrix
        for sizes in [(5, 5), (3, 5, 5), (3, 7, 5, 5)]:
            matsize = sizes[-1]
            batchdims = sizes[:-2]
            M = fullrank(matsize, *batchdims, dtype=dtype, device=device)
            self.assertEqual(torch.eye(matsize, dtype=dtype, device=device).expand(sizes), M.pinverse().matmul(M),
                             atol=1e-7, message='pseudo-inverse for invertible matrix')

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_matrix_rank(self, device):
        a = torch.eye(10, device=device)
        self.assertEqual(torch.matrix_rank(a).item(), 10)
        self.assertEqual(torch.matrix_rank(a, True).item(), 10)

        a[5, 5] = 0
        self.assertEqual(torch.matrix_rank(a).item(), 9)
        self.assertEqual(torch.matrix_rank(a, True).item(), 9)

        a = torch.randn(24, 42, device=device)
        self.assertEqual(torch.matrix_rank(a), torch.matrix_rank(a.t()))
        aaT = torch.mm(a, a.t())
        self.assertEqual(torch.matrix_rank(aaT), torch.matrix_rank(aaT, True))
        aTa = torch.mm(a.t(), a)
        self.assertEqual(torch.matrix_rank(aTa), torch.matrix_rank(aTa, True))

        if TEST_NUMPY:
            from numpy.linalg import matrix_rank
            a = torch.randn(35, 75, device=device)
            self.assertEqual(torch.matrix_rank(a).item(), matrix_rank(a.cpu().numpy()))
            self.assertEqual(torch.matrix_rank(a, 0.01).item(), matrix_rank(a.cpu().numpy(), 0.01))

            aaT = torch.mm(a, a.t())
            self.assertEqual(torch.matrix_rank(aaT).item(), matrix_rank(aaT.cpu().numpy()))
            self.assertEqual(torch.matrix_rank(aaT, 0.01).item(), matrix_rank(aaT.cpu().numpy(), 0.01))

            if np.lib.NumpyVersion(np.__version__) >= '1.14.0':
                self.assertEqual(torch.matrix_rank(aaT, True).item(), matrix_rank(aaT.cpu().numpy(), True))
                self.assertEqual(torch.matrix_rank(aaT, 0.01, True).item(),
                                 matrix_rank(aaT.cpu().numpy(), 0.01, True))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_matrix_power(self, device, dtype):
        def run_test(M, sign=1):
            if sign == -1:
                M = M.inverse()
            MP2 = torch.matrix_power(M, 2)
            self.assertEqual(MP2, torch.matmul(M, M))

            MP3 = torch.matrix_power(M, 3)
            self.assertEqual(MP3, torch.matmul(MP2, M))

            MP4 = torch.matrix_power(M, 4)
            self.assertEqual(MP4, torch.matmul(MP2, MP2))

            MP6 = torch.matrix_power(M, 6)
            self.assertEqual(MP6, torch.matmul(MP3, MP3))

            MP0 = torch.matrix_power(M, 0)
            self.assertEqual(MP0, torch.eye(M.size(-2), dtype=dtype).expand_as(M))

        # Single matrix
        M = torch.randn(5, 5, dtype=dtype, device=device)
        run_test(M)

        # Batch matrices
        M = torch.randn(3, 3, 3, dtype=dtype, device=device)
        run_test(M)

        # Many batch matrices
        M = torch.randn(2, 3, 3, 3, dtype=dtype, device=device)
        run_test(M)

        # This is for negative powers
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value
        M = random_fullrank_matrix_distinct_singular_value(5, dtype=dtype, device=device)
        run_test(M, sign=-1)

        M = random_fullrank_matrix_distinct_singular_value(3, 3, dtype=dtype, device=device)
        run_test(M, sign=-1)

        M = random_fullrank_matrix_distinct_singular_value(3, 2, 3, dtype=dtype, device=device)
        run_test(M, sign=-1)

    @dtypes(torch.double)
    def test_chain_matmul(self, device, dtype):
        def product(matrices):
            for mat in matrices[1:]:
                matrices[0] = matrices[0].mm(mat)
            return matrices[0]

        def run_test(p):
            matrices = []
            for (pi, pi_1) in zip(p[:-1], p[1:]):
                matrices.append(torch.randn(pi, pi_1, dtype=dtype, device=device))
            self.assertEqual(torch.chain_matmul(*matrices), product(matrices))

        run_test([10, 20, 30, 5])
        run_test([15, 5, 10, 20, 25])

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_det_logdet_slogdet(self, device, dtype):
        def reference_slogdet(M):
            if TEST_NUMPY:
                sdet, logabsdet = np.linalg.slogdet(M.detach().cpu().numpy())
                return M.new_tensor(sdet), M.new_tensor(logabsdet)
            else:
                # naive row reduction
                M = M.clone()
                l = M.size(0)
                multiplier = 1
                for i in range(l):
                    if M[i, 0].item() != 0:
                        if i != 0:
                            M[0], M[i] = M[i], M[0]
                            multiplier = -1
                        break
                else:
                    return 0
                for i in range(1, l):
                    row = M[i]
                    for j in range(i):
                        row -= row[j] / M[j, j] * M[j]
                    M[i] = row
            sdet = M.diag().sign().prod()
            logabsdet = M.diag().abs_().log_().sum().add_(math.log(multiplier))
            return sdet, logabsdet

        def test_single_det(M, target, desc):
            target_sdet, target_logabsdet = target

            det = M.det()
            logdet = M.logdet()
            sdet, logabsdet = M.slogdet()

            # Test det
            self.assertEqual(det, target_sdet * target_logabsdet.exp(), atol=1e-7, message='{} (det)'.format(desc))

            # Test slogdet
            # Compare the overall value rather than individual parts because of
            # precision issues when det is near zero.
            self.assertEqual(sdet * logabsdet.exp(), target_sdet * target_logabsdet.exp(),
                             atol=1e-7, message='{} (slogdet)'.format(desc))

            # Test logdet
            # Compare logdet against our own pytorch slogdet because they should
            # be consistent, while it may behave slightly differently with other
            # slogdet implementations when det is near zero due to precision
            # issues.
            if sdet.item() < 0:
                self.assertTrue(logdet.item() != logdet.item(), '{} (logdet negative case)'.format(desc))
            else:
                self.assertEqual(logdet.exp(), target_logabsdet.exp(),
                                 atol=1e-7, message='{} (logdet non-negative case)'.format(desc))

        eye = torch.eye(5, dtype=dtype, device=device)
        test_single_det(eye, (torch.ones((), dtype=dtype, device=device), torch.zeros((), dtype=dtype, device=device)), 'identity')

        def test(M):
            assert M.size(0) >= 5, 'this helper fn assumes M to be at least 5x5'
            M = M.to(device)

            ref_M_sdet, ref_M_logabsdet = reference_slogdet(M)

            test_single_det(M, (ref_M_sdet, ref_M_logabsdet), 'basic')
            if ref_M_logabsdet.exp().item() >= 1e-6:  # skip singular
                M_inv = M.inverse()
                test_single_det(M_inv, reference_slogdet(M_inv), 'inverse')

            test_single_det(M, (ref_M_sdet, ref_M_logabsdet), 'transpose')

            for x in [0, 2, 4]:
                for scale in [-2, -0.1, 0, 10]:
                    if scale > 0:
                        target = ref_M_sdet, ref_M_logabsdet + math.log(scale)
                    elif scale == 0:
                        target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                    else:
                        target = ref_M_sdet.neg(), ref_M_logabsdet + math.log(-scale)

                    # dim 0
                    M_clone = M.clone()
                    M_clone[:, x] *= scale
                    test_single_det(M_clone, target, 'scale a row')
                    # dim 1
                    M_clone = M.clone()
                    M_clone[x, :] *= scale
                    test_single_det(M_clone, target, 'scale a column')

            for x1, x2 in [(0, 3), (4, 1), (3, 2)]:
                assert x1 != x2, 'x1 and x2 needs to be different for this test'
                target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                # dim 0
                M_clone = M.clone()
                M_clone[:, x2] = M_clone[:, x1]
                test_single_det(M_clone, target, 'two rows are same')
                # dim 1
                M_clone = M.clone()
                M_clone[x2, :] = M_clone[x1, :]
                test_single_det(M_clone, target, 'two columns are same')

                for scale1, scale2 in [(0.3, -1), (0, 2), (10, 0.1)]:
                    det_scale = scale1 * scale2 * -1
                    if det_scale > 0:
                        target = ref_M_sdet, ref_M_logabsdet + math.log(det_scale)
                    elif det_scale == 0:
                        target = torch.zeros_like(ref_M_sdet), torch.full_like(ref_M_logabsdet, -inf)
                    else:
                        target = ref_M_sdet.neg(), ref_M_logabsdet + math.log(-det_scale)

                    # dim 0
                    M_clone = M.clone()
                    t = M_clone[:, x1] * scale1
                    M_clone[:, x1] += M_clone[:, x2] * scale2
                    M_clone[:, x2] = t
                    test_single_det(M_clone, target, 'exchanging rows')
                    # dim 1
                    M_clone = M.clone()
                    t = M_clone[x1, :] * scale1
                    M_clone[x1, :] += M_clone[x2, :] * scale2
                    M_clone[x2, :] = t
                    test_single_det(M_clone, target, 'exchanging columns')

        def get_random_mat_scale(n):
            # For matrices with values i.i.d. with 0 mean, unit variance, and
            # subexponential tail, we have:
            #   E[log det(A^2)] \approx log((n-1)!)
            #
            # Notice:
            #   log Var[det(A)] = log E[det(A^2)] >= E[log det(A^2)]
            #
            # So:
            #   stddev[det(A)] >= sqrt( (n-1)! )
            #
            # We use this as an intuitive guideline to scale random generated
            # matrices so our closeness tests can work more robustly:
            #   scale by sqrt( (n-1)! )^(-1/n) = ( (n-1)! )^(-1/(2n))
            #
            # source: https://arxiv.org/pdf/1112.0752.pdf

            # TODO: technically we need subexponential distn for this to hold,
            #       but we mostly use gaussian entries below. Consider switching
            #       to Chi-sq if this turns out not stable enough, since Chi-sq
            #       is easy enough to sample from.
            return math.factorial(n - 1) ** (-1.0 / (2 * n))

        for n in [5, 10, 25]:
            scale = get_random_mat_scale(n)
            test(torch.randn(n, n, dtype=dtype, device=device) * scale)
            r = torch.randn(n, n, dtype=dtype, device=device) * scale
            # symmetric psd
            test(r.mm(r.t()))
            # symmetric pd
            r = torch.randn(n, n, dtype=dtype, device=device) * scale
            test(r.mm(r.t()) + torch.eye(n, dtype=dtype, device=device) * 1e-6)
            # symmetric
            r = torch.randn(n, n, dtype=dtype, device=device) * scale
            for i in range(n):
                for j in range(i):
                    r[i, j] = r[j, i]
            test(r)
            # non-contiguous
            test((torch.randn(n, n, n + 1, dtype=dtype, device=device) * scale)[:, 2, 1:])
            # det = 0
            r = torch.randn(n, n, dtype=dtype, device=device) * scale
            u, s, v = r.svd()
            if reference_slogdet(u)[0] < 0:
                u = -u
            if reference_slogdet(v)[0] < 0:
                v = -v
            s[0] *= -1
            s[-1] = 0
            test(u.mm(s.diag()).mm(v))

        # Small values to test numerical stability. Note that we don't scale
        # this matrix.
        r = torch.randn(512, 512, dtype=dtype, device=device)
        u, s, v = r.svd()
        s.fill_(1. / (100 * s.numel()))
        test(u.mm(s.diag()).mm(v))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_det_logdet_slogdet_batched(self, device, dtype):
        from torch.testing._internal.common_utils import (random_symmetric_matrix, random_symmetric_psd_matrix,
                                                          random_symmetric_pd_matrix, random_square_matrix_of_rank)

        # mat_chars denotes matrix characteristics
        # possible values are: sym, sym_psd, sym_pd, sing, non_sym
        def run_test(matsize, batchdims, mat_chars):
            num_matrices = reduce(lambda x, y: x * y, batchdims, 1)
            list_of_matrices = []

            for idx in range(num_matrices):
                mat_type = idx % len(mat_chars)
                if mat_chars[mat_type] == 'sym':
                    list_of_matrices.append(random_symmetric_matrix(matsize, dtype=dtype, device=device))
                elif mat_chars[mat_type] == 'sym_psd':
                    list_of_matrices.append(random_symmetric_psd_matrix(matsize, dtype=dtype, device=device))
                elif mat_chars[mat_type] == 'sym_pd':
                    list_of_matrices.append(random_symmetric_pd_matrix(matsize, dtype=dtype, device=device))
                elif mat_chars[mat_type] == 'sing':
                    list_of_matrices.append(torch.ones(matsize, matsize, dtype=dtype, device=device))
                elif mat_chars[mat_type] == 'non_sing':
                    list_of_matrices.append(random_square_matrix_of_rank(matsize, matsize, dtype=dtype, device=device))
            full_tensor = torch.stack(list_of_matrices, dim=0).reshape(batchdims + (matsize, matsize))
            # Scaling adapted from `get_random_mat_scale` in _test_det_logdet_slogdet
            full_tensor *= (math.factorial(matsize - 1) ** (-1.0 / (2 * matsize)))

            for fn in [torch.det, torch.logdet, torch.slogdet]:
                expected_value = []
                actual_value = fn(full_tensor)
                for full_idx in product(*map(lambda x: list(range(x)), batchdims)):
                    expected_value.append(fn(full_tensor[full_idx]))

                if fn == torch.slogdet:
                    sign_value = torch.stack([tup[0] for tup in expected_value], dim=0).reshape(batchdims)
                    expected_value = torch.stack([tup[1] for tup in expected_value], dim=0).reshape(batchdims)
                    self.assertEqual(sign_value, actual_value[0], allow_inf=True)
                    self.assertEqual(expected_value, actual_value[1], allow_inf=True)
                else:
                    expected_value = torch.stack(expected_value, dim=0).reshape(batchdims)
                    self.assertEqual(actual_value, expected_value, allow_inf=True)

        for matsize, batchdims in product([3, 5], [(3,), (5, 3)]):
            run_test(matsize, batchdims, mat_chars=['sym_pd'])
            run_test(matsize, batchdims, mat_chars=['sing'])
            run_test(matsize, batchdims, mat_chars=['non_sing'])
            run_test(matsize, batchdims, mat_chars=['sym', 'sym_pd', 'sym_psd'])
            run_test(matsize, batchdims, mat_chars=['sing', 'non_sing'])

    def solve_test_helper(self, A_dims, b_dims, device, dtype):
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        b = torch.randn(*b_dims, dtype=dtype, device=device)
        A = random_fullrank_matrix_distinct_singular_value(*A_dims, dtype=dtype, device=device)
        return b, A

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_solve(self, device, dtype):
        for (k, n) in zip([2, 3, 5], [3, 5, 7]):
            b, A = self.solve_test_helper((n,), (n, k), device, dtype)
            x = torch.solve(b, A)[0]
            self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_solve_batched(self, device, dtype):
        def solve_batch_helper(A_dims, b_dims):
            b, A = self.solve_test_helper(A_dims, b_dims, device, dtype)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.solve(b[i], A[i])[0])
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.solve(b, A)[0]  # Actual output
            self.assertEqual(x_exp, x_act)  # Equality check
            self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 1e-12)  # Correctness check

        for batchsize in [1, 3, 4]:
            solve_batch_helper((5, batchsize), (batchsize, 5, 10))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_solve_batched_non_contiguous(self, device, dtype):
        from numpy.linalg import solve
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value
        A = random_fullrank_matrix_distinct_singular_value(2, 2, dtype=dtype,
                                                           device=device).permute(1, 0, 2)
        b = torch.randn(2, 2, 2, dtype=dtype, device=device).permute(2, 1, 0)
        x, _ = torch.solve(b, A)
        x_exp = torch.Tensor(solve(A.cpu().numpy(), b.cpu().numpy())).to(dtype=dtype, device=device)
        self.assertEqual(x, x_exp)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_solve_batched_many_batches(self, device, dtype):
        b, A = self.solve_test_helper((5, 256, 256), (5, 1), device, dtype)
        x, _ = torch.solve(b, A)
        self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 1)))

        b, A = self.solve_test_helper((3,), (512, 512, 3, 1), device, dtype)
        x, _ = torch.solve(b, A)
        self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_solve_batched_broadcasting(self, device, dtype):
        from numpy.linalg import solve

        def run_test(A_dims, b_dims):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            b, A = self.solve_test_helper((A_matrix_size,) + A_batch_dims, b_dims, device, dtype)
            x, _ = torch.solve(b, A)
            x_exp = torch.Tensor(solve(A.cpu().numpy(), b.cpu().numpy())).to(dtype=dtype, device=device)
            self.assertEqual(x, x_exp)

        # test against numpy.linalg.solve
        for upper in [True, False]:
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6))  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6))  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2))  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5))  # broadcasting A & b

    def cholesky_solve_test_helper(self, A_dims, b_dims, upper, device, dtype):
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix

        b = torch.randn(*b_dims, dtype=dtype, device=device)
        A = random_symmetric_pd_matrix(*A_dims, dtype=dtype, device=device)
        L = torch.cholesky(A, upper=upper)
        return b, A, L

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_solve(self, device, dtype):
        for (k, n), upper in product(zip([2, 3, 5], [3, 5, 7]), [True, False]):
            b, A, L = self.cholesky_solve_test_helper((n,), (n, k), upper, device, dtype)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_solve_batched(self, device, dtype):
        def cholesky_solve_batch_helper(A_dims, b_dims, upper):
            b, A, L = self.cholesky_solve_test_helper(A_dims, b_dims, upper, device, dtype)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.cholesky_solve(b[i], L[i], upper=upper))
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.cholesky_solve(b, L, upper=upper)  # Actual output
            self.assertEqual(x_act, x_exp)  # Equality check
            self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 2e-12)  # Correctness check

        for upper, batchsize in product([True, False], [1, 3, 4]):
            cholesky_solve_batch_helper((5, batchsize), (batchsize, 5, 10), upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_cholesky_solve_batched_non_contiguous(self, device, dtype):
        from numpy.linalg import solve
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix

        for upper in [True, False]:
            A = random_symmetric_pd_matrix(2, 2, dtype=dtype, device='cpu')
            b = torch.randn(2, 2, 2, dtype=dtype, device='cpu')
            x_exp = torch.Tensor(solve(A.permute(0, 2, 1).numpy(), b.permute(2, 1, 0).numpy())).to(dtype=dtype, device=device)
            A = A.to(device).permute(0, 2, 1)
            b = b.to(device).permute(2, 1, 0)
            assert not A.is_contiguous() and not b.is_contiguous(), "contiguous inputs"
            L = torch.cholesky(A, upper)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertEqual(x, x_exp)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_solve_batched_many_batches(self, device, dtype):
        for upper in [True, False]:
            b, A, L = self.cholesky_solve_test_helper((5, 256, 256), (5, 10), upper, device, dtype)
            x = torch.cholesky_solve(b, L, upper)
            self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 10)))

            b, A, L = self.cholesky_solve_test_helper((5,), (512, 512, 5, 10), upper, device, dtype)
            x = torch.cholesky_solve(b, L, upper)
            self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_cholesky_solve_batched_broadcasting(self, device, dtype):
        from numpy.linalg import solve
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix

        def run_test(A_dims, b_dims, upper):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            A = random_symmetric_pd_matrix(A_matrix_size, *A_batch_dims,
                                           dtype=dtype, device='cpu')
            b = torch.randn(*b_dims, dtype=dtype, device='cpu')
            x_exp = torch.tensor(solve(A.numpy(), b.numpy()), dtype=dtype, device=device)
            A, b = A.to(dtype=dtype, device=device), b.to(dtype=dtype, device=device)
            L = torch.cholesky(A, upper)
            x = torch.cholesky_solve(b, L, upper=upper)
            self.assertEqual(x, x_exp)

        # test against numpy.linalg.solve
        for upper in [True, False]:
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), upper)  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6), upper)  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2), upper)  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), upper)  # broadcasting A & b

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_inverse(self, device, dtype):
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix
        a = random_symmetric_pd_matrix(5, dtype=dtype, device=device)

        # compute inverse directly
        inv0 = torch.inverse(a)

        # default case
        chol = torch.cholesky(a)
        inv1 = torch.cholesky_inverse(chol, False)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

        # upper Triangular Test
        chol = torch.cholesky(a, True)
        inv1 = torch.cholesky_inverse(chol, True)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

        # lower Triangular Test
        chol = torch.cholesky(a, False)
        inv1 = torch.cholesky_inverse(chol, False)
        self.assertLessEqual(inv0.dist(inv1), 1e-12)

    @slowTest
    @skipCUDAIf(True, "See issue #26789.")
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_batched_many_batches(self, device, dtype):
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix

        def cholesky_test_helper(n, batchsize, device, upper):
            A = random_symmetric_pd_matrix(n, batchsize, dtype=dtype, device=device)
            chol_fact = torch.cholesky(A, upper=upper)
            if upper:
                # Correctness check
                self.assertEqual(A, chol_fact.transpose(-2, -1).matmul(chol_fact))
                # Upper triangular check
                self.assertEqual(chol_fact, chol_fact.triu())
            else:
                # Correctness check
                self.assertEqual(A, chol_fact.matmul(chol_fact.transpose(-2, -1)))
                # Lower triangular check
                self.assertEqual(chol_fact, chol_fact.tril())

        for upper, batchsize in product([True, False], [262144, 524288]):
            cholesky_test_helper(2, batchsize, device, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky_batched(self, device, dtype):
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix

        def cholesky_test_helper(n, batch_dims, upper):
            A = random_symmetric_pd_matrix(n, *batch_dims, dtype=dtype, device=device)
            cholesky_exp = torch.stack([m.cholesky(upper=upper) for m in A.reshape(-1, n, n)])
            cholesky_exp = cholesky_exp.reshape_as(A)
            self.assertEqual(cholesky_exp, torch.cholesky(A, upper=upper))

        for upper, batchsize in product([True, False], [(3,), (3, 4), (2, 3, 4)]):
            cholesky_test_helper(3, batchsize, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_cholesky(self, device, dtype):
        x = torch.rand(10, 10, dtype=dtype, device=device) + 1e-1
        A = torch.mm(x, x.t())

        # default Case
        C = torch.cholesky(A)
        B = torch.mm(C, C.t())
        self.assertEqual(A, B, 1e-14)

        # test Upper Triangular
        U = torch.cholesky(A, True)
        B = torch.mm(U.t(), U)
        self.assertEqual(A, B, atol=1e-14, message='cholesky (upper) did not allow rebuilding the original matrix')

        # test Lower Triangular
        L = torch.cholesky(A, False)
        B = torch.mm(L, L.t())
        self.assertEqual(A, B, atol=1e-14, message='cholesky (lower) did not allow rebuilding the original matrix')

    def test_view(self, device):
        tensor = torch.rand(15, device=device)
        template = torch.rand(3, 5, device=device)
        empty = torch.empty(0, device=device)
        target = template.size()
        self.assertEqual(tensor.view_as(template).size(), target)
        self.assertEqual(tensor.view(3, 5).size(), target)
        self.assertEqual(tensor.view(torch.Size([3, 5])).size(), target)
        self.assertEqual(tensor.view(-1, 5).size(), target)
        self.assertEqual(tensor.view(3, -1).size(), target)
        tensor_view = tensor.view(5, 3)
        tensor_view.fill_(random.uniform(0, 1))
        self.assertEqual(empty.view_as(empty), empty)
        self.assertEqual(empty.view(0), empty)
        self.assertEqual(empty.view(0, 3, 0, 1).size(), torch.Size([0, 3, 0, 1]))
        self.assertEqual(empty.view(0, 3, 0, 1).view(0), empty)

        # test size inference with empty tensors
        self.assertEqual(empty.view(-1).size(), torch.Size([0]))
        self.assertEqual(empty.view(10, 3, -1).size(), torch.Size([10, 3, 0]))

        with self.assertRaisesRegex(RuntimeError, r"because the unspecified dimension size -1 can be any value"):
            empty.view(-1, 0)

        with self.assertRaisesRegex(RuntimeError, r"because the unspecified dimension size -1 can be any value"):
            empty.view(3, 0, -1, 0)

        self.assertRaises(RuntimeError, lambda: tensor.view(15, 0))
        self.assertRaises(RuntimeError, lambda: tensor.view(7, -1))
        self.assertRaises(RuntimeError, lambda: tensor.view(15, -1, -1))

        # test view when tensor is not contiguous in every dimension, but only
        # contiguous dimensions are touched.
        tensor = torch.rand(4, 2, 5, 1, 6, 2, 9, 3, device=device).transpose(-1, 2).transpose(-2, 3)
        # size:                      [   4,    2,    3,    9,    6,    2,    1,    5]
        # stride:                    [3840, 1620,    1,    3,   54,   27,  324,  324]
        # contiguous dim chunks:     [__________, ____, ____, __________, ____, ____]
        # merging 1 to chunk after:  [__________, ____, ____, __________, __________]
        contig_tensor = tensor.clone()
        # [4, 2] => [8, 1]
        # [3] => [3]
        # [9] => [3, 3]
        # [6, 2] => [4, 1, 3]
        # [1, 5] => [5]
        view_size = [8, 1, 3, 3, 3, 4, 1, 3, 5]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))
        # [4, 2] => [2, 4]
        # [3] => [3]
        # [9] => [1, 9]
        # [6, 2] => [2, 2, 3]
        # [1, 5] => [5, 1]
        view_size = [2, 4, 3, 1, 9, 2, 2, 3, 5, 1]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))
        # adding size 1 dims
        view_size = [1, 1, 2, 1, 4, 3, 1, 1, 9, 1, 2, 1, 2, 3, 1, 5, 1, 1]
        self.assertEqual(tensor.view(*view_size), contig_tensor.view(*view_size))

        # invalid views
        self.assertRaises(RuntimeError, lambda: tensor.view(-1))
        # crossing [4, 2], [3]
        self.assertRaises(RuntimeError, lambda: tensor.view(24, 9, 6, 2, 1, 5))
        # crossing [6, 2], [1, 5]
        self.assertRaises(RuntimeError, lambda: tensor.view(8, 3, 9, 6, 10))
        # crossing [9], [6, 2]
        self.assertRaises(RuntimeError, lambda: tensor.view(8, 3, 54, 2, 1, 5))

        # view with stride 0 dims
        tensor = torch.empty(1, 1, device=device).expand(3, 4)  # all dims are contiguous
        contig_tensor = tensor.clone()
        self.assertEqual(tensor.view(-1), contig_tensor.view(-1))
        self.assertEqual(tensor.view(1, -1, 1), contig_tensor.view(1, -1, 1))
        self.assertEqual(tensor.view(-1, 1), contig_tensor.view(-1, 1))
        self.assertEqual(tensor.view(6, 2, 1), contig_tensor.view(6, 2, 1))
        self.assertEqual(tensor.view(1, 6, 2, 1), contig_tensor.view(1, 6, 2, 1))

    def test_flip(self, device):
        data = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8], device=device).view(2, 2, 2)

        self.assertEqual(torch.tensor([5, 6, 7, 8, 1, 2, 3, 4]).view(2, 2, 2), data.flip(0))
        self.assertEqual(torch.tensor([3, 4, 1, 2, 7, 8, 5, 6]).view(2, 2, 2), data.flip(1))
        self.assertEqual(torch.tensor([2, 1, 4, 3, 6, 5, 8, 7]).view(2, 2, 2), data.flip(2))
        self.assertEqual(torch.tensor([7, 8, 5, 6, 3, 4, 1, 2]).view(2, 2, 2), data.flip(0, 1))
        self.assertEqual(torch.tensor([8, 7, 6, 5, 4, 3, 2, 1]).view(2, 2, 2), data.flip(0, 1, 2))

        # check for wrap dim
        self.assertEqual(torch.tensor([2, 1, 4, 3, 6, 5, 8, 7]).view(2, 2, 2), data.flip(-1))
        # check for permute
        self.assertEqual(torch.tensor([6, 5, 8, 7, 2, 1, 4, 3]).view(2, 2, 2), data.flip(0, 2))
        self.assertEqual(torch.tensor([6, 5, 8, 7, 2, 1, 4, 3]).view(2, 2, 2), data.flip(2, 0))

        # not allow flip on the same dim more than once
        self.assertRaises(RuntimeError, lambda: data.flip(0, 1, 1))
        # not allow empty list as input
        self.assertRaises(TypeError, lambda: data.flip())

        # not allow size of flip dim > total dims
        self.assertRaises(IndexError, lambda: data.flip(0, 1, 2, 3))
        # not allow dim > max dim
        self.assertRaises(IndexError, lambda: data.flip(3))

        # test for non-contiguous case
        expanded_data = torch.arange(1, 4, device=device).view(3, 1).expand(3, 2)
        transposed_data = torch.arange(1, 9, device=device).view(2, 2, 2).transpose(0, 1)
        self.assertEqual(torch.tensor([3, 3, 2, 2, 1, 1]).view(3, 2), expanded_data.flip(0))
        self.assertEqual(torch.tensor([8, 7, 4, 3, 6, 5, 2, 1]).view(2, 2, 2), transposed_data.flip(0, 1, 2))

        # test for shape
        data = torch.randn(2, 3, 4, device=device)
        size = [2, 3, 4]
        test_dims = []
        for i in range(1, 3):
            test_dims += combinations(range(len(size)), i)

        for ds in test_dims:
            self.assertEqual(size, list(data.flip(ds).size()))

        # test rectangular case
        data = torch.tensor([1, 2, 3, 4, 5, 6]).view(2, 3).to(device)
        flip0_result = torch.tensor([[4, 5, 6], [1, 2, 3]]).to(device)
        flip1_result = torch.tensor([[3, 2, 1], [6, 5, 4]]).to(device)

        self.assertEqual(flip0_result, data.flip(0))
        self.assertEqual(flip1_result, data.flip(1))

        # test empty tensor, should just return an empty tensor of the same shape
        data = torch.tensor([])
        self.assertEqual(data, data.flip(0))

        # test bool tensor
        a = torch.tensor([False, True])
        self.assertEqual(a.flip(0), torch.tensor([True, False]))

    def test_rot90(self, device):
        data = torch.arange(1, 5, device=device).view(2, 2)
        self.assertEqual(torch.tensor([1, 2, 3, 4]).view(2, 2), data.rot90(0, [0, 1]))
        self.assertEqual(torch.tensor([2, 4, 1, 3]).view(2, 2), data.rot90(1, [0, 1]))
        self.assertEqual(torch.tensor([4, 3, 2, 1]).view(2, 2), data.rot90(2, [0, 1]))
        self.assertEqual(torch.tensor([3, 1, 4, 2]).view(2, 2), data.rot90(3, [0, 1]))

        # test for default args k=1, dims=[0, 1]
        self.assertEqual(data.rot90(), data.rot90(1, [0, 1]))

        # test for reversed order of dims
        self.assertEqual(data.rot90(3, [0, 1]), data.rot90(1, [1, 0]))

        # test for modulo of k
        self.assertEqual(data.rot90(5, [0, 1]), data.rot90(1, [0, 1]))
        self.assertEqual(data.rot90(3, [0, 1]), data.rot90(-1, [0, 1]))
        self.assertEqual(data.rot90(-5, [0, 1]), data.rot90(-1, [0, 1]))

        # test for dims out-of-range error
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, -3]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 2]))

        # test tensor with more than 2D
        data = torch.arange(1, 9, device=device).view(2, 2, 2)
        self.assertEqual(torch.tensor([2, 4, 1, 3, 6, 8, 5, 7]).view(2, 2, 2), data.rot90(1, [1, 2]))
        self.assertEqual(data.rot90(1, [1, -1]), data.rot90(1, [1, 2]))

        # test for errors
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 3]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [1, 1]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0, 1, 2]))
        self.assertRaises(RuntimeError, lambda: data.rot90(1, [0]))

    def test_signal_window_functions(self, device):
        if not TEST_SCIPY:
            raise unittest.SkipTest('Scipy not found')

        def test(name):
            torch_method = getattr(torch, name + '_window')
            for size in [1, 2, 5, 10, 50, 100, 1024, 2048]:
                for periodic in [True, False]:
                    res = torch_method(size, periodic=periodic, device=device)
                    # NB: scipy always returns a float32 result
                    ref = torch.from_numpy(signal.get_window(name, size, fftbins=periodic))
                    self.assertEqual(res, ref, exact_dtype=False)
            with self.assertRaisesRegex(RuntimeError, r'not implemented for sparse types'):
                torch_method(3, layout=torch.sparse_coo)
            with self.assertRaisesRegex(RuntimeError, r'floating point'):
                torch_method(3, dtype=torch.long)
            self.assertTrue(torch_method(3, requires_grad=True).requires_grad)
            self.assertFalse(torch_method(3).requires_grad)

        for window in ['hann', 'hamming', 'bartlett', 'blackman']:
            test(window)

    def test_broadcast(self, device):

        # all functions
        fns = {
            "dist", "atan2", "pow", "lerp", "add",
            "sub", "mul", "div", "fmod", "remainder",
            "eq", "ge", "gt", "le", "lt", "max", "min", "ne",
            "addcdiv", "addcmul", "masked_scatter", "masked_select", "masked_fill",
            "map", "map2", "copy"
        }
        # functions with three tensor arguments
        fns_3_args = {"map2"}
        fns_value_kwarg = {"addcdiv", "addcmul"}

        for fn in fns:
            (dims_small, dims_large, dims_full) = self._select_broadcastable_dims()
            full1d = torch.randn(*dims_full, device=device).flatten().float()
            small = torch.randn(*dims_small, device=device).float()
            large = torch.randn(*dims_large, device=device).float()
            small_expanded = small.expand(*dims_full)
            large_expanded = large.expand(*dims_full)
            small2 = None
            small2_expanded = None
            if fn in fns_3_args or fn in fns_value_kwarg:
                # create another smaller tensor
                (dims_small2, _, _) = self._select_broadcastable_dims(dims_full)
                small2 = torch.randn(*dims_small2, device=device).float()
                small2_expanded = small2.expand(*dims_full)

            if small.is_cuda and fn in ['map', 'map2']:
                # map and map2 are not implementd on CUDA tensors
                continue

            if hasattr(large_expanded, fn):
                # run through tensor versions of functions
                # and verify fully expanded inputs give same results
                expanded = {large: large_expanded, small: small_expanded, small2: small2_expanded}

                def tensorfn(myfn, t1, t2):
                    if fn == "lerp":
                        return myfn(t1, 0.5)
                    elif fn == "masked_select":
                        return myfn(t1 < 0)
                    elif fn == "masked_scatter":
                        return myfn(t1 < 0.5, full1d)
                    elif fn == "masked_fill":
                        return myfn(t1 < 0.5, 1.0)
                    elif fn in fns_3_args:
                        return myfn(1, t1, t2)
                    elif fn in fns_value_kwarg:
                        return myfn(t1, t2, value=1)
                    else:
                        return myfn(t1)

                # test various orders
                for first, second, third in [(large, small, small2), (small, large, small2),
                                             (small2, small, large), (small2, large, small)]:
                    if first is None:
                        break  # ignore last iter when small2 is None
                    method_expanded = getattr(expanded[first], fn)
                    method = getattr(first, fn)
                    r1 = tensorfn(method_expanded, expanded[second], expanded[third])
                    r2 = tensorfn(method, second, third)
                    self.assertEqual(r1, r2)

            # now for torch. versions of functions
            if hasattr(torch, fn):
                fntorch = getattr(torch, fn)
                expanded = {large: large_expanded, small: small_expanded, small2: small2_expanded}

                def torchfn(t1, t2, t3):
                    if fn == "lerp":
                        return fntorch(t1, t2, 0.5)
                    elif fn == "masked_select":
                        return fntorch(t1, t2 < 0)
                    elif fn == "masked_scatter":
                        return fntorch(t1, t2 < 0.5, full1d)
                    elif fn == "masked_fill":
                        return fntorch(t1, t2 < 0.5, 1.0)
                    elif fn in fns_3_args:
                        return fntorch(t1, 1.0, t2, t3)
                    elif fn in fns_value_kwarg:
                        return fntorch(t1, t2, t3, value=1.0)
                    else:
                        return fntorch(t1, t2)

                # test various orders
                for first, second, third in [(large, small, small2), (small, large, small2),
                                             (small2, small, large), (small2, large, small)]:
                    if first is None:
                        break  # ignore last iter when small2 is None
                    r1 = torchfn(expanded[first], expanded[second], expanded[third])
                    r2 = torchfn(first, second, third)
                    self.assertEqual(r1, r2)

            # now for in place functions
            # in-place tensor is not broadcastable; test only guaranteed
            # to work by broadcasting other argument(s)
            if not hasattr(large_expanded, fn + "_"):
                continue

            # need to clone largeExpanded so we can reuse, since functions are in-place
            large_expanded_clone = large_expanded.clone()

            def tensorfn_inplace(t0, t1, t2=None):
                t0_fn = getattr(t0, fn + "_")
                if fn == "lerp":
                    return t0_fn(t1, 0.5)
                elif fn == "masked_scatter":
                    return t0_fn(t1 < 0.5, full1d)
                elif fn == "masked_fill":
                    return t0_fn(t1 < 0.5, 1.0)
                elif fn == "map":
                    return t0_fn(t1, lambda x, y: x + y)
                elif fn == "map2":
                    return t0_fn(t1, t2, lambda x, y, z: x + y + z)
                elif fn in fns_3_args:
                    return t0_fn(1.0, t1, t2)
                elif fn in fns_value_kwarg:
                    return t0_fn(t1, t2, value=1.0)
                else:
                    return t0_fn(t1)
            # in-place pointwise operations don't actually work if the in-place
            # tensor is 0-strided (numpy has the same issue)
            if (0 not in large_expanded.stride() and 0 not in large_expanded_clone.stride()):
                r1 = tensorfn_inplace(large_expanded, small_expanded, small2_expanded)
                r2 = tensorfn_inplace(large_expanded_clone, small, small2)
                self.assertEqual(r1, r2)

            def broadcastable(t0, t1, t2=None):
                try:
                    t1.expand_as(t0)
                    if t2 is not None:
                        t2.expand_as(t0)
                except RuntimeError:
                    return False
                return True

            def _test_in_place_broadcastable(t0, t1, t2=None):
                if not broadcastable(t0, t1, t2):
                    same_size = t0.numel() == t1.numel() and (t0.numel() == t2.numel() if t2 is not None else True)
                    if not same_size:
                        self.assertRaises(RuntimeError, lambda: tensorfn_inplace(t0, t1, t2))
                else:
                    tensorfn_inplace(t0, t1, t2)

            if fn not in fns_3_args and fn not in fns_value_kwarg:
                _test_in_place_broadcastable(small, large_expanded)
                _test_in_place_broadcastable(small, large)
            else:
                _test_in_place_broadcastable(small2, small_expanded, large_expanded)
                _test_in_place_broadcastable(small2, small, large)

    def test_broadcast_fused_matmul(self, device):
        fns = ["baddbmm", "addbmm", "addmm", "addmv", "addr"]

        for fn in fns:
            batch_dim = random.randint(1, 8)
            n_dim = random.randint(1, 8)
            m_dim = random.randint(1, 8)
            p_dim = random.randint(1, 8)

            def dims_full_for_fn():
                if fn == "baddbmm":
                    return ([batch_dim, n_dim, p_dim], [batch_dim, n_dim, m_dim], [batch_dim, m_dim, p_dim])
                elif fn == "addbmm":
                    return ([n_dim, p_dim], [batch_dim, n_dim, m_dim], [batch_dim, m_dim, p_dim])
                elif fn == "addmm":
                    return ([n_dim, p_dim], [n_dim, m_dim], [m_dim, p_dim])
                elif fn == "addmv":
                    return ([n_dim], [n_dim, m_dim], [m_dim])
                elif fn == "addr":
                    return ([n_dim, m_dim], [n_dim], [m_dim])
                else:
                    raise AssertionError("unknown function")

            (t0_dims_full, t1_dims, t2_dims) = dims_full_for_fn()
            (t0_dims_small, _, _) = self._select_broadcastable_dims(t0_dims_full)

            t0_small = torch.randn(*t0_dims_small, device=device).float()
            t1 = torch.randn(*t1_dims, device=device).float()
            t2 = torch.randn(*t2_dims, device=device).float()

            t0_full = t0_small.expand(*t0_dims_full).to(device)

            fntorch = getattr(torch, fn)
            r0 = fntorch(t0_small, t1, t2)
            r1 = fntorch(t0_full, t1, t2)
            self.assertEqual(r0, r1)

    def test_broadcast_batched_matmul(self, device):
        n_dim = random.randint(1, 8)
        m_dim = random.randint(1, 8)
        p_dim = random.randint(1, 8)
        full_batch_dims = [random.randint(1, 3) for i in range(random.randint(1, 3))]
        (batch_dims_small, _, _) = self._select_broadcastable_dims(full_batch_dims)

        def verify_batched_matmul(full_lhs, one_dimensional):
            if not one_dimensional:
                lhs_dims = [n_dim, m_dim]
                rhs_dims = [m_dim, p_dim]
                result_dims = [n_dim, p_dim]
            else:
                lhs_dims = [n_dim, m_dim] if full_lhs else [m_dim]
                rhs_dims = [m_dim, p_dim] if not full_lhs else [m_dim]
                result_dims = [n_dim] if full_lhs else [p_dim]

            lhs_mat_dims = lhs_dims if len(lhs_dims) != 1 else [1, m_dim]
            rhs_mat_dims = rhs_dims if len(rhs_dims) != 1 else [m_dim, 1]
            full_mat_dims = lhs_mat_dims if full_lhs else rhs_mat_dims
            dim0_dims = rhs_dims if full_lhs else lhs_dims
            small_dims = batch_dims_small + (rhs_mat_dims if full_lhs else lhs_mat_dims)

            small = torch.randn(*(small_dims), device=device).float()
            dim0 = torch.randn(*(dim0_dims), device=device).float()
            full = torch.randn(*(full_batch_dims + full_mat_dims), device=device).float()
            if not one_dimensional:
                (lhsTensors, rhsTensors) = ((full,), (small, dim0)) if full_lhs else ((small, dim0), (full,))
            else:
                (lhsTensors, rhsTensors) = ((full,), (dim0,)) if full_lhs else ((dim0,), (full,))

            def maybe_squeeze_result(l, r, result):
                if len(lhs_dims) == 1 and l.dim() != 1:
                    return result.squeeze(-2)
                elif len(rhs_dims) == 1 and r.dim() != 1:
                    return result.squeeze(-1)
                else:
                    return result

            for lhs in lhsTensors:
                lhs_expanded = lhs.expand(*(torch.Size(full_batch_dims) + torch.Size(lhs_mat_dims)))
                lhs_expanded_matmul_fn = lhs_expanded.matmul
                for rhs in rhsTensors:
                    rhs_expanded = ((rhs if len(rhs_dims) != 1 else rhs.unsqueeze(-1)).
                                    expand(*(torch.Size(full_batch_dims) + torch.Size(rhs_mat_dims))))
                    truth = maybe_squeeze_result(lhs_expanded, rhs_expanded, lhs_expanded_matmul_fn(rhs_expanded))
                    for l in (lhs, lhs_expanded):
                        for r in (rhs, rhs_expanded):
                            l_matmul_fn = l.matmul
                            result = maybe_squeeze_result(l, r, l_matmul_fn(r))
                            self.assertEqual(truth, result)
                            # test torch.matmul function as well
                            torch_result = maybe_squeeze_result(l, r, torch.matmul(l, r))
                            self.assertEqual(truth, torch_result)
                            # test torch.matmul with out
                            out = torch.zeros_like(torch_result)
                            torch.matmul(l, r, out=out)
                            self.assertEqual(truth, maybe_squeeze_result(l, r, out))

                # compare to bmm
                bmm_result = (torch.bmm(lhs_expanded.contiguous().view(-1, *lhs_mat_dims),
                                        rhs_expanded.contiguous().view(-1, *rhs_mat_dims)))
                self.assertEqual(truth.view(-1, *result_dims), bmm_result.view(-1, *result_dims))

        for indices in product((True, False), repeat=2):
            verify_batched_matmul(*indices)

    def test_contiguous(self, device):
        x = torch.randn(1, 16, 5, 5, device=device)
        self.assertTrue(x.is_contiguous())
        stride = list(x.stride())
        stride[0] = 20
        # change the stride in dimension 0. the tensor is still contiguous because size[0] is 1
        x.set_(x.storage(), 0, x.size(), stride)
        self.assertTrue(x.is_contiguous())

    def test_index(self, device):

        def consec(size, start=1):
            sequence = torch.ones(int(torch.Tensor(size).prod(0))).cumsum(0)
            sequence.add_(start - 1)
            return sequence.view(*size)

        reference = consec((3, 3, 3)).to(device)

        # empty tensor indexing
        self.assertEqual(reference[torch.LongTensor().to(device)], reference.new(0, 3, 3))

        self.assertEqual(reference[0], consec((3, 3)), 0)
        self.assertEqual(reference[1], consec((3, 3), 10), 0)
        self.assertEqual(reference[2], consec((3, 3), 19), 0)
        self.assertEqual(reference[0, 1], consec((3,), 4), 0)
        self.assertEqual(reference[0:2], consec((2, 3, 3)), 0)
        self.assertEqual(reference[2, 2, 2], 27, 0)
        self.assertEqual(reference[:], consec((3, 3, 3)), 0)

        # indexing with Ellipsis
        self.assertEqual(reference[..., 2], torch.Tensor([[3, 6, 9],
                                                          [12, 15, 18],
                                                          [21, 24, 27]]), 0)
        self.assertEqual(reference[0, ..., 2], torch.Tensor([3, 6, 9]), 0)
        self.assertEqual(reference[..., 2], reference[:, :, 2], 0)
        self.assertEqual(reference[0, ..., 2], reference[0, :, 2], 0)
        self.assertEqual(reference[0, 2, ...], reference[0, 2], 0)
        self.assertEqual(reference[..., 2, 2, 2], 27, 0)
        self.assertEqual(reference[2, ..., 2, 2], 27, 0)
        self.assertEqual(reference[2, 2, ..., 2], 27, 0)
        self.assertEqual(reference[2, 2, 2, ...], 27, 0)
        self.assertEqual(reference[...], reference, 0)

        reference_5d = consec((3, 3, 3, 3, 3)).to(device)
        self.assertEqual(reference_5d[..., 1, 0], reference_5d[:, :, :, 1, 0], 0)
        self.assertEqual(reference_5d[2, ..., 1, 0], reference_5d[2, :, :, 1, 0], 0)
        self.assertEqual(reference_5d[2, 1, 0, ..., 1], reference_5d[2, 1, 0, :, 1], 0)
        self.assertEqual(reference_5d[...], reference_5d, 0)

        # LongTensor indexing
        reference = consec((5, 5, 5)).to(device)
        idx = torch.LongTensor([2, 4]).to(device)
        self.assertEqual(reference[idx], torch.stack([reference[2], reference[4]]))
        # TODO: enable one indexing is implemented like in numpy
        # self.assertEqual(reference[2, idx], torch.stack([reference[2, 2], reference[2, 4]]))
        # self.assertEqual(reference[3, idx, 1], torch.stack([reference[3, 2], reference[3, 4]])[:, 1])

        # None indexing
        self.assertEqual(reference[2, None], reference[2].unsqueeze(0))
        self.assertEqual(reference[2, None, None], reference[2].unsqueeze(0).unsqueeze(0))
        self.assertEqual(reference[2:4, None], reference[2:4].unsqueeze(1))
        self.assertEqual(reference[None, 2, None, None], reference.unsqueeze(0)[:, 2].unsqueeze(0).unsqueeze(0))
        self.assertEqual(reference[None, 2:5, None, None], reference.unsqueeze(0)[:, 2:5].unsqueeze(2).unsqueeze(2))

        # indexing 0-length slice
        self.assertEqual(torch.empty(0, 5, 5), reference[slice(0)])
        self.assertEqual(torch.empty(0, 5), reference[slice(0), 2])
        self.assertEqual(torch.empty(0, 5), reference[2, slice(0)])
        self.assertEqual(torch.tensor([]), reference[2, 1:1, 2])

        # indexing with step
        reference = consec((10, 10, 10)).to(device)
        self.assertEqual(reference[1:5:2], torch.stack([reference[1], reference[3]], 0))
        self.assertEqual(reference[1:6:2], torch.stack([reference[1], reference[3], reference[5]], 0))
        self.assertEqual(reference[1:9:4], torch.stack([reference[1], reference[5]], 0))
        self.assertEqual(reference[2:4, 1:5:2], torch.stack([reference[2:4, 1], reference[2:4, 3]], 1))
        self.assertEqual(reference[3, 1:6:2], torch.stack([reference[3, 1], reference[3, 3], reference[3, 5]], 0))
        self.assertEqual(reference[None, 2, 1:9:4], torch.stack([reference[2, 1], reference[2, 5]], 0).unsqueeze(0))
        self.assertEqual(reference[:, 2, 1:6:2],
                         torch.stack([reference[:, 2, 1], reference[:, 2, 3], reference[:, 2, 5]], 1))

        lst = [list(range(i, i + 10)) for i in range(0, 100, 10)]
        tensor = torch.DoubleTensor(lst).to(device)
        for _i in range(100):
            idx1_start = random.randrange(10)
            idx1_end = idx1_start + random.randrange(1, 10 - idx1_start + 1)
            idx1_step = random.randrange(1, 8)
            idx1 = slice(idx1_start, idx1_end, idx1_step)
            if random.randrange(2) == 0:
                idx2_start = random.randrange(10)
                idx2_end = idx2_start + random.randrange(1, 10 - idx2_start + 1)
                idx2_step = random.randrange(1, 8)
                idx2 = slice(idx2_start, idx2_end, idx2_step)
                lst_indexed = list(map(lambda l: l[idx2], lst[idx1]))
                tensor_indexed = tensor[idx1, idx2]
            else:
                lst_indexed = lst[idx1]
                tensor_indexed = tensor[idx1]
            self.assertEqual(torch.DoubleTensor(lst_indexed), tensor_indexed)

        self.assertRaises(ValueError, lambda: reference[1:9:0])
        self.assertRaises(ValueError, lambda: reference[1:9:-1])

        self.assertRaises(IndexError, lambda: reference[1, 1, 1, 1])
        self.assertRaises(IndexError, lambda: reference[1, 1, 1, 1:1])
        self.assertRaises(IndexError, lambda: reference[3, 3, 3, 3, 3, 3, 3, 3])

        self.assertRaises(IndexError, lambda: reference[0.0])
        self.assertRaises(TypeError, lambda: reference[0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, :, 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, ..., 0.0:2.0])
        self.assertRaises(IndexError, lambda: reference[0.0, :, 0.0])

        def delitem():
            del reference[0]

        self.assertRaises(TypeError, delitem)

    @dtypes(torch.half, torch.double)
    def test_advancedindex(self, device, dtype):
        # Tests for Integer Array Indexing, Part I - Purely integer array
        # indexing

        def consec(size, start=1):
            # Creates the sequence in float since CPU half doesn't support the
            # needed operations. Converts to dtype before returning.
            numel = reduce(lambda x, y: x * y, size, 1)
            sequence = torch.ones(numel, dtype=torch.float, device=device).cumsum(0)
            sequence.add_(start - 1)
            return sequence.view(*size).to(dtype=dtype)

        # pick a random valid indexer type
        def ri(indices):
            choice = random.randint(0, 2)
            if choice == 0:
                return torch.LongTensor(indices).to(device)
            elif choice == 1:
                return list(indices)
            else:
                return tuple(indices)

        def validate_indexing(x):
            self.assertEqual(x[[0]], consec((1,)))
            self.assertEqual(x[ri([0]), ], consec((1,)))
            self.assertEqual(x[ri([3]), ], consec((1,), 4))
            self.assertEqual(x[[2, 3, 4]], consec((3,), 3))
            self.assertEqual(x[ri([2, 3, 4]), ], consec((3,), 3))
            self.assertEqual(x[ri([0, 2, 4]), ], torch.tensor([1, 3, 5], dtype=dtype, device=device))

        def validate_setting(x):
            x[[0]] = -2
            self.assertEqual(x[[0]], torch.tensor([-2], dtype=dtype, device=device))
            x[[0]] = -1
            self.assertEqual(x[ri([0]), ], torch.tensor([-1], dtype=dtype, device=device))
            x[[2, 3, 4]] = 4
            self.assertEqual(x[[2, 3, 4]], torch.tensor([4, 4, 4], dtype=dtype, device=device))
            x[ri([2, 3, 4]), ] = 3
            self.assertEqual(x[ri([2, 3, 4]), ], torch.tensor([3, 3, 3], dtype=dtype, device=device))
            x[ri([0, 2, 4]), ] = torch.tensor([5, 4, 3], dtype=dtype, device=device)
            self.assertEqual(x[ri([0, 2, 4]), ], torch.tensor([5, 4, 3], dtype=dtype, device=device))

        # Only validates indexing and setting for halfs
        if dtype == torch.half:
            reference = consec((10,))
            validate_indexing(reference)
            validate_setting(reference)
            return

        # Case 1: Purely Integer Array Indexing
        reference = consec((10,))
        validate_indexing(reference)

        # setting values
        validate_setting(reference)

        # Tensor with stride != 1
        # strided is [1, 3, 5, 7]
        reference = consec((10,))
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), storage_offset=0,
                     size=torch.Size([4]), stride=[2])

        self.assertEqual(strided[[0]], torch.tensor([1], dtype=dtype, device=device))
        self.assertEqual(strided[ri([0]), ], torch.tensor([1], dtype=dtype, device=device))
        self.assertEqual(strided[ri([3]), ], torch.tensor([7], dtype=dtype, device=device))
        self.assertEqual(strided[[1, 2]], torch.tensor([3, 5], dtype=dtype, device=device))
        self.assertEqual(strided[ri([1, 2]), ], torch.tensor([3, 5], dtype=dtype, device=device))
        self.assertEqual(strided[ri([[2, 1], [0, 3]]), ],
                         torch.tensor([[5, 3], [1, 7]], dtype=dtype, device=device))

        # stride is [4, 8]
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), storage_offset=4,
                     size=torch.Size([2]), stride=[4])
        self.assertEqual(strided[[0]], torch.tensor([5], dtype=dtype, device=device))
        self.assertEqual(strided[ri([0]), ], torch.tensor([5], dtype=dtype, device=device))
        self.assertEqual(strided[ri([1]), ], torch.tensor([9], dtype=dtype, device=device))
        self.assertEqual(strided[[0, 1]], torch.tensor([5, 9], dtype=dtype, device=device))
        self.assertEqual(strided[ri([0, 1]), ], torch.tensor([5, 9], dtype=dtype, device=device))
        self.assertEqual(strided[ri([[0, 1], [1, 0]]), ],
                         torch.tensor([[5, 9], [9, 5]], dtype=dtype, device=device))

        # reference is 1 2
        #              3 4
        #              5 6
        reference = consec((3, 2))
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])], torch.tensor([1, 3, 5], dtype=dtype, device=device))
        self.assertEqual(reference[ri([0, 1, 2]), ri([1])], torch.tensor([2, 4, 6], dtype=dtype, device=device))
        self.assertEqual(reference[ri([0]), ri([0])], consec((1,)))
        self.assertEqual(reference[ri([2]), ri([1])], consec((1,), 6))
        self.assertEqual(reference[[ri([0, 0]), ri([0, 1])]], torch.tensor([1, 2], dtype=dtype, device=device))
        self.assertEqual(reference[[ri([0, 1, 1, 0, 2]), ri([1])]],
                         torch.tensor([2, 4, 4, 2, 6], dtype=dtype, device=device))
        self.assertEqual(reference[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.tensor([1, 2, 3, 3], dtype=dtype, device=device))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = [0],
        self.assertEqual(reference[rows, columns], torch.tensor([[1, 1],
                                                                 [3, 5]], dtype=dtype, device=device))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([1, 0])
        self.assertEqual(reference[rows, columns], torch.tensor([[2, 1],
                                                                 [4, 5]], dtype=dtype, device=device))
        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([[0, 1],
                      [1, 0]])
        self.assertEqual(reference[rows, columns], torch.tensor([[1, 2],
                                                                 [4, 5]], dtype=dtype, device=device))

        # setting values
        reference[ri([0]), ri([1])] = -1
        self.assertEqual(reference[ri([0]), ri([1])], torch.tensor([-1], dtype=dtype, device=device))
        reference[ri([0, 1, 2]), ri([0])] = torch.tensor([-1, 2, -4], dtype=dtype, device=device)
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])],
                         torch.tensor([-1, 2, -4], dtype=dtype, device=device))
        reference[rows, columns] = torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device)
        self.assertEqual(reference[rows, columns],
                         torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device))

        # Verify still works with Transposed (i.e. non-contiguous) Tensors

        reference = torch.tensor([[0, 1, 2, 3],
                                  [4, 5, 6, 7],
                                  [8, 9, 10, 11]], dtype=dtype, device=device).t_()

        # Transposed: [[0, 4, 8],
        #              [1, 5, 9],
        #              [2, 6, 10],
        #              [3, 7, 11]]

        self.assertEqual(reference[ri([0, 1, 2]), ri([0])],
                         torch.tensor([0, 1, 2], dtype=dtype, device=device))
        self.assertEqual(reference[ri([0, 1, 2]), ri([1])],
                         torch.tensor([4, 5, 6], dtype=dtype, device=device))
        self.assertEqual(reference[ri([0]), ri([0])],
                         torch.tensor([0], dtype=dtype, device=device))
        self.assertEqual(reference[ri([2]), ri([1])],
                         torch.tensor([6], dtype=dtype, device=device))
        self.assertEqual(reference[[ri([0, 0]), ri([0, 1])]],
                         torch.tensor([0, 4], dtype=dtype, device=device))
        self.assertEqual(reference[[ri([0, 1, 1, 0, 3]), ri([1])]],
                         torch.tensor([4, 5, 5, 4, 7], dtype=dtype, device=device))
        self.assertEqual(reference[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.tensor([0, 4, 1, 1], dtype=dtype, device=device))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = [0],
        self.assertEqual(reference[rows, columns],
                         torch.tensor([[0, 0], [1, 2]], dtype=dtype, device=device))

        rows = ri([[0, 0],
                   [1, 2]])
        columns = ri([1, 0])
        self.assertEqual(reference[rows, columns],
                         torch.tensor([[4, 0], [5, 2]], dtype=dtype, device=device))
        rows = ri([[0, 0],
                   [1, 3]])
        columns = ri([[0, 1],
                      [1, 2]])
        self.assertEqual(reference[rows, columns],
                         torch.tensor([[0, 4], [5, 11]], dtype=dtype, device=device))

        # setting values
        reference[ri([0]), ri([1])] = -1
        self.assertEqual(reference[ri([0]), ri([1])],
                         torch.tensor([-1], dtype=dtype, device=device))
        reference[ri([0, 1, 2]), ri([0])] = torch.tensor([-1, 2, -4], dtype=dtype, device=device)
        self.assertEqual(reference[ri([0, 1, 2]), ri([0])],
                         torch.tensor([-1, 2, -4], dtype=dtype, device=device))
        reference[rows, columns] = torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device)
        self.assertEqual(reference[rows, columns],
                         torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device))

        # stride != 1

        # strided is [[1 3 5 7],
        #             [9 11 13 15]]

        reference = torch.arange(0., 24, dtype=dtype, device=device).view(3, 8)
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), 1, size=torch.Size([2, 4]),
                     stride=[8, 2])

        self.assertEqual(strided[ri([0, 1]), ri([0])],
                         torch.tensor([1, 9], dtype=dtype, device=device))
        self.assertEqual(strided[ri([0, 1]), ri([1])],
                         torch.tensor([3, 11], dtype=dtype, device=device))
        self.assertEqual(strided[ri([0]), ri([0])],
                         torch.tensor([1], dtype=dtype, device=device))
        self.assertEqual(strided[ri([1]), ri([3])],
                         torch.tensor([15], dtype=dtype, device=device))
        self.assertEqual(strided[[ri([0, 0]), ri([0, 3])]],
                         torch.tensor([1, 7], dtype=dtype, device=device))
        self.assertEqual(strided[[ri([1]), ri([0, 1, 1, 0, 3])]],
                         torch.tensor([9, 11, 11, 9, 15], dtype=dtype, device=device))
        self.assertEqual(strided[[ri([0, 0, 1, 1]), ri([0, 1, 0, 0])]],
                         torch.tensor([1, 3, 9, 9], dtype=dtype, device=device))

        rows = ri([[0, 0],
                   [1, 1]])
        columns = [0],
        self.assertEqual(strided[rows, columns],
                         torch.tensor([[1, 1], [9, 9]], dtype=dtype, device=device))

        rows = ri([[0, 1],
                   [1, 0]])
        columns = ri([1, 2])
        self.assertEqual(strided[rows, columns],
                         torch.tensor([[3, 13], [11, 5]], dtype=dtype, device=device))
        rows = ri([[0, 0],
                   [1, 1]])
        columns = ri([[0, 1],
                      [1, 2]])
        self.assertEqual(strided[rows, columns],
                         torch.tensor([[1, 3], [11, 13]], dtype=dtype, device=device))

        # setting values

        # strided is [[10, 11],
        #             [17, 18]]

        reference = torch.arange(0., 24, dtype=dtype, device=device).view(3, 8)
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])
        self.assertEqual(strided[ri([0]), ri([1])],
                         torch.tensor([11], dtype=dtype, device=device))
        strided[ri([0]), ri([1])] = -1
        self.assertEqual(strided[ri([0]), ri([1])],
                         torch.tensor([-1], dtype=dtype, device=device))

        reference = torch.arange(0., 24, dtype=dtype, device=device).view(3, 8)
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])
        self.assertEqual(strided[ri([0, 1]), ri([1, 0])],
                         torch.tensor([11, 17], dtype=dtype, device=device))
        strided[ri([0, 1]), ri([1, 0])] = torch.tensor([-1, 2], dtype=dtype, device=device)
        self.assertEqual(strided[ri([0, 1]), ri([1, 0])],
                         torch.tensor([-1, 2], dtype=dtype, device=device))

        reference = torch.arange(0., 24, dtype=dtype, device=device).view(3, 8)
        strided = torch.tensor((), dtype=dtype, device=device)
        strided.set_(reference.storage(), 10, size=torch.Size([2, 2]),
                     stride=[7, 1])

        rows = ri([[0],
                   [1]])
        columns = ri([[0, 1],
                      [0, 1]])
        self.assertEqual(strided[rows, columns],
                         torch.tensor([[10, 11], [17, 18]], dtype=dtype, device=device))
        strided[rows, columns] = torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device)
        self.assertEqual(strided[rows, columns],
                         torch.tensor([[4, 6], [2, 3]], dtype=dtype, device=device))

        # Tests using less than the number of dims, and ellipsis

        # reference is 1 2
        #              3 4
        #              5 6
        reference = consec((3, 2))
        self.assertEqual(reference[ri([0, 2]), ],
                         torch.tensor([[1, 2], [5, 6]], dtype=dtype, device=device))
        self.assertEqual(reference[ri([1]), ...],
                         torch.tensor([[3, 4]], dtype=dtype, device=device))
        self.assertEqual(reference[..., ri([1])],
                         torch.tensor([[2], [4], [6]], dtype=dtype, device=device))

        # verify too many indices fails
        with self.assertRaises(IndexError):
            reference[ri([1]), ri([0, 2]), ri([3])]

        # test invalid index fails
        reference = torch.empty(10, dtype=dtype, device=device)
        # can't test cuda because it is a device assert
        if not reference.is_cuda:
            for err_idx in (10, -11):
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[err_idx]
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[torch.LongTensor([err_idx]).to(device)]
                with self.assertRaisesRegex(IndexError, r'out of'):
                    reference[[err_idx]]

        if TEST_NUMPY:
            # we use numpy to compare against, to verify that our advanced
            # indexing semantics are the same, and also for ease of test
            # writing

            def tensor_indices_to_np(tensor, indices):
                # convert the Torch Tensor to a numpy array
                tensor = tensor.to(device='cpu')
                npt = tensor.numpy()

                # convert indices
                idxs = tuple(i.tolist() if isinstance(i, torch.LongTensor) else
                             i for i in indices)

                return npt, idxs

            def get_numpy(tensor, indices):
                npt, idxs = tensor_indices_to_np(tensor, indices)

                # index and return as a Torch Tensor
                return torch.tensor(npt[idxs], dtype=dtype, device=device)

            def set_numpy(tensor, indices, value):
                if not isinstance(value, int):
                    if self.device_type != 'cpu':
                        value = value.cpu()
                    value = value.numpy()

                npt, idxs = tensor_indices_to_np(tensor, indices)
                npt[idxs] = value
                return npt

            def assert_get_eq(tensor, indexer):
                self.assertEqual(tensor[indexer], get_numpy(tensor, indexer))

            def assert_set_eq(tensor, indexer, val):
                pyt = tensor.clone()
                numt = tensor.clone()
                pyt[indexer] = val
                numt = torch.tensor(set_numpy(numt, indexer, val), dtype=dtype, device=device)
                self.assertEqual(pyt, numt)

            def assert_backward_eq(tensor, indexer):
                cpu = tensor.float().clone().detach().requires_grad_(True)
                outcpu = cpu[indexer]
                gOcpu = torch.rand_like(outcpu)
                outcpu.backward(gOcpu)
                dev = cpu.to(device).detach().requires_grad_(True)
                outdev = dev[indexer]
                outdev.backward(gOcpu.to(device))
                self.assertEqual(cpu.grad, dev.grad)

            def get_set_tensor(indexed, indexer):
                set_size = indexed[indexer].size()
                set_count = indexed[indexer].numel()
                set_tensor = torch.randperm(set_count).view(set_size).double().to(device)
                return set_tensor

            # Tensor is  0  1  2  3  4
            #            5  6  7  8  9
            #           10 11 12 13 14
            #           15 16 17 18 19
            reference = torch.arange(0., 20, dtype=dtype, device=device).view(4, 5)

            indices_to_test = [
                # grab the second, fourth columns
                [slice(None), [1, 3]],

                # first, third rows,
                [[0, 2], slice(None)],

                # weird shape
                [slice(None), [[0, 1],
                               [2, 3]]],
                # negatives
                [[-1], [0]],
                [[0, 2], [-1]],
                [slice(None), [-1]],
            ]

            # only test dupes on gets
            get_indices_to_test = indices_to_test + [[slice(None), [0, 1, 1, 2, 2]]]

            for indexer in get_indices_to_test:
                assert_get_eq(reference, indexer)
                if self.device_type != 'cpu':
                    assert_backward_eq(reference, indexer)

            for indexer in indices_to_test:
                assert_set_eq(reference, indexer, 44)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))

            reference = torch.arange(0., 160, dtype=dtype, device=device).view(4, 8, 5)

            indices_to_test = [
                [slice(None), slice(None), [0, 3, 4]],
                [slice(None), [2, 4, 5, 7], slice(None)],
                [[2, 3], slice(None), slice(None)],
                [slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), [0], [1, 2, 4]],
                [slice(None), [0, 1, 3], [4]],
                [slice(None), [[0, 1], [1, 0]], [[2, 3]]],
                [slice(None), [[0, 1], [2, 3]], [[0]]],
                [slice(None), [[5, 6]], [[0, 3], [4, 4]]],
                [[0, 2, 3], [1, 3, 4], slice(None)],
                [[0], [1, 2, 4], slice(None)],
                [[0, 1, 3], [4], slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None)],
                [[[0, 1], [1, 0]], [[2, 3]], slice(None)],
                [[[0, 1], [2, 3]], [[0]], slice(None)],
                [[[2, 1]], [[0, 3], [4, 4]], slice(None)],
                [[[2]], [[0, 3], [4, 1]], slice(None)],
                # non-contiguous indexing subspace
                [[0, 2, 3], slice(None), [1, 3, 4]],

                # less dim, ellipsis
                [[0, 2], ],
                [[0, 2], slice(None)],
                [[0, 2], Ellipsis],
                [[0, 2], slice(None), Ellipsis],
                [[0, 2], Ellipsis, slice(None)],
                [[0, 2], [1, 3]],
                [[0, 2], [1, 3], Ellipsis],
                [Ellipsis, [1, 3], [2, 3]],
                [Ellipsis, [2, 3, 4]],
                [Ellipsis, slice(None), [2, 3, 4]],
                [slice(None), Ellipsis, [2, 3, 4]],

                # ellipsis counts for nothing
                [Ellipsis, slice(None), slice(None), [0, 3, 4]],
                [slice(None), Ellipsis, slice(None), [0, 3, 4]],
                [slice(None), slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), slice(None), [0, 3, 4], Ellipsis],
                [Ellipsis, [[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], Ellipsis, slice(None)],
                [[[0, 1], [1, 0]], [[2, 1], [3, 5]], slice(None), Ellipsis],
            ]

            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 212)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))
                if torch.cuda.is_available():
                    assert_backward_eq(reference, indexer)

            reference = torch.arange(0., 1296, dtype=dtype, device=device).view(3, 9, 8, 6)

            indices_to_test = [
                [slice(None), slice(None), slice(None), [0, 3, 4]],
                [slice(None), slice(None), [2, 4, 5, 7], slice(None)],
                [slice(None), [2, 3], slice(None), slice(None)],
                [[1, 2], slice(None), slice(None), slice(None)],
                [slice(None), slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), slice(None), [0], [1, 2, 4]],
                [slice(None), slice(None), [0, 1, 3], [4]],
                [slice(None), slice(None), [[0, 1], [1, 0]], [[2, 3]]],
                [slice(None), slice(None), [[0, 1], [2, 3]], [[0]]],
                [slice(None), slice(None), [[5, 6]], [[0, 3], [4, 4]]],
                [slice(None), [0, 2, 3], [1, 3, 4], slice(None)],
                [slice(None), [0], [1, 2, 4], slice(None)],
                [slice(None), [0, 1, 3], [4], slice(None)],
                [slice(None), [[0, 1], [3, 4]], [[2, 3], [0, 1]], slice(None)],
                [slice(None), [[0, 1], [3, 4]], [[2, 3]], slice(None)],
                [slice(None), [[0, 1], [3, 2]], [[0]], slice(None)],
                [slice(None), [[2, 1]], [[0, 3], [6, 4]], slice(None)],
                [slice(None), [[2]], [[0, 3], [4, 2]], slice(None)],
                [[0, 1, 2], [1, 3, 4], slice(None), slice(None)],
                [[0], [1, 2, 4], slice(None), slice(None)],
                [[0, 1, 2], [4], slice(None), slice(None)],
                [[[0, 1], [0, 2]], [[2, 4], [1, 5]], slice(None), slice(None)],
                [[[0, 1], [1, 2]], [[2, 0]], slice(None), slice(None)],
                [[[2, 2]], [[0, 3], [4, 5]], slice(None), slice(None)],
                [[[2]], [[0, 3], [4, 5]], slice(None), slice(None)],
                [slice(None), [3, 4, 6], [0, 2, 3], [1, 3, 4]],
                [slice(None), [2, 3, 4], [1, 3, 4], [4]],
                [slice(None), [0, 1, 3], [4], [1, 3, 4]],
                [slice(None), [6], [0, 2, 3], [1, 3, 4]],
                [slice(None), [2, 3, 5], [3], [4]],
                [slice(None), [0], [4], [1, 3, 4]],
                [slice(None), [6], [0, 2, 3], [1]],
                [slice(None), [[0, 3], [3, 6]], [[0, 1], [1, 3]], [[5, 3], [1, 2]]],
                [[2, 2, 1], [0, 2, 3], [1, 3, 4], slice(None)],
                [[2, 0, 1], [1, 2, 3], [4], slice(None)],
                [[0, 1, 2], [4], [1, 3, 4], slice(None)],
                [[0], [0, 2, 3], [1, 3, 4], slice(None)],
                [[0, 2, 1], [3], [4], slice(None)],
                [[0], [4], [1, 3, 4], slice(None)],
                [[1], [0, 2, 3], [1], slice(None)],
                [[[1, 2], [1, 2]], [[0, 1], [2, 3]], [[2, 3], [3, 5]], slice(None)],

                # less dim, ellipsis
                [Ellipsis, [0, 3, 4]],
                [Ellipsis, slice(None), [0, 3, 4]],
                [Ellipsis, slice(None), slice(None), [0, 3, 4]],
                [slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), slice(None), Ellipsis, [0, 3, 4]],
                [slice(None), [0, 2, 3], [1, 3, 4]],
                [slice(None), [0, 2, 3], [1, 3, 4], Ellipsis],
                [Ellipsis, [0, 2, 3], [1, 3, 4], slice(None)],
                [[0], [1, 2, 4]],
                [[0], [1, 2, 4], slice(None)],
                [[0], [1, 2, 4], Ellipsis],
                [[0], [1, 2, 4], Ellipsis, slice(None)],
                [[1], ],
                [[0, 2, 1], [3], [4]],
                [[0, 2, 1], [3], [4], slice(None)],
                [[0, 2, 1], [3], [4], Ellipsis],
                [Ellipsis, [0, 2, 1], [3], [4]],
            ]

            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 1333)
                assert_set_eq(reference,
                              indexer,
                              get_set_tensor(reference, indexer))
            indices_to_test += [
                [slice(None), slice(None), [[0, 1], [1, 0]], [[2, 3], [3, 0]]],
                [slice(None), slice(None), [[2]], [[0, 3], [4, 4]]],
            ]
            for indexer in indices_to_test:
                assert_get_eq(reference, indexer)
                assert_set_eq(reference, indexer, 1333)
                if self.device_type != 'cpu':
                    assert_backward_eq(reference, indexer)

    def test_advancedindex_big(self, device):
        reference = torch.arange(0, 123344, dtype=torch.int, device=device)

        self.assertEqual(reference[[0, 123, 44488, 68807, 123343], ],
                         torch.tensor([0, 123, 44488, 68807, 123343], dtype=torch.int))

    @dtypes(torch.double)
    def test_kthvalue(self, device, dtype):
        SIZE = 50
        x = torch.rand(SIZE, SIZE, SIZE, dtype=dtype, device=device)
        x0 = x.clone()

        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(x, k, keepdim=False)
        res2val, res2ind = torch.sort(x)

        self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
        self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)
        # test use of result tensors
        k = random.randint(1, SIZE)
        res1val = torch.tensor([], dtype=dtype, device=device)
        res1ind = torch.tensor([], dtype=torch.long, device=device)
        torch.kthvalue(x, k, keepdim=False, out=(res1val, res1ind))
        res2val, res2ind = torch.sort(x)
        self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
        self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)

        # test non-default dim
        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(x, k, 0, keepdim=False)
        res2val, res2ind = torch.sort(x, 0)
        self.assertEqual(res1val, res2val[k - 1], 0)
        self.assertEqual(res1ind, res2ind[k - 1], 0)

        # non-contiguous
        y = x.narrow(1, 0, 1)
        y0 = y.contiguous()
        k = random.randint(1, SIZE)
        res1val, res1ind = torch.kthvalue(y, k)
        res2val, res2ind = torch.kthvalue(y0, k)
        self.assertEqual(res1val, res2val, 0)
        self.assertEqual(res1ind, res2ind, 0)

        # check that the input wasn't modified
        self.assertEqual(x, x0, 0)

        # simple test case (with repetitions)
        y = torch.tensor((3., 5, 4, 1, 1, 5), dtype=dtype, device=device)
        self.assertEqual(torch.kthvalue(y, 3)[0], 3, 0)
        self.assertEqual(torch.kthvalue(y, 2)[0], 1, 0)

        # simple test case (with NaN)
        SIZE = 50
        x = torch.rand(SIZE, SIZE, SIZE, dtype=dtype, device=device)
        x[torch.arange(SIZE), :, torch.randint(50, (50,))] = nan
        ks = [random.randint(1, SIZE), 1, SIZE, SIZE - 1]
        res2val, res2ind = torch.sort(x)
        for k in ks:
            res1val, res1ind = torch.kthvalue(x, k, keepdim=False)
            self.assertEqual(res1val[:, :], res2val[:, :, k - 1], 0)
            self.assertEqual(res1ind[:, :], res2ind[:, :, k - 1], 0)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_lu_solve_batched_non_contiguous(self, device, dtype):
        from numpy.linalg import solve
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        A = random_fullrank_matrix_distinct_singular_value(2, 2, dtype=dtype, device='cpu')
        b = torch.randn(2, 2, 2, dtype=dtype, device='cpu')
        x_exp = torch.as_tensor(solve(A.permute(0, 2, 1).numpy(), b.permute(2, 1, 0).numpy())).to(device)
        A = A.to(device).permute(0, 2, 1)
        b = b.to(device).permute(2, 1, 0)
        assert not A.is_contiguous() and not b.is_contiguous(), "contiguous inputs"
        LU_data, LU_pivots = torch.lu(A)
        x = torch.lu_solve(b, LU_data, LU_pivots)
        self.assertEqual(x, x_exp)

    def lu_solve_test_helper(self, A_dims, b_dims, pivot, device, dtype):
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        b = torch.randn(*b_dims, dtype=dtype, device=device)
        A = random_fullrank_matrix_distinct_singular_value(*A_dims, dtype=dtype, device=device)
        LU_data, LU_pivots, info = torch.lu(A, get_infos=True, pivot=pivot)
        self.assertEqual(info, torch.zeros_like(info))
        return b, A, LU_data, LU_pivots

    @skipCPUIfNoLapack
    @skipCUDAIfNoMagma
    @dtypes(torch.double)
    def test_lu_solve(self, device, dtype):
        def sub_test(pivot):
            for k, n in zip([2, 3, 5], [3, 5, 7]):
                b, A, LU_data, LU_pivots = self.lu_solve_test_helper((n,), (n, k), pivot, device, dtype)
                x = torch.lu_solve(b, LU_data, LU_pivots)
                self.assertLessEqual(b.dist(A.mm(x)), 1e-12)

        sub_test(True)
        if self.device_type == 'cuda':
            sub_test(False)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_lu_solve_batched(self, device, dtype):
        def sub_test(pivot):
            def lu_solve_batch_test_helper(A_dims, b_dims, pivot):
                b, A, LU_data, LU_pivots = self.lu_solve_test_helper(A_dims, b_dims, pivot, device, dtype)
                x_exp_list = []
                for i in range(b_dims[0]):
                    x_exp_list.append(torch.lu_solve(b[i], LU_data[i], LU_pivots[i]))
                x_exp = torch.stack(x_exp_list)  # Stacked output
                x_act = torch.lu_solve(b, LU_data, LU_pivots)  # Actual output
                self.assertEqual(x_exp, x_act)  # Equality check
                self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 1e-12)  # Correctness check

            for batchsize in [1, 3, 4]:
                lu_solve_batch_test_helper((5, batchsize), (batchsize, 5, 10), pivot)

        # Tests tensors with 0 elements
        b = torch.randn(3, 0, 3, dtype=dtype, device=device)
        A = torch.randn(3, 0, 0, dtype=dtype, device=device)
        LU_data, LU_pivots = torch.lu(A)
        self.assertEqual(torch.empty_like(b), b.lu_solve(LU_data, LU_pivots))

        sub_test(True)
        if self.device_type == 'cuda':
            sub_test(False)

    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_lu_solve_batched_many_batches(self, device, dtype):
        def run_test(A_dims, b_dims):
            b, A, LU_data, LU_pivots = self.lu_solve_test_helper(A_dims, b_dims, True, device, dtype)
            x = torch.lu_solve(b, LU_data, LU_pivots)
            b_ = torch.matmul(A, x)
            self.assertEqual(b_, b.expand_as(b_))

        run_test((5, 65536), (65536, 5, 10))
        run_test((5, 262144), (262144, 5, 10))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.double)
    def test_lu_solve_batched_broadcasting(self, device, dtype):
        from numpy.linalg import solve
        from torch.testing._internal.common_utils import random_fullrank_matrix_distinct_singular_value

        def run_test(A_dims, b_dims, pivot=True):
            A_matrix_size = A_dims[-1]
            A_batch_dims = A_dims[:-2]
            A = random_fullrank_matrix_distinct_singular_value(A_matrix_size, *A_batch_dims, dtype=dtype)
            b = torch.randn(*b_dims, dtype=dtype)
            x_exp = torch.as_tensor(solve(A.numpy(), b.numpy())).to(dtype=dtype, device=device)
            A, b = A.to(device), b.to(device)
            LU_data, LU_pivots = torch.lu(A, pivot=pivot)
            x = torch.lu_solve(b, LU_data, LU_pivots)
            self.assertEqual(x, x_exp)

        # test against numpy.linalg.solve
        run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6))  # no broadcasting
        run_test((2, 1, 3, 4, 4), (4, 6))  # broadcasting b
        run_test((4, 4), (2, 1, 3, 4, 2))  # broadcasting A
        run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5))  # broadcasting A & b

    @dtypes(torch.float, torch.double, torch.int64, torch.int32, torch.int16)
    @dtypesIfCUDA(torch.float, torch.double, torch.int64, torch.int32, torch.int16, torch.half)
    def test_dim_arg_reduction_scalar(self, device, dtype):
        example = 4.0

        x = torch.tensor(example, device=device, dtype=dtype)
        self.assertEqual(x.argmax().item(), 0)
        self.assertEqual(x.argmax(dim=None).item(), 0)
        self.assertEqual(x.argmax(dim=0).item(), 0)
        self.assertEqual(x.argmax(dim=0, keepdim=True), torch.tensor(0, dtype=torch.int64))

        x = torch.tensor(example, device=device, dtype=dtype)
        self.assertEqual(x.argmin().item(), 0)
        self.assertEqual(x.argmin(dim=None).item(), 0)
        self.assertEqual(x.argmin(dim=0).item(), 0)
        self.assertEqual(x.argmin(dim=0, keepdim=True), torch.tensor(0, dtype=torch.int64))


    def test_dim_reduction(self, device):
        example = [[-1, 2, 1], [5, 3, 6]]

        types = [torch.double,
                 torch.float,
                 torch.int64,
                 torch.int32,
                 torch.int16]
        if self.device_type == 'cuda':  # 'cpu' and 'xla' do not support half
            types.append(torch.half)

        sum_dtype = {
            torch.double: torch.double,
            torch.float: torch.float,
            torch.half: torch.half,
            torch.int64: torch.int64,
            torch.int32: torch.int64,
            torch.int16: torch.int64,
        }

        # This won't test for 256bit instructions, since we usually
        # only work on 1 cacheline (1024bit) at a time and these
        # examples aren't big enough to trigger that.
        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.sum().item(), 16)
            self.assertEqual(x.sum(0), torch.tensor([4, 5, 7], dtype=sum_dtype[dtype]))
            self.assertEqual(x.sum(1), torch.tensor([2, 14], dtype=sum_dtype[dtype]))
            y = torch.tensor(example, device=device, dtype=sum_dtype[dtype])
            torch.sum(x, 0, out=y)
            self.assertEqual(x.sum(0), y)

        # Mean not supported for Int types
        for dtype in types[:2]:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.mean().item(), 16.0 / 6)
            self.assertEqual(x.mean(0), torch.tensor([2.0, 2.5, 7.0 / 2], dtype=dtype))
            self.assertEqual(x.mean(1), torch.tensor([2.0 / 3, 14.0 / 3], dtype=dtype))
            self.assertEqual(x.mean(), x.mean((0, 1)))

        prod_dtype = {
            torch.double: torch.double,
            torch.float: torch.float,
            torch.half: torch.half,
            torch.int64: torch.int64,
            torch.int32: torch.int64,
            torch.int16: torch.int64
        }

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.prod().item(), -180)
            self.assertEqual(x.prod(0), torch.tensor([-5, 6, 6], dtype=prod_dtype[dtype]))
            self.assertEqual(x.prod(1), torch.tensor([-2, 90], dtype=prod_dtype[dtype]))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.max().item(), 6)
            self.assertEqual(x.max(0), (torch.tensor([5, 3, 6], dtype=dtype),
                                        torch.tensor([1, 1, 1], dtype=torch.int64)))
            self.assertEqual(x.max(1), (torch.tensor([2, 6], dtype=dtype),
                                        torch.tensor([1, 2], dtype=torch.int64)))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.min().item(), -1)
            self.assertEqual(x.min(0), (torch.tensor([-1, 2, 1], dtype=dtype),
                                        torch.tensor([0, 0, 0], dtype=torch.int64)))
            self.assertEqual(x.min(1), (torch.tensor([-1, 3], dtype=dtype),
                                        torch.tensor([0, 1], dtype=torch.int64)))

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.argmax().item(), 5)
            self.assertEqual(x.argmax(dim=None).item(), 5)
            self.assertEqual(x.argmax(dim=0), torch.tensor([1, 1, 1], dtype=torch.int64))
            self.assertEqual(x.argmax(dim=1), torch.tensor([1, 2], dtype=torch.int64))
            self.assertEqual(x.argmax(dim=0, keepdim=True), torch.tensor([[1, 1, 1]], dtype=torch.int64))
            # test that non-contiguous tensors work
            self.assertEqual(x[:, :2].argmax().item(), 2)

        for dtype in types:
            x = torch.tensor(example, device=device, dtype=dtype)
            self.assertEqual(x.argmin().item(), 0)
            self.assertEqual(x.argmin(dim=None).item(), 0)
            self.assertEqual(x.argmin(dim=0), torch.tensor([0, 0, 0], dtype=torch.int64))
            self.assertEqual(x.argmin(dim=1), torch.tensor([0, 1], dtype=torch.int64))
            self.assertEqual(x.argmin(dim=1, keepdim=True), torch.tensor([[0], [1]], dtype=torch.int64))
            # test that non-contiguous tensors work
            self.assertEqual(x[:, :2].argmin().item(), 0)

        dim_red_fns = [
            "mean", "median", "mode", "norm", "prod",
            "std", "sum", "var", "max", "min"]

        def normfn_attr(t, dim, keepdim=False, out=None):
            attr = torch.norm
            return attr(t, 2, dim, keepdim, out=out)

        for fn_name in dim_red_fns:
            fn_attr = getattr(torch, fn_name) if fn_name != "norm" else normfn_attr

            def fn(x, dim, keepdim=False, out=None):
                ans = fn_attr(x, dim, keepdim=keepdim, out=out)
                return ans if not istuple(ans) else ans[0]

            def fn_tuple(x, dim, keepdim=False, out=None):
                return fn_attr(x, dim, keepdim=keepdim, out=out)

            def test_multidim(x, dim):
                self.assertEqual(fn(x, dim).unsqueeze(dim), fn(x, dim, keepdim=True))
                self.assertEqual(x.ndimension() - 1, fn(x, dim).ndimension())
                self.assertEqual(x.ndimension(), fn(x, dim, keepdim=True).ndimension())

            # general case
            x = torch.randn(3, 4, 5, device=device)
            dim = random.randint(0, 2)
            test_multidim(x, dim)

            # check 1-d behavior
            x = torch.randn(1, device=device)
            dim = 0
            self.assertEqual(fn(x, dim).shape, ())
            self.assertEqual(fn(x, dim, keepdim=True).shape, (1,))

            # check reducing of a singleton dimension
            dims = [3, 4, 5]
            singleton_dim = random.randint(0, 2)
            dims[singleton_dim] = 1
            x = torch.randn(dims, device=device)
            test_multidim(x, singleton_dim)

            # check reducing median with NaNs
            # If the element in the median is a NaN, there can be issues
            # when comparining with other nan elements
            if fn_name == 'median':
                y = torch.full((1, 3), np.nan, dtype=torch.float64, device=device)
                y[:, :1] = 1.1
                values, indices = fn_tuple(y, dim=1)
                expected_values = torch.tensor([nan], dtype=torch.float64, device=device)
                self.assertEqual(values, expected_values)
                self.assertTrue(torch.isnan(y.flatten()[indices[0]]))

            # check reducing with output kwargs
            if fn_name in ['median', 'mode', 'max', 'min']:
                y = torch.randn(5, 3, device=device)
                values = torch.randn(5, 3, device=device)
                indices = torch.zeros(5, 3, device=device).long() - 1
                fn_tuple(y, 1, keepdim=False, out=(values[:, 1], indices[:, 1]))
                values_expected, indices_expected = fn_tuple(y, 1, keepdim=False)
                self.assertEqual(values[:, 1], values_expected,
                                 '{} values with out= kwarg'.format(fn_name))
                self.assertEqual(indices[:, 1], indices_expected,
                                 '{} indices with out= kwarg'.format(fn_name))
                continue

            x = torch.randn(5, 3, device=device)
            y = torch.randn(5, 3, device=device)
            fn(y, 1, keepdim=False, out=x[:, 1])
            expected = fn(y, 1, keepdim=False)
            self.assertEqual(x[:, 1], expected, '{} with out= kwarg'.format(fn_name))

    @largeCUDATensorTest('10GB')
    def test_reduction_split(self, device):
        # Test reduction when there is a 32bit-indexing split
        # https://github.com/pytorch/pytorch/issues/37583
        input_ = torch.randn(5, 14400, 14400, device=device)
        result = input_.sum(dim=0)
        expect = input_[0] + input_[1] + input_[2] + input_[3] + input_[4]
        self.assertEqual(result, expect)

    @onlyCUDA
    @dtypes(torch.half, torch.float, torch.double)
    def test_reduction_vectorized_corner(self, device, dtype):
        # 1D case: sum
        size = 1024 * 1024 * 64 + 3
        shift = 1
        x = torch.zeros(size, dtype=dtype, device=device)
        y = x[shift:]
        for i in range(100):
            x.zero_()
            x[i] = 1
            self.assertEqual(x.sum(), 1.0)
            if i < shift:
                self.assertEqual(y.sum(), 0.0)
            else:
                self.assertEqual(y.sum(), 1.0)
        for i in range(1, 100):
            x.zero_()
            x[-i] = 1
            self.assertEqual(x.sum(), 1.0)
            self.assertEqual(y.sum(), 1.0)
        # 1D case: argmax
        size = 1024 * 1024 * 64 + 3
        shift = 1
        ysize = size - shift
        x = torch.zeros(size, dtype=dtype, device=device)
        y = x[shift:]
        for i in range(100):
            x.zero_()
            x[i] = 1
            self.assertEqual(x.argmax().item(), i)
            if i >= shift:
                self.assertEqual(y.argmax().item(), i - shift)
        for i in range(1, 100):
            x.zero_()
            x[-i] = 1
            self.assertEqual(x.argmax().item(), size - i)
            self.assertEqual(y.argmax().item(), ysize - i)
        # 2D case: sum
        size = (7, 1024 * 1024 + 3)
        x = torch.zeros(size, dtype=dtype, device=device)
        for i in range(100):
            x.zero_()
            for j in range(7):
                x[j][i] = j
            xs = x.sum(dim=-1)
            for j in range(7):
                self.assertEqual(xs[j].item(), float(j))
        for i in range(100):
            x.zero_()
            for j in range(7):
                x[j][-i] = j
            xs = x.sum(dim=-1)
            for j in range(7):
                self.assertEqual(xs[j].item(), float(j))
        # 2D case: argmax
        size = (7, 1024 * 1024 + 3)
        x = torch.zeros(size, dtype=dtype, device=device)
        for i in range(100):
            x.zero_()
            for j in range(7):
                x[j][i] = j + 1
            xs = x.argmax(dim=-1)
            for j in range(7):
                self.assertEqual(xs[j].item(), i)
        for i in range(1, 100):
            x.zero_()
            for j in range(7):
                x[j][-i] = j + 1
            xs = x.argmax(dim=-1)
            for j in range(7):
                self.assertEqual(xs[j].item(), size[1] - i)


    @slowTest
    def test_argminmax_large_axis(self, device):
        # Regression test for gh-32863
        # Requires > 8 GB of memory. So, if allocation fails just skip it.
        try:
            x = torch.zeros((2, 2**32), device=device, dtype=torch.int8)
            x[:, -1] = 1
            self.assertEqual(x.argmax(1), [x.shape[1] - 1] * 2)
            x[:, -1] = -1
            self.assertEqual(x.argmin(1), [x.shape[1] - 1] * 2)
        except RuntimeError as e:
            if 'memory' in str(e):
                raise unittest.SkipTest('Insufficient memory')
            raise

    def test_remainder_overflow(self, device):
        # Check Integer Overflows
        x = torch.tensor(23500, dtype=torch.int64, device=device)
        q = 392486996410368
        self.assertEqual(x % q, x)
        self.assertEqual(-x % q, q - x)
        self.assertEqual(x % -q, x - q)
        self.assertEqual(-x % -q, -x)

    def test_rpow(self, device):
        m = torch.randn(10, 10, device=device)
        self.assertEqual(torch.pow(2, m), 2**m)

        # test with scalar
        m = torch.randn(1, device=device).squeeze()
        assert m.dim() == 0, "m is intentionally a scalar"
        self.assertEqual(torch.pow(2, m), 2**m)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_symeig(self, device, dtype):
        from torch.testing._internal.common_utils import random_symmetric_matrix

        def run_test(dims, eigenvectors, upper):
            x = random_symmetric_matrix(*dims, dtype=dtype, device=device)
            oute = torch.empty(dims[1:] + dims[:1], dtype=dtype, device=device)
            outv = torch.empty(dims[1:] + dims[:1] * 2, dtype=dtype, device=device)
            torch.symeig(x, eigenvectors=eigenvectors, upper=upper, out=(oute, outv))

            if eigenvectors:
                x_recon = torch.matmul(torch.matmul(outv, torch.diag_embed(oute)), outv.transpose(-2, -1))
                self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using V @ diag(e) @ V.T')
            else:
                eigvals, _ = torch.symeig(x, eigenvectors=True, upper=upper)
                self.assertEqual(eigvals, oute, 'Eigenvalues mismatch')
                self.assertEqual(torch.empty(0, device=device, dtype=dtype), outv, 'Eigenvector matrix not empty')

            rese, resv = x.symeig(eigenvectors=eigenvectors, upper=upper)
            self.assertEqual(rese, oute, "outputs of symeig and symeig with out don't match")
            self.assertEqual(resv, outv, "outputs of symeig and symeig with out don't match")

            # test non-contiguous
            x = random_symmetric_matrix(*dims, dtype=dtype, device=device)
            n_dim = len(dims) + 1
            # Reverse the batch dimensions and the matrix dimensions and then concat them
            x = x.permute(tuple(range(n_dim - 3, -1, -1)) + (n_dim - 1, n_dim - 2))
            assert not x.is_contiguous(), "x is intentionally non-contiguous"
            rese, resv = torch.symeig(x, eigenvectors=eigenvectors, upper=upper)
            if eigenvectors:
                x_recon = torch.matmul(torch.matmul(resv, torch.diag_embed(rese)), resv.transpose(-2, -1))
                self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using V @ diag(e) @ V.T')
            else:
                eigvals, _ = torch.symeig(x, eigenvectors=True, upper=upper)
                self.assertEqual(eigvals, rese, 'Eigenvalues mismatch')
                self.assertEqual(torch.empty(0, device=device, dtype=dtype), resv, 'Eigenvector matrix not empty')

        batch_dims_set = [(), (3,), (3, 5), (5, 3, 5)]
        for batch_dims, eigenvectors, upper in product(batch_dims_set, (True, False), (True, False)):
            run_test((5,) + batch_dims, eigenvectors, upper)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_svd(self, device, dtype):
        def run_test(dims, some, compute_uv):
            x = torch.randn(*dims, dtype=dtype, device=device)
            outu = torch.tensor((), dtype=dtype, device=device)
            outs = torch.tensor((), dtype=dtype, device=device)
            outv = torch.tensor((), dtype=dtype, device=device)
            torch.svd(x, some=some, compute_uv=compute_uv, out=(outu, outs, outv))

            if compute_uv:
                if some:
                    x_recon = torch.matmul(outu, torch.matmul(outs.diag_embed(), outv.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using U @ diag(S) @ V.T')
                else:
                    narrow_u = outu[..., :min(*dims[-2:])]
                    narrow_v = outv[..., :min(*dims[-2:])]
                    x_recon = torch.matmul(narrow_u, torch.matmul(outs.diag_embed(), narrow_v.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using U @ diag(S) @ V.T')
            else:
                _, singvals, _ = torch.svd(x, compute_uv=True)
                self.assertEqual(singvals, outs, 'Singular values mismatch')
                self.assertEqual(outu, torch.zeros_like(outu), 'U not zero')
                self.assertEqual(outv, torch.zeros_like(outv), 'V not zero')

            resu, ress, resv = torch.svd(x, some=some, compute_uv=compute_uv)
            self.assertEqual(resu, outu, 'outputs of svd and svd with out differ')
            self.assertEqual(ress, outs, 'outputs of svd and svd with out differ')
            self.assertEqual(resv, outv, 'outputs of svd and svd with out differ')

            # test non-contiguous
            x = torch.randn(*dims, dtype=dtype, device=device)
            n_dim = len(dims)
            # Reverse the batch dimensions and the matrix dimensions and then concat them
            x = x.permute(tuple(range(n_dim - 3, -1, -1)) + (n_dim - 1, n_dim - 2))
            assert not x.is_contiguous(), "x is intentionally non-contiguous"
            resu, ress, resv = torch.svd(x, some=some, compute_uv=compute_uv)
            if compute_uv:
                if some:
                    x_recon = torch.matmul(resu, torch.matmul(ress.diag_embed(), resv.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using U @ diag(S) @ V.T')
                else:
                    narrow_u = resu[..., :min(*dims[-2:])]
                    narrow_v = resv[..., :min(*dims[-2:])]
                    x_recon = torch.matmul(narrow_u, torch.matmul(ress.diag_embed(), narrow_v.transpose(-2, -1)))
                    self.assertEqual(x, x_recon, atol=1e-8, message='Incorrect reconstruction using U @ diag(S) @ V.T')
            else:
                _, singvals, _ = torch.svd(x, compute_uv=True)
                self.assertEqual(singvals, ress, 'Singular values mismatch')
                self.assertEqual(resu, torch.zeros_like(resu), 'U not zero')
                self.assertEqual(resv, torch.zeros_like(resv), 'V not zero')

        shapes = [(3, 3), (5, 3, 3), (7, 5, 3, 3),  # square matrices
                  (7, 3), (5, 7, 3), (7, 5, 7, 3),  # fat matrices
                  (3, 7), (5, 3, 7), (7, 5, 3, 7)]  # thin matrices
        for dims, some, compute_uv in product(shapes, [True, False], [True, False]):
            run_test(dims, some, compute_uv)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_svd_no_singularvectors(self, device):
        for size in [(5, 5), (5, 20), (20, 5)]:
            a = torch.randn(*size, device=device)
            u, s_expect, v = torch.svd(a)
            u, s_actual, v = torch.svd(a, compute_uv=False)
            self.assertEqual(s_expect, s_actual, "Singular values don't match")

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_svd_lowrank(self, device):
        import torch
        from torch.testing._internal.common_utils import random_lowrank_matrix, random_sparse_matrix

        dtype = torch.double

        def run_subtest(actual_rank, matrix_size, batches, device, svd_lowrank, **options):
            density = options.pop('density', 1)
            if isinstance(matrix_size, int):
                rows = columns = matrix_size
            else:
                rows, columns = matrix_size
            if density == 1:
                a_input = random_lowrank_matrix(actual_rank, rows, columns, *batches, device=device, dtype=dtype)
                a = a_input
            else:
                assert batches == ()
                a_input = random_sparse_matrix(rows, columns, density, device=device, dtype=dtype)
                a = a_input.to_dense()

            q = min(*size)
            u, s, v = svd_lowrank(a_input, q=q, **options)

            # check if u, s, v is a SVD
            u, s, v = u[..., :q], s[..., :q], v[..., :q]
            A = u.matmul(s.diag_embed()).matmul(v.transpose(-2, -1))
            self.assertEqual(A, a)

            # check if svd_lowrank produces same singular values as torch.svd
            U, S, V = torch.svd(a)
            self.assertEqual(s.shape, S.shape)
            self.assertEqual(u.shape, U.shape)
            self.assertEqual(v.shape, V.shape)
            self.assertEqual(s, S)

            if density == 1:
                # actual_rank is known only for dense inputs
                #
                # check if pairs (u, U) and (v, V) span the same
                # subspaces, respectively
                u, s, v = u[..., :actual_rank], s[..., :actual_rank], v[..., :actual_rank]
                U, S, V = U[..., :actual_rank], S[..., :actual_rank], V[..., :actual_rank]
                self.assertEqual(u.transpose(-2, -1).matmul(U).det().abs(), torch.ones(batches, device=device, dtype=dtype))
                self.assertEqual(v.transpose(-2, -1).matmul(V).det().abs(), torch.ones(batches, device=device, dtype=dtype))

        all_batches = [(), (1,), (3,), (2, 3)]
        for actual_rank, size, all_batches in [
                (2, (17, 4), all_batches),
                (4, (17, 4), all_batches),
                (4, (17, 17), all_batches),
                (10, (100, 40), all_batches),
                (7, (1000, 1000), [()]),
        ]:
            # dense input
            for batches in all_batches:
                run_subtest(actual_rank, size, batches, device, torch.svd_lowrank)
                if size != size[::-1]:
                    run_subtest(actual_rank, size[::-1], batches, device, torch.svd_lowrank)

        # sparse input
        for size in [(17, 4), (4, 17), (17, 17), (100, 40), (40, 100), (1000, 1000)]:
            for density in [0.005, 0.1]:
                run_subtest(None, size, (), device, torch.svd_lowrank, density=density)

        # jitting support
        jitted = torch.jit.script(torch.svd_lowrank)
        actual_rank, size, batches = 2, (17, 4), ()
        run_subtest(actual_rank, size, batches, device, jitted)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_pca_lowrank(self, device):
        from torch.testing._internal.common_utils import random_lowrank_matrix, random_sparse_matrix

        dtype = torch.double

        def run_subtest(guess_rank, actual_rank, matrix_size, batches, device, pca, **options):
            density = options.pop('density', 1)
            if isinstance(matrix_size, int):
                rows = columns = matrix_size
            else:
                rows, columns = matrix_size
            if density == 1:
                a_input = random_lowrank_matrix(actual_rank, rows, columns, *batches, device=device, dtype=dtype)
                a = a_input
            else:
                a_input = random_sparse_matrix(rows, columns, density, device=device, dtype=dtype)
                a = a_input.to_dense()

            u, s, v = pca(a_input, q=guess_rank, **options)

            self.assertEqual(s.shape[-1], guess_rank)
            self.assertEqual(u.shape[-2], rows)
            self.assertEqual(u.shape[-1], guess_rank)
            self.assertEqual(v.shape[-1], guess_rank)
            self.assertEqual(v.shape[-2], columns)

            A1 = u.matmul(s.diag_embed()).matmul(v.transpose(-2, -1))
            ones_m1 = torch.ones(batches + (rows, 1), dtype=a.dtype, device=device)
            c = a.sum(axis=-2) / rows
            c = c.reshape(batches + (1, columns))
            A2 = a - ones_m1.matmul(c)
            self.assertEqual(A1, A2)

            if density == 1:
                # actual rank is known only for dense input
                detect_rank = (s.abs() > 1e-5).sum(axis=-1)
                self.assertEqual(actual_rank * torch.ones(batches, device=device, dtype=torch.int64), detect_rank)
                U, S, V = torch.svd(A2)
                self.assertEqual(s[..., :actual_rank], S[..., :actual_rank])

        all_batches = [(), (1,), (3,), (2, 3)]
        for actual_rank, size, all_batches in [
                (2, (17, 4), all_batches),
                (2, (100, 4), all_batches),
                (6, (100, 40), all_batches),
                (12, (1000, 1000), [()]),
        ]:
            for batches in all_batches:
                for guess_rank in [
                        actual_rank,
                        actual_rank + 2,
                        actual_rank + 6,
                ]:
                    if guess_rank <= min(*size):
                        run_subtest(guess_rank, actual_rank, size, batches, device, torch.pca_lowrank)
                        run_subtest(guess_rank, actual_rank, size[::-1], batches, device, torch.pca_lowrank)

        # sparse input
        for guess_rank, size in [
                (4, (17, 4)), (4, (4, 17)), (16, (17, 17)),
                (21, (100, 40)), (20, (40, 100)), (600, (1000, 1000))]:
            for density in [0.005, 0.1]:
                run_subtest(guess_rank, None, size, (), device, torch.pca_lowrank, density=density)

        # jitting support
        jitted = torch.jit.script(torch.pca_lowrank)
        guess_rank, actual_rank, size, batches = 2, 2, (17, 4), ()
        run_subtest(guess_rank, actual_rank, size, batches, device, jitted)

    def test_lerp(self, device):
        start_end_shapes = [(), (5,), (5, 5), (5, 5, 5)]
        for shapes in product(start_end_shapes, start_end_shapes):
            start = torch.randn(shapes[0], device=device)
            end = torch.randn(shapes[1], device=device)

            # Tensor weights
            for weight in [torch.randn(shapes[0], device=device), random.random()]:
                actual = torch.lerp(start, end, weight)
                actual_method = start.lerp(end, weight)
                self.assertEqual(actual, actual_method)
                actual_out = torch.Tensor().to(device)
                torch.lerp(start, end, weight, out=actual_out)
                self.assertEqual(actual, actual_out)
                expected = start + weight * (end - start)
                self.assertEqual(expected, actual)

    def test_diagflat(self, device):
        dtype = torch.float32
        # Basic sanity test
        x = torch.randn((100,), dtype=dtype, device=device)
        result = torch.diagflat(x)
        expected = torch.diag(x)
        self.assertEqual(result, expected)

        # Test offset
        x = torch.randn((100,), dtype=dtype, device=device)
        result = torch.diagflat(x, 17)
        expected = torch.diag(x, 17)
        self.assertEqual(result, expected)

        # Test where input has more than one dimension
        x = torch.randn((2, 3, 4), dtype=dtype, device=device)
        result = torch.diagflat(x)
        expected = torch.diag(x.contiguous().view(-1))
        self.assertEqual(result, expected)

        # Noncontig input
        x = torch.randn((2, 3, 4), dtype=dtype, device=device).transpose(2, 0)
        self.assertFalse(x.is_contiguous())
        result = torch.diagflat(x)
        expected = torch.diag(x.contiguous().view(-1))
        self.assertEqual(result, expected)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_norm(self, device):
        # full reduction
        x = torch.randn(25, device=device)
        xn = x.cpu().numpy()
        for p in [0, 1, 2, 3, 4, inf, -inf]:
            res = x.norm(p).item()
            expected = np.linalg.norm(xn, p)
            self.assertEqual(res, expected, atol=1e-5, message="full reduction failed for {}-norm".format(p))

        # one dimension
        x = torch.randn(25, 25, device=device)
        xn = x.cpu().numpy()
        for p in [0, 1, 2, 3, 4, inf, -inf]:
            res = x.norm(p, 1).cpu().numpy()
            expected = np.linalg.norm(xn, p, 1)
            self.assertEqual(res.shape, expected.shape)
            self.assertTrue(np.allclose(res, expected), "dim reduction failed for {}-norm".format(p))

        # matrix norm
        for p in ['fro', 'nuc']:
            res = x.norm(p).cpu().numpy()
            expected = np.linalg.norm(xn, p)
            self.assertEqual(res.shape, expected.shape)
            self.assertTrue(np.allclose(res, expected), "dim reduction failed for {}-norm".format(p))

        # larger tensor sanity check
        self.assertEqual(2 * torch.norm(torch.ones(10000)), torch.norm(torch.ones(40000)))

    @skipCUDAIfNoMagma
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_nuclear_norm_axes_small_brute_force(self, device):
        def check_single_nuclear_norm(x, axes):
            if self.device_type != 'cpu' and randrange(100) < 95:
                return  # too many cpu <==> device copies

            a = np.array(x.cpu(), copy=False)
            expected = np.linalg.norm(a, "nuc", axis=axes)

            ans = torch.norm(x, "nuc", dim=axes)
            self.assertTrue(ans.is_contiguous())
            self.assertEqual(ans.shape, expected.shape)
            self.assertTrue(np.allclose(ans.cpu(), expected, rtol=1e-02, atol=1e-03, equal_nan=True))

            out = torch.zeros(expected.shape, dtype=x.dtype, device=x.device)
            ans = torch.norm(x, "nuc", dim=axes, out=out)
            self.assertIs(ans, out)
            self.assertTrue(ans.is_contiguous())
            self.assertEqual(ans.shape, expected.shape)
            self.assertTrue(np.allclose(ans.cpu(), expected, rtol=1e-02, atol=1e-03, equal_nan=True))

        for n in range(1, 3):
            for m in range(1, 3):
                for axes in permutations([0, 1], 2):
                    # 2d, inner dimensions C
                    x = torch.randn(n, m, device=device)
                    check_single_nuclear_norm(x, axes)

                    # 2d, inner dimensions Fortran
                    x = torch.randn(m, n, device=device).transpose(-1, -2)
                    check_single_nuclear_norm(x, axes)

                    # 2d, inner dimensions non-contiguous
                    x = torch.randn(n, 2 * m, device=device)[:, ::2]
                    check_single_nuclear_norm(x, axes)

                    # 2d, all dimensions non-contiguous
                    x = torch.randn(7 * n, 2 * m, device=device)[::7, ::2]
                    check_single_nuclear_norm(x, axes)

                for o in range(1, 3):
                    for axes in permutations([0, 1, 2], 2):
                        # 3d, inner dimensions C
                        x = torch.randn(o, n, m, device=device)
                        check_single_nuclear_norm(x, axes)

                        # 3d, inner dimensions Fortran
                        x = torch.randn(o, m, n, device=device).transpose(-1, -2)
                        check_single_nuclear_norm(x, axes)

                        # 3d, inner dimensions non-contiguous
                        x = torch.randn(o, n, 2 * m, device=device)[:, :, ::2]
                        check_single_nuclear_norm(x, axes)

                        # 3d, all dimensions non-contiguous
                        x = torch.randn(7 * o, 5 * n, 2 * m, device=device)[::7, ::5, ::2]
                        check_single_nuclear_norm(x, axes)

                    for r in range(1, 3):
                        for axes in permutations([0, 1, 2, 3], 2):
                            # 4d, inner dimensions C
                            x = torch.randn(r, o, n, m, device=device)
                            check_single_nuclear_norm(x, axes)

                            # 4d, inner dimensions Fortran
                            x = torch.randn(r, o, n, m, device=device).transpose(-1, -2)
                            check_single_nuclear_norm(x, axes)

                            # 4d, inner dimensions non-contiguous
                            x = torch.randn(r, o, n, 2 * m, device=device)[:, :, :, ::2]
                            check_single_nuclear_norm(x, axes)

                            # 4d, all dimensions non-contiguous
                            x = torch.randn(7 * r, 5 * o, 11 * n, 2 * m, device=device)[::7, ::5, ::11, ::2]
                            check_single_nuclear_norm(x, axes)

    @skipCUDAIfNoMagma
    def test_nuclear_norm_exceptions(self, device):
        for lst in [], [1], [1, 2]:
            for axes in (), (0,), (0, 1):
                x = torch.tensor(lst, dtype=torch.double, device=device)
                self.assertRaises(RuntimeError, torch.norm, x, "nuc", axes)

        x = torch.tensor([[0, 1, 2], [3, 4, 5]], dtype=torch.double, device=device)
        self.assertRaisesRegex(RuntimeError, "duplicate or invalid", torch.norm, x, "nuc", (0, 0))
        self.assertRaisesRegex(RuntimeError, "duplicate or invalid", torch.norm, x, "nuc", (0, 2))

    def test_dist(self, device):
        def run_test(x, y):
            for p in [0, 1, 2, 3, 4, inf, -inf]:
                dist_xy = torch.dist(x, y, p)
                dist_xy_norm = torch.norm(x - y, p)
                self.assertEqual(dist_xy, dist_xy_norm)

        run_test(torch.randn(5, device=device), torch.randn(5, device=device))

        x = torch.zeros(3, device=device)
        y = torch.zeros(3, device=device)
        y[1] = 1.
        run_test(x, y)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_geqrf(self, device):
        a = torch.randn(5, 5, device=device)
        b, c = torch.geqrf(a)
        b_placeholder, c_placeholder = torch.empty_like(b), torch.empty_like(c)
        torch.geqrf(a, out=(b_placeholder, c_placeholder))
        self.assertEqual(b, b_placeholder)
        self.assertEqual(c, c_placeholder)

    def triangular_solve_test_helper(self, A_dims, b_dims, upper, unitriangular,
                                     device, dtype):
        triangle_function = torch.triu if upper else torch.tril
        b = torch.randn(*b_dims, dtype=dtype, device=device)
        A = torch.randn(*A_dims, dtype=dtype, device=device)
        A_triangular = triangle_function(A)
        if unitriangular:
            A_triangular.diagonal(dim1=-2, dim2=-1).fill_(1.)
        return b, A_triangular

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_triangular_solve(self, device, dtype):
        for (k, n), (upper, unitriangular, transpose) in product(zip([2, 3, 5], [3, 5, 7]),
                                                                 product([True, False], repeat=3)):
            b, A = self.triangular_solve_test_helper((n, n), (n, k), upper,
                                                     unitriangular, device, dtype)
            x = torch.triangular_solve(b, A, upper=upper, unitriangular=unitriangular, transpose=transpose)[0]
            if transpose:
                self.assertLessEqual(b.dist(A.t().mm(x)), 4e-12)
            else:
                self.assertLessEqual(b.dist(A.mm(x)), 4e-12)

    @skipCPUIfNoLapack
    @skipCUDAIfNoMagma
    @dtypes(torch.double)
    def test_triangular_solve_batched(self, device, dtype):
        def triangular_solve_batch_helper(A_dims, b_dims, upper, unitriangular, transpose):
            b, A = self.triangular_solve_test_helper(A_dims, b_dims, upper,
                                                     unitriangular, device, dtype)
            x_exp_list = []
            for i in range(b_dims[0]):
                x_exp_list.append(torch.triangular_solve(b[i], A[i], upper=upper,
                                                         unitriangular=unitriangular,
                                                         transpose=transpose)[0])
            x_exp = torch.stack(x_exp_list)  # Stacked output
            x_act = torch.triangular_solve(b, A, upper=upper,
                                           unitriangular=unitriangular,
                                           transpose=transpose)[0]  # Actual output
            self.assertEqual(x_act, x_exp)  # Equality check
            if transpose:
                self.assertLessEqual(b.dist(torch.matmul(A.transpose(-2, -1), x_act)), 3e-12)  # Correctness check
            else:
                self.assertLessEqual(b.dist(torch.matmul(A, x_act)), 3e-12)  # Correctness check

        for (upper, unitriangular, transpose), batchsize in product(product([True, False], repeat=3), [1, 3, 4]):
            triangular_solve_batch_helper((batchsize, 5, 5), (batchsize, 5, 10),
                                          upper, unitriangular, transpose)


    @slowTest
    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_triangular_solve_batched_many_batches(self, device, dtype):
        for upper, transpose, unitriangular in product([True, False], repeat=3):
            b, A = self.triangular_solve_test_helper((256, 256, 5, 5), (5, 1),
                                                     upper, unitriangular, device, dtype)
            x, _ = torch.triangular_solve(b, A,
                                          upper=upper, transpose=transpose, unitriangular=unitriangular)
            if transpose:
                A = A.transpose(-2, -1)
            self.assertEqual(torch.matmul(A, x), b.expand(A.shape[:-2] + (5, 1)))

            b, A = self.triangular_solve_test_helper((3, 3), (512, 512, 3, 1),
                                                     upper, unitriangular, device, dtype)
            x, _ = torch.triangular_solve(b, A, upper=upper, transpose=transpose,
                                          unitriangular=unitriangular)
            if transpose:
                A = A.transpose(-2, -1)
            self.assertEqual(torch.matmul(A, x), b)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @unittest.skipIf(not TEST_SCIPY, "SciPy not found")
    @dtypes(torch.double)
    def test_triangular_solve_batched_broadcasting(self, device, dtype):
        from scipy.linalg import solve_triangular as tri_solve

        def scipy_tri_solve_batched(A, B, upper, trans, diag):
            batch_dims_A, batch_dims_B = A.shape[:-2], B.shape[:-2]
            single_dim_A, single_dim_B = A.shape[-2:], B.shape[-2:]
            expand_dims = tuple(torch._C._infer_size(torch.Size(batch_dims_A),
                                                     torch.Size(batch_dims_B)))
            expand_A = np.broadcast_to(A, expand_dims + single_dim_A)
            expand_B = np.broadcast_to(B, expand_dims + single_dim_B)
            flat_A = expand_A.reshape((-1,) + single_dim_A)
            flat_B = expand_B.reshape((-1,) + single_dim_B)
            flat_X = np.vstack([tri_solve(a, b, lower=(not upper), trans=int(trans), unit_diagonal=diag)
                                for a, b in zip(flat_A, flat_B)])
            return flat_X.reshape(expand_B.shape)

        def run_test(A_dims, b_dims, device, upper, transpose, unitriangular):
            b, A = self.triangular_solve_test_helper(A_dims, b_dims, upper,
                                                     unitriangular, device, dtype)
            x_exp = torch.as_tensor(scipy_tri_solve_batched(A.cpu().numpy(), b.cpu().numpy(),
                                                            upper, transpose, unitriangular))
            x = torch.triangular_solve(b, A, upper=upper, transpose=transpose, unitriangular=unitriangular)[0]

            self.assertEqual(x, x_exp.to(device))

        for upper, transpose, unitriangular in product([True, False], repeat=3):
            # test against scipy.linalg.solve_triangular
            run_test((2, 1, 3, 4, 4), (2, 1, 3, 4, 6), device, upper, transpose, unitriangular)  # no broadcasting
            run_test((2, 1, 3, 4, 4), (4, 6), device, upper, transpose, unitriangular)  # broadcasting b
            run_test((4, 4), (2, 1, 3, 4, 2), device, upper, transpose, unitriangular)  # broadcasting A
            run_test((1, 3, 1, 4, 4), (2, 1, 3, 4, 5), device, upper, transpose, unitriangular)  # broadcasting A & b

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_lstsq(self, device, dtype):
        def _test_underdetermined(a, b, expectedNorm):
            # underdetermined systems are only supported on CPU
            if self.device_type != 'cpu':
                return

            m = a.size()[0]
            n = a.size()[1]
            assert(m <= n)

            a_copy = a.clone()
            b_copy = b.clone()
            res1 = torch.lstsq(b, a)[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            self.assertEqual((torch.mm(a, res1) - b).norm(), expectedNorm, 1e-8)

            ta = torch.tensor((), dtype=dtype, device=device)
            tb = torch.tensor((), dtype=dtype, device=device)
            res2 = torch.lstsq(b, a, out=(tb, ta))[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            self.assertEqual((torch.mm(a, res1) - b).norm(), expectedNorm, 1e-8)

            res3 = torch.lstsq(b, a, out=(b, a))[0]
            self.assertEqual((torch.mm(a_copy, b) - b_copy).norm(), expectedNorm, 1e-8)
            self.assertEqual(res1, tb, 0)
            self.assertEqual(res1, b, 0)
            self.assertEqual(res1, res2, 0)
            self.assertEqual(res1, res3, 0)

        def _test_overdetermined(a, b, expectedNorm):
            m = a.size()[0]
            n = a.size()[1]
            assert(m > n)

            def check_norm(a, b, expected_norm, gels_result):
                # Checks |ax - b| and the residual info from the result

                # The first n rows is the least square solution.
                # Rows n to m-1 contain residual information.
                x = gels_result[:n]
                resid_info = gels_result[n:]

                resid_norm = (torch.mm(a, x) - b).norm()
                self.assertEqual(resid_norm, expectedNorm, 1e-8)
                self.assertEqual(resid_info.norm(), resid_norm, 1e-8)

            a_copy = a.clone()
            b_copy = b.clone()
            res1 = torch.lstsq(b, a)[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            check_norm(a, b, expectedNorm, res1)

            ta = torch.tensor((), dtype=dtype, device=device)
            tb = torch.tensor((), dtype=dtype, device=device)
            res2 = torch.lstsq(b, a, out=(tb, ta))[0]
            self.assertEqual(a, a_copy, 0)
            self.assertEqual(b, b_copy, 0)
            check_norm(a, b, expectedNorm, res2)

            res3 = torch.lstsq(b, a, out=(b, a))[0]
            check_norm(a_copy, b_copy, expectedNorm, res3)

            self.assertEqual(res1, tb, 0)
            self.assertEqual(res1, b, 0)
            self.assertEqual(res1, res2, 0)
            self.assertEqual(res1, res3, 0)

        # basic test
        expectedNorm = 0
        a = torch.tensor(((1.44, -9.96, -7.55, 8.34),
                          (-7.84, -0.28, 3.24, 8.09),
                          (-4.39, -3.24, 6.27, 5.28),
                          (4.53, 3.83, -6.64, 2.06)), dtype=dtype, device=device).t()
        b = torch.tensor(((8.58, 8.26, 8.48, -5.28),
                          (9.35, -4.43, -0.70, -0.26)), dtype=dtype, device=device).t()
        _test_underdetermined(a, b, expectedNorm)

        # test overdetermined
        expectedNorm = 17.390200628863
        a = torch.tensor(((1.44, -9.96, -7.55, 8.34, 7.08, -5.45),
                          (-7.84, -0.28, 3.24, 8.09, 2.52, -5.70),
                          (-4.39, -3.24, 6.27, 5.28, 0.74, -1.19),
                          (4.53, 3.83, -6.64, 2.06, -2.47, 4.70)), dtype=dtype, device=device).t()
        b = torch.tensor(((8.58, 8.26, 8.48, -5.28, 5.72, 8.93),
                          (9.35, -4.43, -0.70, -0.26, -7.36, -2.52)), dtype=dtype, device=device).t()
        _test_overdetermined(a, b, expectedNorm)

        # test underdetermined
        expectedNorm = 0
        a = torch.tensor(((1.44, -9.96, -7.55),
                          (-7.84, -0.28, 3.24),
                          (-4.39, -3.24, 6.27),
                          (4.53, 3.83, -6.64)), dtype=dtype, device=device).t()
        b = torch.tensor(((8.58, 8.26, 8.48),
                          (9.35, -4.43, -0.70)), dtype=dtype, device=device).t()
        _test_underdetermined(a, b, expectedNorm)

        # test reuse
        expectedNorm = 0
        a = torch.tensor(((1.44, -9.96, -7.55, 8.34),
                          (-7.84, -0.28, 3.24, 8.09),
                          (-4.39, -3.24, 6.27, 5.28),
                          (4.53, 3.83, -6.64, 2.06)), dtype=dtype, device=device).t()
        b = torch.tensor(((8.58, 8.26, 8.48, -5.28),
                          (9.35, -4.43, -0.70, -0.26)), dtype=dtype, device=device).t()
        ta = torch.tensor((), dtype=dtype, device=device)
        tb = torch.tensor((), dtype=dtype, device=device)
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)
        torch.lstsq(b, a, out=(tb, ta))
        self.assertEqual((torch.mm(a, tb) - b).norm(), expectedNorm, 1e-8)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_qr(self, device):
        def run_test(tensor_dims, some):
            A = torch.randn(*tensor_dims, device=device)
            Q, R = torch.qr(A, some=some)

            # Check0: Q[-2:] = (m, n_columns), R[-2:] = (n_columns, n)
            m, n = tensor_dims[-2:]
            n_columns = m if (not some) and m > n else min(m, n)
            self.assertEqual(Q.size(-2), m)
            self.assertEqual(R.size(-1), n)
            self.assertEqual(Q.size(-1), n_columns)

            # Check1: A = QR
            self.assertEqual(A, torch.matmul(Q, R))

            # Check2: A = QR (with out)
            Q_out, R_out = torch.Tensor().to(device), torch.Tensor().to(device)
            torch.qr(A, some=some, out=(Q_out, R_out))
            self.assertEqual(A, torch.matmul(Q_out, R_out))

            # Check3: Q == Q_out, R == R_out
            self.assertEqual(Q, Q_out)
            self.assertEqual(R, R_out)

            # Check4: Q^{T}Q = I, triu(R) = R
            self.assertEqual(torch.matmul(Q.transpose(-2, -1), Q),
                             torch.eye(n_columns, device=device).expand(Q.shape[:-2] + (n_columns, n_columns)))
            self.assertEqual(R.triu(), R)

        tensor_dims_list = [(3, 5), (5, 5), (5, 3),  # Single matrix
                            (7, 3, 5), (7, 5, 5), (7, 5, 3),  # 3-dim Tensors
                            (7, 5, 3, 5), (7, 5, 5, 5), (7, 5, 5, 3)]  # 4-dim Tensors
        for tensor_dims, some in product(tensor_dims_list, [True, False]):
            run_test(tensor_dims, some)

    @slowTest
    def test_randperm(self, device):
        if device == 'cpu':
            rng_device = None
        else:
            rng_device = [device]

        # Test core functionality. On CUDA, for small n, randperm is offloaded to CPU instead. For large n, randperm is
        # executed on GPU.
        for n in (100, 50000, 100000):
            # Ensure both integer and floating-point numbers are tested. Half follows an execution path that is
            # different from others on CUDA.
            for dtype in (torch.long, torch.half, torch.float):
                if n > 2049 and dtype == torch.half:  # Large n for torch.half will raise an exception, do not test here.
                    continue
                with torch.random.fork_rng(devices=rng_device):
                    res1 = torch.randperm(n, dtype=dtype, device=device)
                res2 = torch.empty(0, dtype=dtype, device=device)
                torch.randperm(n, out=res2, dtype=dtype, device=device)
                self.assertEqual(res1, res2, 0)

        # Default type is long
        for n in (100, 10000):
            self.assertEqual(torch.randperm(n, device=device).dtype, torch.long)

        # randperm of 0 elements is an empty tensor
        res1 = torch.randperm(0)
        res2 = torch.tensor(5, dtype=dtype, device=device)
        torch.randperm(0, out=res2)
        self.assertEqual(res1.numel(), 0)
        self.assertEqual(res2.numel(), 0)

        # Test exceptions when n is too large for a floating point type
        for dtype, small_n, large_n in ((torch.half, 2**11 + 1, 2**11 + 2),
                                        (torch.float, 2**24 + 1, 2**24 + 2),
                                        (torch.double, 2**25,  # 2**53 + 1 is too large to run
                                         2**53 + 2)):
            res = torch.empty(0, dtype=dtype, device=device)
            torch.randperm(small_n, out=res)  # No exception expected
            self.assertRaises(RuntimeError, lambda: torch.randperm(large_n, out=res, device=device))

        # Test non-contiguous tensors
        for n in (4, 5, 6, 10, 20):
            non_contiguous_tensor = torch.zeros((2, 3), dtype=torch.long, device=device).t()
            self.assertFalse(non_contiguous_tensor.is_contiguous())
            with torch.random.fork_rng(devices=rng_device):
                res = torch.randperm(n, dtype=torch.long, device=device)
            torch.randperm(n, out=non_contiguous_tensor)
            self.assertEqual(non_contiguous_tensor, res)

    def test_random_neg_values(self, device):
        signed_dtypes = [torch.double, torch.float, torch.long, torch.int, torch.short]
        for dtype in signed_dtypes:
            res = torch.rand(SIZE, SIZE).to(device=device, dtype=dtype)
            res.random_(-10, -1)
            self.assertLessEqual(res.max().item(), 9)
            self.assertGreaterEqual(res.min().item(), -10)

    @slowTest
    def test_triu_tril(self, device):
        def gen_mask(shape, diagonal, device, upper):
            mask = torch.zeros(*shape[-2:]).byte()
            for i in range(shape[-2]):
                for j in range(shape[-1]):
                    cond = j - i < diagonal if upper else j - i > diagonal
                    if cond:
                        mask[i, j] = 1
            return mask.expand(*shape).to(device)

        torch_functions = {True: torch.triu, False: torch.tril}
        if TEST_NUMPY:
            numpy_functions = {True: np.triu, False: np.tril}

        # TODO: remove this when bool and half are supported for torch.where
        def bool_half_compat_where(pred, true_tensor, false_tensor, dtype):
            if dtype == torch.bool or dtype == torch.half:
                return torch.where(pred.byte(), true_tensor.byte(), false_tensor.byte()).to(dtype=dtype)
            else:
                return torch.where(pred, true_tensor, false_tensor)

        def run_test(shape, device, diagonal, dtype):
            x = torch.empty(*shape, device=device, dtype=dtype).fill_(2)

            for upper in [True, False]:
                # normal test with mask
                torch_tri_func = torch_functions[upper]
                res1 = torch_tri_func(x, diagonal=diagonal)
                res2 = torch.empty(0, device=device, dtype=dtype)
                torch_tri_func(x, diagonal=diagonal, out=res2)
                exp_mask = gen_mask(shape, diagonal, device, upper)
                expected = bool_half_compat_where(exp_mask, torch.tensor(0).type_as(x), x, dtype)
                self.assertEqual(res1, res2, 0)
                self.assertEqual(expected, res1, 0)

                # non-contiguous and expanded tensors test
                if 0 not in shape:
                    for s in range(-len(shape), -1):
                        # non-contiguous tensors
                        x_nc = x.clone().transpose(s, s + 1)
                        exp_mask = gen_mask(x_nc.size(), diagonal, device, upper)
                        if 1 not in shape:
                            assert not x_nc.is_contiguous(), "x is intentionally non-contiguous"
                        exp_nc = bool_half_compat_where(exp_mask, torch.tensor(0).type_as(x), x_nc, dtype)
                        self.assertEqual(torch_tri_func(x_nc, diagonal), exp_nc, 0)
                        x_nc_is_contiguous = x_nc.is_contiguous()
                        if upper:
                            self.assertEqual(x_nc.triu_(diagonal), exp_nc, 0)
                        else:
                            self.assertEqual(x_nc.tril_(diagonal), exp_nc, 0)

                        self.assertTrue(x_nc.is_contiguous() == x_nc_is_contiguous,
                                        "contiguity of x_nc should not be changed")

                    # expanded tensors
                    expanded_size = (x.size(0),) + x.size()
                    x_expanded = x.clone().expand(*expanded_size)
                    if x.size(0) != 1:
                        assert 0 in x_expanded.stride(), "x intentionally has 0 in its stride"
                    output = torch_tri_func(x_expanded, diagonal)
                    self.assertEqual(output, expected.expand(expanded_size), 0)
                    if x.size(0) != 1:
                        self.assertTrue(0 in x_expanded.stride(),
                                        "geometry of x_expanded should be the same")
                    if upper:
                        self.assertEqual(output, x_expanded.triu_(diagonal), 0)
                    else:
                        self.assertEqual(output, x_expanded.tril_(diagonal), 0)

                if not TEST_NUMPY:
                    continue

                # numpy test
                numpy_tri_func = numpy_functions[upper]
                self.assertEqual(numpy_tri_func(x.to('cpu').numpy(), diagonal), res1.cpu().numpy())

        diagonals = [-2, -1, 0, 1, 2]
        shapes = [(3, 3), (5, 3, 3), (7, 5, 3, 3),  # square matrices
                  (7, 3), (5, 7, 3), (7, 5, 7, 3),  # fat matrices
                  (3, 7), (5, 3, 7), (7, 5, 3, 7),  # thin matrices
                  (3, 0), (0, 3, 3), (3, 3, 0, 0),  # no numel matrices
                  (3, 1), (5, 3, 1), (7, 5, 3, 1),  # very fat matrices
                  (1, 3), (5, 1, 3), (7, 5, 1, 3),  # very thin matrices
                  (1, 3, 3, 3), (3, 1, 3, 3, 3)]    # unsqueezed batch dimensions
        dtypes = [dtype for dtype in torch.testing.get_all_dtypes() if dtype != torch.bfloat16]
        for s, d, dtype in product(shapes, diagonals, dtypes):
            run_test(s, device, d, dtype)

    @skipCUDANonDefaultStreamIf(True)
    def test_multinomial_alias(self, device):
        # Get probs vector to use in setup
        def get_probs(length, is_contiguous):
            probs = torch.softmax(torch.randn(length), 0)
            if not is_contiguous:
                probs = torch.softmax(torch.randn(length, 2), 0)[:, 1]
            assert not (is_contiguous ^ probs.is_contiguous()), "contiguity requirement not met"
            return probs.to(device)

        for is_contiguous in [True, False]:
            probs = get_probs(4, is_contiguous)
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            for n_samples in [-1, 1, 10]:
                if n_samples > 0:
                    samples = torch._multinomial_alias_draw(prob_table, alias_table, n_samples)
                    self.assertEqual(prob_table.size(), torch.Size([4]), "size mismatch: probability table")
                    self.assertEqual(alias_table.size(), torch.Size([4]), "size mismatch: alias table")
                    self.assertEqual(samples.size(), torch.Size([n_samples]), "wrong number of samples")
                else:
                    with self.assertRaisesRegex(RuntimeError, "cannot sample <= 0 samples"):
                        torch._multinomial_alias_draw(prob_table, alias_table, n_samples)

            with self.assertRaisesRegex(RuntimeError, "expected 1-D"):
                probs = probs.view(2, 2)
                torch._multinomial_alias_setup(probs)

            with self.assertRaisesRegex(RuntimeError, "expected 1-D"):
                a_t, p_t = torch._multinomial_alias_setup(probs)
                torch._multinomial_alias_draw(p_t.view(2, 2), a_t.view(2, 2))

        MAX_SAMPLES = 200000
        for probs in [get_probs(4, True),
                      torch.tensor([0.8, 0.2], device=device),
                      torch.tensor([0.7, 0.2, 0.1], device=device)]:
            # Check how different the alias distribution and the original distribution are
            alias_dist = torch.zeros_like(probs)
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            alias_samples = torch._multinomial_alias_draw(prob_table, alias_table, MAX_SAMPLES)
            alias_dist = torch.unique(alias_samples, return_counts=True)[1].to(dtype=probs.dtype) / MAX_SAMPLES
            self.assertTrue(torch.allclose(alias_dist, probs, rtol=0.02, atol=0.0),
                            "Actual: {}\nExpected: {}".format(alias_dist, probs))

        for probs in [torch.tensor([0.2501, 0.25, 0.2499, 0.25], device=device),
                      torch.tensor([0.8, 0.199, 0.001], device=device),
                      torch.tensor([0.25001, 0.25, 0.24999, 0.25], device=device),
                      torch.tensor([0.33, 0.34, 0.33], device=device),
                      torch.tensor([0.8, 0.1999, 0.0001], device=device)]:
            # Check the difference between the original probabilities and the reconstructed
            # probabilities from the alias and probability tables output by _multinomial_alias_setup
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            actual = torch.zeros_like(probs)
            for i, vals in enumerate(zip(alias_table, prob_table)):
                idx, p = vals
                actual[i] += p
                actual[idx] += 1. - p
            actual = actual / len(probs)
            self.assertEqual(actual, probs, 1e-6)

        # Some special cases
        test_cases = [torch.tensor([1.0, 0.0, 0.0], device=device), torch.tensor([0.0, 1.0], device=device)]
        for probs in test_cases:
            alias_table, prob_table = torch._multinomial_alias_setup(probs)
            alias_samples = torch._multinomial_alias_draw(prob_table, alias_table, MAX_SAMPLES)
            self.assertEqual(alias_samples.unique(), probs.nonzero().squeeze(-1))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lapack_empty(self, device):
        # FIXME: these are just a selection of LAPACK functions -- we need a general strategy here.
        # The LAPACK functions themselves generally do NOT work with zero sized dimensions, although
        # numpy/sci often has a direct wrapper (e.g. lu_factor) and a wrapper that "does the right thing"
        # (e.g. lu).  We often name our functions identically to the lapack function, so it will take work
        # to name / migrate-to better wrappers.
        def fn(torchfn, *args):
            return torchfn(*tuple(torch.randn(shape, device=device) if isinstance(shape, tuple) else shape
                                  for shape in args))

        # inverse, pinverse
        self.assertEqual((0, 0), fn(torch.inverse, (0, 0)).shape)
        self.assertEqual((5, 0), fn(torch.pinverse, (0, 5)).shape)
        self.assertEqual((0, 5), fn(torch.pinverse, (5, 0)).shape)
        self.assertEqual((0, 0), fn(torch.pinverse, (0, 0)).shape)

        # det, logdet, slogdet
        self.assertEqual(torch.tensor(1., device=device), fn(torch.det, (0, 0)))
        self.assertEqual(torch.tensor(0., device=device), fn(torch.logdet, (0, 0)))
        self.assertEqual((torch.tensor(1., device=device), torch.tensor(0., device=device)),
                         fn(torch.slogdet, (0, 0)))

        # eig, symeig
        evalues, evectors = fn(torch.eig, (0, 0), True)
        self.assertEqual([(0, 2), (0, 0)], [evalues.shape, evectors.shape])
        evalues, evectors = fn(torch.symeig, (0, 0), True)
        self.assertEqual([(0,), (0, 0)], [evalues.shape, evectors.shape])

        # qr
        q, r = fn(torch.qr, (3, 0), True)
        self.assertEqual([(3, 0), (0, 0)], [q.shape, r.shape])
        q, r = fn(torch.qr, (0, 3), True)
        self.assertEqual([(0, 0), (0, 3)], [q.shape, r.shape])
        q, r = fn(torch.qr, (3, 0), False)
        self.assertEqual([(3, 3), (3, 0)], [q.shape, r.shape])

        # lstsq
        self.assertRaises(RuntimeError, lambda: torch.lstsq(torch.randn(0, 0), torch.randn(0, 0)))
        self.assertRaises(RuntimeError, lambda: torch.lstsq(torch.randn(0,), torch.randn(0, 0)))

    def test_roll(self, device):
        numbers = torch.arange(1, 9, device=device)

        single_roll = numbers.roll(1, 0)
        expected = torch.tensor([8, 1, 2, 3, 4, 5, 6, 7], device=device)
        self.assertEqual(single_roll, expected, "{} did not equal expected result".format(single_roll))

        roll_backwards = numbers.roll(-2, 0)
        expected = torch.tensor([3, 4, 5, 6, 7, 8, 1, 2], device=device)
        self.assertEqual(roll_backwards, expected, "{} did not equal expected result".format(roll_backwards))

        data = numbers.view(2, 2, 2)
        rolled = data.roll(1, 0)
        expected = torch.tensor([5, 6, 7, 8, 1, 2, 3, 4], device=device).view(2, 2, 2)
        self.assertEqual(expected, rolled, "{} did not equal expected result: {}".format(rolled, expected))

        data = data.view(2, 4)
        # roll a loop until back where started
        loop_rolled = data.roll(2, 0).roll(4, 1)
        self.assertEqual(data, loop_rolled, "{} did not equal the original: {}".format(loop_rolled, data))
        # multiple inverse loops
        self.assertEqual(data, data.roll(-20, 0).roll(-40, 1))
        self.assertEqual(torch.tensor([8, 1, 2, 3, 4, 5, 6, 7], device=device), numbers.roll(1, 0))

        # test non-contiguous
        # strided equivalent to numbers.as_strided(size=(4, 2), stride=(1, 4))
        strided = numbers.view(2, 4).transpose(0, 1)
        self.assertFalse(strided.is_contiguous(), "this test needs a non-contiguous tensor")
        expected = torch.tensor([4, 8, 1, 5, 2, 6, 3, 7]).view(4, 2)
        rolled = strided.roll(1, 0)
        self.assertEqual(expected, rolled,
                         "non contiguous tensor rolled to {} instead of {} ".format(rolled, expected))

        # test roll with no dimension specified
        expected = numbers.roll(1, 0).view(2, 4)
        self.assertEqual(expected, data.roll(1), "roll with no dims should flatten and roll.")
        self.assertEqual(expected, data.roll(1, dims=None), "roll with no dims should flatten and roll.")

        # test roll over multiple dimensions
        expected = torch.tensor([[7, 8, 5, 6], [3, 4, 1, 2]], device=device)
        double_rolled = data.roll(shifts=(2, -1), dims=(1, 0))
        self.assertEqual(double_rolled, expected,
                         "should be able to roll over two dimensions, got {}".format(double_rolled))

        self.assertRaisesRegex(RuntimeError, "required", lambda: data.roll(shifts=(), dims=()))
        self.assertRaisesRegex(RuntimeError, "required", lambda: data.roll(shifts=(), dims=1))
        # shifts/dims should align
        self.assertRaisesRegex(RuntimeError, "align", lambda: data.roll(shifts=(1, 2), dims=(1,)))
        self.assertRaisesRegex(RuntimeError, "align", lambda: data.roll(shifts=(1,), dims=(1, 2)))

        # test bool tensor
        t = torch.zeros(6, dtype=torch.bool, device=device)
        t[0] = True
        t[3] = True
        self.assertEqual(torch.tensor([False, True, False, False, True, False]), t.roll(1, 0))

    def test_nonzero_empty(self, device):
        def assert_tuple_empty(tup, dim):
            self.assertEqual(dim, len(tup))
            for t in tup:
                self.assertEqual(torch.Size([0]), t.shape)

        x = torch.randn(0, 2, 0, 5, 0, device=device)
        y = torch.nonzero(x)
        z = torch.nonzero(x, as_tuple=True)

        self.assertEqual(0, y.numel())
        self.assertEqual(torch.Size([0, 5]), y.shape)
        assert_tuple_empty(z, 5)

        x = torch.tensor(0.5, device=device)
        y = torch.nonzero(x)
        # nonzero with as_tuple returns a
        # tuple of len 1 for a zero-dim tensor.
        # This is done to match Numpy behavior.
        z = torch.nonzero(x, as_tuple=True)
        self.assertEqual(1, len(z))
        self.assertEqual(torch.zeros(1, dtype=torch.long), z[0])

        x = torch.zeros((), device=device)
        y = torch.nonzero(x)
        z = torch.nonzero(x, as_tuple=True)
        self.assertEqual(torch.Size([0, 0]), y.shape)
        self.assertEqual(1, len(z))
        self.assertEqual(torch.empty(0, dtype=torch.long), z[0])

    # TODO: add torch.complex64, torch.complex128
    @dtypes(torch.float, torch.double)
    def test_normal(self, device, dtype):

        def helper(self, device, dtype, ptype, t_transform, std_transform):
            q = torch.empty(100, 100, dtype=dtype, device=device)

            q.normal_()
            self.assertEqual(t_transform(q).mean(), 0, 0.2)
            self.assertEqual(t_transform(q).std(), std_transform(1), 0.2)

            q.normal_(2, 3)
            self.assertEqual(t_transform(q).mean(), 2, 0.3)
            self.assertEqual(t_transform(q).std(), std_transform(3), 0.3)

            q = torch.empty(100, 100, dtype=dtype, device=device)
            q_row1 = q[0:1].clone()
            q[99:100].normal_()
            self.assertEqual(t_transform(q[99:100]).mean(), 0, 0.2)
            self.assertEqual(t_transform(q[99:100]).std(), std_transform(1), 0.2)
            self.assertEqual(t_transform(q[0:1]).clone(), t_transform(q_row1))

            mean = torch.empty(100, 100, dtype=dtype, device=device)
            mean[:50].fill_(ptype(0))
            mean[50:].fill_(ptype(1))

            std = torch.empty(100, 100, dtype=torch.float, device=device)
            std[:, :50] = 4
            std[:, 50:] = 1

            r = torch.normal(mean)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r[:50]).mean(), 0, 0.2)
            self.assertEqual(t_transform(r[50:]).mean(), 1, 0.2)
            self.assertEqual(t_transform(r).std(), std_transform(1), 0.2)

            r.fill_(42)
            r = torch.normal(mean, 3)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r[:50]).mean(), 0, 0.2)
            self.assertEqual(t_transform(r[50:]).mean(), 1, 0.2)
            self.assertEqual(t_transform(r).std(), std_transform(3), 0.2)

            r.fill_(42)
            torch.normal(mean, 3, out=r)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r[:50]).mean(), 0, 0.2)
            self.assertEqual(t_transform(r[50:]).mean(), 1, 0.2)
            self.assertEqual(t_transform(r).std(), std_transform(3), 0.2)

            r.fill_(42)
            r = torch.normal(2, std)
            self.assertFalse(r.dtype.is_complex)
            self.assertEqual(str(r.device), device)
            self.assertEqual(r.mean(), 2, 0.2)
            self.assertEqual(r[:, :50].std(), 4, 0.3)
            self.assertEqual(r[:, 50:].std(), 1, 0.2)

            r.fill_(42)
            torch.normal(2, std, out=r)
            self.assertFalse(r.dtype.is_complex)
            self.assertEqual(str(r.device), device)
            self.assertEqual(r.mean(), 2, 0.2)
            self.assertEqual(r[:, :50].std(), 4, 0.3)
            self.assertEqual(r[:, 50:].std(), 1, 0.2)

            r.fill_(42)
            r = torch.normal(mean, std)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r[:50]).mean(), 0, 0.2)
            self.assertEqual(t_transform(r[50:]).mean(), 1, 0.2)
            self.assertEqual(t_transform(r[:, :50]).std(), std_transform(4), 0.3)
            self.assertEqual(t_transform(r[:, 50:]).std(), std_transform(1), 0.2)

            r.fill_(42)
            torch.normal(mean, std, out=r)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r[:50]).mean(), 0, 0.2)
            self.assertEqual(t_transform(r[50:]).mean(), 1, 0.2)
            self.assertEqual(t_transform(r[:, :50]).std(), std_transform(4), 0.3)
            self.assertEqual(t_transform(r[:, 50:]).std(), std_transform(1), 0.2)

            r.fill_(42)
            r = torch.normal(2, 3, (100, 100), dtype=dtype, device=device)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r).mean(), 2, 0.3)
            self.assertEqual(t_transform(r).std(), std_transform(3), 0.3)

            r.fill_(42)
            torch.normal(2, 3, (100, 100), dtype=dtype, device=device, out=r)
            self.assertEqual(r.dtype, dtype)
            self.assertEqual(str(r.device), device)
            self.assertEqual(t_transform(r).mean(), 2, 0.3)
            self.assertEqual(t_transform(r).std(), std_transform(3), 0.3)

        if dtype.is_complex:
            helper(self, device, dtype, lambda x: complex(x, x),
                   lambda t: torch.real(t).to(torch.float), lambda mean: mean / math.sqrt(2))
            helper(self, device, dtype, lambda x: complex(x, x),
                   lambda t: torch.imag(t).to(torch.float), lambda mean: mean / math.sqrt(2))
            self.assertRaisesRegex(
                RuntimeError, "normal expects standard deviation to be non-complex",
                lambda: torch.normal(0, torch.empty(100, 100, dtype=dtype, device=device)))
            out = torch.empty(100, 100, dtype=dtype, device=device)
            self.assertRaisesRegex(
                RuntimeError, "normal expects standard deviation to be non-complex",
                lambda: torch.normal(0, torch.empty(100, 100, dtype=dtype, device=device), out=out))
        else:
            helper(self, device, dtype, lambda x: x, lambda t: t, lambda mean: mean)

    @dtypes(torch.float, torch.double)
    @dtypesIfCUDA(torch.float, torch.double, torch.half, torch.bfloat16)
    def test_uniform_from_to(self, device, dtype):
        # TODO: https://github.com/pytorch/pytorch/issues/33793
        if IS_WINDOWS and device.startswith('cuda') and dtype == torch.bfloat16:
            raise unittest.SkipTest("Crashes with CUDA error: unspecified launch failure")

        size = 2000
        alpha = 0.1

        float_min = torch.finfo(torch.float).min
        float_max = torch.finfo(torch.float).max
        double_min = torch.finfo(torch.double).min
        double_max = torch.finfo(torch.double).max

        if dtype == torch.bfloat16:
            min_val = -3.389531389251535e+38
            max_val = 3.389531389251535e+38
        else:
            min_val = torch.finfo(dtype).min
            max_val = torch.finfo(dtype).max

        values = [double_min, float_min, -42, 0, 42, float_max, double_max]

        for from_ in values:
            for to_ in values:
                t = torch.empty(size, dtype=dtype, device=device)
                if not (min_val <= from_ <= max_val) or not (min_val <= to_ <= max_val):
                    pass
                elif to_ < from_:
                    self.assertRaisesRegex(
                        RuntimeError,
                        "uniform_ expects to return",
                        lambda: t.uniform_(from_, to_)
                    )
                elif to_ - from_ > max_val:
                    self.assertRaisesRegex(
                        RuntimeError,
                        "uniform_ expects to-from",
                        lambda: t.uniform_(from_, to_)
                    )
                else:
                    t.uniform_(from_, to_)
                    range_ = to_ - from_
                    if not (dtype == torch.bfloat16) and not (
                            dtype == torch.half and device == 'cpu') and not torch.isnan(t).all():
                        delta = alpha * range_
                        double_t = t.to(torch.double)
                        if range_ == 0:
                            self.assertTrue(double_t.min() == from_)
                            self.assertTrue(double_t.max() == to_)
                        elif dtype == torch.half:
                            self.assertTrue(from_ <= double_t.min() <= (from_ + delta))
                            self.assertTrue((to_ - delta) <= double_t.max() <= to_)
                        else:
                            self.assertTrue(from_ <= double_t.min() <= (from_ + delta))
                            self.assertTrue((to_ - delta) <= double_t.max() < to_)

    @dtypes(torch.float, torch.double, torch.complex64, torch.complex128)
    def test_randn(self, device, dtype):
        for size in [0, SIZE]:
            torch.manual_seed(123456)
            res1 = torch.randn(size, size, dtype=dtype, device=device)
            res2 = torch.tensor([], dtype=dtype, device=device)
            torch.manual_seed(123456)
            torch.randn(size, size, out=res2)
            self.assertEqual(res1, res2)

    @dtypes(torch.float, torch.double, torch.complex64, torch.complex128)
    def test_rand(self, device, dtype):
        for size in [0, SIZE]:
            torch.manual_seed(123456)
            res1 = torch.rand(size, size, dtype=dtype, device=device)
            res2 = torch.tensor([], dtype=dtype, device=device)
            torch.manual_seed(123456)
            torch.rand(size, size, out=res2)
            self.assertEqual(res1, res2)

    @dtypes(torch.float, torch.double)
    def test_log_normal(self, device, dtype):
        a = torch.tensor([10], dtype=dtype, device=device).log_normal_()
        self.assertEqual(a.dtype, dtype)
        self.assertEqual(a.size(), torch.Size([1]))

    @dtypes(torch.float, torch.double)
    def test_geometric(self, device, dtype):
        a = torch.tensor([10], dtype=dtype, device=device).geometric_(0.5)
        self.assertEqual(a.dtype, dtype)
        self.assertEqual(a.size(), torch.Size([1]))

    @dtypes(torch.float, torch.double)
    def test_exponential(self, device, dtype):
        a = torch.tensor([10], dtype=dtype, device=device).exponential_(0.5)
        self.assertEqual(a.dtype, dtype)
        self.assertEqual(a.size(), torch.Size([1]))

        # Tests extremal behavior
        tests = ((-0, float('inf')), (0, float('inf')), (float('inf'), 0))
        for test in tests:
            t = torch.empty((1,), device=device, dtype=dtype).exponential_(test[0])
            self.assertTrue(t.item() == test[1])

        # Tests that negative lambda fails
        with self.assertRaises(RuntimeError):
            torch.empty((1,), device=device, dtype=dtype).exponential_(-0.5)

    def test_empty_strided(self, device):
        for shape in [(2, 3, 4), (0, 2, 0)]:
            # some of these cases are pretty strange, just verifying that if as_strided
            # allows them then empty_strided can as well.
            for strides in [(12, 4, 1), (2, 4, 6), (0, 0, 0)]:
                empty_strided = torch.empty_strided(shape, strides, device=device)
                # as_strided checks the storage size is big enough to support such a strided tensor;
                # instead of repeating this calculation, we just use empty_strided which does the same
                # calculation when setting the storage size.
                as_strided = torch.empty(empty_strided.storage().size(),
                                         device=device).as_strided(shape, strides)
                self.assertEqual(empty_strided.shape, as_strided.shape)
                self.assertEqual(empty_strided.stride(), as_strided.stride())

    def test_sign(self, device):
        for dtype in torch.testing.get_all_math_dtypes(device):
            if dtype.is_complex:
                continue

            # Include NaN for floating point numbers
            if dtype.is_floating_point:
                dt_info = torch.finfo(dtype)

                # Create tensor (with NaN checking)
                a = torch.tensor([float('nan'), -12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                a_target = torch.tensor([0, -1, 0, 1, -1, 1], device=device, dtype=dtype)

            else:
                dt_info = torch.iinfo(dtype)

                # If unsigned type, everything should be >= 0
                if dt_info.min == 0:
                    a = torch.tensor([12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                    a_target = torch.tensor([1, 0, 1, 0, 1], device=device, dtype=dtype)
                else:
                    a = torch.tensor([-12, 0, 71, dt_info.min, dt_info.max], device=device, dtype=dtype)
                    a_target = torch.tensor([-1, 0, 1, -1, 1], device=device, dtype=dtype)

            self.assertEqual(a.sign(), a_target, 'sign device={} dtype={}'.format(device, dtype))
            self.assertEqual(torch.sign(a), a_target, 'sign device={} dtype={}'.format(device, dtype))

            out = torch.empty_like(a)
            torch.sign(a, out=out)
            self.assertEqual(out, a_target, 'sign_out device={} dtype={}'.format(device, dtype))

            a.sign_()
            self.assertEqual(a, a_target, 'sign_ device={} dtype={}'.format(device, dtype))

        # Include test for bool dtype
        a_bool = torch.tensor([True, True, False, float('nan')], device=device).bool()
        a_bool_target = torch.tensor([True, True, False, True], device=device).bool()
        self.assertEqual(a_bool.sign(), a_bool_target, 'sign device={} dtype=bool'.format(device))
        self.assertEqual(torch.sign(a_bool), a_bool_target, 'sign device={} dtype=bool'.format(device))

        a_out = torch.empty_like(a_bool)
        torch.sign(a_bool, out=a_out)
        self.assertEqual(a_out, a_bool_target, 'sign_out device={} dtype=bool'.format(device))

        a_bool.sign_()
        self.assertEqual(a_bool, a_bool_target, 'sign_ device={} dtype=bool'.format(device))

    def test_logical_any(self, device):
        x = torch.zeros([2, 3, 400], dtype=torch.uint8, device=device)

        self.assertEqual(
            torch.tensor(0, dtype=torch.uint8, device=device),
            x.any())

        self.assertEqual(
            torch.zeros([1, 3, 400], dtype=torch.uint8, device=device),
            x.any(0, keepdim=True))

        self.assertEqual(
            torch.zeros([2, 1, 400], dtype=torch.uint8, device=device),
            x.any(1, keepdim=True))

        self.assertEqual(
            torch.zeros([2, 3, 1], dtype=torch.uint8, device=device),
            x.any(2, keepdim=True))

        # set the last element to 0
        x[-1][-1][-1] = 1

        self.assertEqual(
            torch.tensor(1, dtype=torch.uint8, device=device),
            x.any())

        y = torch.zeros([1, 3, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(0, keepdim=True))

        y = torch.zeros([2, 1, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(1, keepdim=True))

        y = torch.zeros([2, 3, 1], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 1
        self.assertEqual(y, x.any(2, keepdim=True))

    def test_logical_all(self, device):
        x = torch.ones([2, 3, 400], dtype=torch.uint8, device=device)

        self.assertEqual(
            torch.tensor(1, dtype=torch.uint8, device=device),
            x.all())

        self.assertEqual(
            torch.ones([1, 3, 400], dtype=torch.uint8, device=device),
            x.all(0, keepdim=True))

        self.assertEqual(
            torch.ones([2, 1, 400], dtype=torch.uint8, device=device),
            x.all(1, keepdim=True))

        self.assertEqual(
            torch.ones([2, 3, 1], dtype=torch.uint8, device=device),
            x.all(2, keepdim=True))

        # set the last element to 0
        x[-1][-1][-1] = 0

        self.assertEqual(
            torch.tensor(0, dtype=torch.uint8, device=device),
            x.all())

        y = torch.ones([1, 3, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(0, keepdim=True))

        y = torch.ones([2, 1, 400], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(1, keepdim=True))

        y = torch.ones([2, 3, 1], dtype=torch.uint8, device=device)
        y[-1][-1][-1] = 0
        self.assertEqual(y, x.all(2, keepdim=True))

    def test_pairwise_distance_empty(self, device):
        shape = (2, 0)
        x = torch.randn(shape, device=device)
        y = torch.randn(shape, device=device)

        self.assertEqual(torch.zeros(2, device=device), torch.pairwise_distance(x, y))
        self.assertEqual(torch.zeros((2, 1), device=device), torch.pairwise_distance(x, y, keepdim=True))

        shape = (0, 2)
        x = torch.randn(shape, device=device)
        y = torch.randn(shape, device=device)
        self.assertEqual(torch.zeros(0, device=device), torch.pairwise_distance(x, y))
        self.assertEqual(torch.zeros((0, 1), device=device), torch.pairwise_distance(x, y, keepdim=True))

    def test_pdist_empty(self, device):
        shape = (0, 2)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.empty(0, device=device), torch.pdist(x))

        shape = (1, 2)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.empty(0, device=device), torch.pdist(x))

        shape = (3, 0)
        x = torch.randn(shape, device=device)
        self.assertEqual(torch.zeros(3, device=device), torch.pdist(x))

    def test_cdist_empty(self, device):
        x = torch.randn((0, 5), device=device)
        y = torch.randn((4, 5), device=device)
        self.assertEqual(torch.empty(0, 4, device=device), torch.cdist(x, y))

        x = torch.randn((2, 5), device=device)
        y = torch.randn((0, 5), device=device)
        self.assertEqual(torch.empty(2, 0, device=device), torch.cdist(x, y))

        x = torch.randn((2, 0), device=device)
        y = torch.randn((3, 0), device=device)
        self.assertEqual(torch.zeros(2, 3, device=device), torch.cdist(x, y))

        x = torch.randn((2, 0), device=device)
        y = torch.randn((0, 0), device=device)
        self.assertEqual(torch.empty(2, 0, device=device), torch.cdist(x, y))

    def _brute_cdist(self, x, y, p=2):
        r1 = x.shape[-2]
        r2 = y.shape[-2]
        if r1 == 0 or r2 == 0:
            return torch.empty(r1, r2, device=x.device)
        return torch.norm(x[..., None, :] - y[..., None, :, :], p=p, dim=-1)

    def test_cdist_norm(self, device):
        for r1 in [3, 4, 5, 6]:
            for m in [2, 3, 4, 10]:
                for r2 in [4, 6, 7, 8]:
                    for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                        x = torch.randn(r1, m, device=device)
                        y = torch.randn(r2, m, device=device)
                        if p == 2:
                            for cm in ['use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
                                actual = torch.cdist(x, y, p=2, compute_mode=cm)
                                expected = self._brute_cdist(x, y, p=2)
                                self.assertTrue(torch.allclose(expected, actual, rtol=0, atol=0.02))
                        else:
                            actual = torch.cdist(x, y, p=p)
                            expected = self._brute_cdist(x, y, p=p)
                            self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_norm_batch(self, device):
        for r1 in [3, 4, 5, 6]:
            for m in [2, 3, 4, 10]:
                for r2 in [4, 6, 7, 8]:
                    for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                        x = torch.randn(2, 3, 6, r1, m, device=device)
                        y = torch.randn(2, 3, 6, r2, m, device=device)
                        if p == 2:
                            for cm in ['use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
                                actual = torch.cdist(x, y, p=2, compute_mode=cm)
                                expected = self._brute_cdist(x, y, p=2)
                                self.assertTrue(torch.allclose(expected, actual, rtol=0, atol=0.02))
                        else:
                            actual = torch.cdist(x, y, p=p)
                            expected = self._brute_cdist(x, y, p=p)
                            self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_large(self, device):
        for cm in ['use_mm_for_euclid_dist_if_necessary', 'use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
            x = torch.randn(1000, 10, device=device)
            y = torch.randn(1000, 10, device=device)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertTrue(torch.allclose(expected, actual))

    @slowTest
    def test_cdist_large_batch(self, device):
        for cm in ['use_mm_for_euclid_dist_if_necessary', 'use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
            x = torch.randn(4, 3, 1000, 10, device=device)
            y = torch.randn(4, 3, 1000, 10, device=device)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_non_contiguous(self, device):
        for cm in ['use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
            x = torch.randn(5, 7, device=device).transpose(-1, -2)
            y = torch.randn(5, 3, device=device).transpose(-1, -2)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertFalse(x.is_contiguous())
            self.assertFalse(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

            x = torch.randn(7, 5, device=device)
            y = torch.randn(5, 3, device=device).t()
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertTrue(x.is_contiguous())
            self.assertFalse(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

            x = torch.randn(5, 7, device=device).t()
            y = torch.randn(3, 5, device=device)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertFalse(x.is_contiguous())
            self.assertTrue(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

    def test_cdist_non_contiguous_batch(self, device):
        for cm in ['use_mm_for_euclid_dist', 'donot_use_mm_for_euclid_dist']:
            x = torch.randn(4, 3, 2, 5, 7, device=device).transpose(-1, -2)
            y = torch.randn(4, 3, 2, 5, 3, device=device).transpose(-1, -2)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertFalse(x.is_contiguous())
            self.assertFalse(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

            x = torch.randn(7, 2, 7, 5, device=device)
            y = torch.randn(7, 2, 5, 3, device=device).transpose(-1, -2)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertTrue(x.is_contiguous())
            self.assertFalse(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

            x = torch.randn(4, 5, 7, device=device).transpose(-1, -2)
            y = torch.randn(4, 3, 5, device=device)
            actual = torch.cdist(x, y, p=2, compute_mode=cm)
            expected = self._brute_cdist(x, y, p=2)
            self.assertFalse(x.is_contiguous())
            self.assertTrue(y.is_contiguous())
            self.assertTrue(torch.allclose(expected, actual))

    def test_multinomial_constraints(self, device):
        x = torch.empty(1, 2, 3, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "prob_dist must be 1 or 2 dim",
            lambda: torch.multinomial(x, 2))
        x = torch.empty(1, 2, dtype=torch.long, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial only supports floating-point dtypes for input",
            lambda: torch.multinomial(x, 2))
        x = torch.empty(1, 2, dtype=torch.double, device=device)
        y = torch.empty(1, 2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial expects Long tensor out",
            lambda: torch.multinomial(x, 2, out=y))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample <= 0 samples",
            lambda: torch.multinomial(x, 0))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample <= 0 samples",
            lambda: torch.multinomial(x, -1))
        x = torch.empty(2, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "cannot sample n_sample > prob_dist",
            lambda: torch.multinomial(x, 3, False))
        x = torch.empty(16777217, dtype=torch.double, device=device)
        self.assertRaisesRegex(
            RuntimeError, "number of categories cannot exceed",
            lambda: torch.multinomial(x, 3))

    def test_add(self, device):
        dtypes = [torch.float, torch.double] + torch.testing.get_all_complex_dtypes()
        for dtype in dtypes:
            # [res] torch.add([res,] tensor1, tensor2)
            m1 = torch.randn(100, 100, dtype=dtype, device=device)
            v1 = torch.randn(100, dtype=dtype, device=device)

            # contiguous
            res1 = torch.add(m1[4], v1)
            res2 = res1.clone().zero_()
            for i in range(m1.size(1)):
                res2[i] = m1[4, i] + v1[i]
            self.assertEqual(res1, res2)

            m1 = torch.randn(100, 100, device=device)
            v1 = torch.randn(100, device=device)

            # non-contiguous
            res1 = torch.add(m1[:, 4], v1)
            res2 = res1.clone().zero_()
            for i in range(m1.size(0)):
                res2[i] = m1[i, 4] + v1[i]
            self.assertEqual(res1, res2)

            # [res] torch.add([res,] tensor, value)
            m1 = torch.randn(10, 10, device=device)

            # contiguous
            res1 = m1.clone()
            res1[3].add_(2)
            res2 = m1.clone()
            for i in range(m1.size(1)):
                res2[3, i] = res2[3, i] + 2
            self.assertEqual(res1, res2)

            # non-contiguous
            m1 = torch.randn(10, 10, device=device)
            res1 = m1.clone()
            res1[:, 3].add_(2)
            res2 = m1.clone()
            for i in range(m1.size(0)):
                res2[i, 3] = res2[i, 3] + 2
            self.assertEqual(res1, res2)

            # inter-type
            m1 = torch.randn(10, 10, dtype=dtype, device=device)
            self.assertEqual(m1 + 3, m1 + torch.tensor(3))
            self.assertEqual(3 + m1, torch.tensor(3) + m1)

            # contiguous + non-contiguous
            m1 = torch.randn(10, 10, dtype=dtype, device=device)
            m2 = torch.randn(10, 10, dtype=dtype, device=device).t()
            res = m1 + m2
            self.assertTrue(res.is_contiguous())
            self.assertEqual(res, m1 + m2.contiguous())

            # 1d + empty
            m1 = torch.tensor([1.0], dtype=dtype, device=device)
            m2 = torch.tensor([], dtype=dtype, device=device)
            self.assertEqual(m1 + m2, [])

        # inter-type unint8
        one = torch.tensor(1, dtype=torch.uint8, device=device)
        self.assertEqual(torch.add(one, 1), 2)
        self.assertEqual(torch.add(one, 1).dtype, torch.uint8)

        # bool
        m1 = torch.tensor([True, False, False, True, False, False], dtype=torch.bool, device=device)
        m2 = torch.tensor([True, True, False, False, False, True], dtype=torch.bool, device=device)
        expected = torch.tensor([True, True, False, True, False, True], dtype=torch.bool, device=device)
        self.assertEqual(m1 + m2, expected)

        # fused multiply add
        a = torch.zeros(2, 3, dtype=torch.bool, device=device)
        res = torch.add(a, a, alpha=0)
        expected = torch.zeros(2, 3, device=device).bool()
        self.assertEqual(res, expected)

        # bfloat16
        m1 = torch.tensor([1., 2.], dtype=torch.bfloat16)
        m2 = torch.tensor([3., 4.], dtype=torch.bfloat16)
        self.assertEqual(m1 + m2, torch.tensor([4., 6.], dtype=torch.bfloat16))

        # mismatched alpha
        m1 = torch.tensor([1], dtype=torch.int8, device=device)
        m2 = torch.tensor([2], dtype=torch.int8, device=device)
        self.assertRaisesRegex(RuntimeError,
                               r"Boolean alpha only supported for Boolean results\.",
                               lambda: torch.add(m1, m2, alpha=True))
        self.assertRaisesRegex(RuntimeError,
                               r"For integral input tensors, argument alpha must not be a floating point number\.",
                               lambda: torch.add(m1, m2, alpha=1.0))

        # complex
        m1 = torch.tensor((4.0000 + 4.0000j), dtype=torch.complex64)
        m2 = torch.tensor(4., dtype=torch.float64)
        self.assertRaisesRegex(RuntimeError, r"result type ComplexDouble can't be cast to the desired output type Double",
                               lambda: torch.add(m1, m1, out=m2))


    def test_sub_typing(self, device):
        m1 = torch.tensor([True, False, False, True, False, False], dtype=torch.bool, device=device)
        m2 = torch.tensor([True, True, False, False, False, True], dtype=torch.bool, device=device)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with two bool tensors is not supported. "
                               r"Use the `\^` or `logical_xor\(\)` operator instead.",
                               lambda: m1 - m2)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with a bool tensor is not supported. "
                               r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
                               lambda: 1 - m1)
        self.assertRaisesRegex(RuntimeError,
                               r"Subtraction, the `\-` operator, with a bool tensor is not supported. "
                               r"If you are trying to invert a mask, use the `\~` or `logical_not\(\)` operator instead.",
                               lambda: m2 - 1)

        # mismatched alpha
        m1 = torch.tensor([1], dtype=torch.int8, device=device)
        m2 = torch.tensor([2], dtype=torch.int8, device=device)
        self.assertRaisesRegex(RuntimeError,
                               r"Boolean alpha only supported for Boolean results\.",
                               lambda: torch.sub(m1, m2, alpha=True))
        self.assertRaisesRegex(RuntimeError,
                               r"For integral input tensors, argument alpha must not be a floating point number\.",
                               lambda: torch.sub(m1, m2, alpha=1.0))

    def test_mul(self, device):
        m1 = torch.randn(10, 10, device=device)
        res1 = m1.clone()
        res1[:, 3].mul_(2)
        res2 = m1.clone()
        for i in range(res1.size(0)):
            res2[i, 3] = res2[i, 3] * 2
        self.assertEqual(res1, res2)

        a1 = torch.tensor([True, False, False, True], dtype=torch.bool, device=device)
        a2 = torch.tensor([True, False, True, False], dtype=torch.bool, device=device)
        self.assertEqual(a1 * a2, torch.tensor([True, False, False, False], dtype=torch.bool, device=device))

        if device == 'cpu':
            a1 = torch.tensor([0.1, 0.1], dtype=torch.bfloat16, device=device)
            a2 = torch.tensor([1.1, 0.1], dtype=torch.bfloat16, device=device)
            self.assertEqual(a1 * a2, torch.tensor([0.11, 0.01], dtype=torch.bfloat16, device=device), 0.01)
            self.assertEqual(a1.mul(a2), a1 * a2)

    def test_cumsum(self, device):
        x = torch.rand(100, 100, device=device)
        res1 = torch.cumsum(x, 1)
        res2 = torch.Tensor().to(device)
        torch.cumsum(x, 1, out=res2)
        self.assertEqual(res1, res2)

        a = torch.tensor([[True, False, True],
                          [False, False, False],
                          [True, True, True]], device=device)
        b = a.byte()
        aRes = torch.cumsum(a, 0)
        bRes = torch.cumsum(b, 0)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 1],
                                             [1, 0, 1],
                                             [2, 1, 2]]))

        aRes = torch.cumsum(a, 1)
        bRes = torch.cumsum(b, 1)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 1, 2],
                                             [0, 0, 0],
                                             [1, 2, 3]]))

        # Check that cummulative sum over a zero length dimension doesn't crash on backprop.
        # Also check that cumsum over other dimensions in a tensor with a zero-length
        # dimensiuon also works
        # Also include a basic suite of similar tests for other bases cases.
        shapes = [[2, 0], [2, 1, 4], [0, 2, 3], [1], [5]]
        for shape in shapes:
            for dim in range(len(shape)):
                raw_tensor = torch.zeros(*shape, requires_grad=True)
                integrated = raw_tensor.cumsum(dim=dim)
                # Check that backward does not crash
                integrated.sum().backward()
                # Check that output maintained correct shape
                self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

        # Check a scalar example
        raw_tensor = torch.tensor(3., requires_grad=True)
        integrated = raw_tensor.cumsum(dim=-1)
        self.assertEqual(raw_tensor, integrated)
        # Check that backward does not crash
        integrated.sum().backward()
        # Check that output maintained correct shape
        self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

    def test_cumprod(self, device):
        x = torch.rand(100, 100, device=device)
        res1 = torch.cumprod(x, 1)
        res2 = torch.Tensor().to(device)
        torch.cumprod(x, 1, out=res2)
        self.assertEqual(res1, res2)

        a = torch.tensor([[True, False, True],
                          [False, False, False],
                          [True, True, True]], dtype=torch.bool, device=device)
        b = a.byte()
        aRes = torch.cumprod(a, 0)
        bRes = torch.cumprod(b, 0)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 1],
                                             [0, 0, 0],
                                             [0, 0, 0]]))

        aRes = torch.cumprod(a, 1)
        bRes = torch.cumprod(b, 1)
        self.assertEqual(aRes, bRes)
        self.assertEqual(aRes, torch.tensor([[1, 0, 0],
                                             [0, 0, 0],
                                             [1, 1, 1]]))

        # Check that cummulative prod over a zero length dimension doesn't crash on backprop.
        # Also check that cumprod over other dimensions in a tensor with a zero-length
        # dimensiuon also works
        # Also include a basic suite of similar tests for other bases cases.
        shapes = [[2, 0], [2, 1, 4], [0, 2, 3], [1], [5]]
        for shape in shapes:
            for dim in range(len(shape)):
                raw_tensor = torch.zeros(*shape, requires_grad=True)
                integrated = raw_tensor.cumprod(dim=dim)
                # Check that backward does not crash
                integrated.sum().backward()
                # Check that output maintained correct shape
                self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

        # Check a scalar example
        raw_tensor = torch.tensor(3., requires_grad=True)
        integrated = raw_tensor.cumprod(dim=-1)
        self.assertEqual(raw_tensor, integrated)
        # Check that backward does not crash
        integrated.sum().backward()
        # Check that output maintained correct shape
        self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

    def test_cummax_cummin(self, device):
        def test_ops(op, string_of_function_name, expected_output1, expected_output2):
            x = torch.rand(100, 100, device=device)
            out1 = op(x, 1)
            res2 = torch.empty(0, device=device)
            indices2 = torch.empty(0, dtype=torch.int64, device=device)
            op(x, 1, out=(res2, indices2))
            self.assertEqual(out1[0], res2)
            self.assertEqual(out1[1], indices2)

            a = torch.tensor([[True, False, True],
                              [False, False, False],
                              [True, True, True]], dtype=torch.bool, device=device)
            b = a.byte()
            aRes = op(a, 0)
            bRes = op(b, 0)
            self.assertEqual(aRes[0], bRes[0].bool())
            self.assertEqual(aRes[0], expected_output1.bool())

            # test inf and nan input
            x = torch.tensor([4, inf, 1.5, -inf, 0, nan, 1])
            xRes = op(x, 0)[0]
            self.assertEqual(xRes, expected_output2, allow_inf=True)

            # op shouldn't support values, indices with a dtype, device type or layout
            # different from that of input tensor
            t = torch.randn(10)
            values = torch.empty(0, dtype=torch.int16)
            indices = torch.empty(0, dtype=torch.int64)
            with self.assertRaisesRegex(
                    RuntimeError,
                    'expected scalar_type Float but found Short'):
                op(t, 0, out=(values, indices))

            # Check that op over a zero length dimension doesn't crash on backprop.
            # Also check that op over other dimensions in a tensor with a zero-length
            # dimension also works
            # Also include a basic suite of similar tests for other bases cases.
            shapes = [[2, 0], [2, 1, 4], [0, 2, 3], [1], [5]]
            for shape in shapes:
                for dim in range(len(shape)):
                    raw_tensor = torch.zeros(*shape, requires_grad=True)
                    integrated = getattr(raw_tensor, string_of_function_name)(dim=dim)
                    # Check that backward does not crash
                    integrated[0].sum().backward()
                    # Check that output maintained correct shape
                    self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

            # Check a scalar example
            raw_tensor = torch.tensor(3., requires_grad=True)
            integrated = getattr(raw_tensor, string_of_function_name)(dim=-1)
            # Check that backward does not crash
            integrated[0].sum().backward()
            # Check that output maintained correct shape
            self.assertEqual(raw_tensor.shape, raw_tensor.grad.shape)

        expected_out = torch.tensor([4, inf, inf, inf, inf, nan, nan])
        test_ops(torch.cummax, "cummax", torch.tensor([[1, 0, 1],
                                                       [1, 0, 1],
                                                       [1, 1, 1]]), expected_out)

        expected_out = torch.tensor([4, 4, 1.5, -inf, -inf, nan, nan])
        test_ops(torch.cummin, "cummin", torch.tensor([[1, 0, 1],
                                                       [0, 0, 0],
                                                       [0, 0, 0]]), expected_out)

    def test_std_mean(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for dim in range(x.dim()):
            for unbiased in [False, True]:
                for keepdim in [False, True]:
                    std1, mean1 = torch.std_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                    std2 = x.std(dim=dim, unbiased=unbiased, keepdim=keepdim)
                    mean2 = x.mean(dim=dim, keepdim=keepdim)
                    self.assertEqual(std1, std2)
                    self.assertEqual(mean1, mean2)

    def test_std_mean_all_dims(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for unbiased in [False, True]:
            std1, mean1 = torch.std_mean(x, unbiased=unbiased)
            std2 = x.std(unbiased=unbiased)
            mean2 = x.mean()
            self.assertEqual(std1, std2)
            self.assertEqual(mean1, mean2)

    def test_var_mean(self, device):
        x = torch.rand(100, 300, 50, device=device)
        for dim in range(x.dim()):
            for unbiased in [False, True]:
                for keepdim in [False, True]:
                    var1, mean1 = torch.var_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                    var2 = x.var(dim=dim, unbiased=unbiased, keepdim=keepdim)
                    mean2 = x.mean(dim=dim, keepdim=keepdim)
                    self.assertEqual(var1, var2)
                    self.assertEqual(mean1, mean2)

    def test_var_mean_all_dims(self, device):
        x = torch.rand(100, 50, 20, device=device)
        for unbiased in [False, True]:
            var1, mean1 = torch.var_mean(x, unbiased=unbiased)
            var2 = x.var(unbiased=unbiased)
            mean2 = x.mean()
            self.assertEqual(var1, var2)
            self.assertEqual(mean1, mean2)

    def test_std_mean_some_dims(self, device):
        sizes = (4, 6, 7, 5, 3)
        dims = len(sizes)
        x = torch.rand(sizes, device=device)
        for num_of_dims in range(2, dims):
            dim_list = list(combinations(list(range(dims)), r=num_of_dims))
            for dim in dim_list:
                for unbiased in [False, True]:
                    for keepdim in [False, True]:
                        std1, mean1 = torch.std_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                        std2 = x.std(dim=dim, unbiased=unbiased, keepdim=keepdim)
                        mean2 = x.mean(dim=dim, keepdim=keepdim)
                        self.assertEqual(std1, std2)
                        self.assertEqual(mean1, mean2)

    def test_zeros_like(self, device):
        expected = torch.zeros((100, 100,), device=device)

        res1 = torch.zeros_like(expected)
        self.assertEqual(res1, expected)

    def test_histc(self, device):
        # negative nbins throws
        with self.assertRaisesRegex(RuntimeError, 'bins must be > 0'):
            torch.histc(torch.tensor([1], dtype=torch.float, device=device), bins=-1)

        # without nbins
        actual = torch.histc(
            torch.tensor([2, 5], dtype=torch.float, device=device))
        expected = torch.zeros(100, dtype=torch.float, device=device)
        expected[0] = 1
        expected[99] = 1
        self.assertEqual(expected, actual)
        # tensor with the same element
        actual = torch.histc(torch.ones(5, dtype=torch.float, device=device), bins=5)
        self.assertEqual(
            torch.tensor([0, 0, 5, 0, 0], dtype=torch.float, device=device),
            actual)
        # no element falls between [min, max]
        actual = torch.histc(
            torch.ones(5, dtype=torch.float, device=device), bins=5, min=2, max=3)
        self.assertEqual(
            torch.tensor([0, 0, 0, 0, 0], dtype=torch.float, device=device),
            actual)
        # element falls below min + integral bin size and
        actual = torch.histc(
            torch.tensor([2, 4, 2, 2, 5, 4], dtype=torch.float, device=device),
            bins=5, min=1, max=5)
        self.assertEqual(
            torch.tensor([0, 3, 0, 2, 1], dtype=torch.float, device=device),
            actual)
        # non-integral bin size
        actual = torch.histc(
            torch.tensor([1, 2, 1], dtype=torch.float, device=device),
            bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.float, device=device),
            actual)
        # double input
        actual = torch.histc(
            torch.tensor([1, 2, 1], dtype=torch.double, device=device), bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.double, device=device),
            actual)
        self.assertEqual(actual.dtype, torch.double)
        # mixed input
        actual = torch.histc(
            torch.tensor([1., 2, 1], dtype=torch.float, device=device),
            bins=4, min=0, max=3)
        self.assertEqual(
            torch.tensor([0, 2, 1, 0], dtype=torch.float, device=device),
            actual)
        self.assertEqual(actual.dtype, torch.float)
        # scalar input and 1 bin -- should return a 1-dimensional tensor, not a scalar.
        actual = torch.histc(
            torch.tensor(0, dtype=torch.float, device=device),
            bins=1, min=0, max=3)
        self.assertEqual(
            torch.tensor([1], dtype=torch.float, device=device),
            actual)
        # tensors with inf; min, max not provided -- should throw a RuntimeError
        with self.assertRaisesRegex(RuntimeError, r'range of \[inf, inf\] is not finite'):
            torch.histc(torch.tensor([float("inf")], dtype=torch.float, device=device))
        with self.assertRaisesRegex(RuntimeError, r'range of \[1, inf\] is not finite'):
            torch.histc(torch.tensor([1., 2., float("inf")], dtype=torch.float, device=device))
        # tensors with inf; min, max provided
        self.assertEqual(
            torch.histc(torch.tensor([float("inf")], dtype=torch.float, device=device),
                        bins=1, min=0, max=3),
            torch.tensor([0], dtype=torch.float, device=device))
        self.assertEqual(
            torch.histc(torch.tensor([1., 2., float("inf")], dtype=torch.float, device=device),
                        bins=4, max=3),
            torch.tensor([0, 1, 1, 0], dtype=torch.float, device=device))
        # tensor with nan -- should throw a RuntimeError
        with self.assertRaisesRegex(RuntimeError, r'range of \[nan, nan\] is not finite'):
            torch.histc(torch.tensor([float("nan")], dtype=torch.float, device=device))
        # tensors with min > max -- should throw a RuntimeError
        with self.assertRaisesRegex(RuntimeError, "max must be larger than min"):
            torch.histc(torch.tensor([1., 2., 3.], dtype=torch.float, device=device),
                        bins=4, min=5, max=1)

        # test against numpy.histogram()
        def test_against_np(tensor, bins=100, min=0, max=0):
            if min == 0 and max == 0:
                min = tensor.min().item()
                max = tensor.max().item()
            nparr = tensor.cpu().numpy()
            actual = torch.histc(tensor, bins=bins, min=min, max=max)
            expected = torch.from_numpy(np.histogram(nparr, bins=bins, range=(min, max))[0])
            actual_cpu = actual.cpu()
            # NB: Numpy returns a int64 tensor, like normal people...
            self.assertEqual(actual, expected.to(actual_cpu))

        if TEST_NUMPY:
            test_against_np(torch.tensor([1., 2, 1], device=device))
            test_against_np(torch.randn(5000, device=device))

            # Test bins arg
            test_against_np(torch.randn(301, device=device), bins=10)

            # Test truncated range
            test_against_np(torch.randn(201, device=device), min=0.1, max=1)

            noncontig = torch.randn(100, 3, device=device)[:, 2]
            test_against_np(noncontig)

            multidim = torch.randn(3, 5, 7, 2, device=device)
            test_against_np(multidim)

            expanded = torch.randn(1, 5, 1, 2, device=device).expand(3, 5, 7, 2)
            test_against_np(expanded)

    def test_bool_tensor_comparison_ops(self, device):
        a = torch.tensor([True, False, True, False, True, False], dtype=torch.bool, device=device)
        b = torch.tensor([True, False, True, True, True, True], dtype=torch.bool, device=device)
        self.assertEqual(a == b, torch.tensor([1, 1, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a != b, torch.tensor([0, 0, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertEqual(a < b, torch.tensor([0, 0, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertEqual(a > b, torch.tensor([0, 0, 0, 0, 0, 0], dtype=torch.bool, device=device))
        self.assertEqual(a >= b, torch.tensor([1, 1, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a <= b, torch.tensor([1, 1, 1, 1, 1, 1], dtype=torch.bool, device=device))
        self.assertEqual(a > False, torch.tensor([1, 0, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a == torch.tensor(True, dtype=torch.bool, device=device),
                         torch.tensor([1, 0, 1, 0, 1, 0], dtype=torch.bool, device=device))
        self.assertEqual(a == torch.tensor(0, dtype=torch.bool, device=device),
                         torch.tensor([0, 1, 0, 1, 0, 1], dtype=torch.bool, device=device))
        self.assertFalse(a.equal(b))

    def test_bool_tensor_value_change(self, device):
        x = torch.tensor([True, False], dtype=torch.bool, device=device)
        x[0] = False
        x[1] = True
        self.assertEqual(x, torch.tensor([False, True], dtype=torch.bool, device=device))

    def test_unfold_all_devices_and_dtypes(self, device):
        for dt in torch.testing.get_all_dtypes():

            if dt == torch.bfloat16 and device.startswith('cuda') and IS_WINDOWS:
                # TODO: https://github.com/pytorch/pytorch/issues/33793
                self.assertRaises(RuntimeError, lambda: torch.randint(5, (0, 1, 3, 0), dtype=dt, device=device))
            elif dt == torch.bool:
                x = torch.empty((0, 1, 3, 0), dtype=dt, device=device)
                self.assertEqual((0, 1, 1, 0, 3), x.unfold(2, 3, 2).shape)
            else:
                x = torch.empty((0, 1, 3, 0), dtype=dt, device=device)
                self.assertEqual((0, 1, 1, 0, 3), x.unfold(2, 3, 2).shape)

    def test_unfold_scalars(self, device):
        x = torch.tensor(0.5, device=device)
        # unfold on a 0-dimensional tensor should always return a 1-d dimensional
        # tensor of shape [size] (i.e., the second parameter to unfold)

        self.assertEqual(torch.empty(0, device=device), x.unfold(0, 0, 1))
        self.assertEqual(torch.empty(0, device=device), x.unfold(0, 0, 2))
        self.assertEqual(torch.tensor([0.5], device=device), x.unfold(0, 1, 1))

    def test_copy_all_dtypes_and_devices(self, device):
        from copy import copy
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([1, 2, 3, 4], dtype=dt, device=device)
            x_clone = x.clone()
            y = copy(x)
            y.fill_(1)
            # copy is a shallow copy, only copies the tensor view,
            # not the data
            self.assertEqual(x, y)

    def test_resize_all_dtypes_and_devices(self, device):
        shape = (2, 2)
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            x.resize_(shape)
            self.assertEqual(shape, x.shape)

    def test_resize_as_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            y = torch.tensor([[1, 2, 3], [4, 5, 6]], dtype=dt, device=device)
            x.resize_as_(y)
            self.assertEqual(y.shape, x.shape)

    def test_view_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4], [5, 6]], dtype=dt, device=device)
            self.assertEqual(x.view(6).shape, [6])

    def test_fill_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            for x in [torch.tensor((10, 10), dtype=dt, device=device),
                      torch.empty(10000, dtype=dt, device=device)]:  # large tensor
                numel = x.numel()
                bound = 100 if dt in (torch.uint8, torch.int8) else 2000
                for n in range(-bound, bound, bound // 10):
                    x.fill_(n)
                    self.assertEqual(x, torch.tensor([n] * numel, dtype=dt, device=device))
                    self.assertEqual(dt, x.dtype)

    def test_clone_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor((1, 1), dtype=dt, device=device)
            y = x.clone()
            self.assertEqual(x, y)

    def test_clone_zero_stride_dim(self, device):
        # stride zero, size 1 axis, not contiguous
        x = torch.randn(10)
        y = x.as_strided([2, 1, 5], [1, 0, 2])
        self.assertEqual(y, y.clone())

    def test_cat_all_dtypes_and_devices(self, device):
        for dt in torch.testing.get_all_dtypes():
            x = torch.tensor([[1, 2], [3, 4]], dtype=dt, device=device)

            expected1 = torch.tensor([[1, 2], [3, 4], [1, 2], [3, 4]], dtype=dt, device=device)
            self.assertEqual(torch.cat((x, x), 0), expected1)

            expected2 = torch.tensor([[1, 2, 1, 2], [3, 4, 3, 4]], dtype=dt, device=device)
            self.assertEqual(torch.cat((x, x), 1), expected2)

    def test_tensor_factories_empty(self, device):
        # ensure we can create empty tensors from each factory function
        shapes = [(5, 0, 1), (0,), (0, 0, 1, 0, 2, 0, 0)]

        for shape in shapes:
            for dt in torch.testing.get_all_dtypes():

                self.assertEqual(shape, torch.zeros(shape, device=device, dtype=dt).shape)
                self.assertEqual(shape, torch.zeros_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                self.assertEqual(shape, torch.full(shape, 3, device=device, dtype=dt).shape)
                self.assertEqual(shape, torch.full_like(torch.zeros(shape, device=device, dtype=dt), 3).shape)
                self.assertEqual(shape, torch.ones(shape, device=device, dtype=dt).shape)
                self.assertEqual(shape, torch.ones_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                self.assertEqual(shape, torch.empty(shape, device=device, dtype=dt).shape)
                self.assertEqual(shape, torch.empty_like(torch.zeros(shape, device=device, dtype=dt)).shape)
                self.assertEqual(shape, torch.empty_strided(shape, (0,) * len(shape), device=device, dtype=dt).shape)

                if dt == torch.bfloat16 and device.startswith('cuda') and IS_WINDOWS:
                    # TODO: https://github.com/pytorch/pytorch/issues/33793
                    self.assertRaises(RuntimeError, lambda: torch.randint(6, shape, device=device, dtype=dt).shape)
                elif dt == torch.bool:
                    self.assertEqual(shape, torch.randint(2, shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.randint_like(torch.zeros(shape, device=device, dtype=dt), 2).shape)
                elif dt.is_complex:
                    self.assertRaises(RuntimeError, lambda: torch.randint(6, shape, device=device, dtype=dt).shape)
                else:
                    self.assertEqual(shape, torch.randint(6, shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.randint_like(torch.zeros(shape, device=device, dtype=dt), 6).shape)

                if dt not in {torch.double, torch.float, torch.half, torch.bfloat16, torch.complex64, torch.complex128}:
                    self.assertRaises(RuntimeError, lambda: torch.rand(shape, device=device, dtype=dt).shape)

                if dt == torch.double or dt == torch.float or dt.is_complex:
                    self.assertEqual(shape, torch.randn(shape, device=device, dtype=dt).shape)
                    self.assertEqual(shape, torch.randn_like(torch.zeros(shape, device=device, dtype=dt)).shape)

        self.assertEqual((0,), torch.arange(0, device=device).shape)
        self.assertEqual((0, 0), torch.eye(0, device=device).shape)
        self.assertEqual((0, 0), torch.eye(0, 0, device=device).shape)
        self.assertEqual((5, 0), torch.eye(5, 0, device=device).shape)
        self.assertEqual((0, 5), torch.eye(0, 5, device=device).shape)
        self.assertEqual((0,), torch.linspace(1, 1, 0, device=device).shape)
        self.assertEqual((0,), torch.logspace(1, 1, 0, device=device).shape)
        self.assertEqual((0,), torch.randperm(0, device=device).shape)
        self.assertEqual((0,), torch.bartlett_window(0, device=device).shape)
        self.assertEqual((0,), torch.bartlett_window(0, periodic=False, device=device).shape)
        self.assertEqual((0,), torch.hamming_window(0, device=device).shape)
        self.assertEqual((0,), torch.hann_window(0, device=device).shape)
        self.assertEqual((1, 1, 0), torch.tensor([[[]]], device=device).shape)
        self.assertEqual((1, 1, 0), torch.as_tensor([[[]]], device=device).shape)

    @onlyOnCPUAndCUDA
    def test_vander(self, device):
        x = torch.tensor([1, 2, 3, 5], device=device)

        self.assertEqual((0, 0), torch.vander(torch.tensor([]), 0).shape)

        with self.assertRaisesRegex(RuntimeError, "N must be non-negative."):
            torch.vander(x, N=-1)

        with self.assertRaisesRegex(RuntimeError, "x must be a one-dimensional tensor."):
            torch.vander(torch.stack((x, x)))

        # This passes on the xla backend
        if device != 'xla':
            with self.assertRaises(RuntimeError):
                torch.vander(x.to(torch.complex64))

    @unittest.skipIf(not TEST_NUMPY, 'NumPy not found')
    @onlyOnCPUAndCUDA
    @dtypes(torch.bool, torch.uint8, torch.int8, torch.short, torch.int, torch.long, torch.float, torch.double)
    def test_vander_types(self, device, dtype):
        if dtype is torch.uint8:
            # Note: no negative uint8 values
            X = [[1, 2, 3, 5], [0, 1 / 3, 1, math.pi, 3 / 7]]
        elif dtype is torch.bool:
            # Note: see https://github.com/pytorch/pytorch/issues/37398
            # for why this is necessary.
            X = [[True, True, True, True], [False, True, True, True, True]]
        else:
            X = [[1, 2, 3, 5], [-math.pi, 0, 1 / 3, 1, math.pi, 3 / 7]]

        N = [None, 0, 1, 3]
        increasing = [False, True]

        for x, n, inc in product(X, N, increasing):
            numpy_dtype = torch_to_numpy_dtype_dict[dtype]
            pt_x = torch.tensor(x, device=device, dtype=dtype)
            np_x = np.array(x, dtype=numpy_dtype)

            pt_res = torch.vander(pt_x, increasing=inc) if n is None else torch.vander(pt_x, n, inc)
            np_res = np.vander(np_x, n, inc)

            self.assertEqual(
                pt_res,
                torch.from_numpy(np_res),
                atol=1e-3,
                exact_dtype=False)

    def test_eye(self, device):
        for dtype in torch.testing.get_all_dtypes():
            if dtype == torch.bfloat16:
                continue
            for n, m in product([3, 5, 7], repeat=2):
                # Construct identity using diagonal and fill
                res1 = torch.eye(n, m, device=device, dtype=dtype)
                naive_eye = torch.zeros(n, m, dtype=dtype, device=device)
                naive_eye.diagonal(dim1=-2, dim2=-1).fill_(1)
                self.assertEqual(naive_eye, res1)

                # Check eye_out outputs
                res2 = torch.empty(0, device=device, dtype=dtype)
                torch.eye(n, m, out=res2)
                self.assertEqual(res1, res2)

    def test_addcmul(self, device):
        def rand_tensor(size, dtype, device):
            if dtype.is_floating_point or dtype.is_complex:
                return torch.rand(size=size, dtype=dtype, device=device)
            if dtype == torch.uint8:
                return torch.randint(1, 5, size=size, dtype=dtype, device=device)
            else:
                return torch.randint(-5, 5, size=size, dtype=dtype, device=device)

        for dtype in torch.testing.get_all_math_dtypes(device):
            a = rand_tensor((2, 2), dtype=dtype, device=device)
            b = rand_tensor((2, 2), dtype=dtype, device=device)
            c = rand_tensor((2, 2), dtype=dtype, device=device)
            if dtype.is_floating_point:
                alpha = 0.1
            else:
                alpha = 3

            # addcmul is not supported for complex dtypes on cuda yet
            if device.startswith('cuda') and dtype.is_complex:
                continue

            actual = torch.addcmul(a, b, c, value=alpha)
            expected = a + alpha * b * c

            self.assertEqual(expected, actual)

            with self.maybeWarnsRegex(
                    UserWarning, "This overload of addcmul is deprecated"):
                self.assertEqual(actual, torch.addcmul(a, alpha, b, c))

    def test_empty_tensor_props(self, device):
        sizes = [(0,), (0, 3), (5, 0), (5, 0, 3, 0, 2), (0, 3, 0, 2), (0, 5, 0, 2, 0)]
        for size in sizes:
            x = torch.empty(tuple(size), device=device)
            self.assertEqual(size, x.shape)
            self.assertTrue(x.is_contiguous())
            size_ones_instead_of_zeros = (x if x != 0 else 1 for x in size)
            y = torch.empty(tuple(size_ones_instead_of_zeros), device=device)
            self.assertEqual(x.stride(), y.stride())

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_tensordot(self, device):
        a = torch.arange(60., device=device).reshape(3, 4, 5)
        b = torch.arange(24., device=device).reshape(4, 3, 2)
        c = torch.tensordot(a, b, dims=([1, 0], [0, 1])).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy(),
                                           axes=([1, 0], [0, 1])))
        self.assertEqual(c, cn)
        a = torch.randn(2, 3, 4, 5, device=device)
        b = torch.randn(4, 5, 6, 7, device=device)
        c = torch.tensordot(a, b, dims=2).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy(),
                                           axes=2))

        with self.assertRaisesRegex(RuntimeError, "expects dims >= 0"):
            torch.tensordot(a, b, dims=-1)

        self.assertEqual(c, cn)
        c = torch.tensordot(a, b).cpu()
        cn = torch.from_numpy(np.tensordot(a.cpu().numpy(), b.cpu().numpy()))
        self.assertEqual(c, cn)

    def test_narrow_empty(self, device):
        x = torch.randn(2, 3, 4, device=device)
        for d in range(x.dim()):
            y = x.narrow(d, x.size(d), 0)
            sz = list(x.size())
            sz[d] = 0
            self.assertEqual(sz, y.size())

    @precisionOverride({torch.half: 1e-1, torch.float: 1e-5, torch.double: 1e-10})
    @dtypes(torch.uint8, torch.int8, torch.short, torch.int, torch.long, torch.float, torch.double)
    @dtypesIfCUDA(torch.uint8, torch.int8, torch.short, torch.int, torch.long, torch.half, torch.float, torch.double)
    def test_logspace(self, device, dtype):
        _from = random.random()
        to = _from + random.random()
        res1 = torch.logspace(_from, to, 137, device=device, dtype=dtype)
        res2 = torch.tensor((), device=device, dtype=dtype)
        torch.logspace(_from, to, 137, device=device, dtype=dtype, out=res2)
        self.assertEqual(res1, res2, 0)
        self.assertRaises(RuntimeError, lambda: torch.logspace(0, 1, -1, device=device, dtype=dtype))
        self.assertEqual(torch.logspace(0, 1, 1, device=device, dtype=dtype),
                         torch.ones(1, device=device, dtype=dtype), 0)

        # Check precision - start, stop and base are chosen to avoid overflow
        # steps is chosen so that step size is not subject to rounding error
        # a tolerance is needed for gpu tests due to differences in computation
        tol = 0. if device == 'cpu' else self.precision
        self.assertEqual(torch.tensor([2. ** (i / 8.) for i in range(49)], device=device, dtype=dtype),
                         torch.logspace(0, 6, steps=49, base=2, device=device, dtype=dtype),
                         tol)

        # Check non-default base=2
        self.assertEqual(torch.logspace(1, 1, 1, 2, device=device, dtype=dtype),
                         torch.ones(1, device=device, dtype=dtype) * 2)
        self.assertEqual(torch.logspace(0, 2, 3, 2, device=device, dtype=dtype),
                         torch.tensor((1, 2, 4), device=device, dtype=dtype))

        # Check logspace_ for generating with start > end.
        self.assertEqual(torch.logspace(1, 0, 2, device=device, dtype=dtype),
                         torch.tensor((10, 1), device=device, dtype=dtype), 0)

        # Check logspace_ for non-contiguous tensors.
        x = torch.zeros(2, 3, device=device, dtype=dtype)
        y = torch.logspace(0, 3, 4, base=2, device=device, dtype=dtype, out=x.narrow(1, 1, 2))
        self.assertEqual(x, torch.tensor(((0, 1, 2), (0, 4, 8)), device=device, dtype=dtype), 0)

    @dtypes(torch.int8, torch.short, torch.int, torch.long, torch.float, torch.double)
    @dtypesIfCUDA(torch.int8, torch.short, torch.int, torch.long, torch.half, torch.float, torch.double)
    def test_linspace(self, device, dtype):
        _from = random.random()
        to = _from + random.random()
        res1 = torch.linspace(_from, to, 137, device=device, dtype=dtype)
        res2 = torch.tensor((), device=device, dtype=dtype)
        torch.linspace(_from, to, 137, dtype=dtype, out=res2)
        self.assertEqual(res1, res2, 0)

        # small tensor
        self.assertEqual(torch.linspace(10, 20, 11, device=device, dtype=dtype),
                         torch.tensor(list(range(10, 21)), device=device, dtype=dtype))
        # large tensor
        if dtype not in (torch.int8, torch.uint8):
            self.assertEqual(torch.linspace(10, 2000, 1991, device=device, dtype=dtype),
                             torch.tensor(list(range(10, 2001)), device=device, dtype=dtype))

        self.assertRaises(RuntimeError, lambda: torch.linspace(0, 1, -1, device=device, dtype=dtype))
        # steps = 1
        self.assertEqual(torch.linspace(0, 1, 1, device=device, dtype=dtype),
                         torch.zeros(1, device=device, dtype=dtype), 0)
        # steps = 0
        self.assertEqual(torch.linspace(0, 1, 0, device=device, dtype=dtype).numel(), 0)

        # Check linspace for generating the correct output for each dtype.
        expected_lin = torch.tensor([-100. + .5 * i for i in range(401)], device=device, dtype=torch.double)
        actual_lin = torch.linspace(-100, 100, 401, device=device, dtype=dtype)
        # If on GPU, allow for minor error depending on dtype.
        tol = 0.
        if device != 'cpu':
            if dtype == torch.half:
                tol = 1e-1
            elif dtype == torch.float:
                tol = 1e-5
            elif dtype == torch.double:
                tol = 1e-10

        self.assertEqual(expected_lin.to(dtype), actual_lin, tol)

        # Check linspace for generating with start > end.
        self.assertEqual(torch.linspace(2, 0, 3, device=device, dtype=dtype),
                         torch.tensor((2, 1, 0), device=device, dtype=dtype),
                         0)

        # Check for race condition (correctness when applied on a large tensor).
        if dtype not in (torch.int8, torch.uint8, torch.int16, torch.half):
            y = torch.linspace(0, 1000000 - 1, 1000000, device=device, dtype=dtype)
            cond = y[:-1] < y[1:]
            correct = all(cond)
            self.assertTrue(correct)

        # Check linspace for non-contiguous tensors.
        x = torch.zeros(2, 3, device=device, dtype=dtype)
        y = torch.linspace(0, 3, 4, out=x.narrow(1, 1, 2), dtype=dtype)
        self.assertEqual(x, torch.tensor(((0, 0, 1), (0, 2, 3)), device=device, dtype=dtype), 0)

    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @precisionOverride({torch.float: 1e-8, torch.double: 1e-10})
    @dtypes(torch.float, torch.double)
    def test_linspace_vs_numpy(self, device, dtype):
        start = -0.0316082797944545745849609375
        end = .0315315723419189453125

        for steps in [1, 2, 3, 5, 11, 256, 257, 2**22]:
            t = torch.linspace(start, end, steps, device=device, dtype=dtype)
            a = np.linspace(start, end, steps, dtype=torch_to_numpy_dtype_dict[dtype])
            t = t.cpu()
            self.assertEqual(t, torch.from_numpy(a))
            self.assertTrue(t[0] == a[0])
            self.assertTrue(t[steps - 1] == a[steps - 1])

    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @precisionOverride({torch.float: 1e-6, torch.double: 1e-10})
    @dtypes(torch.float, torch.double)
    def test_logspace_vs_numpy(self, device, dtype):
        start = -0.0316082797944545745849609375
        end = .0315315723419189453125

        for steps in [1, 2, 3, 5, 11, 256, 257, 2**22]:
            t = torch.logspace(start, end, steps, device=device, dtype=dtype)
            a = np.logspace(start, end, steps, dtype=torch_to_numpy_dtype_dict[dtype])
            t = t.cpu()
            self.assertEqual(t, torch.from_numpy(a))
            self.assertEqual(t[0], a[0])
            self.assertEqual(t[steps - 1], a[steps - 1])

    @largeCUDATensorTest('16GB')
    def test_range_factories_64bit_indexing(self, device):
        bigint = 2 ** 31 + 1
        t = torch.arange(bigint, dtype=torch.long, device=device)
        self.assertEqual(t[-1].item(), bigint - 1)
        del t
        t = torch.linspace(0, 1, bigint, dtype=torch.float, device=device)
        self.assertEqual(t[-1].item(), 1)
        del t
        t = torch.logspace(0, 1, bigint, 2, dtype=torch.float, device=device)
        self.assertEqual(t[-1].item(), 2)
        del t

    def test_logical(self, device):
        for dt in torch.testing.get_all_dtypes():
            if dt.is_complex:
                continue
            x = torch.tensor([1, 2, 3, 4], device=device, dtype=dt)
            b = torch.tensor([2], device=device, dtype=dt)

            if dt == torch.half and device == 'cpu':
                self.assertRaises(RuntimeError, lambda: x.lt(2))
                continue

            if dt == torch.bool:
                # torch.bool is a special case and is being tested later
                # in this test
                continue

            if self.device_type == 'cuda' and dt == torch.bfloat16 and not TEST_WITH_ROCM:
                self.assertRaises(RuntimeError, lambda: x > b)
                self.assertRaises(RuntimeError, lambda: x < b)
                self.assertRaises(RuntimeError, lambda: x == b)
                self.assertRaises(RuntimeError, lambda: x != b)
                self.assertRaises(RuntimeError, lambda: x >= b)
                self.assertRaises(RuntimeError, lambda: x <= b)
                continue

            self.assertEqual(x.lt(2), torch.tensor([True, False, False, False]))
            self.assertEqual(x.le(2), torch.tensor([True, True, False, False]))
            self.assertEqual(x.ge(2), torch.tensor([False, True, True, True]))
            self.assertEqual(x.gt(2), torch.tensor([False, False, True, True]))
            self.assertEqual(x.eq(2), torch.tensor([False, True, False, False]))
            self.assertEqual(x.ne(2), torch.tensor([True, False, True, True]))

            self.assertEqual(x.lt(b), torch.tensor([True, False, False, False]))
            self.assertEqual(x.le(b), torch.tensor([True, True, False, False]))
            self.assertEqual(x.ge(b), torch.tensor([False, True, True, True]))
            self.assertEqual(x.gt(b), torch.tensor([False, False, True, True]))
            self.assertEqual(x.eq(b), torch.tensor([False, True, False, False]))
            self.assertEqual(x.ne(b), torch.tensor([True, False, True, True]))

        # Bool Tensor
        x = torch.tensor([True, False, True, False], device=device)
        self.assertEqual(x.lt(True), torch.tensor([False, True, False, True]))
        self.assertEqual(x.le(True), torch.tensor([True, True, True, True]))
        self.assertEqual(x.ge(True), torch.tensor([True, False, True, False]))
        self.assertEqual(x.gt(True), torch.tensor([False, False, False, False]))
        self.assertEqual(x.eq(True), torch.tensor([True, False, True, False]))
        self.assertEqual(x.ne(True), torch.tensor([False, True, False, True]))

    def test_index_copy(self, device):
        num_copy, num_dest = 3, 20
        dest = torch.randn(num_dest, 4, 5, device=device)
        src = torch.randn(num_copy, 4, 5, device=device)
        idx = torch.randperm(num_dest, device=device).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_copy_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] = src[i]
        self.assertEqual(dest, dest2, 0)

        dest = torch.randn(num_dest, device=device)
        src = torch.randn(num_copy, device=device)
        idx = torch.randperm(num_dest, device=device).narrow(0, 0, num_copy)
        dest2 = dest.clone()
        dest.index_copy_(0, idx, src)
        for i in range(idx.size(0)):
            dest2[idx[i]] = src[i]
        self.assertEqual(dest, dest2, 0)

        # Bool tensor
        dest = torch.zeros(2, 2, dtype=torch.bool, device=device)
        src = torch.tensor([[True, True], [True, True]], device=device)
        index = torch.tensor([0, 1], device=device)
        dest.index_copy_(0, index, src)
        self.assertEqual(dest, torch.tensor([[True, True], [True, True]], device=device))

        # Error cases
        a = torch.randn(3, 5)
        c = torch.zeros(3)
        self.assertRaises(IndexError, lambda: a.index_copy_(dim=1, index=torch.tensor([3]), source=c))

    def test_index_fill(self, device):
        for dt in torch.testing.get_all_dtypes():
            if dt == torch.half or dt == torch.bfloat16 or dt.is_complex:
                continue

            x = torch.tensor([[1, 2], [4, 5]], dtype=dt, device=device)
            index = torch.tensor([0], device=device)
            x.index_fill_(1, index, 0)
            self.assertEqual(x, torch.tensor([[0, 2], [0, 5]], dtype=dt, device=device))

    def test_index_select(self, device):
        src = torch.randn(3, 4, 5, device=device)
        # Index can be duplicated.
        idx = torch.tensor([2, 1, 0, 1, 2], dtype=torch.long, device=device)
        dest = torch.index_select(src, 0, idx)
        self.assertEqual(dest.shape, (5, 4, 5))
        for i in range(idx.size(0)):
            self.assertEqual(dest[i], src[idx[i]])

        # Check that 'out' is used correctly.
        out = torch.randn(5 * 4 * 5, device=device)
        dest = torch.index_select(src, 0, idx, out=out.view(5, 4, 5))
        self.assertEqual(dest.shape, (5, 4, 5))
        for i in range(idx.size(0)):
            self.assertEqual(dest[i], src[idx[i]])
        out.fill_(0.123)
        self.assertEqual(out, dest.view(-1))  # Must point to the same storage.

        # Bool tensor
        src = torch.tensor([False, True, False, False], device=device, dtype=torch.bool)
        idx = torch.tensor([1], dtype=torch.long, device=device)
        dest = torch.index_select(src, 0, idx)
        self.assertEqual(torch.tensor([True]), dest)

        # Complex Tensor
        src = torch.randn(3, 4, 5, dtype=torch.complex64, device=device)
        idx = torch.tensor([2, 1, 0, 1, 2], dtype=torch.long, device=device)

        # index_select not supported for complex on cuda
        if device.startswith('cuda'):
            with self.assertRaises(RuntimeError):
                torch.index_select(src, 0, idx)
            return

        dest = torch.index_select(src, 0, idx)
        self.assertEqual(dest.shape, (5, 4, 5))
        for i in range(idx.size(0)):
            self.assertEqual(dest[i], src[idx[i]])

    def test_take_empty(self, device):
        for input_shape in [(0,), (0, 1, 2, 0), (1, 2, 3)]:
            for indices_shape in [(0,), (0, 1, 2, 0)]:
                input = torch.empty(input_shape, device=device)
                indices = torch.empty(indices_shape, dtype=torch.int64, device=device)
                self.assertEqual(indices.float(), torch.take(input, indices))

    def test_put_empty(self, device):
        for dst_shape in [(0,), (0, 1, 2, 0), (1, 2, 3)]:
            for indices_shape in [(0,), (0, 1, 2, 0)]:
                for accumulate in [False, True]:
                    dst = torch.randn(dst_shape, device=device)
                    indices = torch.empty(indices_shape, dtype=torch.int64, device=device)
                    src = torch.randn(indices_shape, device=device)
                    self.assertEqual(dst, dst.put_(indices, src, accumulate=accumulate))

    def test_scatter_to_large_input(self, device):
        input = torch.zeros(4, 4, device=device)
        src = torch.ones(2, 2, device=device)
        index = torch.tensor([[1], [2]], device=device, dtype=torch.long)
        input.scatter_(0, index, src)
        self.assertEqual(input, torch.tensor([[0, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [0, 0, 0, 0]], device=device, dtype=torch.float32))

    def test_scatter_add_to_large_input(self, device):
        input = torch.zeros(4, 4, device=device)
        src = torch.ones(2, 2, device=device)
        index = torch.tensor([[1], [2]], device=device, dtype=torch.long)
        input.scatter_add_(0, index, src)
        self.assertEqual(input, torch.tensor([[0, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [1, 0, 0, 0],
                                              [0, 0, 0, 0]], device=device, dtype=torch.float32))

    def test_scatter_bool(self, device):
        x = torch.tensor([[True, True, True], [True, True, True]], device=device)
        res = torch.zeros(3, 3, dtype=torch.bool, device=device)
        res = res.scatter_(0, torch.tensor([[0, 1, 2], [0, 1, 2]], device=device), x)
        self.assertEqual(res, torch.tensor([[True, False, False],
                                            [False, True, False],
                                            [False, False, True]], device=device))

    def test_scatter_add_bool(self, device):
        x = torch.tensor([[True, True, True, True, True], [True, True, True, True, True]], device=device)
        res = torch.zeros(3, 5, dtype=torch.bool, device=device)
        res = res.scatter_add_(0, torch.tensor([[0, 1, 2, 0, 0], [2, 0, 0, 1, 2]], device=device), x)
        self.assertEqual(res, torch.tensor([[True, True, True, True, True],
                                            [False, True, False, True, False],
                                            [True, False, True, False, True]], device=device))

    def test_masked_scatter_bool_tensor(self, device):
        src = torch.tensor([True, True, True], device=device)
        dst = torch.tensor([False, False, False], device=device)
        mask = torch.tensor([False, True, False], device=device)

        dst.masked_scatter_(mask, src)
        self.assertEqual(dst, torch.tensor([False, True, False], device=device))

        mask = torch.tensor([True, False, True], device=device)
        dst = dst.masked_scatter(mask, src)
        self.assertEqual(dst, torch.tensor([True, True, True], device=device))

    @dtypes(*torch.testing.get_all_dtypes())
    def test_masked_select(self, device, dtype):
        if device == 'cpu':
            warn = 'masked_select received a mask with dtype torch.uint8,'
        else:
            warn = 'indexing with dtype torch.uint8 is now deprecated, pl'
        for maskType in [torch.uint8, torch.bool]:
            num_src = 10
            src = torch.tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=dtype, device=device)
            mask = torch.rand(num_src, device=device).clamp(0, 1).mul(2).floor().to(maskType)

            if (dtype.is_complex or dtype == torch.half) and torch.device(device).type == 'cpu':
                self.assertRaises(RuntimeError, lambda: src.masked_select(mask))
                continue

            with warnings.catch_warnings(record=True) as w:
                dst = src.masked_select(mask)
                if maskType is torch.uint8:
                    self.assertEqual(len(w), 1)
                    self.assertEqual(str(w[0].message)[0:53], str(warn))
            dst2 = []
            for i in range(num_src):
                if mask[i]:
                    dst2 += [src[i]]
            self.assertEqual(dst, torch.tensor(dst2), 0)

            dst3 = torch.empty_like(src, device=device)
            torch.masked_select(src, mask, out=dst3)
            self.assertEqual(dst3, torch.tensor(dst2, dtype=dst3.dtype), 0)

        # Since complex and half on CPU is not supported, need to skip the remaining test cases
        if (dtype.is_complex or dtype == torch.half) and torch.device(device).type == 'cpu':
            return

        # Ensure that masks are expanded to match tensor properly
        if IS_WINDOWS and dtype == torch.bfloat16 and torch.device(device).type == 'cuda':
            # TODO .to() for bfloat16 does not work on windows
            a = torch.ones(100, 100, device=device, dtype=dtype)
        else:
            a = torch.rand(100, 100, device=device).mul(100).to(dtype)
        mask_first_el_each_row = torch.zeros(100, device=device).bool()
        mask_first_el_each_row[0] = True
        a_masked = a.masked_select(mask_first_el_each_row)
        self.assertEqual(a_masked, a[:, 0])

        mask_first_row = torch.zeros(100, 1, device=device, dtype=dtype).bool()
        mask_first_row[0][0] = True
        a_masked = a.masked_select(mask_first_row)
        self.assertEqual(a_masked, a[0, :])

        # Ensure that tensor is expanded to match mask properly
        if IS_WINDOWS and dtype == torch.bfloat16 and torch.device(device).type == 'cuda':
            a = torch.ones(100, device=device, dtype=dtype)
        else:
            a = torch.rand(100, device=device).mul(100).to(maskType)
        mask_copy_3_times = torch.tensor([[True], [True], [False], [True]], device=device)
        a_masked = a.masked_select(mask_copy_3_times)
        self.assertEqual(a_masked, a.unsqueeze(0).expand(3, 100).flatten())

    def test_masked_fill_bool_tensor(self, device):
        dst = torch.tensor([True, False, True], device=device)
        mask = torch.tensor([False, True, False], device=device)

        dst.masked_fill_(mask, True)
        self.assertEqual(dst, torch.tensor([True, True, True], device=device))

        dst = dst.masked_fill(mask, False)
        self.assertEqual(dst, torch.tensor([True, False, True], device=device))

    def test_tensor_shape_empty(self, device):
        x = torch.randn((0, 1, 3, 0), device=device)
        # flatten
        self.assertEqual((0,), torch.flatten(x, 0, 3).shape)
        self.assertEqual((0, 0), torch.flatten(x, 0, 2).shape)
        self.assertEqual((0, 3, 0), torch.flatten(x, 1, 2).shape)

        # squeeze, unsqueeze
        self.assertEqual((0, 1, 1, 3, 0), torch.unsqueeze(x, 1).shape)
        self.assertEqual((0, 3, 0), torch.squeeze(x, 1).shape)
        self.assertEqual((0, 3, 0), torch.squeeze(x).shape)

        # transpose, t
        self.assertEqual((0, 0, 3, 1), torch.transpose(x, 1, 3).shape)
        y = torch.randn((5, 0), device=device)
        self.assertEqual((0, 5), y.t().shape)

        # select
        self.assertEqual((0, 1, 0), torch.select(x, 2, 2).shape)

        # repeat, permute
        self.assertEqual((9, 0, 5, 6, 0), x.repeat(9, 7, 5, 2, 3).shape)
        self.assertEqual((3, 0, 0, 1), x.permute(2, 3, 0, 1).shape)

        # diagonal, diagflat
        self.assertEqual((0,), torch.diagonal(torch.randn((5, 0), device=device)).shape)
        self.assertEqual((0,), torch.diagonal(torch.randn((0, 5), device=device)).shape)
        # off the end offsets are valid
        self.assertEqual((0,), torch.diagonal(torch.randn((5, 0), device=device), offset=1).shape)
        self.assertEqual((0,), torch.diagonal(torch.randn((0, 5), device=device), offset=1).shape)
        # check non-zero sized offsets off the end
        self.assertEqual((5, 6, 0), torch.diagonal(torch.randn((3, 4, 5, 6), device=device), offset=45252).shape)
        self.assertEqual((5, 6, 0), torch.diagonal(torch.randn((3, 4, 5, 6), device=device), offset=-45252).shape)

        self.assertEqual((0, 0), torch.diagflat(torch.tensor([], device=device)).shape)
        self.assertEqual(torch.zeros(1, 1), torch.diagflat(torch.tensor([], device=device), offset=1))
        self.assertEqual((0, 0), torch.diagflat(torch.tensor([[]], device=device)).shape)
        self.assertEqual(torch.zeros(1, 1), torch.diagflat(torch.tensor([[]], device=device), offset=1))

        # stack, split, chunk
        self.assertEqual((4, 0, 1, 3, 0), torch.stack((x, x, x, x)).shape)
        self.assertEqual([(0, 1, 3, 0)],
                         [z.shape for z in torch.chunk(x, 1, dim=0)])

        self.assertEqual([(0, 1, 3, 0), ] * 3, [z.shape for z in torch.chunk(x, 3, dim=0)])
        self.assertEqual([(0, 1, 1, 0), ] * 3, [z.shape for z in torch.chunk(x, 3, dim=2)])

        # NOTE: split_with_sizes behaves differently than NumPy in that it
        # takes sizes rather than offsets
        self.assertEqual([(0, 1, 0, 0), (0, 1, 1, 0), (0, 1, 2, 0)],
                         [z.shape for z in torch.split(x, (0, 1, 2), dim=2)])

        self.assertRaises(RuntimeError, lambda: torch.split(x, 0, dim=1))
        # This is strange because the split size is larger than the dim size, but consistent with
        # how split handles that case generally (when no 0s are involved).
        self.assertEqual([(0, 1, 3, 0)], [z.shape for z in torch.split(x, 1, dim=0)])
        self.assertEqual([(0, 1, 3, 0)], [z.shape for z in torch.split(x, 0, dim=0)])

    # functions that operate over a dimension but don't reduce.
    def test_dim_function_empty(self, device):
        shape = (0, 1, 2, 0)
        x = torch.randn(shape, device=device)

        # size stride
        self.assertEqual(0, x.size(3))
        self.assertEqual(2, x.size(2))
        self.assertEqual(2, x.stride(0))
        self.assertEqual(1, x.stride(2))

        self.assertEqual(x, torch.nn.functional.glu(x, 0))
        self.assertEqual((0, 1, 1, 0), torch.nn.functional.glu(x, 2).shape)

        # softmax, logsoftmax
        self.assertEqual(x, torch.nn.functional.softmax(x, 0))
        self.assertEqual(x, torch.nn.functional.softmax(x, 2))
        self.assertEqual(x, torch.nn.functional.softmax(x, 3))

        self.assertEqual(x, torch.nn.functional.log_softmax(x, 0))
        self.assertEqual(x, torch.nn.functional.log_softmax(x, 2))
        self.assertEqual(x, torch.nn.functional.log_softmax(x, 3))

        # cumsum, cumprod, cummax, cummin
        self.assertEqual(shape, torch.cumsum(x, 0).shape)
        self.assertEqual(shape, torch.cumsum(x, 2).shape)
        self.assertEqual(shape, torch.cumprod(x, 0).shape)
        self.assertEqual(shape, torch.cumprod(x, 2).shape)
        self.assertEqual(shape, torch.cummax(x, 0)[0].shape)
        self.assertEqual(shape, torch.cummax(x, 2)[0].shape)
        self.assertEqual(shape, torch.cummin(x, 0)[0].shape)
        self.assertEqual(shape, torch.cummin(x, 2)[0].shape)

        # flip
        self.assertEqual(x, x.flip(0))
        self.assertEqual(x, x.flip(2))

        # roll
        self.assertEqual(x, x.roll(0, 1).roll(0, -1))
        self.assertEqual(x, x.roll(1, x.size(1)))
        self.assertEqual(x, x.roll(1))
        self.assertEqual(x, x.roll((1, 1), (3, 1)))

        # unbind
        self.assertEqual((), x.unbind(0))
        self.assertEqual((torch.empty((0, 1, 0), device=device), torch.empty((0, 1, 0), device=device)),
                         x.unbind(2))

        # cross
        y = torch.randn((0, 1, 3, 0), device=device)
        self.assertEqual(y.shape, torch.cross(y, y).shape)

        # renorm
        self.assertEqual(shape, torch.renorm(x, 1, 0, 5).shape)
        self.assertEqual(shape, torch.renorm(x, 1, 2, 5).shape)

        # sort
        self.assertEqual([shape, shape], [z.shape for z in torch.sort(x, dim=0)])
        self.assertEqual([shape, shape], [z.shape for z in torch.sort(x, dim=2)])

        # topk
        self.assertEqual([shape, shape], [z.shape for z in torch.topk(x, 0, dim=0)])
        self.assertEqual([(0, 1, 1, 0), (0, 1, 1, 0)], [z.shape for z in torch.topk(x, 1, dim=2)])

        y = torch.randn((2, 3, 4), device=device)
        self.assertEqual([(2, 3, 0), (2, 3, 0)], [z.shape for z in torch.topk(y, 0)])

        # gather
        self.assertEqual(shape, torch.gather(x, 0, torch.empty(shape, dtype=torch.int64, device=device)).shape)
        self.assertEqual(shape, torch.gather(x, 2, torch.empty(shape, dtype=torch.int64, device=device)).shape)
        larger_shape = torch.empty((0, 1, 3, 0), dtype=torch.int64, device=device)
        self.assertEqual(larger_shape.shape, torch.gather(x, 2, larger_shape).shape)
        smaller_shape = torch.empty((0, 1, 0, 0), dtype=torch.int64, device=device)
        self.assertEqual(smaller_shape.shape, torch.gather(x, 2, smaller_shape).shape)
        y = torch.randn((2, 3, 4), device=device)
        self.assertEqual((0, 3, 4),
                         torch.gather(y, 0, torch.empty((0, 3, 4), dtype=torch.int64, device=device)).shape)

        # scatter, scatter_add
        for dim in [0, 2]:
            y = torch.randn(shape, device=device)
            y_src = torch.randn(shape, device=device)
            ind = torch.empty(shape, dtype=torch.int64, device=device)
            self.assertEqual(shape, y.scatter_(dim, ind, y_src).shape)
            self.assertEqual(shape, y.scatter_add_(dim, ind, y_src).shape)

        z = torch.randn((2, 3, 4), device=device)
        z_src = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.scatter_(2, torch.empty((2, 3, 0), dtype=torch.int64, device=device), z_src))
        self.assertEqual(z, z.scatter_add_(2, torch.empty((2, 3, 0), dtype=torch.int64, device=device), z_src))

        # index_fill, index_copy, index_add
        c = x.clone()
        c_clone = c.clone()
        ind_empty = torch.tensor([], dtype=torch.int64, device=device)
        ind_01 = torch.tensor([0, 1], dtype=torch.int64, device=device)
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_fill_(2, ind_empty, -1))
        self.assertEqual(c_clone, c.index_fill_(2, torch.tensor([0, 1], dtype=torch.int64, device=device), -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_copy_(2, ind_empty, torch.empty((0, 1, 0, 0), device=device)))
        self.assertEqual(c_clone, c.index_copy_(2, ind_01, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(2, ind_empty, torch.empty((0, 1, 0, 0), device=device)))
        self.assertEqual(c_clone, c.index_add_(2, ind_01, torch.empty((0, 1, 2, 0), device=device)))

        c = torch.randn((0, 1, 2), device=device)
        c_clone = c.clone()
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_fill_(0, ind_empty, -1))
        self.assertEqual(c_clone, c.index_copy_(0, ind_empty, torch.empty((0, 1, 2), device=device)))
        self.assertEqual(c_clone, c.index_add_(0, ind_empty, torch.empty((0, 1, 2), device=device)))

        # index fill/copy/add non-empty
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_fill_(0, ind_empty, -1))
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_copy_(0, ind_empty, torch.empty((0, 3, 4), device=device)))
        z = torch.randn((2, 3, 4), device=device)
        self.assertEqual(z, z.index_add_(0, ind_empty, torch.empty((0, 3, 4), device=device)))

        # index_select
        self.assertEqual(x, x.index_select(0, ind_empty))
        self.assertEqual((0, 1, 0, 0), x.index_select(2, ind_empty).shape)
        self.assertEqual(x, x.index_select(2, ind_01))
        z = torch.randn((2, 3, 4), device=device)  # non-empty
        self.assertEqual((0, 3, 4), z.index_select(0, ind_empty).shape)
        c = torch.randn((0, 1, 2), device=device)
        self.assertEqual(c, c.index_select(0, ind_empty))
        c = torch.randn((0, 1, 2), device=device)
        self.assertEqual(c, c.index_select(0, ind_empty))

    def test_nonzero(self, device):
        num_srcs = [
            12, 12, 12, 12, 12, 125,
        ]

        dtypes = [
            torch.uint8,
            torch.int8,
            torch.short,
            torch.int,
            torch.float,
            torch.double,
            torch.long,
        ]

        shapes = [
            torch.Size((12,)),
            torch.Size((12, 1)),
            torch.Size((1, 12)),
            torch.Size((6, 2)),
            torch.Size((3, 2, 2)),
            torch.Size((5, 5, 5)),
        ]

        def is_lexicographically_sorted(inds):
            """Check sorted ascending with
            i -> j -> k changing slowest to fastest"""
            assert inds.size(1) == 3
            if inds.size(0) > 1:
                i0, j0, k0 = inds[:-1].t()
                i1, j1, k1 = inds[+1:].t()
                i_ok = (i1 >= i0)
                j_ok = (j1 >= j0) | (i1 > i0)
                k_ok = (k1 >= k0) | (j1 > j0) | (i1 > i0)
                lex = torch.stack((i_ok, j_ok, k_ok), dim=1)
                return lex
            return torch.full_like(inds, 1)

        def gen_nontrivial_input(num_src, dtype, device):
            while True:
                tensor = torch.rand(num_src).mul(2).floor().to(device=device, dtype=dtype)
                if tensor.sum() > 0:
                    return tensor

        for dtype in dtypes:
            for shape, num_src in zip(shapes, num_srcs):
                tensor = gen_nontrivial_input(num_src, dtype, device)
                tensor = tensor.clone().resize_(shape)
                dst1 = torch.nonzero(tensor)
                dst2 = tensor.nonzero()
                dst3 = torch.LongTensor().to(device)
                torch.nonzero(tensor, out=dst3)

                self.assertRaisesRegex(
                    TypeError,
                    "received an invalid combination of arguments",
                    lambda: torch.nonzero(tensor, as_tuple=True, out=dst3))
                if len(shape) == 1:
                    dst = []
                    for i in range(num_src):
                        if tensor[i] != 0:
                            dst += [i]
                    dst = torch.LongTensor(dst).to(device)
                    self.assertEqual(dst1.select(1, 0), dst, 0)
                    self.assertEqual(dst2.select(1, 0), dst, 0)
                    self.assertEqual(dst3.select(1, 0), dst, 0)
                elif len(shape) == 2:
                    # This test will allow through some False positives. It only checks
                    # that the elements flagged positive are indeed non-zero.
                    for i in range(dst1.size(0)):
                        self.assertNotEqual(tensor[dst1[i, 0], dst1[i, 1]].item(), 0)
                elif len(shape) == 3:
                    # This test will allow through some False positives. It only checks
                    # that the elements flagged positive are indeed non-zero.
                    for i in range(dst1.size(0)):
                        self.assertNotEqual(tensor[dst1[i, 0], dst1[i, 1], dst1[i, 2]].item(), 0)
                    lex = is_lexicographically_sorted(dst1)
                    self.assertEqual(torch.ones_like(lex), lex)
                if TEST_NUMPY:
                    tup1 = torch.nonzero(tensor, as_tuple=True)
                    tup2 = tensor.nonzero(as_tuple=True)
                    tup3 = torch.where(tensor)
                    np1 = tensor.cpu().numpy().nonzero()
                    for t in (tup1, tup2, tup3):
                        self.assertEqual(len(t), len(np1))
                        for i in range(len(t)):
                            self.assertEqual(t[i].cpu().numpy(), np1[i])

    def test_nonzero_non_diff(self, device):
        x = torch.randn(10, requires_grad=True)
        nz = x.nonzero()
        self.assertFalse(nz.requires_grad)

    def _brute_pdist(self, inp, p=2):
        """Computes the same as torch.pdist using primitives"""
        n = inp.shape[-2]
        k = n * (n - 1) // 2
        if k == 0:
            # torch complains about empty indices
            return torch.empty(inp.shape[:-2] + (0,), dtype=inp.dtype, device=inp.device)
        square = torch.norm(inp[..., None, :] - inp[..., None, :, :], p=p, dim=-1)
        unroll = square.view(square.shape[:-2] + (n * n,))
        inds = torch.ones(k, dtype=torch.int)
        inds[torch.arange(n - 1, 1, -1, dtype=torch.int).cumsum(0)] += torch.arange(2, n, dtype=torch.int)
        return unroll[..., inds.cumsum(0)]

    def _pdist_single(self, shape, device, p, dtype, trans, grad_check=False):
        x = torch.randn(shape, dtype=dtype, device=device)
        if trans:
            x.transpose_(-2, -1)
        if grad_check:
            x.requires_grad_()
            y = x.detach().clone().requires_grad_()
        else:
            y = x
        actual = torch.pdist(x, p=p)
        expected = self._brute_pdist(y, p=p)
        self.assertEqual(expected.shape, actual.shape)
        self.assertTrue(torch.allclose(expected, actual))
        if grad_check and expected.size() != torch.Size([0]):
            g0 = torch.rand_like(actual)
            actual.backward(g0)
            expected.backward(g0)
            self.assertTrue(torch.allclose(x.grad, y.grad))

    @slowTest
    def test_pdist_norm_forward(self, device):
        for shape in [(4, 5), (3, 2), (2, 1), (1500, 1)]:
            for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                for trans in [False, True]:
                    for dtype in [torch.float32, torch.float64]:
                        self._pdist_single(shape, device, p, dtype, trans, grad_check=False)

        # do a simplified comparison with big inputs, see:
        # https://github.com/pytorch/pytorch/issues/15511
        for dtype in [torch.float32, torch.float64]:
            self._pdist_single((1000, 2), device, 2, dtype, trans=False, grad_check=False)

    @slowTest
    def test_pdist_norm_backward(self, device):
        for shape in [(4, 5), (3, 2), (2, 1), (1500, 1)]:
            for p in [0, 1, 2, 3, 1.5, 2.5, float('inf')]:
                for trans in [False, True]:
                    self._pdist_single(shape, device, p, torch.float64, trans, grad_check=True)

    @skipIfRocm
    def test_pdist_norm_large(self, device):
        # use dim0>=46342 for forward, see:
        # https://github.com/pytorch/pytorch/issues/30583
        # Compare output using GPU with the CPU implementation, as brute_pdist uses too much memory
        if 'cuda' in device:
            x = torch.randn(50000, 1, dtype=torch.float32)
            expected_cpu = torch.pdist(x, p=2)
            actual_gpu = torch.pdist(x.to(device), p=2)
            self.assertTrue(torch.allclose(expected_cpu, actual_gpu.cpu()))

    def test_atan2(self, device):
        def _test_atan2_with_size(size, device):
            a = torch.rand(size=size, device=device, dtype=torch.double)
            b = torch.rand(size=size, device=device, dtype=torch.double)
            actual = a.atan2(b)
            x = a.view(-1)
            y = b.view(-1)
            expected = torch.tensor([math.atan2(x[i].item(), y[i].item()) for i in range(x.numel())],
                                    device=device, dtype=torch.double)
            self.assertTrue(torch.allclose(expected, actual.view(-1), rtol=0, atol=0.02))

        _test_atan2_with_size((2, 2), device)
        _test_atan2_with_size((3, 3), device)
        _test_atan2_with_size((5, 5), device)

    def test_atan2_edgecases(self, device):
        def _test_atan2(x, y, expected, device, dtype):
            expected_tensor = torch.tensor([expected], dtype=dtype, device=device)
            x_tensor = torch.tensor([x], dtype=dtype, device=device)
            y_tensor = torch.tensor([y], dtype=dtype, device=device)
            actual = torch.atan2(y_tensor, x_tensor)
            self.assertTrue(torch.allclose(expected_tensor, actual, rtol=0, atol=0.02))

        for dtype in [torch.float, torch.double]:
            _test_atan2(0, 0, 0, device, dtype)
            _test_atan2(0, 1, math.pi / 2, device, dtype)
            _test_atan2(0, -1, math.pi / -2, device, dtype)
            _test_atan2(-1, 0, math.pi, device, dtype)
            _test_atan2(1, 0, 0, device, dtype)
            _test_atan2(-1, -1, math.pi * -3 / 4 , device, dtype)
            _test_atan2(1, 1, math.pi / 4 , device, dtype)
            _test_atan2(1, -1, math.pi / -4 , device, dtype)
            _test_atan2(-1, 1, math.pi * 3 / 4 , device, dtype)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_trapz(self, device):
        def test_dx(sizes, dim, dx, device):
            t = torch.randn(sizes, device=device)
            actual = torch.trapz(t, dx=dx, dim=dim)
            expected = np.trapz(t.cpu().numpy(), dx=dx, axis=dim)
            self.assertEqual(expected.shape, actual.shape)
            self.assertTrue(np.allclose(expected, actual.cpu().numpy()))

        def test_x(sizes, dim, x, device):
            t = torch.randn(sizes, device=device)
            actual = torch.trapz(t, x=torch.tensor(x, device=device), dim=dim)
            expected = np.trapz(t.cpu().numpy(), x=x, axis=dim)
            self.assertEqual(expected.shape, actual.shape)
            self.assertTrue(np.allclose(expected, actual.cpu().numpy()))

        test_dx((2, 3, 4), 1, 1, device)
        test_dx((10, 2), 0, 0.1, device)
        test_dx((1, 10), 0, 2.3, device)
        test_dx((0, 2), 0, 1.0, device)
        test_dx((0, 2), 1, 1.0, device)
        test_x((2, 3, 4), 1, [1.0, 2.0, 3.0], device)
        test_x((10, 2), 0, [2.0, 3.0, 4.0, 7.0, 11.0, 14.0, 22.0, 26.0, 26.1, 30.3], device)
        test_x((1, 10), 0, [1.0], device)
        test_x((0, 2), 0, [], device)
        test_x((0, 2), 1, [1.0, 2.0], device)
        with self.assertRaisesRegex(
                IndexError,
                'Dimension out of range'):
            test_x((2, 3), 2, [], device)
            test_dx((2, 3), 2, 1.0, device)
        with self.assertRaisesRegex(
                RuntimeError,
                'There must be one `x` value for each sample point'):
            test_x((2, 3), 1, [1.0, 2.0], device)
            test_x((2, 3), 1, [1.0, 2.0, 3.0, 4.0], device)

    def test_reduction_empty(self, device):
        fns_to_test = [
            # name, function, identity
            ('max', torch.max, None),
            ('kthvalue', lambda *args, **kwargs: torch.kthvalue(*args, k=1, **kwargs), None),
            ('argmax', torch.argmax, None),
            ('min', torch.min, None),
            ('argmin', torch.argmin, None),
            ('mode', torch.mode, None),
            ('median', torch.median, None),

            ('prod', torch.prod, 1),
            ('sum', torch.sum, 0),
            ('norm', torch.norm, 0),
            ('mean', torch.mean, nan),
            ('var', torch.var, nan),
            ('std', torch.std, nan),
            ('logsumexp', torch.logsumexp, -inf),
        ]

        shape = (2, 0, 4)
        x = torch.randn(shape, device=device)

        for fn in [torch.max, torch.min]:
            ident_err = 'operation does not have an identity'
            self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x))

        for item in fns_to_test:
            name, fn, identity = item
            if identity is None:
                ident_err = 'does not have an identity'
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=2))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=2, keepdim=True))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=1))
                self.assertRaisesRegex(RuntimeError, ident_err, lambda: fn(x, dim=1, keepdim=True))
            else:
                self.assertEqual(torch.empty((2, 0), device=device), fn(x, dim=2))
                self.assertEqual(torch.empty((2, 0, 1), device=device), fn(x, dim=2, keepdim=True))
                # assertEqual doesn't work with inf, -inf, nan and two tensors.
                check = (torch.testing.assert_allclose if math.isnan(identity) or math.isinf(identity) else
                         self.assertEqual)
                check(torch.full((2, 4), identity, device=device), fn(x, dim=1))
                check(torch.full((2, 1, 4), identity, device=device), fn(x, dim=1, keepdim=True))
                try:
                    check(torch.full((), identity, device=device), fn(x))
                except TypeError as err:
                    # ignore if there is no allreduce.
                    self.assertTrue('dim' in str(err))

        # any
        xb = x.to(torch.uint8)
        yb = x.to(torch.uint8)
        self.assertEqual((2, 0), xb.any(2).shape)
        self.assertEqual((2, 0, 1), xb.any(2, keepdim=True).shape)
        self.assertEqual(torch.zeros((2, 4), device=device, dtype=torch.uint8), xb.any(1))
        self.assertEqual(torch.zeros((2, 1, 4), device=device, dtype=torch.uint8), xb.any(1, keepdim=True))
        self.assertEqual(torch.zeros((), device=device, dtype=torch.uint8), xb.any())

        # all
        self.assertEqual((2, 0), xb.all(2).shape)
        self.assertEqual((2, 0, 1), xb.all(2, keepdim=True).shape)
        self.assertEqual(torch.ones((2, 4), device=device, dtype=torch.uint8), xb.all(1))
        self.assertEqual(torch.ones((2, 1, 4), device=device, dtype=torch.uint8), xb.all(1, keepdim=True))
        self.assertEqual(torch.ones((), device=device, dtype=torch.uint8), xb.all())

    def test_addcdiv(self, device):
        def _test_addcdiv(a, alpha, b, c):
            actual = torch.addcdiv(a, b, c, value=alpha)
            # implementation of addcdiv downcasts alpha. arithmetic ops don't.
            if not actual.dtype.is_floating_point:
                alpha = int(alpha)
            expected = a + (alpha * b) / c
            self.assertTrue(torch.allclose(expected, actual, equal_nan=True))

            with self.maybeWarnsRegex(
                    UserWarning, "This overload of addcdiv is deprecated"):
                self.assertEqual(actual, torch.addcdiv(a, alpha, b, c))

        def non_zero_rand(size, dtype, device):
            if dtype.is_floating_point or dtype.is_complex:
                a = torch.rand(size=size, dtype=dtype, device=device)
            elif dtype == torch.uint8:
                a = torch.randint(1, 5, size=size, dtype=dtype, device=device)
            else:
                a = torch.randint(-5, 5, size=size, dtype=dtype, device=device)
            return a + (a == 0).to(dtype)

        for dtype in torch.testing.get_all_math_dtypes(device):
            # TODO: update this after torch.allclose is added for complex
            if not dtype.is_complex:
                _test_addcdiv(
                    non_zero_rand((2, 2), dtype=dtype, device=device),
                    0.5,
                    non_zero_rand((2, 2), dtype=dtype, device=device),
                    non_zero_rand((2, 2), dtype=dtype, device=device))

    # TODO: run on non-native device types
    @dtypes(torch.double)
    def test_unary_out_op_mem_overlap(self, device, dtype):
        sz = 3
        doubles = torch.randn(2 * sz, dtype=dtype, device=device)
        positives = torch.randint(1, 100, (2 * sz,), device=device).double()
        ints = torch.randint(-100, 100, (2 * sz,), device=device)
        unary_mem_overlap_cases = [
            ("abs", doubles, True, True, 'cpu'),
            ("abs", doubles, True, True, 'cuda'),
            ("acos", doubles, True, True, 'cpu'),
            ("acos", doubles, True, True, 'cuda'),
            ("asin", doubles, True, True, 'cpu'),
            ("asin", doubles, True, True, 'cuda'),
            ("atan", doubles, True, True, 'cpu'),
            ("atan", doubles, True, True, 'cuda'),
            ("bitwise_not", ints, True, True, 'cpu'),
            ("bitwise_not", ints, True, True, 'cuda'),
            ("ceil", doubles, True, True, 'cpu'),
            ("ceil", doubles, True, True, 'cuda'),
            ("cos", doubles, True, True, 'cpu'),
            ("cos", doubles, True, True, 'cuda'),
            ("cosh", doubles, True, True, 'cpu'),
            ("cosh", doubles, True, True, 'cuda'),
            ("digamma", doubles, True, True, 'cpu'),
            ("erf", doubles, True, True, 'cpu'),
            ("erf", doubles, True, True, 'cuda'),
            ("erfc", doubles, True, True, 'cpu'),
            ("erfc", doubles, True, True, 'cuda'),
            ("erfinv", doubles, True, True, 'cpu'),
            ("erfinv", doubles, True, True, 'cuda'),
            ("exp", doubles, True, True, 'cpu'),
            ("exp", doubles, True, True, 'cuda'),
            ("expm1", doubles, True, True, 'cpu'),
            ("expm1", doubles, True, True, 'cuda'),
            ("floor", doubles, True, True, 'cpu'),
            ("floor", doubles, True, True, 'cuda'),
            ("frac", doubles, True, True, 'cpu'),
            ("frac", doubles, True, True, 'cuda'),
            ("log", positives, True, True, 'cpu'),
            ("log", positives, True, True, 'cuda'),
            ("log10", positives, True, True, 'cpu'),
            ("log10", positives, True, True, 'cuda'),
            ("log1p", positives, True, True, 'cpu'),
            ("log1p", positives, True, True, 'cuda'),
            ("log2", positives, True, True, 'cpu'),
            ("log2", positives, True, True, 'cuda'),
            ("neg", doubles, True, True, 'cpu'),
            ("neg", doubles, True, True, 'cuda'),
            ("reciprocal", doubles, True, True, 'cpu'),
            ("reciprocal", doubles, True, True, 'cuda'),
            ("round", doubles, True, True, 'cpu'),
            ("round", doubles, True, True, 'cuda'),
            ("rsqrt", positives, True, True, 'cpu'),
            ("rsqrt", positives, True, True, 'cuda'),
            ("sin", doubles, True, True, 'cpu'),
            ("sin", doubles, True, True, 'cuda'),
            ("sinh", doubles, True, True, 'cpu'),
            ("sinh", doubles, False, True, 'cuda'),
            ("sigmoid", doubles, True, True, 'cpu'),
            ("sigmoid", doubles, True, True, 'cuda'),
            ("sqrt", doubles, True, True, 'cpu'),
            ("sqrt", doubles, False, True, 'cuda'),
            ("tan", doubles, True, True, 'cpu'),
            ("tan", doubles, True, True, 'cuda'),
            ("tanh", doubles, True, True, 'cpu'),
            ("tanh", doubles, True, True, 'cuda'),
            ("trunc", doubles, True, True, 'cpu'),
            ("trunc", doubles, True, True, 'cuda')
        ]

        for (fn, inputs, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in unary_mem_overlap_cases:
            if dev != device:
                continue
            out_fn = getattr(torch, fn)
            in_fn = getattr(torch.Tensor, fn + '_')

            self.unary_check_input_output_mem_overlap(inputs, sz, out_fn,
                                                      expected_failure=not has_input_output_mem_overlap_check)

            self.check_internal_mem_overlap(in_fn, 1, dtype, dev,
                                            expected_failure=not has_internal_mem_overlap_check)

    @dtypes(torch.double)
    def test_binary_op_mem_overlap(self, device, dtype):
        ops = [
            ("add", True, True, 'cpu'),
            ("add", True, True, 'cuda'),
            ("mul", True, True, 'cpu'),
            ("mul", True, True, 'cuda'),
            ("sub", True, True, 'cpu'),
            ("sub", True, True, 'cuda'),
            ("div", True, True, 'cpu'),
            ("div", True, True, 'cuda'),
            ("pow", True, True, 'cpu'),
            ("pow", True, True, 'cuda')
        ]

        for (fn, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in ops:
            if dev != device:
                continue
            out_op = getattr(torch, fn)
            inplace_op = getattr(torch.Tensor, fn + '_')
            self.check_internal_mem_overlap(
                inplace_op, 2, dtype, device,
                expected_failure=not has_internal_mem_overlap_check)

            self.binary_check_input_output_mem_overlap(out_op, device,
                                                       expected_failure=not has_input_output_mem_overlap_check)

    @dtypes(torch.double)
    def test_ternary_op_mem_overlap(self, device, dtype):
        ops = [
            ("addcmul", True, True, 'cpu'),
            ("addcmul", True, True, 'cuda'),
            ("addcdiv", True, True, 'cpu'),
            ("addcdiv", True, True, 'cuda'),
            ("lerp", True, True, 'cpu'),
            ("lerp", False, False, 'cuda')
        ]

        for (fn, has_input_output_mem_overlap_check,
             has_internal_mem_overlap_check, dev) in ops:
            if dev != device:
                continue
            out_op = getattr(torch, fn)
            inplace_op = getattr(torch.Tensor, fn + '_')
            self.check_internal_mem_overlap(
                inplace_op, 3, dtype, device,
                expected_failure=not has_internal_mem_overlap_check)
            self.ternary_check_input_output_mem_overlap(out_op, dev,
                                                        expected_failure=not has_input_output_mem_overlap_check)

    @dtypes(torch.double)
    def test_copy_mem_overlap(self, device, dtype):
        self.check_internal_mem_overlap(
            torch.Tensor.copy_, num_inputs=2, dtype=dtype, device=device)
        sz = 3
        doubles = torch.randn(2 * sz, dtype=dtype, device=device)
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: out.copy_(input))

    @dtypes(torch.double)
    def test_pow_scalar_overloads_mem_overlap(self, device, dtype):
        sz = 3
        doubles = torch.randn(2 * sz, dtype=dtype, device=device)
        self.check_internal_mem_overlap(
            lambda t: t.pow_(42), 1, dtype, device)
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: torch.pow(input, 42, out=out))
        self.unary_check_input_output_mem_overlap(
            doubles, sz, lambda input, out: torch.pow(42, input, out=out))

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_int_pow(self, device):

        def _test_integral_pow(dt, range, dev):
            tensor = torch.tensor((3, 3), dtype=dt, device=dev).random_(*range)
            exps = [0, 1, 2, 4,
                    torch.tensor((3, 3), dtype=dt, device=dev).random_(0, 5)]
            for exp in exps:
                self._test_pow(tensor, exp)

        _test_integral_pow(torch.int8, (-3, 4), device)
        _test_integral_pow(torch.uint8, (0, 4), device)
        _test_integral_pow(torch.int16, (-5, 5), device)
        _test_integral_pow(torch.int64, (-10, 10), device)
        _test_integral_pow(torch.int32, (-10, 10), device)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_int_tensor_pow_neg_ints(self, device):
        ints = [torch.iinfo(torch.int32).min,
                -3, -2, -1, 0, 1, 2, 3,
                torch.iinfo(torch.int32).max]
        neg_ints = [torch.iinfo(torch.int32).min, -3, -2, -1]
        tensor = torch.tensor(ints, dtype=torch.int32, device=device)
        for pow in neg_ints:
            self._test_pow(tensor, pow)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_long_tensor_pow_floats(self, device):
        ints = [0, 1, 23, 4567]
        floats = [0.0, 1 / 3, 1 / 2, 1.0, 3 / 2, 2.0]
        tensor = torch.tensor(ints, dtype=torch.int64, device=device)
        for pow in floats:
            self._test_pow(tensor, pow)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_float_scalar_pow_float_tensor(self, device):
        floats = [2.0, -3 / 2, -1.0, -1 / 2, -1 / 3, 0.0,
                  1 / 3, 1 / 2, 1.0, 3 / 2, 2.0]
        tensor = torch.tensor(floats, dtype=torch.float32, device=device)
        for base in floats:
            self._test_pow(base, tensor)

    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    def test_tensor_pow_tensor(self, dev):
        def rotate(l, n):
            return l[-n:] + l[:-n]

        def test_tensor_pow_tensor(values, torch_type, numpy_type):
            vals_tensor = torch.tensor(values, dtype=torch_type, device=dev)
            for i in range(len(values)):
                pows = rotate(values, i)
                pows_tensor = torch.tensor(pows, dtype=torch_type, device=dev)
                self._test_pow(vals_tensor, pows_tensor)

        ints = [0, 1, 2, 3]
        test_tensor_pow_tensor(ints, torch.int32, np.int32)
        test_tensor_pow_tensor(ints, torch.int64, np.int64)

        floats = [-3.0, -2.0, -1.0, -1 / 2, -1 / 3,
                  0.0,
                  1 / 3, 1 / 2, 1.0, 2.0, 3.0]
        test_tensor_pow_tensor(floats, torch.float32, np.float32)
        test_tensor_pow_tensor(floats, torch.float64, np.float64)

    @dtypes(torch.float)
    def test_add_with_tail(self, device, dtype):
        # test tensor where there is a tail which is not a multiple
        # of GPU warp size
        for tail_size in [1, 63, 67, 130]:
            size = 4096 + tail_size
            a = torch.randn(size, device=device, dtype=dtype)
            b = torch.randn(size, device=device, dtype=dtype)
            c = a + b
            for x, y, z in zip(a.tolist(), b.tolist(), c.tolist()):
                self.assertEqual(x + y, z)

    def test_logical_xor_with_nontrivial_alignment(self, device):
        # test tensor that is not aligned to multiple of 16 bytes
        size = 128
        a = (torch.randn(size, device=device) > 0)
        b = (torch.randn(size, device=device) > 0)
        c = (torch.randn(size, device=device) > 0)
        non_trivial_alignment = [1, 2, 4, 8, 15]
        for i in non_trivial_alignment:
            for j in non_trivial_alignment:
                for k in non_trivial_alignment:
                    a_ = a[i: 100 + i]
                    b_ = b[j: 100 + j]
                    c_ = c[k: 100 + k]
                    torch.logical_xor(a_, b_, out=c_)
                    for x, y, z in zip(a_.tolist(), b_.tolist(), c_.tolist()):
                        self.assertEqual(x ^ y, z)

    def test_var_mean_some_dims(self, device):
        sizes = (4, 6, 7, 5, 3)
        dims = len(sizes)

        x = torch.rand(sizes, device=device)
        for num_of_dims in range(2, dims):
            dim_list = list(combinations(list(range(dims)), r=num_of_dims))
            for dim in dim_list:
                for unbiased in [False, True]:
                    for keepdim in [False, True]:
                        var1, mean1 = torch.var_mean(x, dim=dim, unbiased=unbiased, keepdim=keepdim)
                        var2 = x.var(dim=dim, unbiased=unbiased, keepdim=keepdim)
                        mean2 = x.mean(dim=dim, keepdim=keepdim)
                        self.assertEqual(var1, var2)
                        self.assertEqual(mean1, mean2)

    # passes on ROCm w/ python 2.7, fails w/ python 3.6
    @skipCUDAIfRocm
    # stft -> rfft -> _fft -> _fft_with_size -> _fft_mkl
    @skipCPUIfNoMkl
    @dtypes(torch.double)
    def test_stft(self, device, dtype):
        if not TEST_LIBROSA:
            raise unittest.SkipTest('librosa not found')

        def librosa_stft(x, n_fft, hop_length, win_length, window, center):
            if window is None:
                window = np.ones(n_fft if win_length is None else win_length)
            else:
                window = window.cpu().numpy()
            input_1d = x.dim() == 1
            if input_1d:
                x = x.view(1, -1)
            result = []
            for xi in x:
                ri = librosa.stft(xi.cpu().numpy(), n_fft, hop_length, win_length, window, center=center)
                result.append(torch.from_numpy(np.stack([ri.real, ri.imag], -1)))
            result = torch.stack(result, 0)
            if input_1d:
                result = result[0]
            return result

        def _test(sizes, n_fft, hop_length=None, win_length=None, win_sizes=None,
                  center=True, expected_error=None):
            x = torch.randn(*sizes, dtype=dtype, device=device)
            if win_sizes is not None:
                window = torch.randn(*win_sizes, dtype=dtype, device=device)
            else:
                window = None
            if expected_error is None:
                result = x.stft(n_fft, hop_length, win_length, window, center=center)
                # NB: librosa defaults to np.complex64 output, no matter what
                # the input dtype
                ref_result = librosa_stft(x, n_fft, hop_length, win_length, window, center)
                self.assertEqual(result, ref_result, atol=7e-6, message='stft comparison against librosa', exact_dtype=False)
            else:
                self.assertRaises(expected_error,
                                  lambda: x.stft(n_fft, hop_length, win_length, window, center=center))

        for center in [True, False]:
            _test((10,), 7, center=center)
            _test((10, 4000), 1024, center=center)

            _test((10,), 7, 2, center=center)
            _test((10, 4000), 1024, 512, center=center)

            _test((10,), 7, 2, win_sizes=(7,), center=center)
            _test((10, 4000), 1024, 512, win_sizes=(1024,), center=center)

            # spectral oversample
            _test((10,), 7, 2, win_length=5, center=center)
            _test((10, 4000), 1024, 512, win_length=100, center=center)

        _test((10, 4, 2), 1, 1, expected_error=RuntimeError)
        _test((10,), 11, 1, center=False, expected_error=RuntimeError)
        _test((10,), -1, 1, expected_error=RuntimeError)
        _test((10,), 3, win_length=5, expected_error=RuntimeError)
        _test((10,), 5, 4, win_sizes=(11,), expected_error=RuntimeError)
        _test((10,), 5, 4, win_sizes=(1, 1), expected_error=RuntimeError)

    @skipIfRocm
    @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
    def test_fft_input_modification(self, device):
        # FFT functions should not modify their input (gh-34551)

        signal = torch.ones((2, 2, 2), device=device)
        signal_copy = signal.clone()
        spectrum = torch.fft(signal, 2)
        self.assertEqual(signal, signal_copy)

        spectrum_copy = spectrum.clone()
        _ = torch.ifft(spectrum, 2)
        self.assertEqual(spectrum, spectrum_copy)

        half_spectrum = torch.rfft(signal, 2)
        self.assertEqual(signal, signal_copy)

        half_spectrum_copy = half_spectrum.clone()
        _ = torch.irfft(half_spectrum_copy, 2, signal_sizes=(2, 2))
        self.assertEqual(half_spectrum, half_spectrum_copy)

    @onlyOnCPUAndCUDA
    @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
    @dtypes(torch.double)
    def test_istft_round_trip_simple_cases(self, device, dtype):
        """stft -> istft should recover the original signale"""
        def _test(input, n_fft, length):
            stft = torch.stft(input, n_fft=n_fft)
            inverse = torch.istft(stft, n_fft=n_fft, length=length)
            self.assertEqual(input, inverse, exact_dtype=True)

        _test(torch.ones(4, dtype=dtype, device=device), 4, 4)
        _test(torch.zeros(4, dtype=dtype, device=device), 4, 4)

    @onlyOnCPUAndCUDA
    @unittest.skipIf(not TEST_MKL, "PyTorch is built without MKL support")
    @dtypes(torch.double)
    def test_istft_round_trip_various_params(self, device, dtype):
        """stft -> istft should recover the original signale"""
        def _test_istft_is_inverse_of_stft(stft_kwargs):
            # generates a random sound signal for each tril and then does the stft/istft
            # operation to check whether we can reconstruct signal
            data_sizes = [(2, 20), (3, 15), (4, 10)]
            num_trials = 100
            istft_kwargs = stft_kwargs.copy()
            del istft_kwargs['pad_mode']
            for sizes in data_sizes:
                for i in range(num_trials):
                    original = torch.randn(*sizes, dtype=dtype, device=device)
                    stft = torch.stft(original, **stft_kwargs)
                    inversed = torch.istft(stft, length=original.size(1), **istft_kwargs)

                    # trim the original for case when constructed signal is shorter than original
                    original = original[..., :inversed.size(-1)]
                    self.assertEqual(
                        inversed, original, 'istft comparison against original', atol=7e-6, exact_dtype=True)

        patterns = [
            # hann_window, centered, normalized, onesided
            {
                'n_fft': 12,
                'hop_length': 4,
                'win_length': 12,
                'window': torch.hann_window(12, dtype=dtype, device=device),
                'center': True,
                'pad_mode': 'reflect',
                'normalized': True,
                'onesided': True,
            },
            # hann_window, centered, not normalized, not onesided
            {
                'n_fft': 12,
                'hop_length': 2,
                'win_length': 8,
                'window': torch.hann_window(8, dtype=dtype, device=device),
                'center': True,
                'pad_mode': 'reflect',
                'normalized': False,
                'onesided': False,
            },
            # hamming_window, centered, normalized, not onesided
            {
                'n_fft': 15,
                'hop_length': 3,
                'win_length': 11,
                'window': torch.hamming_window(11, dtype=dtype, device=device),
                'center': True,
                'pad_mode': 'constant',
                'normalized': True,
                'onesided': False,
            },
            # hamming_window, not centered, not normalized, onesided
            # window same size as n_fft
            {
                'n_fft': 5,
                'hop_length': 2,
                'win_length': 5,
                'window': torch.hamming_window(5, dtype=dtype, device=device),
                'center': False,
                'pad_mode': 'constant',
                'normalized': False,
                'onesided': True,
            },
            # hamming_window, not centered, not normalized, not onesided
            # window same size as n_fft
            {
                'n_fft': 3,
                'hop_length': 2,
                'win_length': 3,
                'window': torch.hamming_window(3, dtype=dtype, device=device),
                'center': False,
                'pad_mode': 'reflect',
                'normalized': False,
                'onesided': False,
            },
        ]
        for i, pattern in enumerate(patterns):
            _test_istft_is_inverse_of_stft(pattern)

    @onlyOnCPUAndCUDA
    def test_istft_throws(self, device):
        """istft should throw exception for invalid parameters"""
        stft = torch.zeros((3, 5, 2), device=device)
        # the window is size 1 but it hops 20 so there is a gap which throw an error
        self.assertRaises(
            RuntimeError, torch.istft, stft, n_fft=4,
            hop_length=20, win_length=1, window=torch.ones(1))
        # A window of zeros does not meet NOLA
        invalid_window = torch.zeros(4, device=device)
        self.assertRaises(
            RuntimeError, torch.istft, stft, n_fft=4, win_length=4, window=invalid_window)
        # Input cannot be empty
        self.assertRaises(RuntimeError, torch.istft, torch.zeros((3, 0, 2)), 2)
        self.assertRaises(RuntimeError, torch.istft, torch.zeros((0, 3, 2)), 2)

    @onlyOnCPUAndCUDA
    @skipIfRocm
    @dtypes(torch.double)
    def test_istft_of_sine(self, device, dtype):
        def _test(amplitude, L, n):
            # stft of amplitude*sin(2*pi/L*n*x) with the hop length and window size equaling L
            x = torch.arange(2 * L + 1, dtype=dtype)
            original = amplitude * torch.sin(2 * math.pi / L * x * n)
            # stft = torch.stft(original, L, hop_length=L, win_length=L,
            #                   window=torch.ones(L), center=False, normalized=False)
            stft = torch.zeros((L // 2 + 1, 2, 2), dtype=dtype)
            stft_largest_val = (amplitude * L) / 2.0
            if n < stft.size(0):
                stft[n, :, 1] = -stft_largest_val

            if 0 <= L - n < stft.size(0):
                # symmetric about L // 2
                stft[L - n, :, 1] = stft_largest_val

            inverse = torch.istft(
                stft, L, hop_length=L, win_length=L,
                window=torch.ones(L, dtype=dtype), center=False, normalized=False)
            # There is a larger error due to the scaling of amplitude
            original = original[..., :inverse.size(-1)]
            self.assertEqual(inverse, original, 1e-3)

        _test(amplitude=123, L=5, n=1)
        _test(amplitude=150, L=5, n=2)
        _test(amplitude=111, L=5, n=3)
        _test(amplitude=160, L=7, n=4)
        _test(amplitude=145, L=8, n=5)
        _test(amplitude=80, L=9, n=6)
        _test(amplitude=99, L=10, n=7)

    @onlyOnCPUAndCUDA
    @skipIfRocm
    @dtypes(torch.double)
    def test_istft_linearity(self, device, dtype):
        num_trials = 100

        def _test(data_size, kwargs):
            for i in range(num_trials):
                tensor1 = torch.randn(data_size, device=device, dtype=dtype)
                tensor2 = torch.randn(data_size, device=device, dtype=dtype)
                a, b = torch.rand(2, dtype=dtype, device=device)
                istft1 = torch.istft(tensor1, **kwargs)
                istft2 = torch.istft(tensor2, **kwargs)
                istft = a * istft1 + b * istft2
                estimate = torch.istft(a * tensor1 + b * tensor2, **kwargs)
                self.assertEqual(istft, estimate, 1e-5)
        patterns = [
            # hann_window, centered, normalized, onesided
            (
                (2, 7, 7, 2),
                {
                    'n_fft': 12,
                    'window': torch.hann_window(12, device=device, dtype=dtype),
                    'center': True,
                    'normalized': True,
                    'onesided': True,
                },
            ),
            # hann_window, centered, not normalized, not onesided
            (
                (2, 12, 7, 2),
                {
                    'n_fft': 12,
                    'window': torch.hann_window(12, device=device, dtype=dtype),
                    'center': True,
                    'normalized': False,
                    'onesided': False,
                },
            ),
            # hamming_window, centered, normalized, not onesided
            (
                (2, 12, 7, 2),
                {
                    'n_fft': 12,
                    'window': torch.hamming_window(12, device=device, dtype=dtype),
                    'center': True,
                    'normalized': True,
                    'onesided': False,
                },
            ),
            # hamming_window, not centered, not normalized, onesided
            (
                (2, 7, 3, 2),
                {
                    'n_fft': 12,
                    'window': torch.hamming_window(12, device=device, dtype=dtype),
                    'center': False,
                    'normalized': False,
                    'onesided': True,
                },
            )
        ]
        for data_size, kwargs in patterns:
            _test(data_size, kwargs)

    @onlyOnCPUAndCUDA
    @skipIfRocm
    def test_batch_istft(self, device):
        original = torch.tensor([
            [[4., 0.], [4., 0.], [4., 0.], [4., 0.], [4., 0.]],
            [[0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.]],
            [[0., 0.], [0., 0.], [0., 0.], [0., 0.], [0., 0.]]
        ], device=device)

        single = original.repeat(1, 1, 1, 1)
        multi = original.repeat(4, 1, 1, 1)

        i_original = torch.istft(original, n_fft=4, length=4)
        i_single = torch.istft(single, n_fft=4, length=4)
        i_multi = torch.istft(multi, n_fft=4, length=4)

        self.assertEqual(i_original.repeat(1, 1), i_single, 1e-6, exact_dtype=True)
        self.assertEqual(i_original.repeat(4, 1), i_multi, 1e-6, exact_dtype=True)

    @skipCUDAIfRocm
    def test_blas_empty(self, device):

        def fn(torchfn, *args, **kwargs):
            return torchfn(*tuple(torch.randn(shape, device=device) if isinstance(shape, tuple) else shape
                                  for shape in args), **kwargs)

        # mm, addmm
        self.assertEqual((0, 0), fn(torch.mm, (0, 0), (0, 0)).shape)
        self.assertEqual((0, 5), fn(torch.mm, (0, 0), (0, 5)).shape)
        self.assertEqual((5, 0), fn(torch.mm, (5, 0), (0, 0)).shape)
        self.assertEqual((3, 0), fn(torch.mm, (3, 2), (2, 0)).shape)
        self.assertEqual(torch.zeros((5, 6), device=device), fn(torch.mm, (5, 0), (0, 6)))

        self.assertEqual((0, 0), fn(torch.addmm, (0, 0), (0, 0), (0, 0)).shape)
        self.assertEqual((5, 6), fn(torch.addmm, (5, 6), (5, 0), (0, 6)).shape)
        self.assertEqual((0, 1), fn(torch.addmm, (1, ), (0, 17), (17, 1)).shape)

        # mv, addmv
        self.assertEqual((0,), fn(torch.mv, (0, 0), (0,)).shape)
        self.assertEqual((0,), fn(torch.mv, (0, 2), (2,)).shape)
        self.assertEqual(torch.zeros((3,), device=device), fn(torch.mv, (3, 0), (0,)))

        self.assertEqual((0,), fn(torch.addmv, (0,), (0, 0), (0,)).shape)
        self.assertEqual((3,), fn(torch.addmv, (3,), (3, 0), (0,)).shape)

        # ger, addr
        self.assertEqual((0, 0), fn(torch.ger, (0,), (0,)).shape)
        self.assertEqual((5, 0), fn(torch.ger, (5,), (0,)).shape)
        self.assertEqual((0, 4), fn(torch.ger, (0,), (4,)).shape)

        self.assertEqual((0, 0), fn(torch.addr, (0, 0), (0,), (0,)).shape)
        self.assertEqual((5, 0), fn(torch.addr, (5, 0), (5,), (0,)).shape)
        self.assertEqual((0, 4), fn(torch.addr, (0, 4), (0,), (4,)).shape)

        # bmm, baddbmm
        self.assertEqual((0, 0, 0), fn(torch.bmm, (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((3, 0, 5), fn(torch.bmm, (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((0, 5, 6), fn(torch.bmm, (0, 5, 0), (0, 0, 6)).shape)
        self.assertEqual(torch.zeros((3, 5, 6), device=device), fn(torch.bmm, (3, 5, 0), (3, 0, 6)))

        self.assertEqual((0, 0, 0), fn(torch.baddbmm, (0, 0, 0), (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((3, 0, 5), fn(torch.baddbmm, (3, 0, 5), (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((0, 5, 6), fn(torch.baddbmm, (0, 5, 6), (0, 5, 0), (0, 0, 6)).shape)
        self.assertEqual((3, 5, 6), fn(torch.baddbmm, (3, 5, 6), (3, 5, 0), (3, 0, 6)).shape)
        c = torch.arange(30, dtype=torch.float32, device=device).reshape(3, 2, 5)
        self.assertEqual(-2 * c, fn(torch.baddbmm, c, (3, 2, 0), (3, 0, 5), beta=-2))  # Issue #33467

        # addbmm
        self.assertEqual((0, 0), fn(torch.addbmm, (0, 0), (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((0, 5), fn(torch.addbmm, (0, 5), (3, 0, 0), (3, 0, 5)).shape)
        self.assertEqual((5, 6), fn(torch.addbmm, (5, 6), (0, 5, 0), (0, 0, 6)).shape)

        # matmul
        self.assertEqual(torch.tensor(0., device=device), fn(torch.matmul, (0,), (0,)))
        self.assertEqual((0, 0), fn(torch.matmul, (0, 0), (0, 0)).shape)
        self.assertEqual((0, 0, 0), fn(torch.matmul, (0, 0, 0), (0, 0, 0)).shape)
        self.assertEqual((5, 0, 0), fn(torch.matmul, (5, 0, 0), (5, 0, 0)).shape)
        self.assertEqual(torch.zeros((5, 3, 4), device=device), fn(torch.matmul, (5, 3, 0), (5, 0, 4)))

        # dot
        self.assertEqual(torch.tensor(0., device=device), fn(torch.dot, (0,), (0,)))

        if torch._C.has_lapack:
            # lu
            A_LU, pivots = fn(torch.lu, (0, 5, 5))
            self.assertEqual([(0, 5, 5), (0, 5)], [A_LU.shape, pivots.shape])
            A_LU, pivots = fn(torch.lu, (0, 0, 0))
            self.assertEqual([(0, 0, 0), (0, 0)], [A_LU.shape, pivots.shape])
            A_LU, pivots = fn(torch.lu, (2, 0, 0))
            self.assertEqual([(2, 0, 0), (2, 0)], [A_LU.shape, pivots.shape])

    @skipCUDAIfRocm
    @dtypesIfCUDA(*(torch.float, torch.double) +
                  # This test is disabled on CUDA 9, due to:
                  # See: https://github.com/pytorch/pytorch/issues/31006
                  ((torch.half,) if torch.version.cuda and not torch.version.cuda.startswith('9.') else ()))
    @dtypes(*(set(torch.testing.get_all_dtypes()) - {torch.half, torch.bool, torch.complex64, torch.complex128}))
    def test_blas_alpha_beta_empty(self, device, dtype):
        if dtype is torch.bfloat16 and self.device_type == 'xla':
            # TODO (@zasdfgbnm): this causes the following error on test
            # TestTorchDeviceTypeXLA.test_blas_alpha_beta_empty_xla_bfloat16:
            #
            #   RuntimeError: _th_equal not supported on CPUType for BFloat16
            return
        # ensure beta is respected
        value = 11
        input = torch.full((2,), value, dtype=dtype, device=device)
        mat = torch.ones((2, 0), dtype=dtype, device=device)
        vec = torch.ones((0,), dtype=dtype, device=device)
        out = torch.empty((2,), dtype=dtype, device=device)
        alpha = 6
        beta = 3
        self.assertEqual(torch.full((2,), beta * value, dtype=dtype, device=device),
                         torch.addmv(input=input, mat=mat, vec=vec, alpha=alpha, beta=beta))
        self.assertEqual(torch.full((2,), beta * value, dtype=dtype, device=device),
                         torch.addmv(input=input, mat=mat, vec=vec, alpha=alpha, beta=beta, out=out))

        # torch.addmm
        input = torch.full((2, 3), value, dtype=dtype, device=device)
        mat2 = torch.ones((0, 3), dtype=dtype, device=device)
        out = torch.empty((2, 3), dtype=dtype, device=device)
        self.assertEqual(torch.full((2, 3), beta * value, dtype=dtype, device=device),
                         torch.addmm(input=input, mat1=mat, mat2=mat2, alpha=alpha, beta=beta))
        self.assertEqual(torch.full((2, 3), beta * value, dtype=dtype, device=device),
                         torch.addmm(input=input, mat1=mat, mat2=mat2, alpha=alpha, beta=beta, out=out))

    @onlyCPU  # not supported by CUBLAS
    def test_blas_nan_out(self, device):
        # These functions should work correctly with NaN filled outputs,
        # but need special handling, see [NOTE: cpu_zero]
        b = 3
        n = 5
        m = 7
        p = 11

        # torch.mv
        nm = torch.randn((m, n), device=device).t()
        _m = torch.randn((), device=device).expand(m)
        _m_out = torch.full((m,), float('nan'), device=device)
        self.assertEqual(torch.mv(nm, _m), torch.mv(nm, _m, out=_m_out))
        self.assertEqual(0, torch.isnan(torch.mv(nm, _m)).sum())

        # torch.mm
        mp = torch.randn((p, m), device=device).t()
        np_out = torch.full((n, p), float('nan'), device=device)
        self.assertEqual(torch.mm(nm, mp), torch.mm(nm, mp, out=np_out))

        # torch.bmm
        bnm = torch.randn((b, m, n), device=device).transpose(1, 2)
        bmp = torch.randn((b, p, m), device=device).transpose(1, 2)
        bnp_out = torch.full((b, n, p), float('nan'), device=device)
        self.assertEqual(torch.bmm(bnm, bmp), torch.bmm(bnm, bmp, out=bnp_out))

    @onlyCPU  # not supported by CUBLAS
    def test_blas_mv_large_input(self, device):
        # This would previously fail if the allocated output had NaNs, see:
        # https://github.com/pytorch/pytorch/issues/31663 and [NOTE: cpu_zero]
        n = 3000
        m = 200

        nm = torch.randn((m, n), device=device).t()
        _m = torch.randn((), device=device).expand(m)
        _m_out = torch.full((m,), 0., device=device)

        self.assertEqual(torch.mv(nm, _m), torch.mv(nm, _m, out=_m_out))

    @skipCUDAIfRocm
    def test_unique_dim(self, device):
        self.assertFalse(hasattr(torch, 'unique_dim'))

        def run_test(device, dtype):
            x = torch.tensor([[[1., 1.],
                               [0., 1.],
                               [2., 1.],
                               [0., 1.]],
                              [[1., 1.],
                               [0., 1.],
                               [2., 1.],
                               [0., 1.]]],
                             dtype=dtype,
                             device=device)
            x_empty = torch.empty(5, 0, dtype=dtype, device=device)
            x_ill_formed_empty = torch.empty(5, 0, 0, dtype=dtype, device=device)
            x_ill_formed_empty_another = torch.empty(5, 0, 5, dtype=dtype, device=device)
            expected_unique_dim0 = torch.tensor([[[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_inverse_dim0 = torch.tensor([0, 0])
            expected_counts_dim0 = torch.tensor([2])
            expected_unique_dim1 = torch.tensor([[[0., 1.],
                                                  [1., 1.],
                                                  [2., 1.]],
                                                 [[0., 1.],
                                                  [1., 1.],
                                                  [2., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_unique_dim1_bool = torch.tensor([[[False, True], [True, True]],
                                                      [[False, True], [True, True]]],
                                                     dtype=torch.bool,
                                                     device=device)
            expected_inverse_dim1 = torch.tensor([1, 0, 2, 0])
            expected_inverse_dim1_bool = torch.tensor([1, 0, 1, 0])
            expected_counts_dim1 = torch.tensor([2, 1, 1])
            expected_counts_dim1_bool = torch.tensor([2, 2])
            expected_unique_dim2 = torch.tensor([[[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]],
                                                 [[1., 1.],
                                                  [0., 1.],
                                                  [2., 1.],
                                                  [0., 1.]]],
                                                dtype=dtype,
                                                device=device)
            expected_inverse_dim2 = torch.tensor([0, 1])
            expected_counts_dim2 = torch.tensor([1, 1])
            expected_unique_empty = torch.tensor([], dtype=dtype, device=device)
            expected_inverse_empty = torch.tensor([], dtype=torch.long, device=device)
            expected_counts_empty = torch.tensor([], dtype=torch.long, device=device)
            # dim0
            x_unique = torch.unique(x, dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_inverse_dim0, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_counts_dim0, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=0)
            self.assertEqual(expected_unique_dim0, x_unique)
            self.assertEqual(expected_inverse_dim0, x_inverse)
            self.assertEqual(expected_counts_dim0, x_counts)

            # dim1
            x_unique = torch.unique(x, dim=1)
            if x.dtype == torch.bool:
                self.assertEqual(expected_unique_dim1_bool, x_unique)
            else:
                self.assertEqual(expected_unique_dim1, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=1)
            if x.dtype == torch.bool:
                self.assertEqual(expected_unique_dim1_bool, x_unique)
                self.assertEqual(expected_inverse_dim1_bool, x_inverse)
            else:
                self.assertEqual(expected_unique_dim1, x_unique)
                self.assertEqual(expected_inverse_dim1, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=1)
            if x.dtype == torch.bool:
                self.assertEqual(expected_unique_dim1_bool, x_unique)
                self.assertEqual(expected_counts_dim1_bool, x_counts)
            else:
                self.assertEqual(expected_unique_dim1, x_unique)
                self.assertEqual(expected_counts_dim1, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=1)
            if x.dtype == torch.bool:
                self.assertEqual(expected_unique_dim1_bool, x_unique)
                self.assertEqual(expected_inverse_dim1_bool, x_inverse)
                self.assertEqual(expected_counts_dim1_bool, x_counts)
            else:
                self.assertEqual(expected_unique_dim1, x_unique)
                self.assertEqual(expected_inverse_dim1, x_inverse)
                self.assertEqual(expected_counts_dim1, x_counts)

            # dim2
            x_unique = torch.unique(x, dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)

            x_unique, x_inverse = torch.unique(
                x,
                return_inverse=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_inverse_dim2, x_inverse)

            x_unique, x_counts = torch.unique(
                x,
                return_inverse=False,
                return_counts=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_counts_dim2, x_counts)

            x_unique, x_inverse, x_counts = torch.unique(
                x,
                return_inverse=True,
                return_counts=True,
                dim=2)
            self.assertEqual(expected_unique_dim2, x_unique)
            self.assertEqual(expected_inverse_dim2, x_inverse)
            self.assertEqual(expected_counts_dim2, x_counts)

            # test empty tensor
            x_unique, x_inverse, x_counts = torch.unique(
                x_empty,
                return_inverse=True,
                return_counts=True,
                dim=1)
            self.assertEqual(expected_unique_empty, x_unique)
            self.assertEqual(expected_inverse_empty, x_inverse)
            self.assertEqual(expected_counts_empty, x_counts)

            # test not a well formed tensor
            # Checking for runtime error, as this is the expected behaviour
            with self.assertRaises(RuntimeError):
                torch.unique(
                    x_ill_formed_empty,
                    return_inverse=True,
                    return_counts=True,
                    dim=1)

            # test along dim2
            with self.assertRaises(RuntimeError):
                torch.unique(
                    x_ill_formed_empty_another,
                    return_inverse=True,
                    return_counts=True,
                    dim=2)

            # test consecutive version
            y = torch.tensor(
                [[0, 1],
                 [0, 1],
                 [0, 1],
                 [1, 2],
                 [1, 2],
                 [3, 4],
                 [0, 1],
                 [0, 1],
                 [3, 4],
                 [1, 2]],
                dtype=dtype,
                device=device
            )
            expected_y_unique = torch.tensor(
                [[0, 1],
                 [1, 2],
                 [3, 4],
                 [0, 1],
                 [3, 4],
                 [1, 2]],
                dtype=dtype,
                device=device
            )
            expected_y_inverse = torch.tensor([0, 0, 0, 1, 1, 2, 3, 3, 4, 5], dtype=torch.int64, device=device)
            expected_y_counts = torch.tensor([3, 2, 1, 2, 1, 1], dtype=torch.int64, device=device)
            expected_y_inverse_bool = torch.tensor([0, 0, 0, 1, 1, 1, 2, 2, 3, 3], dtype=torch.int64, device=device)
            expected_y_counts_bool = torch.tensor([3, 3, 2, 2], dtype=torch.int64, device=device)
            y_unique, y_inverse, y_counts = torch.unique_consecutive(y, return_inverse=True, return_counts=True, dim=0)
            if x.dtype == torch.bool:
                self.assertEqual(expected_y_inverse_bool, y_inverse)
                self.assertEqual(expected_y_counts_bool, y_counts)
            else:
                self.assertEqual(expected_y_inverse, y_inverse)
                self.assertEqual(expected_y_counts, y_counts)

        run_test(device, torch.float)
        run_test(device, torch.double)
        run_test(device, torch.long)
        run_test(device, torch.uint8)
        run_test(device, torch.bool)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_reverse_binary_ops_multiple_device(self, devices):
        self.assertEqual(2 + torch.tensor(3), 2 + torch.tensor(3).to(devices[1]))    # __radd__
        self.assertEqual(2 - torch.tensor(3), 2 - torch.tensor(3).to(devices[1]))    # __rsub__
        self.assertEqual(2 * torch.tensor(3), 2 * torch.tensor(3).to(devices[1]))    # __rmul__
        self.assertEqual(2 / torch.tensor(3), 2 / torch.tensor(3).to(devices[1]))    # __rtruediv__
        self.assertEqual(2 // torch.tensor(3), 2 // torch.tensor(3).to(devices[1]))  # __rfloordiv__

        self.assertEqual(
            torch.tensor(2).to(devices[1]) + torch.tensor(3).to(devices[0]),
            torch.tensor(2) + torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) - torch.tensor(3).to(devices[0]),
            torch.tensor(2) - torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) * torch.tensor(3).to(devices[0]),
            torch.tensor(2) * torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) / torch.tensor(3).to(devices[0]),
            torch.tensor(2) / torch.tensor(3))
        self.assertEqual(
            torch.tensor(2).to(devices[1]) // torch.tensor(3).to(devices[0]),
            torch.tensor(2) // torch.tensor(3))

    @onlyCUDA
    def test_ceil_out_mismatch(self, device):
        a = torch.randn(1)
        b = torch.randn(1, device=device)
        self.assertRaises(RuntimeError, lambda: torch.ceil(a, out=b))


    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_has_storage_numpy(self, device):
        for dtype in [np.float32, np.float64, np.int64,
                      np.int32, np.int16, np.uint8]:
            arr = np.array([1], dtype=dtype)
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.float32).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.double).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.int).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.long).storage())
            self.assertIsNotNone(torch.tensor(arr, device=device, dtype=torch.uint8).storage())

    def test_all_any_empty(self, device):
        x = torch.ByteTensor().to(device)
        self.assertTrue(x.all())
        self.assertFalse(x.any())

        x = torch.BoolTensor().to(device)
        self.assertTrue(x.all())
        self.assertFalse(x.any())

    @onlyCUDA
    def test_multinomial_device_constrain(self, device):
        x = torch.empty(0, device="cpu")
        y = torch.empty(0, device=device)
        self.assertRaisesRegex(
            RuntimeError, "multinomial arguments must have the same device",
            lambda: torch.multinomial(x, 2, out=y))

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_multinomial_gpu_device_constrain(self, devices):
        x = torch.empty(0, device=devices[0])
        y = torch.empty(0, device=devices[1])
        self.assertRaisesRegex(
            RuntimeError, "multinomial arguments must have the same device",
            lambda: torch.multinomial(x, 2, out=y))

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_device_guard(self, devices):
        # verify that all operators with `device_guard: False` behave properly with multiple devices.
        # TODO: if we had operator introspection we could figure out this set of operators automatically...
        x = torch.randn((1, 2, 3), device=devices[1])
        y = torch.zeros((1, 3, 2), device=devices[1])
        scalar = torch.tensor(5, device=devices[1])

        # property ops
        torch.cudnn_is_acceptable(x)
        x.is_distributed()
        x.is_floating_point()
        x.is_complex()
        x.is_same_size(y)
        x.is_signed()
        x.size(0)
        x.stride(0)
        x.numel()
        x.is_set_to(y)
        x.data_ptr()
        scalar.is_nonzero()

        # sparse property ops
        y[0][1] = 5
        y_sparse = y.to_sparse()
        y_sparse.sparse_dim()
        y_sparse._dimI()
        y_sparse.dense_dim()
        y_sparse._dimV()
        y_sparse._nnz()
        y_sparse.is_coalesced()
        y_sparse._indices()
        y_sparse._values()
        y_sparse.indices()
        y_sparse.values()

        # in-place ops
        def inplace():
            return torch.randn((1, 2, 3), device=devices[1])
        inplace().as_strided_(y.size(), y.stride())
        inplace().resize_(y.size())
        inplace().squeeze_()
        inplace().squeeze_(0)
        inplace().unsqueeze_(2)
        inplace().transpose_(1, 2)
        inplace().squeeze_().t_()
        inplace().set_(x.storage())
        inplace().set_(x.storage(), x.storage_offset(), x.size(), x.stride())
        inplace().set_(x)
        inplace().set_()
        y_sparse._coalesced_(True)

        # shape modification
        x.as_strided(y.size(), y.stride())
        x.expand((5, 2, 3))
        x.expand_as(x)
        x.sum_to_size((1,))
        torch.broadcast_tensors(x , x)
        x.reshape((1, 3, 2))
        x.reshape_as(y)
        x.squeeze()
        x.squeeze(0)
        x.squeeze().t()
        x.transpose(1, 2)
        x.unsqueeze(2)
        x.view((1, 3, 2))
        x.view_as(y)

        # chunk, split, etc.
        x.chunk(2, dim=1)
        x.split(1, dim=2)
        x.split_with_sizes([1, 2], dim=2)
        x.unfold(dimension=2, size=1, step=1)

        x.narrow(1, 1, 1)
        x.select(1, 1)
        torch.isnan(x)

        torch.empty((1, 3, 2), out=y)
        torch.empty_like(x)
        torch.empty_like(x, dtype=torch.int64)

        # to
        x.to(x)
        x.to(y)
        x.to(x, copy=True)

    @onlyCUDA
    def test_tensor_factory_gpu_type_inference(self, device):
        saved_type = torch.Tensor().type()
        torch.set_default_tensor_type(torch.cuda.DoubleTensor)
        torch.set_default_dtype(torch.float32)
        self.assertIs(torch.float32, torch.tensor(0.).dtype)
        self.assertEqual(torch.device(device), torch.tensor(0.).device)
        torch.set_default_dtype(torch.float64)
        self.assertIs(torch.float64, torch.tensor(0.).dtype)
        self.assertEqual(torch.device(device), torch.tensor(0.).device)
        torch.set_default_tensor_type(saved_type)

    @onlyCUDA
    def test_tensor_factory_gpu_type(self, device):
        saved_type = torch.Tensor().type()
        torch.set_default_tensor_type(torch.cuda.FloatTensor)
        x = torch.zeros((5, 5))
        self.assertIs(torch.float32, x.dtype)
        self.assertTrue(x.is_cuda)
        torch.set_default_tensor_type(torch.cuda.DoubleTensor)
        x = torch.zeros((5, 5))
        self.assertIs(torch.float64, x.dtype)
        self.assertTrue(x.is_cuda)
        torch.set_default_tensor_type(saved_type)

    @onlyCPU
    def test_renorm_ps(self, device):
        # full reduction
        x = torch.randn(5, 5)
        xn = x.numpy()
        for p in [1, 2, 3, 4, inf]:
            res = x.renorm(p, 1, 1)
            expected = x / x.norm(p, 0, keepdim=True).clamp(min=1)
            self.assertEqual(res.numpy(), expected.numpy(), "renorm failed for {}-norm".format(p))

    @onlyCUDA
    def test_topk_noncontiguous_gpu(self, device):
        t = torch.randn(20, device=device)[::2]
        top1, idx1 = t.topk(5)
        top2, idx2 = t.contiguous().topk(5)
        self.assertEqual(top1, top2)
        self.assertEqual(idx1, idx2)

    @dtypes(torch.int8, torch.uint8, torch.int16, torch.int32, torch.int64)
    def test_topk_integral(self, device, dtype):
        a = torch.randint(torch.iinfo(dtype).min, torch.iinfo(dtype).max, size=(10,),
                          dtype=dtype, device=device)
        sort_topk = a.sort()[0][-5:].flip(0)
        topk = a.topk(5)
        self.assertEqual(sort_topk, topk[0])      # check values
        self.assertEqual(sort_topk, a[topk[1]])   # check indices

    @dtypesIfCUDA(*([torch.half, torch.float, torch.double]
                    + ([torch.bfloat16] if TEST_WITH_ROCM else [])))
    @dtypes(torch.float, torch.double)
    def test_topk_nonfinite(self, device, dtype):
        x = torch.tensor([float('nan'), float('inf'), 1e4, 0, -1e4, -float('inf')], device=device, dtype=dtype)
        val, idx = x.topk(4)
        expect = torch.tensor([float('nan'), float('inf'), 1e4, 0], device=device, dtype=dtype)
        self.assertEqual(val, expect, allow_inf=True)
        self.assertEqual(idx, [0, 1, 2, 3])

        val, idx = x.topk(4, largest=False)
        expect = torch.tensor([-float('inf'), -1e4, 0, 1e4], device=device, dtype=dtype)
        self.assertEqual(val, expect, allow_inf=True)
        self.assertEqual(idx, [5, 4, 3, 2])

    def test_is_signed(self, device):
        self.assertEqual(torch.IntTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.ByteTensor(5).to(device).is_signed(), False)
        self.assertEqual(torch.CharTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.FloatTensor(5).to(device).is_signed(), True)
        self.assertEqual(torch.HalfTensor(10).to(device).is_signed(), True)

    # Note - reports a leak of 512 bytes on CUDA device 1
    @deviceCountAtLeast(2)
    @skipCUDAMemoryLeakCheckIf(True)
    @onlyCUDA
    def test_tensor_set_errors_multigpu(self, devices):
        f_cuda0 = torch.randn((2, 3), dtype=torch.float32, device=devices[0])
        f_cuda1 = torch.randn((2, 3), dtype=torch.float32, device=devices[1])

        self.assertRaises(RuntimeError, lambda: f_cuda0.set_(f_cuda1.storage()))
        self.assertRaises(RuntimeError,
                          lambda: f_cuda0.set_(f_cuda1.storage(), 0, f_cuda1.size(), f_cuda1.stride()))
        self.assertRaises(RuntimeError, lambda: f_cuda0.set_(f_cuda1))

    @onlyCUDA
    def test_half_tensor(self, device):
        x = torch.randn(5, 5).half()
        self.assertEqual(x.to(device), x)

        xc = x.to(device)
        with tempfile.NamedTemporaryFile() as f:
            torch.save(xc, f)
            f.seek(0)
            xc2 = torch.load(f)
            self.assertIsInstance(xc2, type(xc))
            self.assertEqual(xc.float(), xc2.float())

    @onlyCUDA
    @deviceCountAtLeast(1)  # Note: Tests works with one but prefers more devices
    def test_serialization(self, devices):
        def _test_serialization(filecontext_lambda):
            t0 = torch.cuda.FloatTensor(5).fill_(1)
            with torch.cuda.device(devices[-1]):
                tn = torch.cuda.FloatTensor(3).fill_(2)
            torch.cuda.set_device(devices[0])
            b = (t0, tn)
            with filecontext_lambda() as f:
                torch.save(b, f)
                f.seek(0)
                c = torch.load(f)
                self.assertEqual(b, c, 0)
                u0, un = c
                self.assertEqual(str(u0.device), devices[0])
                self.assertEqual(str(un.device), devices[-1])

        _test_serialization(tempfile.NamedTemporaryFile)
        _test_serialization(BytesIOContext)

    def test_memory_format_preserved_after_permute(self, device):
        x = torch.randn(4, 3, 8, 8, device=device)
        nhwc = x.contiguous(memory_format=torch.channels_last)
        y = nhwc.permute(0, 1, 3, 2).permute(0, 1, 3, 2)
        self.assertTrue(y.is_contiguous(memory_format=torch.channels_last))

        x = torch.randn(4, 3, 8, 8, 8, device=device)
        ndhwc = x.contiguous(memory_format=torch.channels_last_3d)
        y = ndhwc.permute(0, 1, 4, 3, 2).permute(0, 1, 4, 3, 2)
        self.assertTrue(y.is_contiguous(memory_format=torch.channels_last_3d))

    def test_resize_as_preserves_strides(self, device):
        x = torch.empty(2, 3).t()
        old_strides = x.stride()
        x.resize_as_(x)
        self.assertEqual(x.stride(), old_strides)

    def test_memory_format_resize_as(self, device):
        def test_helper(shape, memory_format, device):
            xc = torch.randn(shape, device=device).contiguous(memory_format=memory_format)
            flat = torch.randn(xc.numel(), device=device)
            flat.resize_as_(xc, memory_format=torch.preserve_format)
            self.assertTrue(flat.is_contiguous(memory_format=memory_format))

        test_helper((10, 3, 32, 32), torch.channels_last, device)
        test_helper((3, 10, 3, 32, 32), torch.channels_last_3d, device)

    def test_memory_format_resize_(self, device):
        def test_helper(shape, numel, memory_format, device):
            flat = torch.randn(numel, device=device)
            flat.resize_(shape, memory_format=memory_format)
            self.assertTrue(flat.is_contiguous(memory_format=memory_format))

        test_helper((10, 3, 32, 32), 10 * 3 * 32 * 32, torch.channels_last, device)
        test_helper((3, 10, 3, 32, 32), 3 * 10 * 3 * 32 * 32, torch.channels_last_3d, device)

    def test_memory_format_empty_like(self, device):
        def test_helper(x, memory_format):
            xc = x.contiguous(memory_format=memory_format)

            like = torch.empty_like(xc, memory_format=torch.preserve_format)
            self.assertFalse(like.is_contiguous())
            self.assertTrue(like.is_contiguous(memory_format=memory_format))

            like_x = torch.empty_like(x, memory_format=torch.preserve_format)
            self.assertTrue(like_x.is_contiguous())
            self.assertFalse(like_x.is_contiguous(memory_format=memory_format))

            like = torch.empty_like(x, memory_format=memory_format)
            self.assertFalse(like.is_contiguous())
            self.assertTrue(like.is_contiguous(memory_format=memory_format))

            like = torch.empty_like(xc, memory_format=torch.contiguous_format)
            self.assertTrue(like.is_contiguous())
            self.assertFalse(like.is_contiguous(memory_format=memory_format))

            like = torch.empty_like(xc)
            self.assertFalse(like.is_contiguous())
            self.assertTrue(like.is_contiguous(memory_format=memory_format))

            sparse = x.to_sparse()
            with self.assertRaises(RuntimeError):
                z = torch.empty_like(sparse, memory_format=torch.preserve_format)

        test_helper(torch.randn(4, 3, 8, 8, device=device), torch.channels_last)
        test_helper(torch.randn(4, 3, 8, 8, 8, device=device), torch.channels_last_3d)

    def test_memory_format_consistency(self, device):
        x = torch.randn(10, 3, 1, 1, device=device)
        x_rep = x.as_strided(x.size(), x.stride())
        self.assertEqual(x.size(), x_rep.size())
        self.assertEqual(x.stride(), x_rep.stride())
        self.assertEqual(x.is_contiguous(), x_rep.is_contiguous())
        self.assertEqual(x.is_contiguous(memory_format=torch.channels_last), x_rep.is_contiguous(memory_format=torch.channels_last))
        self.assertEqual(
            x.is_contiguous(memory_format=torch.channels_last_3d), x_rep.is_contiguous(memory_format=torch.channels_last_3d))

    def test_memory_format_operators(self, device):
        def chunk_op(x, y):
            x1, x2 = x.chunk(2, dim=1)
            y1, y2 = x.chunk(2, dim=1)
            y1 = y1.contiguous()
            return y1 + x1

        def unsqueeze_op_add(x, y):
            return x[0].unsqueeze(0) + 3

        def unsqueeze_op_clone(x, y):
            return x[0].unsqueeze(0).clone()

        def test_helper(x, y, memory_format):
            fns = [
                lambda x, y: x.clone(),
                lambda x, y: x + 3,
                lambda x, y: 3 * x,
                lambda x, y: x + y,
                lambda x, y: y + x,
                lambda x, y: x * y,
                lambda x, y: y * x,
                lambda x, y: abs(x),
                lambda x, y: x.abs(),
                lambda x, y: x.abs_(),
                lambda x, y: x.acos(),
                lambda x, y: x.acos_(),
                lambda x, y: x.add(y, alpha=3),
                lambda x, y: x.add_(y, alpha=3),
                lambda x, y: x.addcdiv(y, y, value=2),
                lambda x, y: x.addcdiv_(y, y, value=2),
                lambda x, y: y.addcdiv(x, y, value=2),
                lambda x, y: x.addcmul(y, y, value=2),
                lambda x, y: x.addcmul_(y, y, value=2),
                lambda x, y: y.addcmul(x, y, value=2),
                lambda x, y: x.asin(),
                lambda x, y: x.asin_(),
                lambda x, y: x.atan(),
                lambda x, y: x.atan2(y),
                lambda x, y: x.atan2_(y),
                lambda x, y: x.ceil(),
                lambda x, y: x.ceil_(),
                # lambda x, y: x.clamp(-1, 1), # https://github.com/pytorch/pytorch/issues/24544
                # lambda x, y: x.cos(), # https://github.com/pytorch/pytorch/issues/24545
                # lambda x, y: x.cosh(), # https://github.com/pytorch/pytorch/issues/24546
                lambda x, y: x.div(0.5),
                lambda x, y: x.div_(0.5),
                lambda x, y: x.div(y),
                lambda x, y: x.div_(y),
                lambda x, y: x.digamma(),
                lambda x, y: x.digamma_(),
                # lambda x, y: x.erf(), # https://github.com/pytorch/pytorch/issues/24558
                lambda x, y: x.erfc(),
                lambda x, y: x.erfinv(),
                lambda x, y: x.erfinv_(),
                # lambda x, y: x.exp(), # https://github.com/pytorch/pytorch/issues/24561
                lambda x, y: x.expm1(),
                lambda x, y: x.expm1_(),
                lambda x, y: x.floor(),
                lambda x, y: x.floor_(),
                # lambda x, y: x.fmod(2), # https://github.com/pytorch/pytorch/issues/24565
                # lambda x, y: x.frac(), # https://github.com/pytorch/pytorch/issues/24566
                # lambda x, y: x.lerp(y, 0.5), #  Need to update Lerp.cu with TensorIterator
                lambda x, y: x.log(),
                lambda x, y: x.log_(),
                lambda x, y: x.log10(),
                lambda x, y: x.log10_(),
                lambda x, y: x.log1p(),
                lambda x, y: x.log1p_(),
                lambda x, y: x.log2(),
                lambda x, y: x.log2_(),
                lambda x, y: x.mul(3),
                lambda x, y: x.mul_(3),
                lambda x, y: x.neg(),
                lambda x, y: x.neg_(),
                lambda x, y: x.pow(3),
                lambda x, y: x.pow_(3),
                # lambda x, y: x.pow(0.0), # Need to make resize_as_ memory format aware
                # lambda x, y: x.pow(1.0), # Need to make resize_as_ memory format aware
                # lambda x, y: x.reciprocal(), # Not migrated for CUDA
                # lambda x, y: x.remainder(2),  # https://github.com/pytorch/pytorch/issues/24615
                lambda x, y: x.round(),
                lambda x, y: x.round_(),
                lambda x, y: x.rsqrt(),
                lambda x, y: x.rsqrt_(),
                lambda x, y: x.sigmoid(),
                lambda x, y: x.sigmoid_(),
                lambda x, y: x.sign(),
                lambda x, y: x.sign_(),
                lambda x, y: x.sin(),
                lambda x, y: x.sin_(),
                lambda x, y: x.sinh(),
                lambda x, y: x.sinh_(),
                lambda x, y: x.sqrt(),
                lambda x, y: x.sqrt_(),
                # lambda x, y: x.tan(), # https://github.com/pytorch/pytorch/issues/24641
                # lambda x, y: x.tanh(), # https://github.com/pytorch/pytorch/issues/24642
                lambda x, y: x.trunc(),
                lambda x, y: x.trunc_(),
                chunk_op,
                unsqueeze_op_add,
                # unsqueeze_op_clone,
            ]
            for fn in fns:
                x_c = x.contiguous()
                y_c = y.contiguous()
                result_c = fn(x_c, y_c)
                result = fn(x, y)
                self.assertEqual(result, result_c)
                self.assertTrue(
                    result.is_contiguous(memory_format=memory_format),
                    "result of the '{}' is not in '{}' format".format(inspect.getsource(fn).strip(), memory_format))

        test_helper(
            torch.randn((4, 3, 8, 8), device=device).contiguous(memory_format=torch.channels_last),
            abs(torch.randn((4, 3, 8, 8), device=device)) + 1,
            torch.channels_last)
        test_helper(
            torch.randn((4, 3, 8, 8, 8), device=device).contiguous(memory_format=torch.channels_last_3d),
            abs(torch.randn((4, 3, 8, 8, 8), device=device)) + 1,
            torch.channels_last_3d)

    def _test_unique_scalar_empty(self, dtype, device, f):
        # test scalar
        x = torch.tensor(0, dtype=dtype, device=device)
        unique, inverse, counts = f(x, return_inverse=True, return_counts=True)
        expected_unique = torch.tensor([0], dtype=dtype, device=device)
        expected_inverse = torch.tensor(0, device=device)
        expected_counts = torch.tensor([1], device=device)
        self.assertEqual(unique, expected_unique)
        self.assertEqual(inverse, expected_inverse)
        self.assertEqual(counts, expected_counts)

        # test zero sized tensor
        x = torch.zeros((0, 0, 3), dtype=dtype, device=device)
        unique, inverse, counts = f(x, return_inverse=True, return_counts=True)
        expected_unique = torch.tensor([], dtype=dtype, device=device)
        expected_inverse = torch.empty((0, 0, 3), dtype=torch.long, device=device)
        expected_counts = torch.tensor([], dtype=torch.long, device=device)
        self.assertEqual(unique, expected_unique)
        self.assertEqual(inverse, expected_inverse)
        self.assertEqual(counts, expected_counts)

    def _test_unique_with_expects(self, device, dtype, f, x, expected_unique, expected_inverse, expected_counts, additional_shape):
        def ensure_tuple(x):
            if isinstance(x, torch.Tensor):
                return (x,)
            return x

        for return_inverse in [True, False]:
            for return_counts in [True, False]:
                # test with expected
                ret = ensure_tuple(f(x, return_inverse=return_inverse, return_counts=return_counts))
                self.assertEqual(len(ret), 1 + int(return_inverse) + int(return_counts))
                self.assertEqual(expected_unique, ret[0])
                if return_inverse:
                    self.assertEqual(expected_inverse, ret[1])
                if return_counts:
                    count_index = 1 + int(return_inverse)
                    self.assertEqual(expected_counts, ret[count_index])

                # tests per-element unique on a higher rank tensor.
                y = x.view(additional_shape)
                y_unique, y_inverse, y_counts = f(y, return_inverse=True, return_counts=True)
                self.assertEqual(expected_unique, y_unique)
                self.assertEqual(expected_inverse.view(additional_shape), y_inverse)
                self.assertEqual(expected_counts, y_counts)

    @dtypes(*set(torch.testing.get_all_dtypes()) - {torch.bfloat16, torch.complex64, torch.complex128})
    def test_unique(self, device, dtype):
        if dtype is torch.half and self.device_type == 'cpu':
            return  # CPU does not have half support

        def ensure_tuple(x):
            if isinstance(x, torch.Tensor):
                return (x,)
            return x

        if dtype is torch.bool:
            x = torch.tensor([True, False, False, False, True, False, True, False], dtype=torch.bool, device=device)
            expected_unique = torch.tensor([False, True], dtype=torch.bool, device=device)
            expected_inverse = torch.tensor([1, 0, 0, 0, 1, 0, 1, 0], dtype=torch.long, device=device)
            expected_counts = torch.tensor([5, 3], dtype=torch.long, device=device)
        else:
            x = torch.tensor([1, 2, 3, 2, 8, 5, 2, 3], dtype=dtype, device=device)
            expected_unique = torch.tensor([1, 2, 3, 5, 8], dtype=dtype, device=device)
            expected_inverse = torch.tensor([0, 1, 2, 1, 4, 3, 1, 2], device=device)
            expected_counts = torch.tensor([1, 3, 2, 1, 1], device=device)

        # test sorted unique
        fs = [
            lambda x, **kwargs: torch.unique(x, sorted=True, **kwargs),
            lambda x, **kwargs: x.unique(sorted=True, **kwargs),
        ]
        for f in fs:
            self._test_unique_with_expects(device, dtype, f, x, expected_unique, expected_inverse, expected_counts, (2, 2, 2))
            self._test_unique_scalar_empty(dtype, device, f)

        # test unsorted unique
        fs = [
            lambda x, **kwargs: torch.unique(x, sorted=False, **kwargs),
            lambda x, **kwargs: x.unique(sorted=False, **kwargs)
        ]
        for f in fs:
            self._test_unique_scalar_empty(dtype, device, f)
            for return_inverse in [True, False]:
                for return_counts in [True, False]:
                    ret = ensure_tuple(f(x, return_inverse=return_inverse, return_counts=return_counts))
                    self.assertEqual(len(ret), 1 + int(return_inverse) + int(return_counts))
                    x_list = x.tolist()
                    x_unique_list = ret[0].tolist()
                    self.assertEqual(expected_unique.tolist(), sorted(x_unique_list))
                    if return_inverse:
                        x_inverse_list = ret[1].tolist()
                        for i, j in enumerate(x_inverse_list):
                            self.assertEqual(x_list[i], x_unique_list[j])
                    if return_counts:
                        count_index = 1 + int(return_inverse)
                        x_counts_list = ret[count_index].tolist()
                        for i, j in zip(x_unique_list, x_counts_list):
                            count = 0
                            for k in x_list:
                                if k == i:
                                    count += 1
                            self.assertEqual(j, count)

    @dtypes(*set(torch.testing.get_all_dtypes()) - {torch.bfloat16, torch.complex64, torch.complex128})
    def test_unique_consecutive(self, device, dtype):
        if dtype is torch.half and self.device_type == 'cpu':
            return  # CPU does not have half support

        if dtype is torch.bool:
            x = torch.tensor([True, False, False, False, True, True, False, False, False], dtype=torch.bool, device=device)
            expected_unique = torch.tensor([True, False, True, False], dtype=torch.bool, device=device)
            expected_inverse = torch.tensor([0, 1, 1, 1, 2, 2, 3, 3, 3], dtype=torch.long, device=device)
            expected_counts = torch.tensor([1, 3, 2, 3], dtype=torch.long, device=device)
        else:
            x = torch.tensor([1, 2, 2, 2, 5, 5, 2, 2, 3], dtype=dtype, device=device)
            expected_unique = torch.tensor([1, 2, 5, 2, 3], dtype=dtype, device=device)
            expected_inverse = torch.tensor([0, 1, 1, 1, 2, 2, 3, 3, 4], device=device)
            expected_counts = torch.tensor([1, 3, 2, 2, 1], device=device)

        for f in [torch.unique_consecutive, lambda x, **kwargs: x.unique_consecutive(**kwargs)]:
            self._test_unique_with_expects(device, dtype, f, x, expected_unique, expected_inverse, expected_counts, (3, 3))
            self._test_unique_scalar_empty(dtype, device, f)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_erfinv(self, device, dtype):
        # general testing. Narrow the range to avoid accuracy issues
        input_values = torch.randn(4, 4, dtype=dtype, device=device).clamp(-0.3, 0.3)
        self.assertEqual(input_values.erf().erfinv(), input_values)
        # test inf
        self.assertTrue(torch.equal(torch.tensor([-1, 1], dtype=dtype, device=device).erfinv(),
                                    torch.tensor([-inf, inf], dtype=dtype, device=device)))
        # test nan
        self.assertEqual(torch.tensor([-2, 2], dtype=dtype, device=device).erfinv(),
                         torch.tensor([nan, nan], dtype=dtype, device=device))

        if dtype == torch.double:
            # double precision
            a = torch.tensor([0.5, 0.8], dtype=torch.double, device=device).erfinv()
            self.assertAlmostEqual(a[0].item(), 0.47693627620447, places=13)
            self.assertAlmostEqual(a[1].item(), 0.90619380243682, places=13)

    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_ctor_with_numpy_array(self, device):
        correct_dtypes = [
            np.double,
            np.float,
            np.float16,
            np.int64,
            np.int32,
            np.int16,
            np.int8,
            np.uint8,
            np.bool,
        ]

        incorrect_byteorder = '>' if sys.byteorder == 'little' else '<'
        incorrect_dtypes = map(lambda t: incorrect_byteorder + t, ['d', 'f'])

        for dtype in correct_dtypes:
            array = np.array([1, 2, 3, 4], dtype=dtype)

            # Upcast
            tensor = torch.DoubleTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

            # Downcast (sometimes)
            tensor = torch.FloatTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

            tensor = torch.HalfTensor(array).to(device)
            for i in range(len(array)):
                self.assertEqual(tensor[i], array[i])

    def test_dlpack_conversion(self, device):
        x = torch.randn(1, 2, 3, 4, device=device, dtype=torch.float)
        z = from_dlpack(to_dlpack(x))
        self.assertEqual(z, x)

    @onlyCUDA
    @unittest.skipIf(PYTORCH_CUDA_MEMCHECK, "is_pinned uses failure to detect pointer property")
    def test_pin_memory_from_constructor(self, device):
        def _get_like(t, **kwargs):
            return [
                torch.rand_like(t, **kwargs),
                torch.randn_like(t, **kwargs),
                torch.empty_like(t, **kwargs),
                torch.full_like(t, 4, **kwargs),
                torch.zeros_like(t, **kwargs),
                torch.ones_like(t, **kwargs),
            ]

        def _get_tensors(**kwargs):
            return [
                torch.tensor([10, 11], **kwargs),
                torch.randn(3, 5, **kwargs),
                torch.rand(3, **kwargs),
                # torch.randint(3, 5, **kwargs), // unsupported
                torch.zeros(3, **kwargs),
                torch.randperm(3, **kwargs),
                torch.empty(6, **kwargs),
                torch.ones(6, **kwargs),
                torch.eye(6, **kwargs),
                torch.arange(3, 5, **kwargs)]

        pinned_tensors = _get_tensors(pin_memory=True) + _get_like(torch.empty(5, dtype=torch.float64), pin_memory=True)
        for x in pinned_tensors:
            self.assertTrue(x.is_pinned())

        tensors = _get_tensors() + _get_like(torch.empty(5, dtype=torch.float64, pin_memory=True))
        for x in tensors:
            self.assertFalse(x.is_pinned())

    def test_storage_device(self, device):
        x = torch.tensor([], device=device)
        self.assertEqual(x.dtype, x.storage().dtype)

    @deviceCountAtLeast(2)
    @onlyCUDA
    def test_storage_multigpu(self, devices):
        for device in devices:
            x = torch.tensor([], device=device)
            self.assertEqual(x.dtype, x.storage().dtype)

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    def test_lu(self, device):
        from torch.testing._internal.common_utils import random_matrix

        def run_test(device, pivot):
            def run_subtest(matrix_size, batches, device, pivot, singular=False, a=None):
                if isinstance(matrix_size, int):
                    rows = columns = matrix_size
                else:
                    rows, columns = matrix_size
                if a is None:
                    a = random_matrix(rows, columns, *batches, **dict(singular=singular)).to(device)
                a_LU_info, pivots_info, info_ = a.lu(pivot=pivot, get_infos=True)
                self.assertEqual(a_LU_info.size(), torch.Size(batches + (rows, columns)))
                self.assertEqual(pivots_info.size(), torch.Size(batches + (min(rows, columns),)))
                self.assertEqual(info_.size(), torch.Size(batches))
                # If a randomly generated input matrix is singular,
                # then info_ contains indices i such that U[i, i] ==
                # 0. This however conveys that the factorization was
                # successful albeit with a singular input. Therefore,
                # we require info.min() >= 0
                self.assertGreaterEqual(info_.min(), 0)
                a_LU, pivots = a.lu(pivot=pivot)
                self.assertEqual(a_LU, a_LU_info)
                self.assertEqual(pivots_info, pivots)

                P, L, U = torch.lu_unpack(a_LU, pivots)
                self.assertEqual(P.matmul(L.matmul(U)), a)

                if self.device_type == 'cuda':
                    # lu without pivoting is implemented only for cuda device
                    a_LU_info_nopiv, nopiv, info_nopiv = a.lu(pivot=False, get_infos=True)
                    P_nopiv, L_nopiv, U_nopiv = torch.lu_unpack(a_LU_info_nopiv, nopiv)
                    self.assertEqual(P_nopiv.matmul(L_nopiv.matmul(U_nopiv)), a)
                    k = min(rows, columns)
                    self.assertEqual(nopiv, torch.arange(1, 1 + k, device=device, dtype=torch.int32).expand(a.shape[:-2] + (k, )))
                    if not singular:
                        # It is not guaranteed that LU factorization
                        # without pivoting is able to determine if a
                        # matrix is singular while LU factorization
                        # with pivoting is. Therefore, we require the
                        # equality of info-s only for non-singular
                        # matrices.
                        self.assertEqual(info_, info_nopiv)

            for ms, batch in product([3, 5, 7, (4, 2), (3, 4)], [(), (2,), (3,), (3, 5)]):
                run_subtest(ms, batch, device, pivot)
                run_subtest(ms, batch, device, pivot, singular=True)

                # Reproducer of a magma bug, see https://bitbucket.org/icl/magma/issues/13/getrf_batched-kernel-produces-nans-on
                a = torch.ones(batch + (ms if isinstance(ms, tuple) else (ms, ms)), dtype=torch.double, device=device)
                run_subtest(ms, batch, device, pivot, singular=True, a=a)

            # Info should be positive for rank deficient matrices
            a = torch.ones(5, 3, 3, device=device)
            self.assertGreater(a.lu(pivot=pivot, get_infos=True)[2][0], 0)

        run_test(device, True)

        if self.device_type == 'cpu':
            # Error checking, no pivoting variant on CPU
            with self.assertRaisesRegex(RuntimeError, 'lu without pivoting is not implemented on the CPU'):
                torch.lu(torch.empty(1, 2, 2), pivot=False)
        else:
            run_test(device, False)

    @skipCPUIfNoLapack
    @skipCUDAIfNoMagma
    @dtypes(torch.double)
    def test_lu_unpack(self, device, dtype):
        def run_test(pivot):
            for shape in ((3, 3), (5, 3, 3), (7, 3, 5, 5), (7, 5, 3, 3, 3)):
                a = torch.randn(*shape, dtype=dtype, device=device)
                a_lu, p = torch.lu(a, pivot=pivot)
                p_ref, l_ref, u_ref = torch.lu_unpack(a_lu, p)
                self.assertEqual(p_ref.matmul(l_ref.matmul(u_ref)), a)

        run_test(True)

        if self.device_type == 'cuda':
            run_test(False)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_max_with_inf(self, device, dtype):
        a = torch.tensor([[-inf, -inf, inf, 3], [inf, inf, -inf, -1]], dtype=dtype, device=device)
        self.assertTrue(torch.all(torch.max(a, dim=1)[0] == inf).item())
        self.assertTrue(torch.max(a).item() == inf)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_min_with_inf(self, device, dtype):
        a = torch.tensor([[-inf, -inf, inf, 3], [inf, inf, -inf, -1]], dtype=dtype, device=device)
        self.assertTrue(torch.all(torch.min(a, dim=1)[0] == (-inf)).item())
        self.assertTrue(torch.min(a).item() == -inf)

    def test_bincount(self, device):
        # negative input throws
        with self.assertRaisesRegex(RuntimeError, '1-d non-negative integral'):
            torch.bincount(torch.tensor([1, -1], device=device))
        # n-d input, with n > 1 throws
        with self.assertRaisesRegex(RuntimeError, '1-d non-negative integral'):
            torch.bincount(torch.tensor([[1, 2], [3, 4]], device=device))
        # floating input type throws
        with self.assertRaisesRegex(RuntimeError, 'not implemented'):
            torch.bincount(torch.tensor([1., 0.3], device=device))
        # minlength < 0 throws
        with self.assertRaisesRegex(RuntimeError, 'minlength should be >= 0'):
            torch.bincount(torch.tensor([1, 3], device=device),
                           torch.tensor([.2, .2], device=device),
                           minlength=-1)
        # input and weights dim mismatch
        with self.assertRaisesRegex(RuntimeError, 'same length'):
            torch.bincount(torch.tensor([1, 0], device=device),
                           torch.tensor([1., 0.3, 0.5], device=device))
        # 1-d input with no elements and default minlength
        self.assertEqual(torch.bincount(torch.tensor([], device=device, dtype=torch.long)),
                         torch.zeros(0, dtype=torch.long, device=device))
        # 1-d input with no elements and specified minlength
        self.assertEqual(torch.bincount(torch.tensor([], device=device, dtype=torch.long), minlength=10),
                         torch.zeros(10, dtype=torch.long, device=device))

        # test tensor method without weights
        long_counts = torch.tensor(
            [0, 3, 2, 1, 3], dtype=torch.uint8, device=device).bincount()
        self.assertEqual(
            torch.tensor([1, 1, 1, 2], dtype=torch.int64, device=device),
            long_counts)
        # test minlength functionality
        int_counts = torch.bincount(
            torch.tensor([1, 1, 1, 1], device=device), minlength=5)
        self.assertEqual(
            torch.tensor([0, 4, 0, 0, 0], dtype=torch.int64, device=device),
            int_counts)
        # test weights
        byte_counts = torch.bincount(
            torch.tensor([0, 1, 1, 1, 4], device=device),
            torch.tensor([.1, .2, .3, .4, .5], device=device))
        self.assertEqual(
            torch.tensor([0.1, 0.9, 0, 0, 0.5], device=device), byte_counts)
        byte_counts = torch.bincount(
            torch.tensor([0, 1, 1, 1, 4], device=device),
            torch.tensor([1, 2, 3, 4, 5], dtype=torch.int8, device=device))
        self.assertEqual(
            torch.tensor([1, 9, 0, 0, 5], device=device, dtype=torch.float64), byte_counts)
        # test non-contiguous inputs and weights
        inputs = torch.tensor([[0, 0], [3, 1], [2, 1], [1, 1], [3, 4]], device=device)
        weights = torch.tensor([[.1, 1], [.2, 2], [.3, 3], [.4, 4], [.5, 5]], device=device)
        for i in [0, 1]:
            assert not inputs[:, i].is_contiguous(), "Inputs are supposed to be non-contiguous"
            assert not weights[:, i].is_contiguous(), "Weights are supposed to be non-contiguous"
        # inputs are non-contiguous but weights are contiguous
        self.assertEqual(inputs[:, 0].bincount(), torch.tensor([1, 1, 1, 2]))
        # inputs and weights are non-contiguous
        self.assertEqual(
            inputs[:, 1].bincount(weights[:, 1]),
            torch.tensor([1, 9, 0, 0, 5], dtype=torch.float32))
        # weights are non-contiguous but inputs are contiguous
        self.assertEqual(inputs[:, 1].contiguous().bincount(weights[:, 1]),
                         torch.tensor([1, 9, 0, 0, 5], dtype=torch.float32))

        # test bincount on non-contiguous slices
        all0s = torch.zeros((32, 2), dtype=torch.int64, device=device)
        self.assertEqual(all0s[:, 0].bincount(), torch.tensor([32]))

        all1s = torch.ones((32, 2), dtype=torch.int64, device=device)
        self.assertEqual(all1s[:, 0].bincount(), torch.tensor([0, 32]))

        # test large number of bins - global memory use
        big_exp = torch.zeros(10000000, device=device)
        big_exp[-1] = 50.0
        big_w = torch.tensor([.5] * 100, device=device)
        big_out = torch.tensor([9999999] * 100, device=device).bincount(big_w)
        self.assertEqual(big_exp, big_out)
        # test large input size
        big_exp = torch.zeros(2, device=device, dtype=torch.int64)
        big_exp[1] = 1000000
        big_out = torch.ones(1000000, dtype=torch.int8, device=device).bincount()
        self.assertEqual(big_exp, big_out)

    @dtypes(torch.float, torch.double, torch.half)
    def test_multinomial(self, device, dtype):
        def make_prob_dist(shape, is_contiguous):
            if is_contiguous:
                if dtype == torch.half:
                    return torch.zeros(shape, device=device).uniform_().to(dtype=torch.half)
                return torch.zeros(shape, device=device, dtype=dtype).uniform_()
            elif len(shape) == 1:
                if dtype == torch.half:
                    return torch.zeros((shape + [5]), device=device).uniform_().to(dtype=torch.half)[:, 2]
                return torch.zeros((shape + [5]), device=device, dtype=dtype).uniform_()[:, 2]
            else:
                # num dim = 2
                new_shape = [2, shape[1], 7, 1, shape[0], 1, 10]
                if dtype == torch.half:
                    prob_dist = torch.zeros(new_shape, device=device).uniform_().to(dtype=torch.half)
                else:
                    prob_dist = torch.zeros(new_shape, device=device, dtype=dtype).uniform_()
                prob_dist = prob_dist.transpose(1, 4)
                prob_dist = prob_dist[1, :, 5, 0, :, 0, 4]
                assert not prob_dist.is_contiguous()  # sanity check
                return prob_dist

        for is_contiguous in (True, False):
            # with replacement
            n_row = 3
            for n_col in range(4, 5 + 1):
                prob_dist = make_prob_dist([n_row, n_col], is_contiguous)
                # indices that shouldn't be sampled (<0 means none)
                zero_prob_indices = torch.LongTensor(n_row).random_(-2, n_col).tolist()
                for i, j in enumerate(zero_prob_indices):
                    if j >= 0:
                        prob_dist[i, j] = 0
                n_sample = n_col * 3
                sample_indices = torch.multinomial(prob_dist, n_sample, True)
                self.assertEqual(prob_dist.dim(), 2)
                self.assertEqual(sample_indices.size(1), n_sample)
                for i in range(n_row):
                    zero_prob_idx = zero_prob_indices[i]
                    if zero_prob_idx < 0:
                        continue
                    for j in range(n_sample):
                        self.assertNotEqual(sample_indices[i, j], zero_prob_idx,
                                            "sampled an index with zero probability")

            # without replacement
            n_row = 3
            for n_col in range(2, 10 + 1, 2):
                prob_dist = make_prob_dist([n_row, n_col], is_contiguous)
                # indices that shouldn't be sampled (<0 means none)
                zero_prob_indices = torch.LongTensor(n_row).random_(-1, n_col).tolist()
                for i, j in enumerate(zero_prob_indices):
                    if j >= 0:
                        prob_dist[i, j] = 0
                n_sample = max(1, n_col - 2)
                sample_indices = torch.multinomial(prob_dist, n_sample, False)
                self.assertEqual(prob_dist.dim(), 2)
                self.assertEqual(sample_indices.size(1), n_sample)
                for i in range(n_row):
                    row_samples = {}
                    zero_prob_idx = zero_prob_indices[i]
                    for j in range(n_sample):
                        sample_idx = sample_indices[i, j]
                        if zero_prob_idx >= 0:
                            self.assertNotEqual(sample_idx, zero_prob_idx,
                                                "sampled an index with zero probability")
                        self.assertNotIn(sample_idx, row_samples, "sampled an index twice")
                        row_samples[sample_idx] = True

            # vector
            n_col = 4
            prob_dist = make_prob_dist([n_col], is_contiguous).fill_(1)
            zero_prob_idx = 1  # index that shouldn't be sampled
            prob_dist[zero_prob_idx] = 0
            n_sample = 20
            sample_indices = torch.multinomial(prob_dist, n_sample, True)
            for sample_index in sample_indices:
                self.assertNotEqual(sample_index, zero_prob_idx, "sampled an index with zero probability")
            s_dim = sample_indices.dim()
            self.assertEqual(sample_indices.dim(), 1, "wrong number of dimensions")
            self.assertEqual(prob_dist.dim(), 1, "wrong number of prob_dist dimensions")
            self.assertEqual(sample_indices.size(0), n_sample, "wrong number of samples")

    @slowTest
    @dtypes(torch.float)
    def test_multinomial_rng_state_advance(self, device, dtype):
        corpus_size = 100000
        freqs = torch.ones(corpus_size, dtype=torch.float, device=device)
        n_sample = 100
        samples1 = torch.multinomial(freqs, n_sample, replacement=True)
        samples2 = torch.multinomial(freqs, n_sample, replacement=True)
        samples = torch.cat([samples1, samples2])
        # expect no more than 1 repeating elements generated in 2 attempts
        # the probability of at least element being repeated is surprisingly large, 18%
        self.assertLessEqual(2 * n_sample - samples.unique().size(0), 2)
        samples1 = torch.multinomial(freqs, n_sample, replacement=False)
        samples2 = torch.multinomial(freqs, n_sample, replacement=False)
        samples = torch.cat([samples1, samples2])
        # expect no more than 1 repeating elements generated in 2 attempts
        self.assertLessEqual(2 * n_sample - samples.unique().size(0), 1)

    def test_var_unbiased(self, device):
        tensor = torch.randn(100, device=device)
        self.assertEqual(tensor.var(0), tensor.var(0, unbiased=True))
        self.assertEqual(tensor.var(), tensor.var(unbiased=True))
        self.assertEqual(tensor.var(unbiased=False), tensor.var(0, unbiased=False))

        tensor = torch.FloatTensor([1.0, 2.0]).to(device)
        self.assertEqual(tensor.var(unbiased=True), 0.5)
        self.assertEqual(tensor.var(unbiased=False), 0.25)

        tensor = torch.randn(100, device=device)
        self.assertEqual(tensor.std(0), tensor.std(0, unbiased=True))
        self.assertEqual(tensor.std(), tensor.std(unbiased=True))
        self.assertEqual(tensor.std(unbiased=False), tensor.std(0, unbiased=False))

    def test_var_stability(self, device):
        tensor = torch.FloatTensor([2281.5, 2281.25]).to(device)

        # Stability for inner dim
        self.assertEqual(tensor.var(0), 0.03125)

        # General stability
        self.assertEqual(tensor.var(), 0.03125)

        # Stability for outer dimensions
        tensor = tensor.unsqueeze(1)
        self.assertEqual(tensor.var(0), 0.03125)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_mul_intertype_scalar(self, device, dtype):
        x = torch.tensor(1.5, dtype=dtype, device=device)
        y = torch.tensor(3, dtype=torch.int32, device=device)

        self.assertEqual(x * y, 4.5)
        self.assertEqual(y * x, 4.5)

        with self.assertRaisesRegex(RuntimeError, "can't be cast to the desired output type"):
            y *= x
        x *= y
        self.assertEqual(x, 4.5)

    @onlyCPU
    @dtypes(torch.float, torch.double)
    def test_hardshrink(self, device, dtype):
        data = torch.tensor([1, 0.5, 0.3, 0.6], dtype=dtype, device=device).view(2, 2)
        self.assertEqual(torch.tensor([1, 0.5, 0, 0.6], dtype=dtype, device=device).view(2, 2),
                         data.hardshrink(0.3))
        self.assertEqual(torch.tensor([1, 0, 0, 0.6], dtype=dtype, device=device).view(2, 2),
                         data.hardshrink(0.5))

        # test default lambd=0.5
        self.assertEqual(data.hardshrink(), data.hardshrink(0.5))

        # test non-contiguous case
        self.assertEqual(torch.tensor([1, 0, 0.5, 0.6], dtype=dtype, device=device).view(2, 2),
                         data.t().hardshrink(0.3))

    @onlyCPU
    @dtypes(torch.float, torch.double)
    def test_hardshrink_edge_cases(self, device, dtype):
        def h(values, l_expected):
            for l, expected in l_expected.items():
                values_tensor = torch.tensor([float(v) for v in values],
                                             dtype=dtype, device=device)
                expected_tensor = torch.tensor([float(v) for v in expected],
                                               dtype=dtype, device=device)
                self.assertEqual(expected_tensor == values_tensor.hardshrink(l),
                                 torch.ones_like(values_tensor, dtype=torch.bool))

        def test_helper(min, max):
            h([0.0, min, -min, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
              {0.0: [0.0, min, -min, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
               min: [0.0, 0.0, 0.0, 0.1, -0.1, 1.0, -1.0, max, -max, inf, -inf],
               0.1: [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, max, -max, inf, -inf],
               1.0: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, max, -max, inf, -inf],
               max: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, inf, -inf],
               inf: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]})

        test_helper(torch.finfo(dtype).tiny, torch.finfo(dtype).max)

    @onlyCPU
    @slowTest
    @unittest.skipIf(not TEST_NUMPY, 'Numpy not found')
    @dtypes(torch.double)
    def test_einsum(self, device, dtype):
        # test cases taken from https://gist.github.com/rockt/15ee013889d65342088e9260a377dc8f
        x = torch.randn(5, dtype=dtype, device=device)
        y = torch.randn(7, dtype=dtype, device=device)
        A = torch.randn(3, 5, dtype=dtype, device=device)
        B = torch.randn(2, 5, dtype=dtype, device=device)
        C = torch.randn(2, 3, 5, dtype=dtype, device=device)
        D = torch.randn(2, 5, 7, dtype=dtype, device=device)
        E = torch.randn(7, 9, dtype=dtype, device=device)
        F = torch.randn(2, 3, 5, 7, dtype=dtype, device=device)
        G = torch.randn(7, 11, 13, dtype=dtype, device=device)
        H = torch.randn(4, 4, dtype=dtype, device=device)
        I = torch.randn(3, 4, 4, dtype=dtype, device=device)
        l = torch.randn(5, 10, dtype=dtype, device=device)
        r = torch.randn(5, 20, dtype=dtype, device=device)
        w = torch.randn(30, 10, 20, dtype=dtype, device=device)
        test_list = [
            # -- Vector
            ("i->", x),                 # sum
            ("i,i->", x, x),            # dot
            ("i,i->i", x, x),           # vector element-wise mul
            ("i,j->ij", x, y),          # outer
            # -- Matrix
            ("ij->ji", A),              # transpose
            ("ij->j", A),               # row sum
            ("ij->i", A),               # col sum
            ("ij,ij->ij", A, A),        # matrix element-wise mul
            ("ij,j->i", A, x),          # matrix vector multiplication
            ("ij,kj->ik", A, B),        # matmul
            ("ij,ab->ijab", A, E),      # matrix outer product
            # -- Tensor
            ("aij,ajk->aik", C, D),     # batch matmul
            ("ijk,jk->i", C, A),        # tensor matrix contraction
            ("aij,jk->aik", D, E),      # tensor matrix contraction
            ("abcd,dfg->abcfg", F, G),  # tensor tensor contraction
            ("ijk,jk->ik", C, A),       # tensor matrix contraction with double indices
            ("ijk,jk->ij", C, A),       # tensor matrix contraction with double indices
            ("ijk,ik->j", C, B),        # non contiguous
            ("ijk,ik->jk", C, B),       # non contiguous with double indices
            # -- Diagonal
            ("ii", H),                 # trace
            ("ii->i", H),              # diagonal
            # -- Ellipsis
            ("i...->...", H),
            ("ki,...k->i...", A.t(), B),
            ("k...,jk", A.t(), B),
            ("...ii->...i", I),       # batch diagonal
            # -- Other
            ("bn,anm,bm->ba", l, w, r),  # as torch.bilinear
            ("... ii->...i  ", I),       # batch diagonal with spaces
        ]
        for test in test_list:
            actual = torch.einsum(test[0], test[1:])
            expected = np.einsum(test[0], *[t.numpy() for t in test[1:]])
            self.assertEqual(expected.shape, actual.shape, test[0])
            self.assertTrue(np.allclose(expected, actual.numpy()), test[0])
            # test vararg
            actual2 = torch.einsum(test[0], *test[1:])
            self.assertEqual(expected.shape, actual2.shape, test[0])
            self.assertTrue(np.allclose(expected, actual2.numpy()), test[0])

            def do_einsum(*args):
                return torch.einsum(test[0], args)
            # FIXME: following test cases fail gradcheck
            if test[0] not in {"i,i->", "i,i->i", "ij,ij->ij"}:
                gradcheck_inps = tuple(t.detach().requires_grad_() for t in test[1:])
                self.assertTrue(torch.autograd.gradcheck(do_einsum, gradcheck_inps))
            self.assertTrue(A._version == 0)  # check that we do not use inplace ops

    @onlyCPU
    @dtypes(torch.bool, torch.double)
    def test_sum_all(self, device, dtype):
        def check_sum_all(tensor):
            pylist = tensor.reshape(-1).tolist()
            self.assertEqual(tensor.sum(), sum(pylist))

        if dtype != torch.bool:
            check_sum_all(torch.tensor([1, 2, 3, 4, 5], dtype=dtype, device=device))
            check_sum_all(torch.randn(200000, dtype=dtype, device=device))
            check_sum_all(torch.randn(2000, 2, dtype=dtype, device=device)[:, 0])
        else:
            check_sum_all(torch.tensor([True, False, True], dtype=torch.bool, device=device))

    def _test_memory_format_transformations(self, device, input_generator_fn, transformation_fn,
                                            memory_format, compare_data=True, default_is_preserve=False):

        assert(memory_format == torch.channels_last or memory_format == torch.channels_last_3d)

        # xc is a channels last tensor
        xc = input_generator_fn(device)
        # xc is not memory dense, but looks like channels last
        if memory_format == torch.channels_last:
            xc = xc[..., ::2, ::2]
        else:
            xc = xc[..., ::2, ::2, ::2]

        clone = transformation_fn(xc, memory_format=torch.preserve_format)
        self.assertFalse(clone.is_contiguous())
        self.assertTrue(clone.is_contiguous(memory_format=memory_format))
        self.assertFalse(xc.is_contiguous())
        self.assertFalse(xc.is_contiguous(memory_format=memory_format))
        if compare_data:
            self.assertEqual(xc, clone.to(xc))

        xc = input_generator_fn(device)
        clone = transformation_fn(xc, memory_format=torch.contiguous_format)
        self.assertTrue(clone.is_contiguous())
        self.assertFalse(clone.is_contiguous(memory_format=memory_format))
        if compare_data:
            self.assertEqual(xc, clone.to(xc))

        xc = input_generator_fn(device)
        clone = transformation_fn(xc)

        if default_is_preserve:
            self.assertFalse(clone.is_contiguous())
            self.assertTrue(clone.is_contiguous(memory_format=memory_format))
        else:
            self.assertTrue(clone.is_contiguous())
            self.assertFalse(clone.is_contiguous(memory_format=memory_format))
        if compare_data:
            self.assertEqual(xc, clone.to(xc))

        x = torch.randn((3, 4, 5, 6, 7, 8, 9), device=device)
        for _ in range(10):
            permutation = list(range(len(x.shape)))
            random.shuffle(permutation)
            x = x.permute(permutation)
            self.assertEqual(x.stride(), transformation_fn(x, memory_format=torch.preserve_format).stride())

    def test_memory_format_to(self, device):
        def get_generator(memory_format, shape):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=torch.float32).contiguous(memory_format=memory_format)
            return input_generator_fn

        def transformation_fn(tensor, **kwargs):
            return tensor.to(dtype=torch.float64, **kwargs)

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape in formats_shapes:
            self._test_memory_format_transformations(
                device, get_generator(mf, shape), transformation_fn, mf, default_is_preserve=True)

    def test_memory_format_type(self, device):
        def get_generator(memory_format, shape):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=torch.float32).contiguous(memory_format=memory_format)
            return input_generator_fn

        def transformation_fn(tensor, **kwargs):
            return tensor.to(torch.float64, **kwargs)

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape in formats_shapes:
            self._test_memory_format_transformations(
                device, get_generator(mf, shape), transformation_fn, mf, default_is_preserve=True)

    def test_memory_format_clone(self, device):
        def get_generator(memory_format, shape):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=torch.float32).contiguous(memory_format=memory_format)
            return input_generator_fn

        def transformation_fn(tensor, **kwargs):
            return tensor.clone(**kwargs)

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape in formats_shapes:
            self._test_memory_format_transformations(
                device, get_generator(mf, shape), transformation_fn, mf, True, default_is_preserve=True)

    @onlyCPU
    @dtypes(torch.double)
    def test_sum_out(self, device, dtype):
        x = torch.rand(100, 100, dtype=dtype, device=device)
        res1 = torch.sum(x, 1)
        res2 = torch.tensor((), dtype=dtype, device=device)
        torch.sum(x, 1, out=res2)
        self.assertEqual(res1, res2)
        x = torch.rand(100, 100, 100, dtype=dtype, device=device)
        res1 = x.sum(2).sum(1)
        res2 = torch.tensor((), dtype=dtype, device=device)
        torch.sum(x, (2, 1), out=res2)
        self.assertEqual(res1, res2)

    def test_memory_format_factory_like_functions_preserve(self, device):
        def get_generator(memory_format, shape):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=torch.float32).contiguous(memory_format=memory_format)
            return input_generator_fn

        transformation_fns = [
            lambda t, **kwargs: torch.zeros_like(t, **kwargs),
            lambda t, **kwargs: torch.ones_like(t, **kwargs),
            lambda t, **kwargs: torch.randint_like(t, 10, 100, **kwargs),
            lambda t, **kwargs: torch.randint_like(t, 100, **kwargs),
            lambda t, **kwargs: torch.randn_like(t, **kwargs),
            lambda t, **kwargs: torch.rand_like(t, **kwargs),
            lambda t, **kwargs: torch.full_like(t, 7, **kwargs),
            lambda t, **kwargs: torch.empty_like(t, **kwargs)]

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape, in formats_shapes:
            for transformation_fn in transformation_fns:
                self._test_memory_format_transformations(
                    device, get_generator(mf, shape), transformation_fn, mf, compare_data=False, default_is_preserve=True)

    def test_memory_format_type_shortcuts(self, device):
        def get_generator(memory_format, shape, dtype):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=dtype).clamp(0, 1) \
                    .round().contiguous(memory_format=memory_format)
            return input_generator_fn


        def get_fn(fn_name):
            def transformation_fn(tensor, **kwargs):
                fn = getattr(tensor, fn_name)
                return fn(**kwargs)
            return transformation_fn

        shortcuts = ['byte', 'char', 'double', 'bool', 'half', 'int', 'long', 'short']
        if device == 'cpu':
            shortcuts += ['bfloat16']

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape in formats_shapes:
            for fn_name in shortcuts:
                self._test_memory_format_transformations(
                    device, get_generator(mf, shape, torch.float32), get_fn(fn_name), mf, default_is_preserve=True)

        # Test 'float' separately to avoid float->float no-op.
        for mf, shape in formats_shapes:
            self._test_memory_format_transformations(
                device, get_generator(mf, shape, torch.float64), get_fn('float'), mf, default_is_preserve=True)

    @onlyCUDA
    def test_memory_format_cpu_and_cuda_ops(self, device):
        def get_generator(memory_format, shape):
            def input_generator_fn(device):
                return torch.randn(shape, device=device, dtype=torch.float32).contiguous(memory_format=memory_format)
            return input_generator_fn

        def transformation_cpu_fn(tensor, **kwargs):
            return tensor.cpu(**kwargs)

        def transformation_cuda_fn(tensor, **kwargs):
            return tensor.cuda(**kwargs)

        formats_shapes = (
            (torch.channels_last, (4, 3, 8, 8)),
            (torch.channels_last_3d, (4, 3, 8, 8, 8)))

        for mf, shape in formats_shapes:
            self._test_memory_format_transformations(
                'cuda', get_generator(mf, shape), transformation_cpu_fn, mf, default_is_preserve=True)
            self._test_memory_format_transformations(
                'cpu', get_generator(mf, shape), transformation_cuda_fn, mf, default_is_preserve=True)

    @onlyCPU
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_eig(self, device, dtype):
        a = torch.Tensor(((1.96, 0.00, 0.00, 0.00, 0.00),
                          (-6.49, 3.80, 0.00, 0.00, 0.00),
                          (-0.47, -6.39, 4.17, 0.00, 0.00),
                          (-7.20, 1.50, -1.51, 5.70, 0.00),
                          (-0.65, -6.34, 2.67, 1.80, -7.10))).t().contiguous().to(dtype=dtype, device=device)
        e = torch.eig(a)[0]
        ee, vv = torch.eig(a, True)
        te = torch.tensor((), dtype=dtype, device=device)
        tv = torch.tensor((), dtype=dtype, device=device)
        eee, vvv = torch.eig(a, True, out=(te, tv))
        self.assertEqual(e, ee, 1e-12)
        self.assertEqual(ee, eee, 1e-12)
        self.assertEqual(ee, te, 1e-12)
        self.assertEqual(vv, vvv, 1e-12)
        self.assertEqual(vv, tv, 1e-12)

        # test reuse
        X = torch.randn(4, 4, dtype=dtype, device=device)
        X = torch.mm(X.t(), X)
        e = torch.zeros(4, 2, dtype=dtype, device=device)
        v = torch.zeros(4, 4, dtype=dtype, device=device)
        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(torch.mm(v, torch.diag(e.select(1, 0))), v.t())
        self.assertEqual(X, Xhat, atol=1e-8, message='VeV\' wrong')
        self.assertFalse(v.is_contiguous(), 'V is contiguous')

        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(v, torch.mm(e.select(1, 0).diag(), v.t()))
        self.assertEqual(X, Xhat, atol=1e-8, message='VeV\' wrong')
        self.assertFalse(v.is_contiguous(), 'V is contiguous')

        # test non-contiguous
        X = torch.randn(4, 4, dtype=dtype, device=device)
        X = torch.mm(X.t(), X)
        e = torch.zeros(4, 2, 2, dtype=dtype, device=device)[:, 1]
        v = torch.zeros(4, 2, 4, dtype=dtype, device=device)[:, 1]
        self.assertFalse(v.is_contiguous(), 'V is contiguous')
        self.assertFalse(e.is_contiguous(), 'E is contiguous')
        torch.eig(X, True, out=(e, v))
        Xhat = torch.mm(torch.mm(v, torch.diag(e.select(1, 0))), v.t())
        self.assertEqual(X, Xhat, atol=1e-8, message='VeV\' wrong')

        # test invalid input
        self.assertRaisesRegex(
            RuntimeError,
            'A should be 2 dimensional',
            lambda: torch.eig(torch.ones((2))))
        self.assertRaisesRegex(
            RuntimeError,
            'A should be square',
            lambda: torch.eig(torch.ones((2, 3))))
        self.assertRaisesRegex(
            RuntimeError,
            'A should not contain infs or NaNs',
            lambda: torch.eig(np.inf * torch.ones((2, 2))))
        self.assertRaisesRegex(
            RuntimeError,
            'A should not contain infs or NaNs',
            lambda: torch.eig(np.nan * torch.ones((2, 2))))

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_lobpcg_basic(self, device, dtype):
        self._test_lobpcg_method(device, dtype, 'basic')

    @skipCUDAIfNoMagma
    @skipCPUIfNoLapack
    @dtypes(torch.double)
    def test_lobpcg_ortho(self, device, dtype):
        self._test_lobpcg_method(device, dtype, 'ortho')

    def _test_lobpcg_method(self, device, dtype, method):
        from torch.testing._internal.common_utils import random_symmetric_pd_matrix, random_sparse_pd_matrix
        from torch._linalg_utils import matmul, qform
        from torch._lobpcg import lobpcg

        def test_tracker(worker):
            k = worker.iparams['k']
            nc = worker.ivars['converged_count']
            if k <= nc:
                tol = worker.fparams['tol']
                rerr = worker.tvars['rerr']
                X = worker.X
                E = worker.E
                B = worker.B
                A = worker.A
                dtype = X.dtype
                device = X.device

                # Check convergence
                self.assertLessEqual(rerr[:k].max(), tol)

                # Check B-orthogonality
                I = torch.eye(k, k, dtype=dtype, device=device)
                self.assertEqual(qform(B, X[:, :k]), I)

                # Check block equation
                self.assertEqual(qform(A, X[:, :k]) / E[:k], I, atol=0.2)

        orig_lobpcg = lobpcg

        def lobpcg(*args, **kwargs):
            kwargs['tracker'] = test_tracker
            kwargs['niter'] = 1000
            kwargs['method'] = method
            kwargs['tol'] = 1e-8
            return orig_lobpcg(*args, **kwargs)
        prec = 5e-4

        # check dense input
        mm = torch.matmul
        for batches in [(), (2,), (2, 3)]:
            for m, n, k in [
                    (9, 3, 1),
                    (9, 3, 2),
                    (9, 2, 2),
                    (100, 15, 5),
            ]:
                # skip tests that are known to fail with the basic
                # LOBPCG method due to calling cholesky on singular
                # input
                if method == 'basic' and (m, n, k) in [(9, 2, 2), (100, 15, 5)]:
                    continue
                A = random_symmetric_pd_matrix(m, *batches, device=device, dtype=dtype)
                B = random_symmetric_pd_matrix(m, *batches, device=device, dtype=dtype)

                # classical eigenvalue problem, smallest eigenvalues
                E, V = lobpcg(A, k=k, n=n, largest=False)
                self.assertEqual(E.shape, batches + (k,))
                self.assertEqual(V.shape, batches + (m, k))
                self.assertEqual(matmul(A, V), mm(V, E.diag_embed()), atol=prec)
                e = torch.symeig(A)[0]
                e_smallest = e[..., :k]
                self.assertEqual(E, e_smallest)

                # classical eigenvalue problem, largest eigenvalues
                E, V = lobpcg(A, k=k, n=n, largest=True)
                e_largest, _ = torch.sort(e[..., -k:], descending=True)
                self.assertEqual(E, e_largest, atol=prec)
                self.assertEqual(matmul(A, V), mm(V, E.diag_embed()), atol=prec)

                # generalized eigenvalue problem, smallest eigenvalues
                E, V = lobpcg(A, B=B, k=k, n=n, largest=False)
                self.assertEqual(matmul(A, V), mm(matmul(B, V), E.diag_embed()), atol=prec)

                # generalized eigenvalue problem, largest eigenvalues
                E, V = lobpcg(A, B=B, k=k, n=n, largest=True)
                self.assertEqual(matmul(A, V) / E.max(), mm(matmul(B, V), (E / E.max()).diag_embed()),
                                 atol=prec)

        # check sparse input
        for m, n, k, density in [
                (5, 1, 1, 0.8),
                (9, 3, 2, 0.5),
                (100, 1, 1, 0.1),
                (1000, 7, 3, 0.01),
        ]:
            # skip tests that are known to fail with the basic LOBCG
            # method due to insufficient accuracy
            if method == 'basic' and (m, n, k, density) in [(1000, 7, 3, 0.01)]:
                continue
            A = random_sparse_pd_matrix(m, density=density, device=device, dtype=dtype)
            B = random_sparse_pd_matrix(m, density=density, device=device, dtype=dtype)
            A_eigenvalues = torch.arange(1, m + 1, dtype=dtype) / m
            e_smallest = A_eigenvalues[..., :k]
            e_largest, _ = torch.sort(A_eigenvalues[..., -k:], descending=True)

            # classical eigenvalue problem, smallest eigenvalues
            E, V = lobpcg(A, k=k, n=n, largest=False)
            self.assertEqual(E, e_smallest)
            self.assertEqual(matmul(A, V), mm(V, E.diag_embed()), atol=prec)

            # classical eigenvalue problem, largest eigenvalues
            E, V = lobpcg(A, k=k, n=n, largest=True)
            self.assertEqual(matmul(A, V), mm(V, E.diag_embed()), atol=prec)
            self.assertEqual(E, e_largest)

            # generalized eigenvalue problem, smallest eigenvalues
            E, V = lobpcg(A, B=B, k=k, n=n, largest=False)
            self.assertEqual(matmul(A, V), matmul(B, mm(V, E.diag_embed())), atol=prec)

            # generalized eigenvalue problem, largest eigenvalues
            E, V = lobpcg(A, B=B, k=k, n=n, largest=True)
            self.assertEqual(matmul(A, V) / E.max(), mm(matmul(B, V), (E / E.max()).diag_embed()),
                             atol=prec)

    @skipCPUIfNoLapack
    @onlyCPU
    @dtypes(torch.double)
    def test_lobpcg_torchscript(self, device, dtype):
        from torch.testing._internal.common_utils import random_sparse_pd_matrix
        from torch._linalg_utils import matmul as mm

        lobpcg = torch.jit.script(torch.lobpcg)

        m = 500
        k = 5
        A1 = random_sparse_pd_matrix(m, density=2.0 / m, device=device, dtype=dtype)
        X1 = torch.randn((m, k), dtype=dtype, device=device)
        E1, V1 = lobpcg(A1, X=X1)
        eq_err = torch.norm((mm(A1, V1) - V1 * E1), 2) / E1.max()
        self.assertLess(eq_err, 1e-6)

    @unittest.skipIf(not TEST_SCIPY or (TEST_SCIPY and scipy.__version__ < '1.4.1'), "Scipy not found or older than 1.4.1")
    @skipCPUIfNoLapack
    @onlyCPU
    @dtypes(torch.double)
    def test_lobpcg_scipy(self, device, dtype):
        """Compare torch and scipy.sparse.linalg implementations of lobpcg
        """
        import time
        import scipy
        from torch.testing._internal.common_utils import random_sparse_pd_matrix
        from torch._linalg_utils import matmul as mm
        from scipy.sparse.linalg import lobpcg as scipy_lobpcg
        import scipy.sparse

        def toscipy(A):
            if A.layout == torch.sparse_coo:
                values = A.coalesce().values().cpu().numpy().copy()
                indices = A.coalesce().indices().cpu().numpy().copy()
                return scipy.sparse.coo_matrix((values, (indices[0], indices[1])), A.shape)
            return A.cpu().numpy().copy()

        niter = 1000
        repeat = 10
        m = 500   # size of the square matrix
        k = 7     # the number of requested eigenpairs
        A1 = random_sparse_pd_matrix(m, density=2.0 / m, device=device, dtype=dtype)
        B1 = random_sparse_pd_matrix(m, density=2.0 / m, device=device, dtype=dtype)
        X1 = torch.randn((m, k), dtype=dtype, device=device)

        A2 = toscipy(A1)
        B2 = toscipy(B1)
        X2 = toscipy(X1)

        lambdas1 = []

        def tracker(worker):
            lambdas1.append(worker.E[:])

        tol = 1e-8
        # tol for scipy lobpcg will be choosed so that the number of
        # iterations will be equal or very close to pytorch lobpcg
        # (that is around 170-180)

        # Standard eigenvalue problem
        E1, V1 = torch.lobpcg(A1, X=X1, niter=niter, largest=True, tracker=tracker, tol=tol)
        E2, V2, lambdas2 = scipy_lobpcg(A2, X2, maxiter=niter, largest=True, retLambdaHistory=True, tol=1.1 * tol)
        iters1 = len(lambdas1)
        iters2 = len(lambdas2)
        self.assertLess(abs(iters1 - iters2), 0.05 * max(iters1, iters2))

        E2a, V2a = scipy_lobpcg(A2, X2, maxiter=niter, largest=False)

        eq_err = torch.norm((mm(A1, V1) - V1 * E1), 2) / E1.max()
        eq_err_scipy = (abs(A2.dot(V2) - V2 * E2)**2).sum() ** 0.5 / E2.max()
        self.assertLess(eq_err, 1e-6)        # std
        self.assertLess(eq_err_scipy, 1e-6)  # std

        self.assertEqual(E1, torch.from_numpy(E2.copy()))

        # Generalized eigenvalue problem
        lambdas1 = []

        def tracker(worker):
            lambdas1.append(worker.E[:])

        E1, V1 = torch.lobpcg(A1, B=B1, X=X1, niter=niter, largest=True, tracker=tracker, tol=tol)
        E2, V2, lambdas2 = scipy_lobpcg(A2, X2, B=B2, maxiter=niter, largest=True, retLambdaHistory=True, tol=39 * tol)
        E2a, V2a = scipy_lobpcg(A2, X2, B=B2, maxiter=niter, largest=False)
        iters1 = len(lambdas1)
        iters2 = len(lambdas2)
        self.assertLess(abs(iters1 - iters2), 0.05 * max(iters1, iters2))

        eq_err = torch.norm((mm(A1, V1) - mm(B1, V1) * E1), 2) / E1.max()
        eq_err_scipy = (abs(A2.dot(V2) - B2.dot(V2) * E2)**2).sum() ** 0.5 / E2.max()
        self.assertLess(eq_err, 1e-6)        # general
        self.assertLess(eq_err_scipy, 1e-6)  # general

        self.assertEqual(E1, torch.from_numpy(E2.copy()))

        # Timings
        elapsed_ortho = 0
        elapsed_ortho_general = 0
        elapsed_scipy = 0
        elapsed_general_scipy = 0
        for i in range(repeat):
            start = time.time()
            torch.lobpcg(A1, X=X1, niter=niter, method='ortho', tol=tol)
            end = time.time()
            elapsed_ortho += end - start

            start = time.time()
            torch.lobpcg(A1, X=X1, B=B1, niter=niter, method='ortho', tol=tol)
            end = time.time()
            elapsed_ortho_general += end - start

            start = time.time()
            scipy_lobpcg(A2, X2, maxiter=niter, tol=1.1 * tol)
            end = time.time()
            elapsed_scipy += end - start

            start = time.time()
            scipy_lobpcg(A2, X2, B=B2, maxiter=niter, tol=39 * tol)
            end = time.time()
            elapsed_general_scipy += end - start

        elapsed_ortho_ms = 1000.0 * elapsed_ortho / repeat
        elapsed_ortho_general_ms = 1000.0 * elapsed_ortho_general / repeat
        elapsed_scipy_ms = 1000.0 * elapsed_scipy / repeat
        elapsed_general_scipy_ms = 1000.0 * elapsed_general_scipy / repeat

        print('''
CPU timings: torch.lobpcg vs scipy.sparse.linalg.lobpcg
-------------------------------------------------------
              | standard    | generalized | method
torch.lobpcg  | {:10.2f}  | {:10.2f}  | ortho
scipy_lobpcg  | {:10.2f}  | {:10.2f}  | N/A
-(input size: {:4}, eigenpairs:{:2}, units: ms per call)-
        '''.format(elapsed_ortho_ms, elapsed_ortho_general_ms,
                   elapsed_scipy_ms, elapsed_general_scipy_ms,
                   m, k))

        # Handling of very small tolerence
        tol = 1e-100

        lambdas1 = []

        def tracker(worker):
            lambdas1.append(worker.E[:])

        E1, V1 = torch.lobpcg(A1, X=X1, niter=niter, largest=True, tracker=tracker, tol=tol)
        iters1 = len(lambdas1)
        eq_err = torch.norm((mm(A1, V1) - V1 * E1), 2) / E1.max()

        try:
            E2, V2, lambdas2 = scipy_lobpcg(A2, X2, maxiter=niter, largest=True, retLambdaHistory=True, tol=tol)
            iters2 = len(lambdas2)
            eq_err_scipy = (abs(A2.dot(V2) - V2 * E2)**2).sum() ** 0.5 / E2.max()
        except Exception as msg:
            print('Calling scipy_lobpcg failed [standard]:', msg)
            iters2 = -1
            eq_err_scipy = -1

        lambdas1 = []

        def tracker(worker):
            lambdas1.append(worker.E[:])

        E1, V1 = torch.lobpcg(A1, X=X1, B=B1, niter=niter, largest=True, tracker=tracker, tol=tol)
        iters1_general = len(lambdas1)
        eq_err_general = torch.norm((mm(A1, V1) - mm(B1, V1) * E1), 2) / E1.max()

        try:
            E2, V2, lambdas2 = scipy_lobpcg(A2, X2, B=B2, maxiter=niter, largest=True, retLambdaHistory=True, tol=tol)
            iters2_general = len(lambdas2)
            eq_err_general_scipy = (abs(A2.dot(V2) - B2.dot(V2) * E2)**2).sum() ** 0.5 / E2.max()
        except Exception as msg:
            print('Calling scipy_lobpcg failed [generalized]:', msg)
            iters2_general = -1
            eq_err_general_scipy = -1

        print('''\
Handling of small tol={:6.0e}: torch.lobpcg vs scipy.sparse.linalg.lobpcg
----------------------------------------------------------------------------
              | standard    | generalized |  niter | method
torch.lobpcg  | {:10.2e}  | {:10.2e}  | {:6} | ortho
scipy_lobpcg  | {:10.2e}  | {:10.2e}  | {:6} | N/A
---(input size: {:4}, eigenpairs:{:2}, units: relative error, maxiter={:4})---
'''.format(tol, eq_err, eq_err_general, iters1, eq_err_scipy, eq_err_general_scipy, iters2, m, k, niter))

    @slowTest
    @onlyCPU
    @dtypes(torch.bfloat16, torch.float, torch.double)
    def test_ger(self, device, dtype):
        def run_test(v0, v1):
            res0 = torch.ger(v0, v1)
            res1 = torch.zeros(100, 100, dtype=dtype, device=device)
            for i in range(100):
                for j in range(100):
                    res1[i, j] = v0[i] * v1[j]
            self.assertEqual(res0, res1)

        v0 = torch.randn(100, dtype=torch.float, device=device).to(dtype=dtype)
        v1 = torch.randn(100, dtype=torch.float, device=device).to(dtype=dtype)
        run_test(v0, v1)

        # Tests 0-strided
        v0 = torch.randn(1, dtype=torch.float, device=device).expand(100).to(dtype=dtype)
        v1 = torch.randn(100, dtype=torch.float, device=device).to(dtype=dtype)
        run_test(v0, v1)

    @slowTest
    @onlyCPU
    @dtypes(torch.bfloat16, torch.float, torch.double)
    def test_addr(self, device, dtype):
        def run_test(m, v1, v2, m_transform=lambda x: x):
            m = m_transform(m.clone())
            ref = m.clone()
            torch.addr(m, v1, v2, out=m)
            for i in range(m.size(0)):
                for j in range(m.size(1)):
                    ref[i, j] += v1[i] * v2[j]
            self.assertEqual(m, ref)

        for h, w in [(100, 110), (1, 20), (200, 2)]:
            m = torch.randn(h, w, dtype=torch.float, device=device).to(dtype=dtype)
            v1 = torch.randn(h, dtype=torch.float, device=device).to(dtype=dtype)
            v2 = torch.randn(w, dtype=torch.float, device=device).to(dtype=dtype)
            run_test(m, v1, v2)
            # test transpose
            run_test(m, v2, v1, lambda x: x.transpose(0, 1))
            # test 0 strided
            v1 = torch.randn(1, dtype=torch.float, device=device).expand(h).to(dtype=dtype)
            run_test(m, v1, v2)
            run_test(m, v2, v1, lambda x: x.transpose(0, 1))

    @onlyCPU
    @precisionOverride({torch.bfloat16: 1e-0, torch.float: 1e-4, torch.double: 1e-8,
                        torch.cfloat: 1e-4, torch.cdouble: 1e-8})
    @dtypes(torch.bfloat16, torch.float, torch.double, torch.cfloat, torch.cdouble)
    def test_addmv(self, device, dtype):
        t = torch.randn(10, device=device).to(dtype)
        m = torch.randn(10, 100, device=device).to(dtype)
        v = torch.randn(100, device=device).to(dtype)
        res1 = torch.addmv(t, m, v)
        res2 = torch.zeros(10, dtype=dtype, device=device)
        res2 += t
        for i in range(10):
            for j in range(100):
                res2[i] += m[i, j] * v[j]

        self.assertEqual(res1, res2, atol=self.precision)

        # Test 0-strided
        t = torch.randn(1, device=device).to(dtype).expand(10)
        m = torch.randn(10, 1, device=device).to(dtype).expand(10, 100)
        v = torch.randn(100, device=device).to(dtype)
        res1 = torch.addmv(t, m, v)
        res2 = torch.zeros(10, dtype=dtype, device=device)
        res2 += t
        for i in range(10):
            for j in range(100):
                res2[i] += m[i, j] * v[j]

        self.assertEqual(res1, res2, atol=self.precision)

    @dtypesIfCUDA(*([torch.half, torch.float, torch.double]
                    + ([torch.bfloat16] if TEST_WITH_ROCM else [])))
    @dtypes(torch.float, torch.double)
    def test_addmv_rowmajor_colmajor_incx_incy_lda(self, device, dtype):
        # tests (o, s)*(s).  o is output size, s is summed size.
        o = 5
        s = 3
        a_data = torch.arange(1, o * s + 1, device=device, dtype=dtype).view(o, s)
        x_data = torch.arange(1, s + 1, 1, device=device, dtype=dtype)
        y_data = torch.ones(o, device=device, dtype=dtype)
        control = torch.tensor([15., 33., 51., 69., 87.], device=device, dtype=dtype)

        def _test(use_out, row_major, incx, incy, lda_tail):
            if row_major:
                a_storage = torch.full((o, s + lda_tail), float('nan'), device=device, dtype=dtype)
            else:
                a_storage = torch.full((s, o + lda_tail), float('nan'), device=device, dtype=dtype).permute(1, 0)
            a = a_storage[:o, :s].copy_(a_data)

            x_storage = torch.full((s, incx), float('nan'), device=device, dtype=dtype)
            x = x_storage[:, 0].copy_(x_data)

            y_storage = torch.full((o, incy), float('nan'), device=device, dtype=dtype)
            y = y_storage[:, 0].copy_(y_data)

            if use_out:
                out = torch.addmv(y, a, x)
            else:
                out = torch.empty_like(y)
                torch.addmv(y, a, x, out=out)

            self.assertEqual(out, control, atol=1.e-4)

        for use_out, row_major, incx, incy, lda_tail in product((False, True), (False, True), (1, 2), (1, 2), (0, 1)):
            _test(use_out, row_major, incx, incy, lda_tail)

    @slowTest
    @onlyCPU
    def test_addmm(self, device):
        dtypes = {
            torch.double: 1e-8,
            torch.float: 1e-4,
            torch.bfloat16: 1e-1,
        }
        for dtype, prec in dtypes.items():
            M = torch.randn(10, 25).to(device=device, dtype=dtype)
            m1 = torch.randn(10, 50).to(device=device, dtype=dtype)
            m2 = torch.randn(50, 25).to(device=device, dtype=dtype)
            res1 = torch.addmm(M, m1, m2)
            res2 = torch.zeros(10, 25, device=device, dtype=dtype)
            res2 += M
            for i in range(10):
                for j in range(25):
                    for k in range(50):
                        res2[i, j] += m1[i, k] * m2[k, j]
            self.assertEqual(res1, res2, prec)

        # Test 0-strided
        for dtype, prec in dtypes.items():
            M = torch.randn(10, 1).to(device=device, dtype=dtype).expand(10, 25)
            m1 = torch.randn(10, 1).to(device=device, dtype=dtype).expand(10, 50)
            m2 = torch.randn(50, 25).to(device=device, dtype=dtype)
            res1 = torch.addmm(M, m1, m2)
            res2 = torch.zeros(10, 25, device=device, dtype=dtype)
            res2 += M
            for i in range(10):
                for j in range(25):
                    for k in range(50):
                        res2[i, j] += m1[i, k] * m2[k, j]
            self.assertEqual(res1, res2, prec)

    @dtypes(torch.float, torch.double)
    def test_addmm_sizes(self, device, dtype):
        for m in [0, 1, 25]:
            for n in [0, 1, 10]:
                for k in [0, 1, 8]:
                    M = torch.randn(n, m, device=device, dtype=dtype)
                    m1 = torch.randn(n, k, device=device, dtype=dtype)
                    m2 = torch.randn(k, m, device=device, dtype=dtype)
                    res1 = torch.addmm(M, m1, m2)
                    res2 = torch.zeros(n, m, device=device, dtype=dtype)
                    res2 += M
                    for i in range(n):
                        for j in range(m):
                            for l in range(k):
                                res2[i, j] += m1[i, l] * m2[l, j]
                    self.assertEqual(res1, res2)

    @onlyCPU
    @dtypes(torch.float, torch.double)
    def test_dot(self, device, dtype):
        v1 = torch.randn(100, dtype=dtype, device=device)
        v2 = torch.randn(100, dtype=dtype, device=device)
        res1 = torch.dot(v1, v2)
        res2 = 0
        for i, j in zip(v1, v2):
            res2 += i * j
        self.assertEqual(res1, res2)
        out = torch.randn((), dtype=dtype, device=device)
        torch.dot(v1, v2, out=out)
        self.assertEqual(res1, out)

        # Test 0-strided
        v1 = torch.randn(1, dtype=dtype, device=device).expand(100)
        v2 = torch.randn(100, dtype=dtype, device=device)
        res1 = torch.dot(v1, v2)
        res2 = 0
        for i, j in zip(v1, v2):
            res2 += i * j
        self.assertEqual(res1, res2)
        out = torch.randn((), dtype=dtype, device=device)
        torch.dot(v1, v2, out=out)
        self.assertEqual(res1, out)

    @onlyCPU
    @slowTest
    @dtypes(torch.float)
    def test_exp_slow(self, device, dtype):
        # Test for https://github.com/pytorch/pytorch/issues/17271
        # This is pretty slow on my Macbook but it only takes a few
        # seconds on a beefy Xeon server
        a = torch.exp(torch.ones(2 ** 31, dtype=dtype, device=device))
        b = torch.exp(torch.ones(1, dtype=dtype, device=device))
        self.assertEqual(a, b.expand(2 ** 31))

    @dtypes(torch.float, torch.double)
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_hardswish(self, device, dtype):
        inputValues = [-1000, -4, -3, -2, 0, 2, 3, 4, 1000]
        expectedOutput = np.multiply(
            inputValues,
            np.minimum(np.maximum((np.add(inputValues, 3)), 0), 6) / 6.0)
        precision_4dps = 0.0002

        inputTensor = torch.tensor(inputValues, dtype=dtype, device=device)
        expectedOutputTensor = \
            torch.tensor(expectedOutput, dtype=dtype, device=device)

        # normal
        self.assertEqual(torch.nn.functional.hardswish(inputTensor),
                         expectedOutputTensor, precision_4dps)

        # inplace
        inputTensorCpy = inputTensor.clone().detach()
        torch.nn.functional.hardswish(inputTensorCpy, inplace=True)
        self.assertEqual(inputTensorCpy, expectedOutputTensor, precision_4dps)

    @onlyCPU
    @dtypes(torch.float, torch.double)
    def test_sigmoid(self, device, dtype):
        # TODO: why not simulate math.sigmoid like with rsqrt?
        inputValues = [-1000, -1, 0, 0.5, 1, 2, 1000]
        expectedOutput = [0.0000, 0.2689, 0.5, 0.6225, 0.7311, 0.8808, 1.000]
        precision_4dps = 0.0002

        self.assertEqual(torch.tensor(inputValues, dtype=dtype, device=device).sigmoid(),
                         torch.tensor(expectedOutput, dtype=dtype, device=device), precision_4dps)

    @dtypes(torch.float, torch.double)
    @unittest.skipIf(not TEST_NUMPY, "Numpy not found")
    def test_hardsigmoid(self, device, dtype):
        inputValues = [-1000, -4, -3, -2, 0, 2, 3, 4, 1000]
        expectedOutput = np.minimum(np.maximum((np.add(inputValues, 3)), 0), 6) / 6.0

        inputTensor = torch.tensor(inputValues, dtype=dtype, device=device)
        precision_4dps = 0.0002

        # normal
        self.assertEqual(torch.nn.functional.hardsigmoid(inputTensor),
                         torch.tensor(expectedOutput, dtype=dtype, device=device), precision_4dps)

        # inplace
        inputTensorCpy = inputTensor.clone().detach()
        self.assertEqual(torch.nn.functional.hardsigmoid(inputTensorCpy, inplace=True),
                         torch.tensor(expectedOutput, dtype=dtype, device=device), precision_4dps)

    @onlyCPU
    @dtypes(torch.float)
    def test_diag_embed(self, device, dtype):
        x = torch.arange(3 * 4, dtype=dtype, device=device).view(3, 4)
        result = torch.diag_embed(x)
        expected = torch.stack([torch.diag(r) for r in x], 0)
        self.assertEqual(result, expected)

        result = torch.diag_embed(x, offset=1, dim1=0, dim2=2)
        expected = torch.stack([torch.diag(r, 1) for r in x], 1)
        self.assertEqual(result, expected)

    @onlyCPU
    @dtypes(*torch.testing.get_all_dtypes())
    def test_sub(self, device, dtype):
        m1 = torch.tensor([2.34, 4.44], dtype=dtype, device=device)
        m2 = torch.tensor([1.23, 2.33], dtype=dtype, device=device)

        if dtype == torch.bool:
            self.assertRaises(RuntimeError, lambda: m1 - m2)
        elif (dtype == torch.bfloat16 or dtype == torch.half):
            # bfloat16 has a lower precision so we have to have a separate check for it
            self.assertEqual(m1 - m2, torch.tensor([1.11, 2.11], dtype=dtype), 0.01)
        else:
            self.assertEqual(m1 - m2, torch.tensor([1.11, 2.11], dtype=dtype))

    @onlyCPU
    @dtypes(torch.float)
    def test_csub(self, device, dtype):
        # with a tensor
        a = torch.randn(100, 90, dtype=dtype, device=device)
        b = a.clone().normal_()

        res_add = torch.add(a, b, alpha=-1)
        res_csub = a.clone()
        res_csub.sub_(b)
        self.assertEqual(res_add, res_csub)

        # with a scalar
        a = torch.randn(100, 100, dtype=dtype, device=device)

        scalar = 123.5
        res_add = torch.add(a, -scalar)
        res_csub = a.clone()
        res_csub.sub_(scalar)
        self.assertEqual(res_add, res_csub)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_min_max_binary_op_nan(self, device, dtype):
        a = torch.rand(1000, dtype=dtype, device=device)
        b = torch.rand(1000, dtype=dtype, device=device)

        # 0:250: a -- nan, b -- not nan
        a[:250] = float('nan')
        # 250:500: a -- not nan, b -- nan
        b[250:500] = float('nan')
        # 500:750: a and b both nan
        a[500:750] = float('nan')
        b[500:750] = float('nan')
        # 750:1000: neither nan

        ma = torch.max(a, b)
        mi = torch.min(a, b)

        for i in range(750):
            self.assertTrue(torch.isnan(ma[i]), "max(a, b): {}, a: {}, b: {}".format(ma[i], a[i], b[i]))
            self.assertTrue(torch.isnan(mi[i]), "min(a, b): {}, a: {}, b: {}".format(mi[i], a[i], b[i]))

        for i in range(750, 1000):
            self.assertFalse(torch.isnan(ma[i]), "max(a, b): {}, a: {}, b: {}".format(ma[i], a[i], b[i]))
            self.assertFalse(torch.isnan(mi[i]), "min(a, b): {}, a: {}, b: {}".format(mi[i], a[i], b[i]))

    @onlyCPU
    @dtypes(*torch.testing.get_all_math_dtypes('cpu'))
    def test_threshold(self, device, dtype):
        if dtype != torch.uint8 and dtype != torch.float16 and not dtype.is_complex:
            # 100 is wide enough to use AVX2 instructions for all types
            x = torch.randn(100, dtype=torch.float, device=device).sign().to(dtype=dtype)
            y = torch.threshold(x, 0, 0)
            self.assertTrue(y.le(0).any())

    @onlyCPU
    @dtypes(torch.float, torch.double)
    def test_reciprocal(self, device, dtype):
        a = torch.randn(100, 89, device=device, dtype=dtype)
        res_div = 1 / a
        res_reciprocal = a.clone()
        res_reciprocal.reciprocal_()
        self.assertEqual(res_reciprocal, res_div)

    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.float, torch.double, torch.complex64, torch.complex128)
    def test_reciprocal_complex(self, device, dtype):
        t = torch.randn(10, 10, dtype=dtype, device=device)
        expected = torch.from_numpy(np.reciprocal(t.cpu().numpy()))
        actual = torch.reciprocal(t).cpu()
        self.assertEqual(expected, actual)

    @onlyCUDA
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.complex64, torch.complex128)
    def test_reciprocal_complex_extremal(self, device, dtype):
        vals = (
            # Inf and Zeros
            complex(float('inf'), float('inf')),
            complex(float('inf'), 0.),
            complex(0., float('inf')),
            complex(0., 0.),

            # Nans and Zeros
            complex(float('nan'), 0.),
            complex(0., float('nan')),
            complex(float('nan'), float('nan')),

            # Inf and Nans
            complex(float('nan'), float('inf')),
            complex(float('inf'), float('nan')),

            # Extremal and Normal Number
            complex(float('nan'), 2.0),
            complex(float('inf'), 2.0),
            complex(2.0, float('nan')),
            complex(2.0, float('inf')),
            complex(2.0, 0.0),
            complex(0.0, 2.0))

        self._np_compare('reciprocal', vals, device, dtype)

    @onlyCPU
    @dtypes(torch.bfloat16, torch.float)
    def test_div(self, device, dtype):
        m1 = torch.randn(10, 10, dtype=torch.float, device=device).to(dtype=dtype)
        res1 = m1.clone()
        res1[:, 3].div_(2)
        res2 = m1.clone()
        for i in range(m1.size(0)):
            res2[i, 3] = res2[i, 3] / 2
        self.assertEqual(res1, res2)

        if dtype == torch.bfloat16:
            a1 = torch.tensor([4.2, 6.2], dtype=dtype, device=device)
            a2 = torch.tensor([2., 2.], dtype=dtype, device=device)
            self.assertEqual(a1 / a2,
                             torch.tensor([2.1, 3.1], dtype=dtype, device=device),
                             0.01)
            self.assertEqual(a1.div(a2), a1 / a2)

    @dtypesIfCUDA(*set(torch.testing.get_all_math_dtypes('cuda')) - {torch.complex64, torch.complex128})
    @dtypes(*set(torch.testing.get_all_math_dtypes('cpu')) - {torch.complex64, torch.complex128})
    def test_floor_divide_tensor(self, device, dtype):
        x = torch.randn(10, device=device).mul(30).to(dtype)
        y = torch.arange(1, 11, dtype=dtype, device=device)

        z = x // y
        z_alt = torch.trunc(x.double() / y.double()).to(dtype)

        self.assertEqual(z.dtype, x.dtype)
        self.assertEqual(z, z_alt)

    @dtypesIfCUDA(*set(torch.testing.get_all_math_dtypes('cuda')) - {torch.complex64, torch.complex128})
    @dtypes(*set(torch.testing.get_all_math_dtypes('cpu')) - {torch.complex64, torch.complex128})
    def test_floor_divide_scalar(self, device, dtype):
        x = torch.randn(100, device=device).mul(10).to(dtype)

        z = x // 3
        z_alt = torch.tensor([math.trunc(v.item() / 3.) for v in x], dtype=x.dtype, device=device)

        self.assertEqual(z.dtype, x.dtype)
        self.assertEqual(z, z_alt)

    # Note: this tests fails on XLA
    @onlyOnCPUAndCUDA
    @dtypes(torch.float, torch.long)
    def test_floor_divide_out(self, device, dtype):
        x = torch.randn(10, device=device).mul(10).to(dtype)
        y = torch.arange(1, 11, dtype=dtype, device=device)
        o = torch.empty(10, dtype=dtype, device=device)

        torch.floor_divide(x, y, out=o)
        self.assertEqual(o, x // y)

        # Tests scalar with out
        torch.floor_divide(x, 2, out=o)
        self.assertEqual(o, x // 2)

        if dtype == torch.int:
            o = torch.empty(10, dtype=torch.float, device=device)
            torch.floor_divide(x, y, out=o)
            self.assertEqual(o, torch.floor_divide(x.float(), y.float()))

    @onlyCPU
    @dtypes(*torch.testing.get_all_math_dtypes('cpu'))
    def test_rdiv(self, device, dtype):
        if dtype is torch.float16:
            return
        elif dtype.is_complex:
            x = torch.rand(100, dtype=dtype, device=device).add(1).mul(4)
        else:
            x = torch.rand(100, device=device).add(1).mul(4).to(dtype)
        y = 30 / x
        if dtype.is_floating_point or dtype.is_complex:
            z = torch.tensor([30 / v.item() for v in x], dtype=dtype, device=device)
        else:
            z = torch.tensor([math.trunc(30. / v.item()) for v in x], dtype=dtype, device=device)
        self.assertEqual(y, z)

    @onlyCPU
    @dtypes(torch.float)
    def test_fmod(self, device, dtype):
        m1 = torch.Tensor(10, 10).uniform_(-10., 10.).to(dtype=dtype, device=device)
        res1 = m1.clone()
        q = 2.1
        res1[:, 3].fmod_(q)
        res2 = m1.clone()
        for i in range(m1.size(1)):
            res2[i, 3] = math.fmod(res2[i, 3], q)
        self.assertEqual(res1, res2)

    @onlyCPU
    @dtypes(torch.float, torch.long)
    def test_remainder(self, device, dtype):
        for use_item in [True, False]:
            if dtype == torch.float:
                m1 = torch.Tensor(10, 10).uniform_(-10., 10.).to(dtype=dtype, device=device)
                res1 = m1.clone()
                res2 = m1.clone()
                qs = torch.arange(-5.1, 4.1, dtype=dtype, device=device)
                # Check the case where the divisor is a simple float
                for col_idx, q in enumerate(qs):
                    # Reference
                    for i in range(m1.size(0)):
                        res2[i, col_idx] = res2[i, col_idx] % q
                    # To test
                    res1[:, col_idx].remainder_(q if not use_item else q.item())
                self.assertEqual(res1, res2)
                # Check the case where the divisor is a tensor
                res1 = m1.clone()
                res1.remainder_(qs.unsqueeze(0).expand_as(res1))
                self.assertEqual(res1, res2)
            elif dtype == torch.long:
                long_m1 = torch.LongTensor(10, 10).random_(-10, 10)
                long_res1 = long_m1.clone()
                long_res2 = long_m1.clone()
                long_qs = torch.arange(-5, 5, dtype=dtype, device=device)
                long_qs[5] = 5  # Can't handle the divisor=0 case
                for col_idx, long_q in enumerate(long_qs):
                    # Reference
                    for i in range(long_m1.size(0)):
                        long_res2[i, col_idx] = long_res2[i, col_idx] % long_q
                    # To test
                    long_res1[:, col_idx].remainder_(long_q if not use_item else long_q.item())
                self.assertEqual(long_res1, long_res2)
                # Divisor is a tensor case
                long_res1 = long_m1.clone()
                long_res1.remainder_(long_qs.unsqueeze(0).expand_as(long_res1))

    # remove onlyCUDA after CPU impl of remainder_kernel be fixed
    @onlyCUDA
    @dtypes(torch.float, torch.double)
    def test_remainder_fmod_large_dividend(self, device, dtype):
        alarge = 1e9
        pi = 3.14159265358979
        for avalue in [alarge, -alarge]:
            for bvalue in [pi, -pi]:
                a = torch.tensor([avalue], dtype=dtype, device=device)
                b = torch.tensor([bvalue], dtype=dtype, device=device)
                c = torch.remainder(a, b)
                d = torch.fmod(a, b)
                self.assertTrue((b[0] > 0) == (c[0] > 0))  # remainder has same sign as divisor
                self.assertTrue((a[0] > 0) == (d[0] > 0))  # fmod has same sign as dividend
                self.assertTrue(abs(c[0]) < abs(b[0]))     # remainder is within range of divisor
                self.assertTrue(abs(d[0]) < abs(b[0]))     # fmod is within range of divisor
                if ((a[0] > 0) == (b[0] > 0)):
                    self.assertTrue(c[0] == d[0])   # remainder is same as fmod
                else:
                    self.assertTrue(abs(c[0] - d[0]) == abs(b[0]))  # differ by one divisor

    @dtypes(torch.int64, torch.float64)
    def test_remainder_edge_cases(self, device, dtype):
        # Test variations of negative values used as input
        a = torch.tensor([6, -6, -6, 6, 27, -27, -27, 27], dtype=dtype, device=device)
        b = torch.tensor([-3, 3, -3, 3, -5, 5, -5, 5], dtype=dtype, device=device)
        r = a.remainder(b)
        r_expected = torch.tensor([0, 0, 0, 0, -3, 3, -2, 2], dtype=dtype, device=device)
        self.assertEqual(r, r_expected)

        if dtype == torch.float64:
            # Test cases where result should be nan
            a = torch.tensor([-34, 0, 34], dtype=dtype, device=device)
            b = torch.zeros(3, dtype=dtype, device=device)
            self.assertTrue(torch.isnan(a.remainder(b)).all())

            # Need to test a fairly large tensor with float cpu to run
            # the Vec256 implementation
            if device == 'cpu':
                a = torch.tensor([6, -6, -6, 6, 27, -27, -27, 27] * 10000, dtype=dtype, device=device)
                b = torch.tensor([-3, 3, -3, 3, -5, 5, -5, 5] * 10000, dtype=dtype, device=device)
                r = a.remainder(b)
                r_expected = torch.tensor([0, 0, 0, 0, -3, 3, -2, 2] * 10000, dtype=dtype, device=device)
                self.assertEqual(r, r_expected)

                # Test nan cases
                a = torch.tensor([-34, 0, 34] * 20000, dtype=dtype, device=device)
                b = torch.zeros(3 * 20000, dtype=dtype, device=device)
                self.assertTrue(torch.isnan(a.remainder(b)).all())

        elif dtype == torch.int64:
            if device == 'cpu':
                # Test int divide by zero causes an exception
                a = torch.ones(1000, dtype=dtype, device=device)
                b = torch.ones(1000, dtype=dtype, device=device)
                b[500] = 0
                self.assertRaises(RuntimeError, lambda: a.remainder(b))

        # Check scalar type is promoted to match tensor
        a = torch.ones(1, dtype=dtype, device=device)
        b = 1.0 if dtype == torch.int64 else 1
        r = a.remainder(b)
        self.assertEqual(r.dtype, a.dtype)

    @slowTest
    @onlyOnCPUAndCUDA
    @dtypes(torch.float32, torch.float64, torch.bfloat16, torch.int32, torch.int64)
    @dtypesIfCUDA(torch.float32, torch.float64)
    def test_mm(self, device, dtype):
        def _test_mm(n, m, p, dtype, genf):
            # helper function
            def matrixmultiply(mat1, mat2):
                n = mat1.size(0)
                m = mat1.size(1)
                p = mat2.size(1)
                res = torch.zeros(n, p, dtype=dtype, device=device)
                for i, j in iter_indices(res):
                    res[i, j] = sum(mat1[i, k] * mat2[k, j] for k in range(m))
                return res

            # contiguous case
            mat1 = genf(n, m)
            mat2 = genf(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 1
            mat1 = genf(n, m)
            mat2 = genf(p, m).t()
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 2
            mat1 = genf(m, n).t()
            mat2 = genf(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # non contiguous case 3
            mat1 = genf(m, n).t()
            mat2 = genf(p, m).t()
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # test with zero stride
            mat1 = genf(n, m)
            mat2 = genf(m, 1).expand(m, p)
            res = torch.mm(mat1, mat2)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # explicitly exercise the _out variant in torch.mm().
            # contiguous case
            mat1 = genf(n, m)
            mat2 = genf(m, p)
            res = genf(n, p)
            torch.mm(mat1, mat2, out=res)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

            # explicitly exercise the _out variant in torch.mm().
            # non contiguous case 3
            mat1 = genf(m, n).t()
            mat2 = genf(p, m).t()
            res = genf(n, p)
            torch.mm(mat1, mat2, out=res)

            res2 = matrixmultiply(mat1, mat2)
            self.assertEqual(res, res2)

        def genf_int(x, y):
            return torch.randint(0, 100, (x, y), dtype=dtype, device=device)

        def genf_bfloat(x, y):
            return torch.randn(x, y, dtype=torch.float32, device=device).to(dtype)

        def genf_float(x, y):
            return torch.randn(x, y, dtype=dtype, device=device)

        for (n, m, p) in [(20, 10, 5), (15, 5, 10), (5, 18, 10)]:
            if (dtype == torch.int32) or (dtype == torch.int64):
                genf = genf_int
            elif (dtype == torch.bfloat16):
                genf = genf_bfloat
            else:
                genf = genf_float

            _test_mm(n, m, p, dtype, genf)

    @onlyCPU
    @dtypes(torch.float)
    def test_bmm(self, device, dtype):
        num_batches = 10
        M, N, O = 23, 8, 12
        b1 = torch.randn(num_batches, M, N, dtype=dtype, device=device)
        b2 = torch.randn(num_batches, N, O, dtype=dtype, device=device)
        res = torch.bmm(b1, b2)
        for i in range(num_batches):
            r = torch.mm(b1[i], b2[i])
            self.assertEqual(r, res[i])
        if torch.cuda.is_available():
            # check that mixed arguments are rejected
            self.assertRaises(RuntimeError, lambda: torch.bmm(b1, b2.cuda()))
            self.assertRaises(RuntimeError, lambda: torch.bmm(b1.cuda(), b2))

    @onlyCPU
    @dtypes(torch.float)
    def test_addbmm(self, device, dtype):
        # num_batches = 10
        # M, N, O = 12, 8, 5
        num_batches = 2
        M, N, O = 2, 3, 4
        b1 = torch.randn(num_batches, M, N, dtype=dtype, device=device)
        b2 = torch.randn(num_batches, N, O, dtype=dtype, device=device)
        res = torch.bmm(b1, b2)
        res2 = torch.tensor((), dtype=dtype, device=device).resize_as_(res[0]).zero_()
        res3 = torch.tensor((), dtype=dtype, device=device).resize_as_(res[0]).zero_()

        res2.addbmm_(b1, b2)
        self.assertEqual(res2, res.sum(0, False))
        res3.copy_(res2)

        with self.maybeWarnsRegex(
                UserWarning, "This overload of addbmm_ is deprecated"):
            res2.addbmm_(1, b1, b2)
        self.assertEqual(res2, res.sum(0, False) * 2),
        res3.addbmm_(b1, b2, beta=1)
        self.assertEqual(res2, res3)

        with self.maybeWarnsRegex(
                UserWarning, "This overload of addbmm_ is deprecated"):
            res2.addbmm_(1., .5, b1, b2)
        self.assertEqual(res2, res.sum(0, False) * 2.5)
        res3.addbmm_(b1, b2, beta=1., alpha=.5)
        self.assertEqual(res2, res3)

        with self.maybeWarnsRegex(
                UserWarning, "This overload of addbmm is deprecated"):
            self.assertEqual(res2, torch.addbmm(1, res2, 0, b1, b2))

        res4 = torch.addbmm(res2, b1, b2, beta=1, alpha=.5)
        self.assertEqual(res4, res.sum(0, False) * 3),

        res5 = torch.addbmm(res2, b1, b2, beta=0, alpha=1)
        self.assertEqual(res5, res.sum(0, False))

        res6 = torch.addbmm(res2, b1, b2, beta=.1, alpha=.5)
        self.assertEqual(res6, res2 * .1 + .5 * res.sum(0)),

    @onlyCPU
    @dtypes(torch.float)
    def test_baddbmm(self, device, dtype):
        num_batches = 10
        M, N, O = 12, 8, 5
        b1 = torch.randn(num_batches, M, N, dtype=dtype, device=device)
        b2 = torch.randn(num_batches, N, O, dtype=dtype, device=device)
        res = torch.bmm(b1, b2)
        res2 = torch.tensor((), dtype=dtype, device=device).resize_as_(res).zero_()
        res3 = torch.tensor((), dtype=dtype, device=device).resize_as_(res).zero_()

        res2.baddbmm_(b1, b2)
        self.assertEqual(res2, res)
        res3.copy_(res2)

        with self.maybeWarnsRegex(
                UserWarning, "This overload of baddbmm_ is deprecated"):
            res2.baddbmm_(1, b1, b2)
        self.assertEqual(res2, res * 2)
        res3.baddbmm_(b1, b2, beta=1)
        self.assertEqual(res3, res2)

        with self.maybeWarnsRegex(
                UserWarning, "This overload of baddbmm_ is deprecated"):
            res2.baddbmm_(1, .5, b1, b2)
        self.assertEqual(res2, res * 2.5)
        res3.baddbmm_(b1, b2, beta=1, alpha=.5)
        self.assertEqual(res3, res2)


        with self.maybeWarnsRegex(
                UserWarning, "This overload of baddbmm is deprecated"):
            self.assertEqual(torch.baddbmm(1, res2, 0, b1, b2), res2)

        res4 = torch.baddbmm(res2, b1, b2, beta=1, alpha=.5)
        self.assertEqual(res4, res * 3, atol=2e-5)

        res5 = torch.baddbmm(res2, b1, b2, beta=0, alpha=1)
        self.assertEqual(res5, res)

        res6 = torch.baddbmm(res2, b1, b2, beta=.1, alpha=.5)
        self.assertEqual(res6, res2 * .1 + res * .5)

    def _test_cop(self, torchfn, mathfn, dtype, device):
        def reference_implementation(res2):
            for i, j in iter_indices(sm1):
                idx1d = i * sm1.size(0) + j
                res2[i, j] = mathfn(sm1[i, j], sm2[idx1d])
            return res2

        # contiguous
        m1 = torch.randn(10, 10, 10, dtype=dtype, device=device)
        m2 = torch.randn(10, 10 * 10, dtype=dtype, device=device)
        sm1 = m1[4]
        sm2 = m2[4]

        res1 = torchfn(sm1, sm2.view(10, 10))
        res2 = reference_implementation(res1.clone())
        self.assertEqual(res1, res2)

        # non-contiguous
        m1 = torch.randn(10, 10, 10, dtype=dtype, device=device)
        m2 = torch.randn(10 * 10, 10 * 10, dtype=dtype, device=device)
        sm1 = m1[:, 4]
        sm2 = m2[:, 4]
        # view as sm1.size()
        sm2.set_(sm2.storage(), sm2.storage_offset(), sm1.size(), (sm2.stride()[0] * 10, sm2.stride()[0]))
        res1 = torchfn(sm1, sm2)
        # reference_implementation assumes 1-d sm2
        sm2.set_(sm2.storage(), sm2.storage_offset(), m2[:, 4].size(), m2[:, 4].stride())
        res2 = reference_implementation(res1.clone())
        self.assertEqual(res1, res2)

    @onlyCPU
    @dtypes(torch.float)
    def test_cdiv(self, device, dtype):
        self._test_cop(torch.div, lambda x, y: x / y, dtype, device)

    @onlyCPU
    @dtypes(torch.float)
    def test_cfmod(self, device, dtype):
        self._test_cop(torch.fmod, math.fmod, dtype, device)

    @onlyCPU
    @dtypes(torch.float)
    def test_cremainder(self, device, dtype):
        self._test_cop(torch.remainder, lambda x, y: x % y, dtype, device)

    @onlyCPU
    @dtypes(torch.float)
    def test_cmul(self, device, dtype):
        self._test_cop(torch.mul, lambda x, y: x * y, dtype, device)

    @onlyCPU
    @dtypes(torch.float)
    def test_cpow(self, device, dtype):
        self._test_cop(torch.pow, lambda x, y: nan if x < 0 else math.pow(x, y), dtype, device)

    @onlyCUDA
    @dtypes(torch.float16, torch.float32)
    def test_prod_gpu(self, device, dtype):
        x = torch.tensor([2, 3, 6, 9, 8], dtype=dtype, device=device)

        # Check all combinations: fp16 input - fp16 output, fp16 input - fp32
        # output, fp32 input - fp16 output, fp32 input - fp32 output
        for dtype_output in [torch.float16, torch.float32]:
            result_expected = torch.tensor(2592, dtype=dtype_output, device=device)
            output = torch.prod(x, dtype=dtype_output)
            self.assertEqual(output, result_expected)

            output = x.prod(dtype=dtype_output)
            self.assertEqual(output, result_expected)

    @onlyCPU
    @dtypes(torch.float)
    def test_prod(self, device, dtype):
        x = torch.rand(100, 100, dtype=dtype, device=device)
        res1 = torch.prod(x, 1)
        res2 = torch.tensor((), dtype=dtype, device=device)
        torch.prod(x, 1, out=res2)
        self.assertEqual(res1, res2)

    @onlyCPU
    @dtypes(torch.float)
    def test_cross(self, device, dtype):
        x = torch.rand(100, 3, 100, dtype=dtype, device=device)
        y = torch.rand(100, 3, 100, dtype=dtype, device=device)
        res1 = torch.cross(x, y)
        res2 = torch.tensor((), dtype=dtype, device=device)
        torch.cross(x, y, out=res2)
        self.assertEqual(res1, res2)

    @onlyCPU
    @dtypes(torch.float)
    def test_cross_with_and_without_dim(self, device, dtype):
        x = torch.rand(100, 3, dtype=dtype, device=device)
        y = torch.rand(100, 3, dtype=dtype, device=device)
        res1 = torch.cross(x, y, dim=1)
        res2 = torch.cross(x, y, dim=-1)
        res3 = torch.cross(x, y)
        self.assertEqual(res1, res2)
        self.assertEqual(res1, res3)

    @dtypes(torch.float, torch.double, torch.int8, torch.int16, torch.int32, torch.int64)
    def test_random(self, device, dtype):
        # This test is flaky with p<=(2/(ub-lb))^200=6e-36
        t = torch.empty(200, dtype=dtype, device=device)
        lb = 1
        ub = 4

        t.fill_(-1)
        t.random_(lb, ub)
        self.assertEqual(t.min(), lb)
        self.assertEqual(t.max(), ub - 1)

        t.fill_(-1)
        t.random_(ub)
        self.assertEqual(t.min(), 0)
        self.assertEqual(t.max(), ub - 1)

    def test_random_bool(self, device):
        size = 2000
        t = torch.empty(size, dtype=torch.bool, device=device)

        t.fill_(False)
        t.random_()
        self.assertEqual(t.min(), False)
        self.assertEqual(t.max(), True)
        self.assertTrue(0.4 < (t.eq(True)).to(torch.int).sum().item() / size < 0.6)

        t.fill_(True)
        t.random_()
        self.assertEqual(t.min(), False)
        self.assertEqual(t.max(), True)
        self.assertTrue(0.4 < (t.eq(True)).to(torch.int).sum().item() / size < 0.6)

    def test_random_from_to_bool(self, device):
        size = 2000

        int64_min_val = torch.iinfo(torch.int64).min
        int64_max_val = torch.iinfo(torch.int64).max

        min_val = 0
        max_val = 1

        froms = [int64_min_val, -42, min_val - 1, min_val, max_val, max_val + 1, 42]
        tos = [-42, min_val - 1, min_val, max_val, max_val + 1, 42, int64_max_val]

        for from_ in froms:
            for to_ in tos:
                t = torch.empty(size, dtype=torch.bool, device=device)
                if to_ > from_:
                    if not (min_val <= from_ <= max_val):
                        self.assertRaisesRegex(
                            RuntimeError,
                            "from is out of bounds",
                            lambda: t.random_(from_, to_)
                        )
                    elif not (min_val <= (to_ - 1) <= max_val):
                        self.assertRaisesRegex(
                            RuntimeError,
                            "to - 1 is out of bounds",
                            lambda: t.random_(from_, to_)
                        )
                    else:
                        t.random_(from_, to_)
                        range_ = to_ - from_
                        delta = 1
                        self.assertTrue(from_ <= t.to(torch.int).min() < (from_ + delta))
                        self.assertTrue((to_ - delta) <= t.to(torch.int).max() < to_)
                else:
                    self.assertRaisesRegex(
                        RuntimeError,
                        "random_ expects 'from' to be less than 'to', but got from=" + str(from_) + " >= to=" + str(to_),
                        lambda: t.random_(from_, to_)
                    )

    @dtypes(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
            torch.float, torch.double, torch.half, torch.bfloat16)
    @dtypesIfCUDA(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
                  torch.float, torch.double, torch.half, torch.bfloat16)
    def test_random_full_range(self, device, dtype):
        # TODO: https://github.com/pytorch/pytorch/issues/33793
        if IS_WINDOWS and device.startswith('cuda') and dtype == torch.bfloat16:
            raise unittest.SkipTest("Crashes with CUDA error: unspecified launch failure")

        size = 2000
        alpha = 0.1

        int64_min_val = torch.iinfo(torch.int64).min
        int64_max_val = torch.iinfo(torch.int64).max

        if dtype == torch.double:
            fp_limit = 2**53
        elif dtype == torch.float:
            fp_limit = 2**24
        elif dtype == torch.half:
            fp_limit = 2**11
        elif dtype == torch.bfloat16:
            fp_limit = 2**8
        else:
            fp_limit = 0

        t = torch.empty(size, dtype=dtype, device=device)

        if dtype in [torch.float, torch.double, torch.half, torch.bfloat16]:
            from_ = int(max(-fp_limit, int64_min_val))
            to_inc_ = int(min(fp_limit, int64_max_val))
        else:
            from_ = int(max(torch.iinfo(dtype).min, int64_min_val))
            to_inc_ = int(min(torch.iinfo(dtype).max, int64_max_val))
        range_ = to_inc_ - from_ + 1

        t.random_(from_, None)
        delta = max(1, alpha * range_)
        self.assertTrue(from_ <= t.to(torch.double).min() < (from_ + delta))
        self.assertTrue((to_inc_ - delta) < t.to(torch.double).max() <= to_inc_)

    @dtypes(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
            torch.float, torch.double, torch.half, torch.bfloat16)
    @dtypesIfCUDA(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
                  torch.float, torch.double, torch.half, torch.bfloat16)
    def test_random_from_to(self, device, dtype):
        # TODO: https://github.com/pytorch/pytorch/issues/33793
        if IS_WINDOWS and device.startswith('cuda') and dtype == torch.bfloat16:
            raise unittest.SkipTest("Crashes with CUDA error: unspecified launch failure")

        size = 2000
        alpha = 0.1

        int64_min_val = torch.iinfo(torch.int64).min
        int64_max_val = torch.iinfo(torch.int64).max

        if dtype in [torch.float, torch.double, torch.half]:
            min_val = int(max(torch.finfo(dtype).min, int64_min_val))
            max_val = int(min(torch.finfo(dtype).max, int64_max_val))
            froms = [min_val, -42, 0, 42]
            tos = [-42, 0, 42, max_val >> 1]
        elif dtype == torch.bfloat16:
            min_val = int64_min_val
            max_val = int64_max_val
            froms = [min_val, -42, 0, 42]
            tos = [-42, 0, 42, max_val >> 1]
        elif dtype == torch.uint8:
            min_val = torch.iinfo(dtype).min
            max_val = torch.iinfo(dtype).max
            froms = [int64_min_val, -42, min_val - 1, min_val, 42, max_val, max_val + 1]
            tos = [-42, min_val - 1, min_val, 42, max_val, max_val + 1, int64_max_val]
        elif dtype == torch.int64:
            min_val = int64_min_val
            max_val = int64_max_val
            froms = [min_val, -42, 0, 42]
            tos = [-42, 0, 42, max_val]
        else:
            min_val = torch.iinfo(dtype).min
            max_val = torch.iinfo(dtype).max
            froms = [int64_min_val, min_val - 1, min_val, -42, 0, 42, max_val, max_val + 1]
            tos = [min_val - 1, min_val, -42, 0, 42, max_val, max_val + 1, int64_max_val]

        if dtype == torch.double:
            fp_limit = 2**53
        elif dtype == torch.float:
            fp_limit = 2**24
        elif dtype == torch.half:
            fp_limit = 2**11
        elif dtype == torch.bfloat16:
            fp_limit = 2**8
        else:
            fp_limit = 0

        for from_ in froms:
            for to_ in tos:
                t = torch.empty(size, dtype=dtype, device=device)
                if to_ > from_:
                    if not (min_val <= from_ <= max_val):
                        self.assertRaisesRegex(
                            RuntimeError,
                            "from is out of bounds",
                            lambda: t.random_(from_, to_)
                        )
                    elif not (min_val <= (to_ - 1) <= max_val):
                        self.assertRaisesRegex(
                            RuntimeError,
                            "to - 1 is out of bounds",
                            lambda: t.random_(from_, to_)
                        )
                    else:
                        if dtype.is_floating_point and (
                                not (-fp_limit <= from_ <= fp_limit) or not (-fp_limit <= (to_ - 1) <= fp_limit)):
                            if not (-fp_limit <= from_ <= fp_limit):
                                self.assertWarnsRegex(UserWarning, "from is out of bounds",
                                                      lambda: t.random_(from_, to_))
                            if not (-fp_limit <= (to_ - 1) <= fp_limit):
                                self.assertWarnsRegex(UserWarning, "to - 1 is out of bounds",
                                                      lambda: t.random_(from_, to_))
                        else:
                            t.random_(from_, to_)
                            range_ = to_ - from_
                            delta = max(1, alpha * range_)
                            if dtype == torch.bfloat16:
                                # Less strict checks because of rounding errors
                                # TODO investigate rounding errors
                                self.assertTrue(from_ <= t.to(torch.double).min() < (from_ + delta))
                                self.assertTrue((to_ - delta) < t.to(torch.double).max() <= to_)
                            else:
                                self.assertTrue(from_ <= t.to(torch.double).min() < (from_ + delta))
                                self.assertTrue((to_ - delta) <= t.to(torch.double).max() < to_)
                else:
                    self.assertRaisesRegex(
                        RuntimeError,
                        "random_ expects 'from' to be less than 'to', but got from=" + str(from_) + " >= to=" + str(to_),
                        lambda: t.random_(from_, to_)
                    )

    @dtypes(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
            torch.float, torch.double, torch.half, torch.bfloat16)
    @dtypesIfCUDA(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
                  torch.float, torch.double, torch.half, torch.bfloat16)
    def test_random_to(self, device, dtype):
        # TODO: https://github.com/pytorch/pytorch/issues/33793
        if IS_WINDOWS and device.startswith('cuda') and dtype == torch.bfloat16:
            raise unittest.SkipTest("Crashes with CUDA error: unspecified launch failure")

        size = 2000
        alpha = 0.1

        int64_min_val = torch.iinfo(torch.int64).min
        int64_max_val = torch.iinfo(torch.int64).max

        if dtype in [torch.float, torch.double, torch.half]:
            min_val = int(max(torch.finfo(dtype).min, int64_min_val))
            max_val = int(min(torch.finfo(dtype).max, int64_max_val))
            tos = [-42, 0, 42, max_val >> 1]
        elif dtype == torch.bfloat16:
            min_val = int64_min_val
            max_val = int64_max_val
            tos = [-42, 0, 42, max_val >> 1]
        elif dtype == torch.uint8:
            min_val = torch.iinfo(dtype).min
            max_val = torch.iinfo(dtype).max
            tos = [-42, min_val - 1, min_val, 42, max_val, max_val + 1, int64_max_val]
        elif dtype == torch.int64:
            min_val = int64_min_val
            max_val = int64_max_val
            tos = [-42, 0, 42, max_val]
        else:
            min_val = torch.iinfo(dtype).min
            max_val = torch.iinfo(dtype).max
            tos = [min_val - 1, min_val, -42, 0, 42, max_val, max_val + 1, int64_max_val]

        from_ = 0
        for to_ in tos:
            t = torch.empty(size, dtype=dtype, device=device)
            if to_ > from_:
                if not (min_val <= (to_ - 1) <= max_val):
                    self.assertRaisesRegex(
                        RuntimeError,
                        "to - 1 is out of bounds",
                        lambda: t.random_(from_, to_)
                    )
                else:
                    t.random_(to_)
                    range_ = to_ - from_
                    delta = max(1, alpha * range_)
                    if dtype == torch.bfloat16:
                        # Less strict checks because of rounding errors
                        # TODO investigate rounding errors
                        self.assertTrue(from_ <= t.to(torch.double).min() < (from_ + delta))
                        self.assertTrue((to_ - delta) < t.to(torch.double).max() <= to_)
                    else:
                        self.assertTrue(from_ <= t.to(torch.double).min() < (from_ + delta))
                        self.assertTrue((to_ - delta) <= t.to(torch.double).max() < to_)
            else:
                self.assertRaisesRegex(
                    RuntimeError,
                    "random_ expects 'from' to be less than 'to', but got from=" + str(from_) + " >= to=" + str(to_),
                    lambda: t.random_(from_, to_)
                )

    @dtypes(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
            torch.float, torch.double, torch.half, torch.bfloat16)
    @dtypesIfCUDA(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64,
                  torch.float, torch.double, torch.half, torch.bfloat16)
    def test_random_default(self, device, dtype):
        # TODO: https://github.com/pytorch/pytorch/issues/33793
        if IS_WINDOWS and device.startswith('cuda') and dtype == torch.bfloat16:
            raise unittest.SkipTest("Crashes with CUDA error: unspecified launch failure")

        size = 2000
        alpha = 0.1

        if dtype == torch.float:
            to_inc = 1 << 24
        elif dtype == torch.double:
            to_inc = 1 << 53
        elif dtype == torch.half:
            to_inc = 1 << 11
        elif dtype == torch.bfloat16:
            to_inc = 1 << 8
        else:
            to_inc = torch.iinfo(dtype).max

        t = torch.empty(size, dtype=dtype, device=device)
        t.random_()
        self.assertTrue(0 <= t.to(torch.double).min() < alpha * to_inc)
        self.assertTrue((to_inc - alpha * to_inc) < t.to(torch.double).max() <= to_inc)

    @onlyCPU
    @dtypes(torch.half, torch.double, torch.int)
    def test_cat(self, device, dtype):
        SIZE = 10
        for dim in range(-3, 3):
            pos_dim = dim if dim >= 0 else 3 + dim
            x = torch.randint(low=-100, high=100, size=(13, SIZE, SIZE), device=device).to(dtype).transpose(0, pos_dim)
            y = torch.randint(low=-100, high=100, size=(17, SIZE, SIZE), device=device).to(dtype).transpose(0, pos_dim)
            z = torch.randint(low=-100, high=100, size=(19, SIZE, SIZE), device=device).to(dtype).transpose(0, pos_dim)

            res1 = torch.cat((x, y, z), dim)
            self.assertEqual(res1.narrow(pos_dim, 0, 13), x, 0)
            self.assertEqual(res1.narrow(pos_dim, 13, 17), y, 0)
            self.assertEqual(res1.narrow(pos_dim, 30, 19), z, 0)

        x = torch.randint(low=-100, high=100, size=(20, SIZE, SIZE), device=device).to(dtype)
        self.assertEqual(torch.cat(torch.split(x, 7)), x)
        self.assertEqual(torch.cat(torch.chunk(x, 7)), x)

        y = torch.randint(low=-100, high=100, size=(1, SIZE, SIZE), device=device).to(dtype)
        z = torch.cat([x, y])
        self.assertEqual(z.size(), (21, SIZE, SIZE))

        self.assertRaises(RuntimeError, lambda: torch.cat([]))
        self.assertRaisesRegex(TypeError, 'got None', lambda: torch.cat([x, None]))

    @onlyCPU
    def test_cat_scalars(self, device):
        x = torch.tensor(0, device=device)
        y = torch.tensor(1, device=device)
        with self.assertRaisesRegex(RuntimeError, 'zero-dimensional.*cannot be concatenated'):
            torch.cat([x, y])

    @onlyCPU
    @dtypes(torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64)
    def test_div_zero(self, device, dtype):
        a = torch.tensor([0, 1], dtype=dtype, device=device)
        b = torch.tensor([0, 1], dtype=dtype, device=device)
        with self.assertRaisesRegex(RuntimeError, 'ZeroDivisionError'):
            a.div(b)

    @onlyCPU
    def test_cat_bad_input_sizes(self, device):
        x = torch.randn(2, 1, device=device)
        y = torch.randn(2, 1, 1, device=device)
        z = torch.randn(2, 1, 1, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, y, z]))

        x = torch.randn(2, 1, 2, device=device)
        y = torch.randn(2, 1, 1, device=device)
        z = torch.randn(2, 2, 1, device=device)
        self.assertRaises(RuntimeError, lambda: torch.cat([x, y, z], dim=1))

    @slowTest
    @onlyCPU
    def test_cat_big(self, device):
        SIZE1 = 6500
        SIZE2 = 4500
        concat_list = []
        concat_list.append(torch.ones((SIZE1, 1024 * 512), dtype=torch.uint8, device=device))
        concat_list.append(torch.ones((SIZE2, 1024 * 512), dtype=torch.uint8, device=device))
        result = torch.cat(concat_list)
        self.assertEqual(result.size(0), SIZE1 + SIZE2)


    @onlyCPU
    def test_max_mixed_devices(self, device):
        a = torch.randn(10, device=device)
        if torch.cuda.is_available():
            values = torch.randn(10).cuda()
            indices = torch.cuda.LongTensor()
            self.assertRaises(RuntimeError,
                              lambda: torch.max(a, 0, out=(values, indices)))

    @onlyCPU
    def test_min_mixed_devices(self, device):
        a = torch.randn(10, device=device)
        if torch.cuda.is_available():
            values = torch.randn(10).cuda()
            indices = torch.cuda.LongTensor()
            self.assertRaises(RuntimeError,
                              lambda: torch.min(a, 0, out=(values, indices)))

    def test_full_deprecation_warning(self, device):
        size = (2, 2)
        # Tests bool and integer fill_values deprecated without specific dtype set
        with self.maybeWarnsRegex(UserWarning, 'Deprecation warning: .+'):
            self.assertEqual(torch.full(size, True).dtype, torch.float)
        with self.maybeWarnsRegex(UserWarning, 'Deprecation warning: .+'):
            self.assertEqual(torch.full(size, 1).dtype, torch.float)

        # Explicitly setting the dtype doesn't warn
        with self.maybeWarnsRegex(UserWarning, ''):
            self.assertEqual(torch.full(size, 1, dtype=torch.long).dtype, torch.long)
        with self.maybeWarnsRegex(UserWarning, ''):
            self.assertEqual(torch.full(size, True, dtype=torch.bool).dtype,
                             torch.bool)

        # Performs same tests with named tensor
        with self.maybeWarnsRegex(UserWarning, 'Deprecation warning: .+|Named tensors .+'):
            self.assertEqual(torch.full(size, True, names=('a', 'b')).dtype, torch.float)
        with self.maybeWarnsRegex(UserWarning, 'Deprecation warning: .+|Named tensors .+'):
            self.assertEqual(torch.full(size, 1, names=('a', 'b')).dtype, torch.float)

        with self.maybeWarnsRegex(UserWarning, 'Named tensors .+'):
            dt = torch.full(size, True, names=('a', 'b'), dtype=torch.bool).dtype
            self.assertEqual(dt, torch.bool)
        with self.maybeWarnsRegex(UserWarning, 'Named tensors .+'):
            dt = torch.full(size, 1, names=('a', 'b'), dtype=torch.long).dtype
            self.assertEqual(dt, torch.long)

    @onlyOnCPUAndCUDA
    @dtypes(torch.half, torch.float, torch.double)
    def test_full_inference(self, device, dtype):
        size = (2, 2)

        prev_default = torch.get_default_dtype()
        torch.set_default_dtype(dtype)

        # Tests bool fill value inference
        # Note: in the future this will return a tensor of torch.bool dtype
        t = torch.full(size, True)
        self.assertEqual(t.dtype, dtype)

        # Tests integer fill value inference
        # Note: in the future this will return a tensor of torch.long dtype
        t = torch.full(size, 1)
        self.assertEqual(t.dtype, dtype)

        # Tests float fill value inference
        t = torch.full(size, 1.)
        self.assertEqual(t.dtype, dtype)

        # Tests complex inference
        t = torch.full(size, (1 + 1j))
        ctype = torch.complex128 if dtype is torch.double else torch.complex64
        self.assertEqual(t.dtype, ctype)

        torch.set_default_dtype(prev_default)

    # Full-like precedence is the explicit dtype then the dtype of the "like"
    # tensor.
    @onlyOnCPUAndCUDA
    def test_full_like_inference(self, device):
        size = (2, 2)
        like = torch.empty((5,), device=device, dtype=torch.long)

        self.assertEqual(torch.full_like(like, 1.).dtype, torch.long)
        self.assertEqual(torch.full_like(like, 1., dtype=torch.complex64).dtype,
                         torch.complex64)

    def test_full_out(self, device):
        o = torch.empty((5,), device=device, dtype=torch.long)

        # verifies dtype/out conflict throws a RuntimeError
        with self.assertRaises(RuntimeError):
            torch.full(o.shape, 1., dtype=torch.float, out=o)

        # verifies out dtype overrides inference
        self.assertEqual(torch.full(o.shape, 1., out=o).dtype, o.dtype)

    def _float_to_int_conversion_helper(self, vals, device, dtype):
        assert TEST_NUMPY

        a = np.array(vals, dtype=np.float32).astype(torch_to_numpy_dtype_dict[dtype])
        t = torch.tensor(vals, device=device, dtype=torch.float).to(dtype)
        self.assertEqual(torch.from_numpy(a), t.cpu())

    # Checks that float->integer casts don't produce undefined behavior errors.
    # Note: In C++, casting from a floating value to an integral dtype
    # is undefined if the floating point value is not within the integral
    # dtype's dynamic range. This can (and should) cause undefined behavior
    # errors with UBSAN. These casts are deliberate in PyTorch, however, and
    # NumPy has the same behavior.
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @dtypes(torch.bool, torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64)
    def test_float_to_int_conversion_finite(self, device, dtype):
        min = torch.finfo(torch.float).min
        max = torch.finfo(torch.float).max

        # Note: CUDA max float -> integer conversion is divergent on some dtypes
        vals = (min, -2, -1.5, -.5, 0, .5, 1.5, 2, max)
        if self.device_type == 'cuda':
            if torch.version.hip:
                # HIP min float -> int64 conversion is divergent
                vals = (-2, -1.5, -.5, 0, .5, 1.5, 2)
            else:
                vals = (min, -2, -1.5, -.5, 0, .5, 1.5, 2)

        self._float_to_int_conversion_helper(vals, device, dtype)

    # Note: CUDA will fail this test on most dtypes, often dramatically.
    @unittest.skipIf(not TEST_NUMPY, "NumPy not found")
    @onlyCPU
    @dtypes(torch.bool, torch.uint8, torch.int8, torch.int16, torch.int32, torch.int64)
    def test_float_to_int_conversion_nonfinite(self, device, dtype):
        vals = (float('-inf'), float('inf'), float('nan'))

        self._float_to_int_conversion_helper(vals, device, dtype)

    # TODO: re-enable this test
    @unittest.skipIf(True, "real and imag not implemented for complex")
    @onlyOnCPUAndCUDA
    def test_complex_type_conversions(self, device):
        dtypes = [torch.float, torch.complex64, torch.complex128]
        for from_type in dtypes:
            for to_type in dtypes:
                from_tensor = torch.randn(4, dtype=from_type, device=device)
                to_tensor = from_tensor.to(to_type)
                if from_type.is_complex and not to_type.is_complex:
                    self.assertEqual(torch.real(from_tensor), to_tensor, exact_dtype=False)
                elif not from_type.is_complex and to_type.is_complex:
                    self.assertEqual(from_tensor, torch.real(to_tensor), exact_dtype=False)
                    self.assertEqual(torch.zeros_like(torch.imag(to_tensor)), torch.imag(to_tensor), exact_dtype=False)
                else:
                    self.assertEqual(from_tensor, to_tensor, exact_dtype=False)

    @dtypes(torch.complex64, torch.complex128)
    def test_complex_unsupported(self, device, dtype):
        t = torch.tensor((1 + 1j), device=device, dtype=dtype)
        # Note: this is consistent with NumPy
        with self.assertRaises(RuntimeError):
            torch.floor(t)
        with self.assertRaises(RuntimeError):
            torch.ceil(t)
        with self.assertRaises(RuntimeError):
            torch.trunc(t)

        # Tests min and max variants with complex inputs
        # Note: whether PyTorch should support min and max on complex
        # tensors is an open question.
        # See https://github.com/pytorch/pytorch/issues/36374
        with self.assertRaises(RuntimeError):
            torch.min(t)
        with self.assertRaises(RuntimeError):
            t.min()
        with self.assertRaises(RuntimeError):
            torch.min(t, dim=0)
        with self.assertRaises(RuntimeError):
            torch.min(t, t)
        with self.assertRaises(RuntimeError):
            torch.min(t, t, out=t)

        with self.assertRaises(RuntimeError):
            torch.max(t)
        with self.assertRaises(RuntimeError):
            t.max()
        with self.assertRaises(RuntimeError):
            torch.max(t, dim=0)
        with self.assertRaises(RuntimeError):
            torch.max(t, t)
        with self.assertRaises(RuntimeError):
            torch.max(t, t, out=t)

        # Tests clamp variants with complex inputs
        # Note: whether PyTorch should support clamp on complex
        # tensors is an open question.
        # See https://github.com/pytorch/pytorch/issues/33568
        min_val = 1 + 1j
        max_val = 4 + 4j
        out = torch.empty((0,), device=device, dtype=dtype)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, min=min_val)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, max=max_val)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, min_val, max_val)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, min=min_val, out=out)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, max=max_val, out=out)
        with self.assertRaises(RuntimeError):
            torch.clamp(t, min_val, max_val, out=out)

    @dtypes(torch.long)
    def test_abs_big_number(self, device, dtype):
        bignumber = 2 ** 31 + 1
        res = torch.tensor([bignumber], device=device, dtype=dtype)
        self.assertGreater(res.abs()[0], 0)

    @dtypes(torch.float, torch.double)
    def test_abs_signed_zero(self, device, dtype):
        # Both abs(0.0) and abs(-0.0) should result in 0.0
        size = 128 + 1  # pick a large enough number with remainder so that
        # both vectorized and nonvectorized op is tested
        inp = torch.zeros(size, device=device, dtype=dtype)
        inp[::2] = -0.0
        inp = inp.abs()
        for v in inp:
            self.assertGreater(math.copysign(1.0, v), 0.0)

    @dtypes(torch.float)
    def test_absolute(self, device, dtype):
        # absolute is an alias for abs. Just check to see that results
        # are the same.
        t = torch.randn(10, 10, device=device, dtype=dtype)
        r_abs = t.abs()
        r_absolute = t.absolute()
        self.assertEqual(r_abs, r_absolute)

        r_abs = torch.abs(t)
        r_absolute = torch.absolute(t)
        self.assertEqual(r_abs, r_absolute)

        r_abs = torch.empty((10, 10), device=device, dtype=dtype)
        r_absolute = torch.empty((10, 10), device=device, dtype=dtype)
        torch.abs(t, out=r_abs)
        torch.absolute(t, out=r_absolute)
        self.assertEqual(r_abs, r_absolute)

        from copy import deepcopy
        t_copy = deepcopy(t)
        t.absolute_()
        t_copy.abs_()
        self.assertEqual(t, t_copy)

    def test_bucketization(self, device):
        values_1d = torch.tensor([1, 2, 3, 4, 5, 6, 7, 8, 9], device=device)
        values_3d = torch.tensor([[[1, 3, 5], [2, 4, 6]], [[1, 2, 3], [4, 5, 6]]], device=device)

        # regular case 3d boundary and 3d input value
        boundaries = torch.tensor([[[1, 2, 3, 4], [3, 4, 5, 6]], [[1, 3, 5, 7], [2, 4, 6, 8]]], device=device)
        expected_result = torch.tensor([[[0, 2, 4], [0, 1, 3]], [[0, 1, 1], [1, 2, 2]]], device=device)
        output = torch.empty(2, 2, 3, device=device, dtype=torch.int64)
        self.assertEqual(torch.searchsorted(boundaries, values_3d), expected_result)
        self.assertEqual(torch.searchsorted(boundaries, values_3d, out=output), expected_result)
        expected_result = torch.tensor([[[1, 3, 4], [0, 2, 4]], [[1, 1, 2], [2, 2, 3]]], device=device)
        self.assertEqual(torch.searchsorted(boundaries, values_3d, right=True), expected_result)
        self.assertEqual(torch.searchsorted(boundaries, values_3d, right=True, out=output), expected_result)

        # simple 1d boundary and 3d input value
        boundaries = torch.tensor([1, 2, 3, 4, 5, 6], device=device)
        expected_result = torch.tensor([[[0, 2, 4], [1, 3, 5]], [[0, 1, 2], [3, 4, 5]]], device=device)
        output = torch.empty(2, 2, 3, device=device, dtype=torch.int64)
        self.assertEqual(torch.searchsorted(boundaries, values_3d), expected_result)
        self.assertEqual(torch.bucketize(values_3d, boundaries), expected_result)
        self.assertEqual(torch.bucketize(values_3d, boundaries, out=output), expected_result)
        expected_result = torch.tensor([[[1, 3, 5], [2, 4, 6]], [[1, 2, 3], [4, 5, 6]]], device=device)
        self.assertEqual(torch.searchsorted(boundaries, values_3d, right=True), expected_result)
        self.assertEqual(torch.bucketize(values_3d, boundaries, right=True), expected_result)
        self.assertEqual(torch.bucketize(values_3d, boundaries, out=output, right=True), expected_result)

        # simple float 1d boundary and 1d input with output int32 type
        values_1d_float = values_1d.to(torch.float32)
        boundaries = torch.tensor([0.9, 1, 2, 2, 3, 3, 4, 4.1, 9, 9], device=device, dtype=torch.float32)
        expected_result = torch.tensor([1, 2, 4, 6, 8, 8, 8, 8, 8], device=device, dtype=torch.int32)
        self.assertEqual(torch.searchsorted(boundaries, values_1d_float, out_int32=True), expected_result)
        self.assertEqual(torch.bucketize(values_1d_float, boundaries, out_int32=True), expected_result)

        # multiple dimension input with 0 elements
        boundaries = torch.tensor([1, 2, 3, 4, 5, 6], device=device, dtype=torch.int64)
        values_0_el = torch.tensor([[[]]], device=device, dtype=torch.int64)
        expected_result = values_0_el.to(torch.int64)
        self.assertEqual(torch.searchsorted(boundaries, values_0_el), expected_result)
        self.assertEqual(torch.bucketize(values_0_el, boundaries), expected_result)

        # nan input
        values_nan = torch.tensor([1.0, float('nan'), 2.0, float('nan')], device=device, dtype=torch.float64)
        boundaries = torch.tensor([0.0, 1.0, 2.0, 3.0], device=device, dtype=torch.float64)
        expected_result = torch.tensor([1, 4, 2, 4], device=device)
        self.assertEqual(torch.searchsorted(boundaries, values_nan), expected_result)
        expected_result = torch.tensor([2, 4, 3, 4], device=device)
        self.assertEqual(torch.searchsorted(boundaries, values_nan, right=True), expected_result)

        # type promotion and non contiguous tensors
        values_3d_permute = values_3d.permute(2, 1, 0).to(torch.int32)
        boundaries_permute = values_3d.permute(2, 1, 0).to(torch.float64)
        expected_result = torch.tensor([[[0, 0], [0, 1]], [[2, 0], [0, 1]], [[2, 0], [0, 0]]], device=device)
        if self.device_type != 'xla':
            self.assertWarnsRegex(
                UserWarning, "tensor is non-contiguous",
                lambda: self.assertEqual(torch.searchsorted(boundaries_permute, values_3d_permute), expected_result))
        else:
            # All tensors in XLA is contiguous even doing permute, no warning msg will be generate in XLA
            self.assertEqual(torch.searchsorted(boundaries_permute, values_3d_permute), expected_result)

        # scalar type
        boundaries = torch.tensor([1.5, 2.5, 3.5], device=device)
        expected_result = torch.tensor(1, device=device)
        self.assertEqual(torch.searchsorted(boundaries, 2), expected_result)
        self.assertEqual(torch.bucketize(torch.tensor(2, device=device), boundaries), expected_result)
        expected_result = torch.tensor(3, device=device)
        scalar_tensor_nan = torch.tensor(float('nan'), device=device)
        self.assertEqual(torch.searchsorted(boundaries, scalar_tensor_nan), expected_result)
        self.assertEqual(torch.bucketize(float('nan'), boundaries, right=True), expected_result)

        # invalid input dimensions
        boundaries = torch.tensor([[1, 2, 3], [4, 5, 6]], device=device)
        with self.assertRaisesRegex(
                RuntimeError, "first N-1 dimensions of boundaries tensor and input value tensor must match"):
            torch.searchsorted(boundaries, values_3d)
        with self.assertRaisesRegex(
                RuntimeError, "boundaries tensor must be 1 dimension"):
            torch.bucketize(values_3d, boundaries)
        with self.assertRaisesRegex(
                RuntimeError, "only when boundaries tensor dimension is 1"):
            torch.searchsorted(boundaries, 1)

        # incompatiable output tensor's dtype
        def test_output_dtype(dtype, is_int32):
            output = values_1d.to(dtype)
            with self.assertRaisesRegex(
                    RuntimeError, "output tensor's dtype is wrong"):
                torch.searchsorted(values_1d, values_1d, out=output, out_int32=is_int32)

        test_output_dtype(torch.float32, False)
        test_output_dtype(torch.int32, False)
        test_output_dtype(torch.int64, True)


# NOTE [Linspace+Logspace precision override]
# Our Linspace and logspace torch.half CUDA kernels are not very precise.
# Since linspace/logspace are deterministic, we can compute an expected
# amount of error (by testing without a precision override), adding a tiny
# amount (EPS) to that, and using that value as the override.
LINSPACE_LOGSPACE_EXTRA_EPS = 1e-5

# Tests that compare a device's computation with the (gold-standard) CPU's.
class TestDevicePrecision(TestCase):
    exact_dtype = True

    # The implementation of linspace+logspace goes through a different path
    # when the steps arg is equal to 0 or 1. For other values of `steps`
    # they call specialized linspace (or logspace) kernels.
    LINSPACE_LOGSPACE_SPECIAL_STEPS = [0, 1]

    def _test_linspace(self, device, dtype, steps):
        a = torch.linspace(0, 10, steps=steps, dtype=dtype, device=device)
        b = torch.linspace(0, 10, steps=steps)
        self.assertEqual(a, b, atol=self.precision, exact_dtype=False)

    # See NOTE [Linspace+Logspace precision override]
    @precisionOverride({torch.half: 0.0039 + LINSPACE_LOGSPACE_EXTRA_EPS})
    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_linspace(self, device, dtype):
        self._test_linspace(device, dtype, steps=10)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_linspace_special_steps(self, device, dtype):
        for steps in self.LINSPACE_LOGSPACE_SPECIAL_STEPS:
            self._test_linspace(device, dtype, steps=steps)

    def _test_logspace(self, device, dtype, steps):
        a = torch.logspace(1, 1.1, steps=steps, dtype=dtype, device=device)
        b = torch.logspace(1, 1.1, steps=steps)
        self.assertEqual(a, b, atol=self.precision, exact_dtype=False)

    def _test_logspace_base2(self, device, dtype, steps):
        a = torch.logspace(1, 1.1, steps=steps, base=2, dtype=dtype, device=device)
        b = torch.logspace(1, 1.1, steps=steps, base=2)
        self.assertEqual(a, b, atol=self.precision, exact_dtype=False)

    # See NOTE [Linspace+Logspace precision override]
    @precisionOverride({torch.half: 0.0157 + LINSPACE_LOGSPACE_EXTRA_EPS})
    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_logspace(self, device, dtype):
        self._test_logspace(device, dtype, steps=10)

    # See NOTE [Linspace+Logspace precision override]
    @precisionOverride({torch.half: 0.00201 + LINSPACE_LOGSPACE_EXTRA_EPS})
    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_logspace_base2(self, device, dtype):
        self._test_logspace_base2(device, dtype, steps=10)

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_logspace_special_steps(self, device, dtype):
        for steps in self.LINSPACE_LOGSPACE_SPECIAL_STEPS:
            self._test_logspace(device, dtype, steps=steps)
            self._test_logspace_base2(device, dtype, steps=steps)

    # Note: ROCm fails when using float tensors
    @dtypes(torch.double)
    def test_polygamma(self, device, dtype):
        cpu_tensor = torch.randn(10, 10, 10, dtype=dtype)
        device_tensor = cpu_tensor.to(device)
        zeros = torch.zeros(10, 10, 10, dtype=dtype)
        for n in [0, 1]:
            cpu_out = cpu_tensor.polygamma(n)
            device_out = device_tensor.polygamma(n)
            norm_errors = (device_out - cpu_out.to(device)) / device_out
            self.assertEqual(norm_errors, zeros)

    # Note: fails when using float tensors
    @dtypes(torch.double)
    def test_digamma(self, device, dtype):
        cpu_tensor = torch.randn(10, 10, 10, dtype=dtype)
        device_tensor = cpu_tensor.to(device)
        zeros = torch.zeros(10, 10, 10, dtype=dtype)
        cpu_out = cpu_tensor.digamma()
        device_out = device_tensor.digamma()
        norm_errors = (device_out - cpu_out.to(device)) / device_out
        self.assertEqual(norm_errors, zeros)

        # Tests pole behavior
        cpu_tensor = torch.tensor([-0.999999994, -1.999999994, -2.0000000111,
                                   -100.99999994, -1931.99999994, 0.000000111,
                                   -0.000000111, 0, -1, -2, -931], dtype=dtype)
        expected_errors = torch.tensor([0, 0, 0, 0, 0, 0, 0, nan, nan, nan, nan], dtype=dtype)
        device_tensor = cpu_tensor.to(device)
        cpu_out = cpu_tensor.digamma()
        device_out = device_tensor.digamma()
        norm_errors = (device_out - cpu_out.to(device)) / device_out
        self.assertEqual(norm_errors, expected_errors)

    def test_var(self, device):
        cpu_tensor = torch.randn(2, 3, 3)
        device_tensor = cpu_tensor.to(device)
        self.assertEqual(device_tensor.var(), cpu_tensor.var())
        self.assertEqual(device_tensor.var(1), cpu_tensor.var(1))
        self.assertEqual(device_tensor.var(2), cpu_tensor.var(2))
        self.assertEqual(device_tensor.std(), cpu_tensor.std())
        self.assertEqual(device_tensor.std(1), cpu_tensor.std(1))
        self.assertEqual(device_tensor.var(2), cpu_tensor.var(2))

        cpu_tensor = torch.randn(100)
        device_tensor = cpu_tensor.to(device)
        self.assertEqual(device_tensor.var(), cpu_tensor.var())

    def test_var_large_input(self, device):
        # Large, not-nice input
        cpu_tensor = torch.randn(2 * 32 * 1024 + 1, 2, 67)
        device_tensor = cpu_tensor.to(device)

        self.assertEqual(cpu_tensor.var(2), device_tensor.var(2))

    @dtypesIfCUDA(torch.half, torch.float, torch.double)
    @dtypes(torch.float, torch.double)
    def test_device_rounding(self, device, dtype):
        # test half-to-even
        a = [-5.8, -3.5, -2.3, -1.5, -0.5, 0.5, 1.5, 2.3, 3.5, 5.8]
        res = [-6., -4., -2., -2., 0., 0., 2., 2., 4., 6.]

        a_tensor = torch.tensor(a, device=device).round()
        res_tensor = torch.tensor(res, device='cpu')
        self.assertEqual(a_tensor, res_tensor)

    @dtypes(torch.int, torch.long, torch.float, torch.double)
    def test_arange(self, device, dtype):
        cpu_tensor = torch.arange(0, 10, dtype=dtype, device='cpu')
        device_tensor = torch.arange(0, 10, dtype=dtype, device=device)
        self.assertEqual(cpu_tensor, device_tensor)

    @onlyCUDA
    @skipCUDAIfNotRocm
    def test_arange_bfloat16(self, device):
        ref_tensor = torch.tensor([0, 1, 2, 3], dtype=torch.bfloat16, device=device)
        bfloat16_tensor = torch.arange(0, 4, dtype=torch.bfloat16, device=device)
        self.assertEqual(ref_tensor, bfloat16_tensor)

        # step=2
        ref_tensor = torch.tensor([0, 2, 4], dtype=torch.bfloat16, device=device)
        bfloat16_tensor = torch.arange(0, 6, step=2, dtype=torch.bfloat16, device=device)
        self.assertEqual(ref_tensor, bfloat16_tensor)

    @onlyCUDA
    @skipCUDAIfNotRocm
    def test_index_add_bfloat16(self, device):
        inp_tensor = torch.randn(5, 3, device='cpu').bfloat16()
        t = torch.tensor([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=torch.bfloat16, device='cpu')
        index = torch.tensor([0, 4, 2], device='cpu')
        out_cpu = inp_tensor.index_add(0, index, t)

        inp_tensor = inp_tensor.to(device=device)
        t = t.to(device=device)
        index = index.to(device=device)
        out_gpu = inp_tensor.index_add(0, index, t)

        self.assertEqual(out_cpu, out_gpu, atol=1e-2)

    @skipCUDAIfRocm
    @dtypes(torch.double)
    def test_sum_noncontig(self, device, dtype):
        x = torch.randn(1, 75, 57, 20, dtype=dtype, device=device).permute(0, 3, 1, 2)
        y = x.cpu()
        self.assertEqual(x.sum().cpu(), y.sum())
        self.assertEqual(x.sum(dim=(-1, -2)).cpu(), y.sum(dim=(-1, -2)))
        self.assertEqual(x.sum(dim=(1, 3)).cpu(), y.sum(dim=(1, 3)))

    def test_device_serialization(self, device):
        x = torch.randn(4, 4, device=device)

        with tempfile.NamedTemporaryFile() as f:
            torch.save(x, f)
            f.seek(0)
            x_copy = torch.load(f)

        self.assertEqual(x_copy, x)
        self.assertIs(type(x_copy), type(x))
        self.assertEqual(x_copy.device, x.device)

    @deviceCountAtLeast(2)
    def test_multidevice_serialization(self, devices):
        x = [torch.randn(4, 4, device=devices[0]),
             torch.randn(4, 4, device=devices[1])]

        with tempfile.NamedTemporaryFile() as f:
            torch.save(x, f)
            f.seek(0)
            x_copy = torch.load(f)

        for original, cp in zip(x, x_copy):
            self.assertEqual(cp, original)
            self.assertIs(type(cp), type(original))
            self.assertEqual(cp.device, original.device)

    @deviceCountAtLeast(1)
    def test_copy_noncontig(self, devices):
        def do_test(d0, d1):
            x = torch.tensor([1.5, 2.5, 3.5, 4.5, 5.5, 6.5], device=d0)
            y = torch.tensor([0, 0, 0, 0, 0, 0], device=d1)
            self.assertNotEqual(x.dtype, y.dtype)

            y[::2].copy_(x[::2])
            self.assertEqual(y, [1, 0, 3, 0, 5, 0])

        do_test('cpu', devices[0])
        do_test(devices[0], 'cpu')

        if len(devices) > 1:
            do_test(devices[0], devices[1])

    @dtypes(torch.float, torch.double)
    def test_abs_zero(self, device, dtype):
        # Both abs(0.0) and abs(-0.0) should result in 0.0
        abs_zeros = torch.tensor([0.0, -0.0], device=device, dtype=dtype).abs().tolist()
        for num in abs_zeros:
            self.assertGreater(math.copysign(1.0, num), 0.0)

    @deviceCountAtLeast(2)
    def test_type_conversions_same_device(self, devices):
        x = torch.randn(5, 5, device=devices[1])
        self.assertEqual(x.int().device, torch.device(devices[1]))
        self.assertEqual(x.type(torch.int).device, torch.device(devices[1]))
        self.assertEqual(x.to(torch.int).device, torch.device(devices[1]))

    def test_min_max_nan(self, device):
        tests = [(lambda x: x.min(), 'min'),
                 (lambda x: x.max(), 'max'),
                 (lambda x: x.min(0)[0], 'min_dim'),
                 (lambda x: x.max(0)[0], 'max_dim')]
        for f, name in tests:
            a = torch.arange(25.0).view(5, 5)
            a[2, 2] = nan
            actual = f(a.to(device)).cpu()
            expected = f(a).cpu()
            self.assertEqual(torch.isnan(actual), torch.isnan(expected), 'nans for {}'.format(name))
            self.assertEqual(actual[~torch.isnan(actual)],
                             expected[~torch.isnan(expected)], 'nans for {}'.format(name))

    @dtypesIfCUDA(torch.half, torch.float, torch.double,
                  torch.int8, torch.short, torch.int, torch.long,
                  torch.uint8)
    @dtypes(torch.float, torch.double,
            torch.int8, torch.short, torch.int, torch.long,
            torch.uint8)
    def test_from_sequence(self, device, dtype):
        seq = [list(range(i * 4, i * 4 + 4)) for i in range(5)]
        reference = torch.arange(0, 20).resize_(5, 4)
        self.assertEqual(torch.tensor(seq, dtype=dtype, device=device), reference, exact_dtype=False)

    def test_cat(self, device):
        SIZE = 10
        for dim in range(-3, 3):
            pos_dim = dim if dim >= 0 else 3 + dim
            x = torch.rand(13, SIZE, SIZE, device=device).transpose(0, pos_dim)
            y = torch.rand(17, SIZE, SIZE, device=device).transpose(0, pos_dim)
            z = torch.rand(19, SIZE, SIZE, device=device).transpose(0, pos_dim)

            res1 = torch.cat((x, y, z), dim)
            self.assertEqual(res1.narrow(pos_dim, 0, 13), x, 0)
            self.assertEqual(res1.narrow(pos_dim, 13, 17), y, 0)
            self.assertEqual(res1.narrow(pos_dim, 30, 19), z, 0)

        x = torch.randn(20, SIZE, SIZE, device=device)
        self.assertEqual(torch.cat(torch.split(x, 7)), x)
        self.assertEqual(torch.cat(torch.chunk(x, 7)), x)

        y = torch.randn(1, SIZE, SIZE, device=device)
        z = torch.cat([x, y])
        self.assertEqual(z.size(), (21, SIZE, SIZE))

    def test_sum_cpu_device_mismatch(self, device):
        x = torch.randn(20, dtype=torch.float32, device=device)
        y = torch.randn(1, dtype=torch.float32)

        err_string = "output with device cpu doesn't match the desired device {0}".format(device)

        with self.assertRaisesRegex(RuntimeError, err_string):
            torch.sum(x, dim=[0], dtype=torch.float32, out=y)

        # tests half to float promotion
        if self.device_type == 'cuda':
            x = x.half()
            with self.assertRaisesRegex(RuntimeError, err_string):
                torch.sum(x, dim=[0], dtype=torch.float32, out=y)

    @deviceCountAtLeast(1)
    def test_advancedindex_mixed_cpu_devices(self, devices):
        def test(x, ia, ib):
            # test getitem
            self.assertEqual(x[:, ia, None, ib, 0].cpu(),
                             x.cpu()[:, ia.cpu(), None, ib.cpu(), 0])
            self.assertEqual(x[ia], x.cpu()[ia.cpu()])
            # test setitem
            x_clone1 = x.clone()
            x_clone2 = x.clone()
            first_shape = x[:, ia, None, ib, 0].shape
            second_shape = x[ia].shape
            x_clone1[:, ia, None, ib, 0] = torch.randn(first_shape).to(x_clone1)
            x_clone2[ia] = torch.randn(second_shape).to(x_clone2)

        cpu = torch.device('cpu')
        for device in devices:
            # Index cpu tensor with device tensor
            x = torch.randn(3, 4, 4, 4, 3)
            ia = torch.tensor([0, 2, 1]).to(device)
            ib = torch.tensor([0, 2, 1]).to(device)
            test(x, ia, ib)

            # Index device tensor with cpu tensor
            x = x.to(device)
            ia = ia.to(cpu)
            ib = ib.to(cpu)
            test(x, ia, ib)

            # Index cpu tensor with mixed cpu, device tensors
            x = x.to(cpu)
            ia = ia.to(cpu)
            ib = ib.to(device)
            test(x, ia, ib)

            # Index device tensor with mixed cpu, device tensors
            x = x.to(device)
            ia = ia.to(cpu)
            ib = ib.to(device)
            test(x, ia, ib)

            if len(devices) > 1:
                other_device = devices[0]
                if device == devices[0]:
                    other_device = devices[1]
                # Index device tensor with mixed cpu, device tensors on different devices
                x = x.to(device)
                ia = ia.to(cpu)
                ib = ib.to(other_device)
                test(x, ia, ib)

    def test_copy_broadcast(self, device):
        x = torch.randn(10, 5)
        y = torch.randn(5, device=device)
        x.copy_(y)
        self.assertEqual(x[3], y)

        x = torch.randn(10, 5, device=device)
        y = torch.randn(5)
        x.copy_(y)
        self.assertEqual(x[3], y)

    def test_solve_methods_arg_device(self, device):
        for b_device, A_device in product(['cpu', device], repeat=2):
            if b_device == A_device:
                continue

            b = torch.randn(3, 1, device=b_device)
            A = torch.randn(3, 3, device=A_device)
            err_str = "Expected b and A to be on the same device"
            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.solve(b, A)

            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.cholesky_solve(b, A)

            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.triangular_solve(b, A)

            # b and A have to be modified to match accepted inputs sizes for lu_solve
            b = b.unsqueeze(0)
            A = A.unsqueeze(0)
            with self.assertRaisesRegex(RuntimeError, err_str):
                torch.lu_solve(b, A, torch.rand(A.shape[:-1], device=A_device).int())

            # This checks if a suitable error message is thrown
            # when LU output and pivots are on the same device
            with self.assertRaisesRegex(RuntimeError,
                                        "Expected LU_pivots and LU_data to be on the same device"):
                torch.lu_solve(b, A, torch.rand(A.shape[:-1], device=b_device).int())

    @deviceCountAtLeast(2)
    def test_zeros_like_multiple_device(self, devices):
        expected = torch.zeros(100, 100, device=devices[0])
        x = torch.randn(100, 100, device=devices[1], dtype=torch.float32)
        output = torch.zeros_like(x)
        self.assertEqual(output, expected)

    def test_ones_like(self, device):
        expected = torch.ones(100, 100, device=device)

        res1 = torch.ones_like(expected)
        self.assertEqual(res1, expected)

    @deviceCountAtLeast(2)
    def test_ones_like_multiple_device(self, devices):
        expected = torch.ones(100, 100, device=devices[0])
        x = torch.randn(100, 100, device=devices[1], dtype=torch.float32)
        output = torch.ones_like(x)
        self.assertEqual(output, expected)


# Tests ops and indexing to ensure they return views (and new tensors) as
# appropriate.
class TestViewOps(TestCase):
    exact_dtype = True

    def is_view_of(self, base, other):
        if (not other._is_view() or
                other is base or
                other._base is not base or
                base.device != other.device):
            return False

        # Note: only validates storage on native device types
        # because some accelerators, like XLA, do not expose storage
        if base.device.type == 'cpu' or base.device.type == 'cuda':
            if base.storage().data_ptr() != other.storage().data_ptr():
                return False

        return True

    @onlyOnCPUAndCUDA
    def test_real_self(self, device):
        t = torch.ones((5, 5), device=device)
        s = torch.real(t)
        self.assertTrue(s is t)

        # TODO: update when the imag attribute is implemented
        self.assertTrue(not hasattr(t, 'real'))

    # TODO: update after torch.real is implemented for complex tensors
    @onlyOnCPUAndCUDA
    def test_real_view(self, device):
        t = torch.tensor((1 + 1j), device=device)
        with self.assertRaises(RuntimeError):
            v = torch.real(t)
            self.assertTrue(self.is_view_of(t, v))

            v[0] = 0
            self.assertEqual(t.float()[0], v[0])
            self.assertTrue(t[0] == complex(0, 1))

    def test_imag_noncomplex(self, device):
        t = torch.ones((5, 5), device=device)

        with self.assertRaises(RuntimeError):
            torch.imag(t)

        # TODO: update when the imag attribute is implemented
        self.assertTrue(not hasattr(t, 'imag'))

    # TODO: update after torch.imag is implemented for complex tensors
    def test_imag_complex(self, device):
        t = torch.tensor((1 + 1j), device=device)
        with self.assertRaises(RuntimeError):
            v = torch.imag(t)
            self.assertTrue(self.is_view_of(t, v))

            v[0] = 0
            self.assertTrue(t[0] == complex(1, 0))

    def test_diagonal_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = torch.diagonal(t)
        self.assertTrue(self.is_view_of(t, v))

        v[0] = 0
        self.assertEqual(t[0, 0], v[0])

        t = torch.ones((3, 3, 3), device=device)
        v = torch.diagonal(t, offset=1, dim1=1, dim2=2)
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0] = 0
        self.assertEqual(t[0, 0, 1], v[0, 0])

    def test_select_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = t.select(0, 2)
        self.assertTrue(self.is_view_of(t, v))

        v[0] = 0
        self.assertEqual(t[2, 0], v[0])

    def test_unbind_view(self, device):
        t = torch.zeros((5, 5), device=device)
        tup = torch.unbind(t)

        for idx, v in enumerate(tup):
            self.assertTrue(self.is_view_of(t, v))

            v[0] = idx + 1
            self.assertEqual(t[idx, 0], v[0])

    def test_expand_view(self, device):
        t = torch.ones((5, 1), device=device)
        v = t.expand(5, 5)
        self.assertTrue(self.is_view_of(t, v))

        v[2, 2] = 0
        self.assertEqual(t[2, 0], v[2, 2])

    def test_expand_as_view(self, device):
        t = torch.ones((5, 1), device=device)
        e = torch.empty((5, 5), device=device)
        v = t.expand_as(e)
        self.assertTrue(self.is_view_of(t, v))

        v[2, 2] = 0
        self.assertEqual(t[2, 0], v[2, 2])

    def test_narrow_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = torch.narrow(t, 1, 2, 2)
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0] = 0
        self.assertEqual(t[0, 2], v[0, 0])

    def test_permute_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = t.permute(1, 0)
        self.assertTrue(self.is_view_of(t, v))

        v[0, 1] = 0
        self.assertEqual(t[1, 0], v[0, 1])

    def test_transpose_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = torch.transpose(t, 0, 1)
        self.assertTrue(self.is_view_of(t, v))

        v[0, 1] = 0
        self.assertEqual(t[1, 0], v[0, 1])

    def test_t_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = t.t()
        self.assertTrue(self.is_view_of(t, v))

        v[0, 1] = 0
        self.assertEqual(t[1, 0], v[0, 1])

    def test_T_view(self, device):
        t = torch.ones((5, 5), device=device)
        v = t.T
        self.assertTrue(self.is_view_of(t, v))

        v[0, 1] = 0
        self.assertEqual(t[1, 0], v[0, 1])

    def test_unfold_view(self, device):
        t = torch.ones(10, device=device)
        v = t.unfold(0, 3, 2)
        self.assertTrue(self.is_view_of(t, v))

        v[1, 0] = 0
        self.assertEqual(t[2], v[1, 0])

    def test_squeeze_view(self, device):
        t = torch.ones(5, 1, 5, device=device)
        v = torch.squeeze(t)
        self.assertTrue(self.is_view_of(t, v))
        v[0, 1] = 0
        self.assertEqual(t, v._base)

    def test_unsqueeze_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = torch.unsqueeze(t, 1)
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0, 1] = 0
        self.assertEqual(t[0, 1], v[0, 0, 1])

    def test_as_strided_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = torch.as_strided(t, (25,), (1,))
        self.assertTrue(self.is_view_of(t, v))

        v[6] = 0
        self.assertEqual(t[1, 1], v[6])

    def test_view_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = t.view(25)
        self.assertTrue(self.is_view_of(t, v))

        v[6] = 0
        self.assertEqual(t[1, 1], v[6])

    def test_view_as_view(self, device):
        t = torch.ones(5, 5, device=device)
        e = torch.empty((25,))
        v = t.view_as(e)
        self.assertTrue(self.is_view_of(t, v))

        v[6] = 0
        self.assertEqual(t[1, 1], v[6])

    def test_contiguous_self(self, device):
        t = torch.ones(5, 5, device=device)
        s = t.contiguous()
        self.assertTrue(s is t)

    def test_contiguous_nonview(self, device):
        t = torch.ones(5, 5, device=device)
        nv = t.t().contiguous()
        self.assertTrue(not self.is_view_of(t, nv))

        nv[0, 0] = 0
        self.assertNotEqual(t[0, 0], nv[0, 0])

    def test_reshape_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = torch.reshape(t, (25,))
        self.assertTrue(self.is_view_of(t, v))

        v[6] = 0
        self.assertEqual(t[1, 1], v[6])

    def test_reshape_as_view(self, device):
        t = torch.ones(5, 5, device=device)
        e = torch.empty((25,), device=device)
        v = t.reshape_as(e)
        self.assertTrue(self.is_view_of(t, v))

        v[6] = 0
        self.assertEqual(t[1, 1], v[6])

    def test_reshape_nonview(self, device):
        t = torch.ones(5, 5, device=device)
        nv = torch.reshape(t.t(), (25,))
        self.assertTrue(not self.is_view_of(t, nv))

        nv[6] = 0
        self.assertNotEqual(t[1, 1], nv[6])

    def test_basic_indexing_slice_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = t[:2, :3]
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0] = 0
        self.assertEqual(t[0, 0], v[0, 0])

    def test_basic_indexing_ellipses_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = t[..., :2]
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0] = 0
        self.assertEqual(t[0, 0], v[0, 0])

    def test_basic_indexing_newaxis_view(self, device):
        t = torch.ones(5, 5, device=device)
        v = t[None, :2, 3]
        self.assertTrue(self.is_view_of(t, v))

        v[0, 0] = 0
        self.assertEqual(t[0, 3], v[0, 0])

    def test_advanced_indexing_nonview(self, device):
        t = torch.ones(3, 3, device=device)
        rows = torch.tensor([[0, 0], [2, 2]], device=device)
        cols = torch.tensor([[0, 1], [2, 2]], device=device)
        nv = t[rows, cols]
        self.assertTrue(not self.is_view_of(t, nv))

        nv[1, 1] = 0
        self.assertNotEqual(t[2, 2], nv[1, 1])

    def test_advanced_indexing_assignment(self, device):
        t = torch.ones(3, 3, device=device)
        rows = torch.tensor([[0, 0], [2, 2]], device=device)
        cols = torch.tensor([[0, 1], [2, 2]], device=device)
        t[rows, cols] = 0
        self.assertEqual(t[2, 2], 0)

    @unittest.skip("See https://github.com/pytorch/pytorch/pull/32720")
    def test_chunk_view(self, device):
        t = torch.zeros(3, 3, device=device)
        l = torch.chunk(t, 3)

        for idx, v in enumerate(l):
            self.assertTrue(self.is_view_of(t, v))

            v[0, 0] = idx + 1
            self.assertEqual(t[idx, 0], v[0, 0])

    @unittest.skip("See https://github.com/pytorch/pytorch/pull/32720")
    def test_split_view(self, device):
        t = torch.zeros(3, 3, device=device)
        l = torch.split(t, [1, 1, 1])

        for idx, v in enumerate(l):
            self.assertTrue(self.is_view_of(t, v))

            v[0, 0] = idx + 1
            self.assertEqual(t[idx, 0], v[0, 0])


# Below are fixtures and functions that generate tensor op comparison tests
# These tests run a single op on both a CPU and device tensor and compare the
# the results. In-place variants of the ops can also be run.

# Lists of dtypes to instantiate tensor op test variants.
_types = [
    torch.half, torch.float, torch.double,
    torch.int8, torch.short, torch.int, torch.long,
    torch.uint8
]

_types_no_half = [
    torch.float, torch.double,
    torch.int8, torch.short, torch.int, torch.long,
    torch.uint8
]

# _types2 adds bfloat16 type to  _types only on ROCm. Should eventually be unified
# with _types when bfloat16 bringup is complete on all platforms.
_types2 = _types + [torch.bfloat16] if TEST_WITH_ROCM else _types

_float_types = [torch.half, torch.float, torch.double]

_float_types_no_half = [torch.float, torch.double]

# _float_types2 adds bfloat16 type to _float_types only on ROCm. Should eventually be unified
# with _float_types when bfloat16 bringup is complete on all platforms
_float_types2 = _float_types + [torch.bfloat16] if TEST_WITH_ROCM else _float_types

_signed_types = [
    torch.half, torch.float, torch.double,
    torch.int8, torch.short, torch.int, torch.long
]

_signed_types_no_half = [
    torch.float, torch.double,
    torch.int8, torch.short, torch.int, torch.long
]

_cpu_types = []

_unsigned_types = [torch.uint8]

# Helper values and functions for producing tensors and scalars to use in tensor op tests.
# Tensor dimension sizes (Small, Medium, Large, Giant)
_S = 5
_M = 50
_L = 1000
_G = 275000000

# Value to clamp divisors to since dividing by small numbers can be unstable
# on devices.
_div_min = 2**-8

# Returns floating or integral scalar corresponding to dtype
def _number(floating, integer, dtype):
    if dtype in [torch.half, torch.float, torch.double, torch.bfloat16]:
        return floating
    return integer

# Converts half/bfloat16 dtype to float when device is cpu
def _convert_t(dtype, device):
    if device == 'cpu' and dtype in {torch.half, torch.bfloat16}:
        return torch.float
    return dtype

# Returns a tensor of the requested shape, dtype, and device
# Requesting a half CPU tensor returns a float CPU tensor with
# values representable by a half.
# Initialization uses randint for non-float types and randn for float types.
def _make_tensor(shape, dtype, device, fill_ones=False):
    # Returns a tensor filled with ones
    if fill_ones:
        return torch.ones(*shape, dtype=_convert_t(dtype, device), device=device)

    # Returns a tensor with random integer values
    if not dtype.is_floating_point:
        t = torch.randint(0, 10, shape, device=device)
        if dtype != torch.uint8:
            t = t - 5  # generate negative values also
        return t.to(_convert_t(dtype, device))

    # Populates the CPU tensor with floats representable as half/bfloat16
    if dtype == torch.half and device == 'cpu':
        return torch.randn(*shape, dtype=torch.float, device=device).half().float()
    if dtype == torch.bfloat16 and device == 'cpu':
        return torch.randn(*shape, dtype=torch.float, device=device).bfloat16().float()

    # Default: returns a tensor with random float values
    return torch.randn(shape, dtype=dtype, device=device).to(dtype=dtype)

def _small_0d(dtype, device):
    return _make_tensor((1,), dtype, device).squeeze()

def _small_2d(dtype, device, has_zeros=True, fill_ones=False, oneish=False):
    t = _make_tensor((_S, _S), dtype, device, fill_ones=fill_ones)
    if oneish:
        return t.clamp(min=_number(.99, 1, dtype), max=1.01)
    if not has_zeros:
        return t.clamp(min=(_number(_div_min, 1, dtype)))
    return t

def _small_3d(dtype, device, has_zeros=True, fill_ones=False, oneish=False):
    t = _make_tensor((_S, _S, _S), dtype, device, fill_ones=fill_ones)
    if oneish:
        return t.clamp(min=_number(.99, 1, dtype), max=1.01)
    if not has_zeros:
        return t.clamp(min=(_number(_div_min, 1, dtype)))
    return t

def _small_3d_ones(dtype, device):
    return _small_3d(dtype, device, fill_ones=True)

def _small_3d_unique(dtype, device):
    return (torch.randperm(_S * _S * _S,
                           dtype=_convert_t(dtype, device), device=device) + 1).view(_S, _S, _S)

def _medium_1d(dtype, device):
    return _make_tensor((_M,), dtype, device)

def _medium_2d(dtype, device):
    return _make_tensor((_M, _M), dtype, device)

def _large_2d(dtype, device):
    t = _make_tensor((_L, _L), dtype, device)
    return t.normal_()

def _giant_1d(dtype, device):
    return _make_tensor((_G), dtype, device)

# Helper method that returns a function which takes dtype and device and
# instantiates tensors of the given shape.
# Useful for tensor op tests with custom shapes.
def _new_t(shape):
    def tmp(dtype, device):
        return _make_tensor(shape, dtype, device)
    return tmp

def _wrap_maybe_warns(regex):
    def decorator(fn):
        def inner(self, device, dtype):
            with self.maybeWarnsRegex(UserWarning, regex):
                fn(self, device, dtype)
        return inner
    return decorator


# TODO: random functions, cat, gather, scatter, index*, masked*,
#       resize, resizeAs, storage_offset, storage, stride, unfold
# Each tests is defined in tensor_op_tests as a tuple of:
# - op name (string)
# - (sub)test name (string)
# - tensor constructor, takes dtype and device and constructs the tensor to run the op on
# - arg constructor, takes dtype and device and constructs op arguments
# - torch.half precision (=1e-5)
# - torch.bfloat16 precision (=1e-5)
# - precision (=1e-5), precision to use for all other dtypes
# - dtype_list (=_types), a list of torch dtypes to test the op(s) with
# - cpu_dtype_list (=[]), a list of torch dtypes to test the op(s) on cpu
# - make_inplace_variant (=True), if true the inplace version of the op (op_) is also tested
# - decorators (=[]), a list of decorators to apply to the test
tensor_op_tests = [
    ('add', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-2),
    ('add', 'tensor', _small_3d, lambda t, d: [_small_3d(t, d)], 1e-2),
    ('sub', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-2),
    ('sub', 'tensor', _small_3d, lambda t, d: [_small_3d(t, d)], 1e-2),
    ('mul', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-2),
    ('mul', 'tensor', _small_3d, lambda t, d: [_small_3d(t, d)], 1e-2),
    ('mul', 'scalar', _small_0d, lambda t, d: [_small_0d(torch.int32, d)], 1e-2),
    ('div', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-1),
    ('div', 'tensor', _small_3d,
        lambda t, d: [_small_3d(t, d, has_zeros=False)], 1e-1),
    ('true_divide', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-1,
        1e-5, 1e-5, _types, _cpu_types, False),
    ('true_divide', 'with_inplace', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-1,
        1e-5, 1e-5, _float_types),
    ('true_divide', 'tensor', _small_3d,
        lambda t, d: [_small_3d(t, d, has_zeros=False)], 1e-1,
        1e-5, 1e-5, _types, _cpu_types, False),
    ('true_divide', 'tensor_with_inplace', _small_3d,
        lambda t, d: [_small_3d(t, d, has_zeros=False)], 1e-1,
        1e-5, 1e-5, _float_types),
    ('floor_divide', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1, 1e-5, 1e-5, _types),
    ('floor_divide', 'tensor', _small_3d,
        lambda t, d: [_small_3d(t, d, has_zeros=False)], 1, 1e-5, 1e-5, _types),
    ('pow', '', _small_3d, lambda t, d: [_number(3.14, 3, t)], 1e-1, 1e-5, 1e-5, _float_types),
    ('pow', '1', _small_3d, lambda t, d: [_number(1., 1, t)], 1e-1),
    ('pow', '2', _small_3d, lambda t, d: [_number(2., 2, t)], 1e-1),
    ('pow', '3', _small_3d, lambda t, d: [_number(3., 3, t)], 1e-1),
    ('pow', '-1', _small_3d, lambda t, d: [_number(-1., -1, t)], 1e-1, 1e-5, 1e-5, _float_types),
    ('pow', '-2', _small_3d, lambda t, d: [_number(-2., -2, t)],
        1e-1, 1e-5, 1e-5, _float_types_no_half, _cpu_types, False, [skipCUDAIfRocm]),
    ('pow', 'tensor', _small_3d, lambda t, d: [_small_3d(t, d).abs()],
        1e-1, 1e-5, 1e-5, _float_types),
    ('addbmm', '', _small_2d, lambda t, d: [_small_3d(t, d), _small_3d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2),
    ('addbmm', 'scalar', _small_2d, lambda t, d: [_number(0.4, 2, t), _small_3d(t, d), _small_3d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addbmm_? is deprecated")]),
    ('addbmm', 'two_scalars', _small_2d, lambda t, d: [_number(0.5, 3, t), _number(0.4, 2, t), _small_3d(t, d), _small_3d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addbmm_? is deprecated")]),
    ('baddbmm', '', _small_3d, lambda t, d: [_small_3d(t, d), _small_3d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2),
    ('baddbmm', 'scalar', _small_3d, lambda t, d: [_number(0.4, 2, t), _small_3d(t, d), _small_3d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of baddbmm_? is deprecated")]),
    ('baddbmm', 'two_scalars', _small_3d, lambda t, d: [_number(0.5, 3, t), _number(0.4, 2, t), _small_3d(t, d), _small_3d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of baddbmm_? is deprecated")]),
    ('bmm', '', _small_3d, lambda t, d: [_small_3d(t, d)],
        1e-5, 1e-5, 1e-5, _float_types_no_half, _cpu_types, False),
    ('addcdiv', '', _small_2d,
        lambda t, d: [_small_2d(t, d),
                      _small_2d(t, d, has_zeros=False)], 1, 1, 1e-3,
        _types2, _cpu_types, True,
        [_wrap_maybe_warns("Integer division .+")]),
    ('addcdiv', 'scalar', _small_2d,
        lambda t, d: [_number(2.8, 1, t), _small_2d(t, d),
                      _small_2d(t, d, has_zeros=False)], 1, 1e-5, 1e-3,
        _types, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addcdiv_? is deprecated|Integer division .+")]),
    ('addcmul', '', _small_3d, lambda t, d: [_small_3d(t, d), _small_3d(t, d)], 1e-2, 1e-1, 1e-3, _types2),
    ('addcmul', 'scalar', _small_3d,
        lambda t, d: [_number(0.4, 2, t), _small_3d(t, d), _small_3d(t, d)], 1e-2,
        1e-1, 1e-5, _types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addcmul_? is deprecated")]),
    ('addmm', '', _medium_2d, lambda t, d: [_medium_2d(t, d), _medium_2d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2),
    ('addmm', 'scalar', _medium_2d,
        lambda t, d: [_number(0.4, 2, t), _medium_2d(t, d), _medium_2d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addmm_? is deprecated")]),
    ('addmm', 'two_scalars', _medium_2d,
        lambda t, d: [_number(0.5, 3, t), _number(0.4, 2, t), _medium_2d(t, d), _medium_2d(t, d)],
        1e-1, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addmm_? is deprecated")]),
    ('addmv', '', _medium_1d, lambda t, d: [_medium_2d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2),
    ('addmv', 'scalar', _medium_1d,
        lambda t, d: [_number(0.4, 2, t), _medium_2d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addmv_? is deprecated")]),
    ('addmv', 'two_scalars', _medium_1d,
        lambda t, d: [_number(0.5, 3, t), _number(0.4, 2, t), _medium_2d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addmv_? is deprecated")]),
    ('addr', '', _medium_2d, lambda t, d: [_medium_1d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2),
    ('addr', 'scalar', _medium_2d,
        lambda t, d: [_number(0.4, 2, t), _medium_1d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addr_? is deprecated")]),
    ('addr', 'two_scalars', _medium_2d,
        lambda t, d: [_number(0.5, 3, t), _number(0.4, 2, t), _medium_1d(t, d), _medium_1d(t, d)],
        1e-2, 1e-1, 1e-4, _float_types2, _cpu_types, True,
        [_wrap_maybe_warns("This overload of addr_? is deprecated")]),
    ('atan2', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-2, 1e-5, 1e-5, _float_types),
    ('angle', '', _small_3d, lambda t, d: [], 0, 0, 0, _types_no_half, [torch.bfloat16], False),
    ('fmod', 'value', _small_3d, lambda t, d: [3], 1e-3),
    ('fmod', 'tensor', _small_3d, lambda t, d: [_small_3d(t, d, has_zeros=False)], 1e-3),
    ('chunk', '', _medium_2d, lambda t, d: [4], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('chunk', 'dim', _medium_2d, lambda t, d: [4, 1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('chunk', 'neg_dim', _medium_2d, lambda t, d: [4, -2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('clamp', 'neg', _medium_2d, lambda t, d: [-1, 5], 1e-5, 1e-2, 1e-5, _signed_types, [torch.bfloat16]),
    ('clamp', 'pos', _medium_2d, lambda t, d: [1, 5], 1e-5, 1e-2, 1e-5, _unsigned_types, [torch.bfloat16]),
    ('clamp_min', '', _medium_2d, lambda t, d: [1], 1e-2, 1e-2, 1e-5, _types, [torch.bfloat16]),
    ('clamp_max', '', _medium_2d, lambda t, d: [1], 1e-2, 1e-2, 1e-5, _types, [torch.bfloat16]),
    ('clone', '', _medium_2d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('contiguous', '', _medium_2d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('conj', '', _small_3d, lambda t, d: [], 1e-5, 0, 1e-5, _types_no_half, [torch.bfloat16], False),
    ('cross', '', _new_t((_M, 3, _M)), lambda t, d: [_new_t((_M, 3, _M))(t, d)],
        1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cummax', '', _small_3d_unique, lambda t, d: [1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cummax', 'neg_dim', _small_3d_unique, lambda t, d: [-1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cummin', '', _small_3d_unique, lambda t, d: [1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cummin', 'neg_dim', _small_3d_unique, lambda t, d: [-1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cumprod', '', _small_3d, lambda t, d: [1], 1e-2, 1e-5, 1e-4, _types, _cpu_types, False),
    ('cumprod', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-2, 1e-5, 1e-4, _types, _cpu_types, False),
    ('cumsum', '', _small_3d, lambda t, d: [1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('cumsum', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('dim', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('dist', '', _small_2d, lambda t, d: [_small_2d(t, d)], 1e-2, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('dist', '3_norm', _small_2d, lambda t, d: [_small_2d(t, d), 3], 1e-2, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('dist', '2_5_norm', _small_2d, lambda t, d: [_small_2d(t, d), 2.5],
        1e-2, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('dot', '', _medium_1d, lambda t, d: [_medium_1d(t, d)],
        1e-2, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('element_size', '', _medium_1d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _float_types_no_half, _cpu_types, False),
    ('eq', '', _small_3d_ones, lambda t, d: [_small_3d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('eq', 'equal', _small_3d_ones, lambda t, d: [_small_3d_ones(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('ne', '', _small_3d_ones, lambda t, d: [_small_3d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('ne', 'equal', _small_3d_ones, lambda t, d: [_small_3d_ones(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('equal', 'equal', _small_3d_ones, lambda t, d: [_small_3d_ones(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('equal', '', _small_3d_ones, lambda t, d: [_small_3d(t, d)], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('expand', '', _new_t((_M, 1, _M)), lambda t, d: [_M, 4, _M], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('expand_as', '', _new_t((_M, 1, _M)), lambda t, d: [_new_t((_M, 4, _M))(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('fill_', '', _medium_2d, lambda t, d: [_number(3.14, 3, t)], 1e-3, 1e-5, 1e-5, _types, _cpu_types, False),
    ('ge', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('le', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('gt', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('lt', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-5, 1e-5, 1e-5, _types2),
    ('is_contiguous', '', _medium_2d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    # TODO: can't check negative case - cross-device copy is contiguous
    ('is_same_size', 'negative', _medium_2d, lambda t, d: [_small_3d(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('is_same_size', 'positive', _medium_2d, lambda t, d: [_medium_2d(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('is_set_to', '', _medium_2d, lambda t, d: [_medium_2d(t, d)], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    # TODO: positive case
    ('kthvalue', '', _small_3d_unique, lambda t, d: [3], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('kthvalue', 'dim', _small_3d_unique, lambda t, d: [3, 1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('kthvalue', 'neg_dim', _small_3d_unique, lambda t, d: [3, -1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('lerp', '', _small_3d, lambda t, d: [_small_3d(t, d), 0.3],
        1e-2, 1e-5, 1e-5, _float_types_no_half),
    ('max', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('max', 'dim', _small_3d_unique, lambda t, d: [1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('max', 'neg_dim', _small_3d_unique, lambda t, d: [-1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('max', 'elementwise', _medium_2d, lambda t, d: [_medium_2d(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('min', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('min', 'dim', _small_3d_unique, lambda t, d: [1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('min', 'neg_dim', _small_3d_unique, lambda t, d: [-1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('min', 'elementwise', _medium_2d, lambda t, d: [_medium_2d(t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('mean', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types2, _cpu_types, False),
    ('mean', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-3, 1e-2, 1e-5, _float_types2, _cpu_types, False),
    ('mean', 'dim', _small_3d, lambda t, d: [1], 1e-3, 1e-2, 1e-2, _float_types2, _cpu_types, False),
    # Double here because the CPU result will be wrong otherwise
    ('mean', '64bit_indexing', _giant_1d, lambda t, d: [],
        1e-3, 1e-5, 1e-5, [torch.double], _cpu_types, False, [slowTest]),
    ('mode', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('mode', 'dim', _small_3d, lambda t, d: [1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('mode', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('mvlgamma', '2d_p=1', lambda t, d: _small_2d(t, d).clamp(0.1, 10), lambda t, d: [1],
        1e-5, 1e-5, 1e-5, _float_types_no_half),
    ('mvlgamma', '2d_p=2', lambda t, d: _small_2d(t, d).clamp(0.6, 10), lambda t, d: [2],
        1e-5, 1e-5, 1e-5, _float_types_no_half),
    ('remainder', 'value', _small_3d, lambda t, d: [3], 1e-1, 1e-5, 1e-5, _signed_types),
    ('remainder', 'negative_value', _small_3d, lambda t, d: [-3], 1e-1, 1e-5, 1e-5, _signed_types),
    ('remainder', 'tensor', _small_3d,
        lambda t, d: [_small_3d(t, d, has_zeros=False)],
        1e-1, 1e-5, 1e-5, _signed_types),
    ('remainder', 'negative_tensor', _small_3d,
        lambda t, d: [0 - _small_3d(t, d, has_zeros=False)],
        1e-1, 1e-5, 1e-5, _signed_types),
    ('std', '', _small_3d, lambda t, d: [], 1e-3, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('std', 'dim', _small_3d, lambda t, d: [1], 1e-3, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('std', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-3, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('var', '', _small_3d, lambda t, d: [], 1e-3, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('var', 'dim', _small_3d, lambda t, d: [1], 1e-3, 1e-5, 1e-5, _float_types, _cpu_types, False),
    ('var', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-3, 1e-2, 1e-5, _float_types2, _cpu_types, False),
    ('ndimension', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('nelement', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('numel', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('narrow', '', _small_3d, lambda t, d: [1, 3, 2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('narrow', 'neg_dim', _small_3d, lambda t, d: [-1, 3, 2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('nonzero', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('norm', '', _small_3d, lambda t, d: [], 1e-1, 1e-1, 1e-5, _float_types2, _cpu_types, False),
    ('norm', '3_norm', _small_3d, lambda t, d: [3], 1e-1, 1e-1, 1e-5, _float_types2, _cpu_types, False),
    ('norm', '3_norm_dim', _small_3d, lambda t, d: [3, 0], 1e-1, 1e-1, 1e-5, _float_types2, _cpu_types, False),
    ('norm', '3_norm_neg_dim', _small_3d, lambda t, d: [3, -2], 1e-1, 1e-1, 1e-5, _float_types2, _cpu_types, False),
    ('new_ones', '', _small_3d, lambda t, d: [1, 2, 3, 4, 5], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('permute', '', _new_t((1, 2, 3, 4)), lambda t, d: [2, 1, 3, 0], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('put_', '', _new_t((2, 5, 3)),
        lambda t, d: [torch.LongTensor([[0], [-2]]).to(device=d),
                      torch.LongTensor([[3], [4]]).to(dtype=_convert_t(t, d), device=d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('put_', 'empty', _new_t((2, 3)),
        lambda t, d: [torch.LongTensor([]).to(device=d), torch.LongTensor([]).to(dtype=_convert_t(t, d), device=d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('put_', 'accumulate', _new_t((2, 2)),
        lambda t, d: [torch.LongTensor([[1], [-3]]).to(device=d),
                      torch.LongTensor([[1], [2]]).to(dtype=_convert_t(t, d), device=d),
                      True],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('prod', '', lambda t, d: _small_2d(t, d, oneish=True),
        lambda t, d: [], 1e-2, 1e-1, 1e-5, _types2, _cpu_types, False),
    ('prod', 'dim', _small_3d, lambda t, d: [1], 1e-3, 1e-1, 1e-5, _types2, _cpu_types, False),
    ('prod', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-3, 1e-1, 1e-5, _types2, _cpu_types, False),
    ('sum', '', _small_2d, lambda t, d: [], 1e-2, 1e-2, 1e-5, _types2, _cpu_types, False),
    ('sum', 'dim', _small_3d, lambda t, d: [1], 1e-2, 1e-2, 1e-5, _types2, _cpu_types, False),
    ('sum', 'neg_dim', _small_3d, lambda t, d: [-1], 1e-2, 1e-5, 1e-5, _types, _cpu_types, False),
    ('renorm', '2_norm', _small_3d, lambda t, d: [2, 1, 1], 1e-3, 1e-5, 1e-5, _float_types),
    ('renorm', '2_norm_neg_dim', _small_3d, lambda t, d: [2, -1, 1], 1e-3, 1e-5, 1e-5, _float_types),
    ('renorm', '1_5_norm', _small_3d, lambda t, d: [1.5, 1, 1], 1e-3, 1e-5, 1e-5, _float_types),
    ('repeat', '', _small_2d, lambda t, d: [2, 2, 2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('size', '', _new_t((1, 2, 3, 4)), lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('size', 'dim', _new_t((1, 2, 3, 4)), lambda t, d: [1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('size', 'neg_dim', _new_t((1, 2, 3, 4)), lambda t, d: [-2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('sort', '', _small_3d_unique, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('sort', 'dim', _small_3d_unique, lambda t, d: [1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('sort', 'neg_dim', _small_3d_unique, lambda t, d: [-1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('sort', 'dim_descending', _small_3d_unique, lambda t, d: [1, True], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('sort', 'neg_dim_descending', _small_3d_unique, lambda t, d: [-1, True], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('split', '', _small_3d, lambda t, d: [2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('split', 'dim', _small_3d, lambda t, d: [2, 1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('split', 'neg_dim', _small_3d, lambda t, d: [2, -3], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('squeeze', '', _new_t((1, 2, 1, 4)), lambda t, d: [],),
    ('squeeze', 'dim', _new_t((1, 2, 1, 4)), lambda t, d: [2], ),
    ('squeeze', 'neg_dim', _new_t((1, 2, 1, 4)), lambda t, d: [-2], ),
    ('t', '', _new_t((1, 2)), lambda t, d: [],),
    ('take', '', _new_t((3, 4)),
        lambda t, d: [torch.LongTensor([[0], [-2]]).to(device=d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('transpose', '', _new_t((1, 2, 3, 4)), lambda t, d: [1, 2],),
    ('transpose', 'neg_dim', _new_t((1, 2, 3, 4)), lambda t, d: [-1, -2], ),
    ('tolist', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('topk', 'dim_sort', _small_3d_unique, lambda t, d: [2, 1, False, True],
        1e-5, 1e-5, 1e-5, _types2, _cpu_types, False),
    ('topk', 'neg_dim_sort', _small_3d_unique, lambda t, d: [2, -1, False, True],
        1e-5, 1e-5, 1e-5, _types2, _cpu_types, False),
    ('topk', 'dim_desc_sort', _small_3d_unique, lambda t, d: [2, 1, True, True],
        1e-5, 1e-5, 1e-5, _types2, _cpu_types, False),
    ('trace', '', _medium_2d, lambda t, d: [], 1e-3, 1e-5, 1e-5, _types, _cpu_types, False),
    ('tril', '', _medium_2d, lambda t, d: [],),
    ('tril', 'zero_stride', _medium_2d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('tril', 'positive', _medium_2d, lambda t, d: [2], ),
    ('tril', 'negative', _medium_2d, lambda t, d: [-2], ),
    ('triu', '', _medium_2d, lambda t, d: [],),
    ('triu', 'zero_stride', _medium_2d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('triu', 'positive', _medium_2d, lambda t, d: [2], ),
    ('triu', 'negative', _medium_2d, lambda t, d: [-2], ),
    ('unsqueeze', '', _new_t((2, 3, 4)), lambda t, d: [2],),
    ('unsqueeze', 'neg_dim', _new_t((2, 3, 4)), lambda t, d: [-2], ),
    ('view', 'contiguous', _small_3d, lambda t, d: [25, 5], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('view_as', '', _small_3d, lambda t, d: [_make_tensor((25, 5), t, d)],
        1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('zero_', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('new_zeros', '', _small_3d, lambda t, d: [1, 2, 3, 4], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('flip', 'd0', _small_3d, lambda t, d: [0], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('flip', 'd012', _small_3d, lambda t, d: [0, 1, 2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('flip', 'd02', _small_3d, lambda t, d: [0, 2], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('flip', 'd20', _small_3d, lambda t, d: [2, 0], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('flip', 'neg_d', _small_3d, lambda t, d: [-1], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('rot90', 'k1_d01', _small_2d, lambda t, d: [1, [0, 1]], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('rot90', 'k1_d12', _small_3d, lambda t, d: [1, [1, 2]], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('rot90', 'k1_neg_d', _small_3d, lambda t, d: [1, [1, -1]], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('rot90', 'default', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types, _cpu_types, False),
    ('rsqrt', '', lambda t, d: _small_3d(t, d) + 1, lambda t, d: [], 1e-2, 1e-5, 1e-4, _float_types_no_half),
    ('sinh', '', lambda t, d: _small_3d(t, d).clamp(-1, 1), lambda t, d: [], 1e-3, 1e-5, 1e-5, _float_types),
    ('tan', '', lambda t, d: _small_3d(t, d).clamp(-1, 1), lambda t, d: [], 1e-3, 1e-5, 1e-5, _float_types),
    ('__lshift__', '',
        lambda t, d: torch.pow(2, torch.arange(1, 5).to(dtype=_convert_t(t, d), device=d)),
        lambda t, d: [2],
        1e-3, 1e-5, 1e-3, _signed_types, _cpu_types, False),
    ('__rshift__', '',
        lambda t, d: torch.pow(2, torch.arange(3, 7).to(dtype=_convert_t(t, d), device=d)),
        lambda t, d: [2],
        1e-3, 1e-5, 1e-3, _signed_types, _cpu_types, False),
    # lapack tests
    ('qr', 'square', _small_2d, lambda t, d: [],
        1e-5, 1e-5, 3e-4, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('qr', 'skinny', _new_t((3, 4)), lambda t, d: [],
        1e-5, 1e-5, 3e-4, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('qr', 'fat', _new_t((4, 3)), lambda t, d: [],
        1e-5, 1e-5, 3e-4, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('qr', 'big', _large_2d, lambda t, d: [],
        1e-5, 1e-5, 3e-4, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('geqrf', '', _new_t((20, 20)), lambda t, d: [],
        1e-5, 1e-5, 3e-4, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('eig', 'with_eigvec', _new_t((10, 10)), lambda t, d: [True],
        1e-5, 1e-5, 1e-5, _float_types_no_half, _cpu_types, False, [skipCUDAIfNoMagma]),
    ('abs', '', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e-5, _types2, [torch.bfloat16]),
    ('sign', '', _small_3d, lambda t, d: []),
    ('log', '', _small_3d, lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types2, [torch.bfloat16]),
    ('log10', '', _small_3d, lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types2, [torch.bfloat16]),
    ('log1p', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types_no_half, [torch.bfloat16]),
    ('log2', '', _small_3d, lambda t, d: [], 1e-2, 1e-1, 1e-5, _float_types2, [torch.bfloat16]),
    ('sigmoid', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types2),
    ('sin', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('sqrt', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types2, [torch.bfloat16]),
    ('tanh', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types2, [torch.bfloat16]),
    ('acos', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('asin', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('atan', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('cos', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('cosh', '', _small_3d, lambda t, d: [], 1e-2, 1e-5, 1e-5, _float_types),
    ('erf', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('erfc', '', _small_3d, lambda t, d: [], 1e-3, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('exp', '', _small_3d, lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types),
    ('exp', 'samll', lambda t, d: _small_3d(t, d).clamp(-1, 1),
        lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('expm1', '', _small_3d, lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types),
    ('expm1', 'small', lambda t, d: _small_3d(t, d).clamp(-1, 1),
        lambda t, d: [], 1e-2, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('reciprocal', '', _small_3d, lambda t, d: [], 1e-1, 1e-1, 1e-5, _float_types2, [torch.bfloat16]),
    ('floor', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('frac', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('neg', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types2, [torch.bfloat16]),
    ('round', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('trunc', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('ceil', '', _small_3d, lambda t, d: [], 1e-5, 1e-2, 1e-5, _float_types, [torch.bfloat16]),
    ('lgamma', '', _small_3d, lambda t, d: [], 1e-2, 1e-1, 1e-5, _float_types_no_half, [torch.bfloat16]),
    ('digamma', 'op', _small_3d, lambda t, d: [], 1e-5, 1e-5, 1e0, _float_types_no_half),
]

# Creates and decorates a generic test and adds it to the class.
def generate_test_function(cls,
                           op_str,
                           subtest_str,
                           tensor_ctor,
                           arg_ctor,
                           half_precision,
                           bfloat16_precision,
                           float_precision,
                           dtype_list,
                           dtype_cpu_list,
                           decorators):
    def fn(self, device, dtype):
        # Generates the CPU inputs
        # Note: CPU tensors are never torch.half
        cpu_tensor = tensor_ctor(dtype, 'cpu')
        cpu_args = arg_ctor(dtype, 'cpu')

        # Converts CPU tensors to device tensors
        device_tensor = cpu_tensor.to(dtype=dtype, device=device)
        device_args = [arg.to(device=device) if isinstance(arg, torch.Tensor) else arg for arg in cpu_args]

        # Converts float device tensors to half/bfloat16 when the dtype is half/bfloat16
        # Note: CPU half tensors don't support many operations.
        if dtype in {torch.half, torch.bfloat16}:
            device_args = [arg.to(dtype=dtype) if
                           (isinstance(arg, torch.Tensor) and arg.dtype == torch.float) else arg
                           for arg in device_args]

        # Runs the tensor op on CPU and device
        cpu_result = getattr(cpu_tensor, op_str)(*cpu_args)
        device_result = getattr(device_tensor, op_str)(*device_args)

        dtype2precision = {torch.half : half_precision,
                           torch.bfloat16 : bfloat16_precision}

        # Compares CPU and device inputs and outputs
        precision = dtype2precision.get(dtype, float_precision)

        self.assertEqual(cpu_tensor, device_tensor, atol=precision, exact_dtype=False, allow_inf=True)
        self.assertEqual(cpu_args, device_args, atol=precision, exact_dtype=False, allow_inf=True)
        self.assertEqual(cpu_result, device_result, atol=precision, exact_dtype=False, allow_inf=True)

    test_name = "test_" + op_str + subtest_str
    assert not hasattr(cls, test_name), "{0} already in TestDevicePrecision".format(test_name)

    # Constructs decorator list and applies decorators
    if decorators is None:
        decorators = [dtypes(*dtype_list)]
    else:
        decorators = decorators + [dtypes(*dtype_list)]
    decorators = decorators + [dtypesIfCPU(*dtype_cpu_list)]

    for dec in decorators:
        fn = dec(fn)

    setattr(cls, test_name, fn)

# Instantiates variants of tensor_op_tests and adds them to the given class.
def generate_tensor_op_tests(cls):

    def caller(cls,
               op_str,
               subtest_str,
               tensor_ctor,
               arg_ctor,
               half_precision=1e-5,
               bfloat16_precision=1e-5,
               float_precision=1e-5,
               dtype_list=_types,
               dtype_cpu_list=_cpu_types,
               make_inplace_variant=True,
               decorators=None):
        if subtest_str:
            subtest_str = '_' + subtest_str

        generate_test_function(cls, op_str, subtest_str, tensor_ctor, arg_ctor, half_precision,
                               bfloat16_precision, float_precision, dtype_list, dtype_cpu_list, decorators)

        if make_inplace_variant:
            op_str = op_str + '_'
            subtest_str = 'inplace' + subtest_str
            generate_test_function(cls, op_str, subtest_str, tensor_ctor, arg_ctor, half_precision,
                                   bfloat16_precision, float_precision, dtype_list, dtype_cpu_list, decorators)

    for test in tensor_op_tests:
        caller(cls, *test)

def _generate_reference_input(dtype, device):
    input = []
    input.append(list(range(-5, 5)))
    input.append([0 for x in range(-5, 5)])
    input.append([x + 1e-6 for x in range(-5, 5)])
    # Some vectorized implementations don't support large values
    input.append([x + 1e10 for x in range(-5, 5)])
    input.append([x - 1e10 for x in range(-5, 5)])
    input.append(torch.randn(10).tolist())
    input.append((torch.randn(10) * 1e6).tolist())
    input.append([math.pi * (x / 2) for x in range(-5, 5)])
    return torch.tensor(input, dtype=dtype, device=device)

def _generate_gamma_input(dtype, device, test_poles=True):
    input = []
    input.append((torch.randn(10).abs() + 1e-4).tolist())
    input.append((torch.randn(10).abs() + 1e6).tolist())
    zeros = torch.linspace(-9.5, -0.5, 10)
    input.append(zeros.tolist())
    input.append((zeros - 0.49).tolist())
    input.append((zeros + 0.49).tolist())
    input.append((zeros + (torch.rand(10) * 0.99) - 0.5).tolist())
    if test_poles:
        input.append([-0.999999994, -1.999999994, -2.0000000111,
                      -100.99999994, -1931.99999994, 0.000000111,
                      -0.000000111, 0, -2, -329])
    return torch.tensor(input, dtype=dtype, device=device)

# this class contains information needed to generate tests for torch math functions
# the generated tests compare torch implementation with the reference numpy/scipy implementation,
# and also check proper behavior for contiguous/discontiguous/inplace outputs.
class _TorchMathTestMeta(object):
    def __init__(self,
                 opstr,
                 args=(),
                 reffn=None,
                 refargs=lambda x: (x.numpy(),),
                 input_fn=_generate_reference_input,
                 inputargs=(),
                 substr='',
                 make_inplace=True,
                 decorators=None,
                 ref_backend='numpy',
                 rtol=None,
                 atol=None,
                 dtypes=_float_types_no_half,
                 replace_inf_with_nan=False):
        self.opstr = opstr
        self.args = args
        self.reffn = reffn  # reffn is either callable or ref_backend attribute, set to opstr if not specified
        self.refargs = refargs
        self.input_fn = input_fn
        self.inputargs = inputargs
        self.substr = substr
        self.make_inplace = make_inplace
        assert ref_backend == 'numpy' or ref_backend == 'scipy'
        self.ref_backend = ref_backend
        if ref_backend == 'numpy':
            self.ref_decorator = [unittest.skipIf(not TEST_NUMPY, "Numpy not found")]
        elif ref_backend == 'scipy':
            self.ref_decorator = [unittest.skipIf(not TEST_SCIPY, "Scipy not found")]
        self.decorators = decorators
        self.rtol = rtol
        self.atol = atol
        self.dtypes = dtypes
        self.replace_inf_with_nan = replace_inf_with_nan

torch_op_tests = [_TorchMathTestMeta('sin'),
                  _TorchMathTestMeta('asin', reffn='arcsin'),
                  _TorchMathTestMeta('sinh'),
                  _TorchMathTestMeta('cos'),
                  _TorchMathTestMeta('acos', reffn='arccos'),
                  _TorchMathTestMeta('cosh'),
                  _TorchMathTestMeta('tan'),
                  _TorchMathTestMeta('atan', reffn='arctan'),
                  _TorchMathTestMeta('tanh'),
                  _TorchMathTestMeta('log'),
                  _TorchMathTestMeta('log10'),
                  _TorchMathTestMeta('log1p'),
                  _TorchMathTestMeta('log2'),
                  _TorchMathTestMeta('sqrt'),
                  _TorchMathTestMeta('erf', ref_backend='scipy'),
                  _TorchMathTestMeta('erfc', ref_backend='scipy'),
                  _TorchMathTestMeta('exp'),
                  _TorchMathTestMeta('expm1'),
                  _TorchMathTestMeta('floor'),
                  _TorchMathTestMeta('ceil'),
                  _TorchMathTestMeta('rsqrt', reffn=lambda x: np.reciprocal(np.sqrt(x))),
                  _TorchMathTestMeta('frac', reffn='fmod', refargs=lambda x: (x.numpy(), 1)),
                  _TorchMathTestMeta('trunc'),
                  _TorchMathTestMeta('round'),
                  _TorchMathTestMeta('lgamma', reffn='gammaln', ref_backend='scipy'),
                  _TorchMathTestMeta('polygamma', args=[0], substr='_0', reffn='polygamma',
                                     refargs=lambda x: (0, x.numpy()), input_fn=_generate_gamma_input, inputargs=[False],
                                     ref_backend='scipy'),
                  _TorchMathTestMeta('polygamma', args=[1], substr='_1', reffn='polygamma',
                                     refargs=lambda x: (1, x.numpy()), input_fn=_generate_gamma_input, inputargs=[False],
                                     ref_backend='scipy', rtol=0.0008, atol=1e-5),
                  _TorchMathTestMeta('digamma',
                                     input_fn=_generate_gamma_input, inputargs=[True], ref_backend='scipy',
                                     replace_inf_with_nan=True),
                  _TorchMathTestMeta('abs', input_fn=_medium_2d, dtypes=_types_no_half, rtol=0., atol=0.)]


def generate_torch_test_functions(cls, testmeta, inplace):
    opstr = testmeta.opstr if not inplace else testmeta.opstr + "_"

    def torchfn(x):
        return getattr(x, opstr)(*testmeta.args)

    def fn_check_reference(self, device, dtype):
        def reffn(x):
            backend = np if testmeta.ref_backend == 'numpy' else scipy.special
            opstr = None
            if testmeta.reffn is None:
                opstr = testmeta.opstr
            elif isinstance(testmeta.reffn, str):
                opstr = testmeta.reffn
            if callable(testmeta.reffn):
                fn = testmeta.reffn
            else:
                assert opstr is not None, "invalid reffn"
                fn = getattr(backend, opstr)
            return fn(*testmeta.refargs(x))

        inp = testmeta.input_fn(dtype, device, *testmeta.inputargs)
        with warnings.catch_warnings():
            warnings.simplefilter("ignore")
            expected = torch.from_numpy(reffn(inp))
        actual = torchfn(inp)
        if testmeta.replace_inf_with_nan:
            actual[(actual == -inf) | (actual == inf)] = nan
            expected[(expected == -inf) | (expected == inf)] = nan

        torch.testing.assert_allclose(actual, expected, rtol=testmeta.rtol, atol=testmeta.atol)

    def fn_non_contig(self, device, dtype):
        shapes = [(5, 7), (1024,)]
        for shape in shapes:
            contig = _make_tensor(shape, dtype=dtype, device=device)
            non_contig = torch.empty(shape + (2,), dtype=dtype)[..., 0]
            non_contig.copy_(contig)
            self.assertFalse(non_contig.is_contiguous())
            self.assertEqual(torchfn(contig), torchfn(non_contig), 'non-contiguous')

    def fn_non_contig_index(self, device, dtype):
        contig = _make_tensor((2, 2, 1, 2), dtype=dtype, device=device)
        non_contig = contig[:, 1, ...]
        contig = non_contig.clone()
        self.assertFalse(non_contig.is_contiguous())
        self.assertEqual(torchfn(contig), torchfn(non_contig), 'non-contiguous index')

    def fn_non_contig_expand(self, device, dtype):
        shapes = [(1, 3), (1, 7), (5, 7)]
        for shape in shapes:
            contig = _make_tensor(shape, dtype=dtype, device=device)
            non_contig = contig.clone().expand(3, -1, -1)
            self.assertFalse(non_contig.is_contiguous())
            contig = torchfn(contig)
            non_contig = torchfn(non_contig)
            for i in range(3):
                self.assertEqual(contig, non_contig[i], 'non-contiguous expand[' + str(i) + ']')

    def fn_contig_size1(self, device, dtype):
        contig = _make_tensor((5, 100), dtype=dtype, device=device)
        contig = contig[:1, :50]
        contig2 = torch.empty(contig.size(), dtype=dtype)
        contig2.copy_(contig)
        self.assertTrue(contig.is_contiguous())
        self.assertTrue(contig2.is_contiguous())
        self.assertEqual(torchfn(contig), torchfn(contig2), 'contiguous size1')

    def fn_contig_size1_large_dim(self, device, dtype):
        contig = _make_tensor((5, 2, 3, 1, 4, 5, 3, 2, 1, 2, 3, 4), dtype=dtype, device=device)
        contig = contig[:1, :, :, :, :, :, :, :, :, :, :, :]
        contig2 = torch.empty(contig.size(), dtype=dtype)
        contig2.copy_(contig)
        self.assertTrue(contig.is_contiguous())
        self.assertTrue(contig2.is_contiguous())
        self.assertEqual(torchfn(contig), torchfn(contig2), 'contiguous size1')

    def fn_large(self, device, dtype):
        input = _make_tensor((1024, 512), dtype=dtype, device=device)
        # clone input to properly test inplace functions
        actual = torchfn(input.clone())
        expected = torch.stack([torchfn(slice) for slice in input])
        self.assertEqual(actual, expected, 'large')

    test_functions = {"test_reference_": fn_check_reference,
                      "test_non_contig_": fn_non_contig,
                      "test_non_contig_index_": fn_non_contig_index,
                      "test_non_contig_expand_": fn_non_contig_expand,
                      "test_contig_size1_": fn_contig_size1,
                      "test_check_contig_size1_large_dim_": fn_contig_size1_large_dim,
                      "test_large_": fn_large}
    for name in test_functions:
        if inplace and 'expand' in name:
            continue
        test_name = name + testmeta.opstr + testmeta.substr
        if inplace:
            test_name += "_inplace"
        assert not hasattr(cls, test_name), "{0} already in TestTorchMathOps".format(test_name)

        decorators = [] if testmeta.decorators is None else testmeta.decorators
        if 'reference' in name:
            decorators = decorators + testmeta.ref_decorator
        decorators = decorators + [dtypes(*testmeta.dtypes)]
        fn_test = test_functions[name]
        for dec in decorators:
            fn_test = dec(fn_test)
        setattr(cls, test_name, fn_test)




def generate_torch_op_tests(cls):
    for t in torch_op_tests:
        generate_torch_test_functions(cls, t, False)
        if t.make_inplace:
            generate_torch_test_functions(cls, t, True)





tensor_binary_ops = [
    '__lt__', '__le__',
    '__gt__', '__ge__',
    '__eq__', '__ne__',

    '__add__', '__radd__', '__iadd__',
    '__sub__', '__rsub__', '__isub__',
    '__mul__', '__rmul__', '__imul__',
    '__matmul__', '__rmatmul__', '__imatmul__',
    '__truediv__', '__rtruediv__', '__itruediv__',
    '__floordiv__', '__rfloordiv__', '__ifloordiv__',
    '__mod__', '__rmod__', '__imod__',
    '__divmod__', '__rdivmod__', '__idivmod__',
    '__pow__', '__rpow__', '__ipow__',
    '__lshift__', '__rlshift__', '__ilshift__',
    '__rshift__', '__rrshift__', '__irshift__',
    '__and__', '__rand__', '__iand__',
    '__xor__', '__rxor__', '__ixor__',
    '__or__', '__ror__', '__ior__',
]


# Test that binary math operations return NotImplemented for unknown types.
def generate_not_implemented_tests(cls):
    class UnknownType:
        pass

    for op in tensor_binary_ops:
        @dtypes(*_types)
        def test(self, device, dtype):
            # Generate the inputs
            tensor = _small_2d(dtype, device)

            # Runs the tensor op on the device
            result = getattr(tensor, op)(UnknownType())
            self.assertEqual(result, NotImplemented)

        test_name = "test_{}_not_implemented".format(op)
        assert not hasattr(cls, test_name), "{0} already in {1}".format(
            test_name, cls.__name__)

        setattr(cls, test_name, test)


class TestTensorDeviceOps(TestCase):
    exact_dtype = True

    def _test_svd_helper(self, shape, some, col_maj, device, dtype):
        cpu_tensor = torch.randn(shape, device='cpu').to(dtype)
        device_tensor = cpu_tensor.to(device=device)
        if col_maj:
            cpu_tensor = cpu_tensor.t()
            device_tensor = device_tensor.t()
        cpu_result = torch.svd(cpu_tensor, some=some)
        device_result = torch.svd(device_tensor, some=some)
        m = min(cpu_tensor.shape[-2:])
        # torch.svd returns torch.return_types.svd which is a tuple of (U, V, S).
        # - When some==False, U[..., m:] can be arbitrary.
        # - When some==True, U shape: [..., m], V shape: [m, m]
        # - Signs are not deterministic. If the sign of a column of U is changed
        #   then the corresponding column of the V has to be changed.
        # Thus here we only compare result[..., :m].abs() from CPU and device.
        for x, y in zip(cpu_result, device_result):
            self.assertEqual(x[..., :m].abs(), y[..., :m].abs(), atol=1e-5)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_square(self, device, dtype):
        self._test_svd_helper((10, 10), True, False, device, dtype)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_square_col_maj(self, device, dtype):
        self._test_svd_helper((10, 10), True, True, device, dtype)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_tall_some(self, device, dtype):
        self._test_svd_helper((20, 5), True, False, device, dtype)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_tall_all(self, device, dtype):
        self._test_svd_helper((20, 5), False, False, device, dtype)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_tall_some_col_maj(self, device, dtype):
        self._test_svd_helper((5, 20), True, True, device, dtype)

    @skipCUDAIfNoMagma
    @dtypes(*_float_types_no_half)
    def test_svd_tall_all_col_maj(self, device, dtype):
        self._test_svd_helper((5, 20), False, True, device, dtype)

class TestTorchMathOps(TestCase):
    exact_dtype = True

class TestTorch(TestCase, _TestTorchMixin):
    exact_dtype = True


# Generates tests
# Note: test generation must be done at file scope, not within main, or
# pytest will fail.
add_neg_dim_tests()
generate_tensor_op_tests(TestTensorDeviceOps)
generate_not_implemented_tests(TestTorchDeviceType)
generate_torch_op_tests(TestTorchMathOps)
instantiate_device_type_tests(TestTorchDeviceType, globals())
instantiate_device_type_tests(TestViewOps, globals())
instantiate_device_type_tests(TestDevicePrecision, globals(), except_for='cpu')
instantiate_device_type_tests(TestTensorDeviceOps, globals())
instantiate_device_type_tests(TestTorchMathOps, globals(), only_for='cpu')

if __name__ == '__main__':
    run_tests()