diff --git a/Orange/distance/__init__.py b/Orange/distance/__init__.py index 17973c03a79..4f998778aac 100644 --- a/Orange/distance/__init__.py +++ b/Orange/distance/__init__.py @@ -1,261 +1,6 @@ -import numpy as np -from scipy import stats -import sklearn.metrics as skl_metrics +from .distance import (Distance, DistanceModel, + Euclidean, Manhattan, Cosine, Jaccard, + SpearmanR, SpearmanRAbsolute, PearsonR, PearsonRAbsolute, + Mahalanobis, MahalanobisDistance) -from Orange import data -from Orange.misc import DistMatrix -from Orange.preprocess import SklImpute - -__all__ = ['Euclidean', 'Manhattan', 'Cosine', 'Jaccard', 'SpearmanR', - 'SpearmanRAbsolute', 'PearsonR', 'PearsonRAbsolute', 'Mahalanobis', - 'MahalanobisDistance'] - - -def _preprocess(table): - """Remove categorical attributes and impute missing values.""" - if not len(table): - return table - new_domain = data.Domain( - [a for a in table.domain.attributes if a.is_continuous], - table.domain.class_vars, - table.domain.metas) - new_data = table.transform(new_domain) - new_data = SklImpute()(new_data) - return new_data - - -def _orange_to_numpy(x): - """Convert :class:`Orange.data.Table` and :class:`Orange.data.RowInstance` - to :class:`numpy.ndarray`. - """ - if isinstance(x, data.Table): - return x.X - elif isinstance(x, data.Instance): - return np.atleast_2d(x.x) - elif isinstance(x, np.ndarray): - return np.atleast_2d(x) - else: - return x # e.g. None - - -class Distance: - def __call__(self, e1, e2=None, axis=1, impute=False): - """ - :param e1: input data instances, we calculate distances between all - pairs - :type e1: :class:`Orange.data.Table` or - :class:`Orange.data.RowInstance` or :class:`numpy.ndarray` - :param e2: optional second argument for data instances if provided, - distances between each pair, where first item is from e1 and - second is from e2, are calculated - :type e2: :class:`Orange.data.Table` or - :class:`Orange.data.RowInstance` or :class:`numpy.ndarray` - :param axis: if axis=1 we calculate distances between rows, if axis=0 - we calculate distances between columns - :type axis: int - :param impute: if impute=True all NaN values in matrix are replaced - with 0 - :type impute: bool - :return: the matrix with distances between given examples - :rtype: :class:`Orange.misc.distmatrix.DistMatrix` - """ - raise NotImplementedError( - 'Distance is an abstract class and should not be used directly.') - - -class SklDistance(Distance): - """Generic scikit-learn distance.""" - def __init__(self, metric, name, supports_sparse): - """ - Args: - metric: The metric to be used for distance calculation - name (str): Name of the distance - supports_sparse (boolean): Whether this metric works on sparse data - or not. - """ - self.metric = metric - self.name = name - self.supports_sparse = supports_sparse - - def __call__(self, e1, e2=None, axis=1, impute=False): - x1 = _orange_to_numpy(e1) - x2 = _orange_to_numpy(e2) - if axis == 0: - x1 = x1.T - if x2 is not None: - x2 = x2.T - dist = skl_metrics.pairwise.pairwise_distances( - x1, x2, metric=self.metric) - if isinstance(e1, data.Table) or isinstance(e1, data.RowInstance): - dist = DistMatrix(dist, e1, e2, axis) - else: - dist = DistMatrix(dist) - return dist - -Euclidean = SklDistance('euclidean', 'Euclidean', True) -Manhattan = SklDistance('manhattan', 'Manhattan', True) -Cosine = SklDistance('cosine', 'Cosine', True) -Jaccard = SklDistance('jaccard', 'Jaccard', False) - - -class SpearmanDistance(Distance): - """ Generic Spearman's rank correlation coefficient. """ - def __init__(self, absolute, name): - """ - Constructor for Spearman's and Absolute Spearman's distances. - - Args: - absolute (boolean): Whether to use absolute values or not. - name (str): Name of the distance - - Returns: - If absolute=True return Spearman's Absolute rank class else return - Spearman's rank class. - """ - self.absolute = absolute - self.name = name - self.supports_sparse = False - - def __call__(self, e1, e2=None, axis=1, impute=False): - x1 = _orange_to_numpy(e1) - x2 = _orange_to_numpy(e2) - if x2 is None: - x2 = x1 - slc = len(x1) if axis == 1 else x1.shape[1] - rho, _ = stats.spearmanr(x1, x2, axis=axis) - if np.isnan(rho).any() and impute: - rho = np.nan_to_num(rho) - if self.absolute: - dist = (1. - np.abs(rho)) / 2. - else: - dist = (1. - rho) / 2. - if isinstance(dist, np.float): - dist = np.array([[dist]]) - elif isinstance(dist, np.ndarray): - dist = dist[:slc, slc:] - if isinstance(e1, data.Table) or isinstance(e1, data.RowInstance): - dist = DistMatrix(dist, e1, e2, axis) - else: - dist = DistMatrix(dist) - return dist - -SpearmanR = SpearmanDistance(absolute=False, name='Spearman') -SpearmanRAbsolute = SpearmanDistance(absolute=True, name='Spearman absolute') - - -class PearsonDistance(Distance): - """ Generic Pearson's rank correlation coefficient. """ - def __init__(self, absolute, name): - """ - Constructor for Pearson's and Absolute Pearson's distances. - - Args: - absolute (boolean): Whether to use absolute values or not. - name (str): Name of the distance - - Returns: - If absolute=True return Pearson's Absolute rank class else return - Pearson's rank class. - """ - self.absolute = absolute - self.name = name - self.supports_sparse = False - - def __call__(self, e1, e2=None, axis=1, impute=False): - x1 = _orange_to_numpy(e1) - x2 = _orange_to_numpy(e2) - if x2 is None: - x2 = x1 - if axis == 0: - x1 = x1.T - x2 = x2.T - rho = np.array([[stats.pearsonr(i, j)[0] for j in x2] for i in x1]) - if np.isnan(rho).any() and impute: - rho = np.nan_to_num(rho) - if self.absolute: - dist = (1. - np.abs(rho)) / 2. - else: - dist = (1. - rho) / 2. - if isinstance(e1, data.Table) or isinstance(e1, data.RowInstance): - dist = DistMatrix(dist, e1, e2, axis) - else: - dist = DistMatrix(dist) - return dist - -PearsonR = PearsonDistance(absolute=False, name='Pearson') -PearsonRAbsolute = PearsonDistance(absolute=True, name='Pearson absolute') - - -class MahalanobisDistance(Distance): - """Mahalanobis distance.""" - def __init__(self, data=None, axis=1, name='Mahalanobis'): - self.name = name - self.supports_sparse = False - self.axis = None - self.VI = None - if data is not None: - self.fit(data, axis) - - def fit(self, data, axis=1): - """ - Compute the covariance matrix needed for calculating distances. - - Args: - data: The dataset used for calculating covariances. - axis: If axis=1 we calculate distances between rows, if axis=0 we - calculate distances between columns. - """ - x = _orange_to_numpy(data) - if axis == 0: - x = x.T - self.axis = axis - try: - c = np.cov(x.T) - except: - raise MemoryError("Covariance matrix is too large.") - try: - self.VI = np.linalg.inv(c) - except: - raise ValueError("Computation of inverse covariance matrix failed.") - - def __call__(self, e1, e2=None, axis=None, impute=False): - assert self.VI is not None, \ - "Mahalanobis distance must be initialized with the fit() method." - - x1 = _orange_to_numpy(e1) - x2 = _orange_to_numpy(e2) - - if axis is not None: - assert axis == self.axis, \ - "Axis must match its value at initialization." - if self.axis == 0: - x1 = x1.T - if x2 is not None: - x2 = x2.T - if not x1.shape[1] == self.VI.shape[0] or \ - x2 is not None and not x2.shape[1] == self.VI.shape[0]: - raise ValueError('Incorrect number of features.') - - dist = skl_metrics.pairwise.pairwise_distances( - x1, x2, metric='mahalanobis', VI=self.VI) - if np.isnan(dist).any() and impute: - dist = np.nan_to_num(dist) - if isinstance(e1, data.Table) or isinstance(e1, data.RowInstance): - dist = DistMatrix(dist, e1, e2, self.axis) - else: - dist = DistMatrix(dist) - return dist - - -# Only retain this to raise errors on use. Remove in some future version. -class __MahalanobisDistanceError(MahalanobisDistance): - def _raise_error(self, *args, **kwargs): - raise RuntimeError( - "Invalid use of MahalanobisDistance.\n" - "Create a new MahalanobisDistance instance first, e.g.\n" - ">>> metric = MahalanobisDistance(data)\n" - ">>> dist = metric(data)" - ) - fit = _raise_error - __call__ = _raise_error -Mahalanobis = __MahalanobisDistanceError() +from .base import _preprocess, remove_discrete_features, impute diff --git a/Orange/distance/_distance.c b/Orange/distance/_distance.c new file mode 100644 index 00000000000..765b89125cd --- /dev/null +++ b/Orange/distance/_distance.c @@ -0,0 +1,31088 @@ +/* Generated by Cython 0.26 */ + +#define PY_SSIZE_T_CLEAN +#include "Python.h" +#ifndef Py_PYTHON_H + #error Python headers needed to compile C extensions, please install development version of Python. +#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03020000) + #error Cython 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PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b)) +#define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b)) +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b) +#else + #define __Pyx_PyString_Format(a, b) PyString_Format(a, b) +#endif +#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII) + #define PyObject_ASCII(o) PyObject_Repr(o) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBaseString_Type PyUnicode_Type + #define PyStringObject PyUnicodeObject + #define PyString_Type PyUnicode_Type + #define PyString_Check PyUnicode_Check + #define PyString_CheckExact PyUnicode_CheckExact +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj) + #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj) +#else + #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj)) + #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj)) +#endif +#ifndef PySet_CheckExact + #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type) +#endif +#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) +#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception) +#if PY_MAJOR_VERSION >= 3 + #define PyIntObject PyLongObject + #define PyInt_Type PyLong_Type + #define PyInt_Check(op) PyLong_Check(op) + #define PyInt_CheckExact(op) PyLong_CheckExact(op) + #define PyInt_FromString PyLong_FromString + #define PyInt_FromUnicode PyLong_FromUnicode + #define PyInt_FromLong PyLong_FromLong + #define PyInt_FromSize_t PyLong_FromSize_t + #define PyInt_FromSsize_t PyLong_FromSsize_t + #define PyInt_AsLong PyLong_AsLong + #define PyInt_AS_LONG PyLong_AS_LONG + #define PyInt_AsSsize_t PyLong_AsSsize_t + #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask + #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask + #define PyNumber_Int PyNumber_Long +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBoolObject PyLongObject +#endif +#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY + #ifndef PyUnicode_InternFromString + #define PyUnicode_InternFromString(s) PyUnicode_FromString(s) + #endif +#endif +#if PY_VERSION_HEX < 0x030200A4 + typedef long Py_hash_t; + #define __Pyx_PyInt_FromHash_t PyInt_FromLong + #define __Pyx_PyInt_AsHash_t PyInt_AsLong +#else + #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t + #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func)) +#else + #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass) +#endif +#ifndef __has_attribute + #define __has_attribute(x) 0 +#endif +#ifndef __has_cpp_attribute + #define __has_cpp_attribute(x) 0 +#endif +#if CYTHON_USE_ASYNC_SLOTS + #if PY_VERSION_HEX >= 0x030500B1 + #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods + #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async) + #else + typedef struct { + unaryfunc am_await; + unaryfunc am_aiter; + unaryfunc am_anext; + } __Pyx_PyAsyncMethodsStruct; + #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved)) + #endif +#else + #define __Pyx_PyType_AsAsync(obj) NULL +#endif +#ifndef CYTHON_RESTRICT + #if defined(__GNUC__) + #define CYTHON_RESTRICT __restrict__ + #elif defined(_MSC_VER) && _MSC_VER >= 1400 + #define CYTHON_RESTRICT __restrict + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_RESTRICT restrict + #else + #define CYTHON_RESTRICT + #endif +#endif +#ifndef CYTHON_UNUSED +# if defined(__GNUC__) +# if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +#endif +#ifndef CYTHON_MAYBE_UNUSED_VAR +# if defined(__cplusplus) + template void CYTHON_MAYBE_UNUSED_VAR( const T& ) { } +# else +# define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x) +# endif +#endif +#ifndef CYTHON_NCP_UNUSED +# if CYTHON_COMPILING_IN_CPYTHON +# define CYTHON_NCP_UNUSED +# else +# define CYTHON_NCP_UNUSED CYTHON_UNUSED +# endif +#endif +#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None) +#ifdef _MSC_VER + #ifndef _MSC_STDINT_H_ + #if _MSC_VER < 1300 + typedef unsigned char uint8_t; + typedef unsigned int uint32_t; + #else + typedef unsigned __int8 uint8_t; + typedef unsigned __int32 uint32_t; + #endif + #endif +#else + #include +#endif +#ifndef CYTHON_FALLTHROUGH + #ifdef __cplusplus + #if __has_cpp_attribute(fallthrough) + #define CYTHON_FALLTHROUGH [[fallthrough]] + #elif __has_cpp_attribute(clang::fallthrough) + #define CYTHON_FALLTHROUGH [[clang::fallthrough]] + #endif + #endif + #ifndef CYTHON_FALLTHROUGH + #if __has_attribute(fallthrough) || (defined(__GNUC__) && defined(__attribute__)) + #define CYTHON_FALLTHROUGH __attribute__((fallthrough)) + #else + #define CYTHON_FALLTHROUGH + #endif + #endif +#endif + +#ifndef CYTHON_INLINE + #if defined(__clang__) + #define CYTHON_INLINE __inline__ __attribute__ ((__unused__)) + #elif defined(__GNUC__) + #define CYTHON_INLINE __inline__ + #elif defined(_MSC_VER) + #define CYTHON_INLINE __inline + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_INLINE inline + #else + #define CYTHON_INLINE + #endif +#endif + +#if defined(WIN32) || defined(MS_WINDOWS) + #define _USE_MATH_DEFINES +#endif +#include +#ifdef NAN +#define __PYX_NAN() ((float) NAN) +#else +static CYTHON_INLINE float __PYX_NAN() { + float value; + memset(&value, 0xFF, sizeof(value)); + return value; +} +#endif +#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL) +#define __Pyx_truncl trunc +#else +#define __Pyx_truncl truncl +#endif + + +#define __PYX_ERR(f_index, lineno, Ln_error) \ +{ \ + __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \ +} + +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y) +#else + #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y) +#endif + +#ifndef __PYX_EXTERN_C + #ifdef __cplusplus + #define __PYX_EXTERN_C extern "C" + #else + #define __PYX_EXTERN_C extern + #endif +#endif + +#define __PYX_HAVE__Orange__distance___distance +#define __PYX_HAVE_API__Orange__distance___distance +#include +#include +#include +#include "numpy/arrayobject.h" +#include "numpy/ufuncobject.h" +#include "numpy/npy_math.h" +#include "math.h" +#include "pythread.h" +#include "pystate.h" +#ifdef _OPENMP +#include +#endif /* _OPENMP */ + +#ifdef PYREX_WITHOUT_ASSERTIONS +#define CYTHON_WITHOUT_ASSERTIONS +#endif + +typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding; + const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry; + +#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0 +#define __PYX_DEFAULT_STRING_ENCODING "" +#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString +#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#define __Pyx_uchar_cast(c) ((unsigned char)c) +#define __Pyx_long_cast(x) ((long)x) +#define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\ + (sizeof(type) < sizeof(Py_ssize_t)) ||\ + (sizeof(type) > sizeof(Py_ssize_t) &&\ + likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX) &&\ + (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\ + v == (type)PY_SSIZE_T_MIN))) ||\ + (sizeof(type) == sizeof(Py_ssize_t) &&\ + (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX))) ) +#if defined (__cplusplus) && __cplusplus >= 201103L + #include + #define __Pyx_sst_abs(value) std::abs(value) +#elif SIZEOF_INT >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) abs(value) +#elif SIZEOF_LONG >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) labs(value) +#elif defined (_MSC_VER) && defined (_M_X64) + #define __Pyx_sst_abs(value) _abs64(value) +#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define __Pyx_sst_abs(value) llabs(value) +#elif defined (__GNUC__) + #define __Pyx_sst_abs(value) __builtin_llabs(value) +#else + #define __Pyx_sst_abs(value) ((value<0) ? -value : value) +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*); +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length); +#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s)) +#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l) +#define __Pyx_PyBytes_FromString PyBytes_FromString +#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*); +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#else + #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize +#endif +#define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s) +#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) +#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) +#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) +#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) +#if PY_MAJOR_VERSION < 3 +static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) +{ + const Py_UNICODE *u_end = u; + while (*u_end++) ; + return (size_t)(u_end - u - 1); +} +#else +#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen +#endif +#define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u)) +#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode +#define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode +#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj) +#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) +#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False)) +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*); +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x); +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*); +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t); +#if CYTHON_ASSUME_SAFE_MACROS +#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x)) +#else +#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x) +#endif +#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x)) +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x)) +#else +#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x)) +#endif +#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x)) +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII +static int __Pyx_sys_getdefaultencoding_not_ascii; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + PyObject* ascii_chars_u = NULL; + PyObject* ascii_chars_b = NULL; + const char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + if (strcmp(default_encoding_c, "ascii") == 0) { + __Pyx_sys_getdefaultencoding_not_ascii = 0; + } else { + char ascii_chars[128]; + int c; + for (c = 0; c < 128; c++) { + ascii_chars[c] = c; + } + __Pyx_sys_getdefaultencoding_not_ascii = 1; + ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL); + if (!ascii_chars_u) goto bad; + ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL); + if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) { + PyErr_Format( + PyExc_ValueError, + "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.", + default_encoding_c); + goto bad; + } + Py_DECREF(ascii_chars_u); + Py_DECREF(ascii_chars_b); + } + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + Py_XDECREF(ascii_chars_u); + Py_XDECREF(ascii_chars_b); + return -1; +} +#endif +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3 +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL) +#else +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL) +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +static char* __PYX_DEFAULT_STRING_ENCODING; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c)); + if (!__PYX_DEFAULT_STRING_ENCODING) goto bad; + strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c); + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + return -1; +} +#endif +#endif + + +/* Test for GCC > 2.95 */ +#if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))) + #define likely(x) __builtin_expect(!!(x), 1) + #define unlikely(x) __builtin_expect(!!(x), 0) +#else /* !__GNUC__ or GCC < 2.95 */ + #define likely(x) (x) + #define unlikely(x) (x) +#endif /* __GNUC__ */ +static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; } + +static PyObject *__pyx_m; +static PyObject *__pyx_d; +static PyObject *__pyx_b; +static PyObject *__pyx_cython_runtime; +static PyObject *__pyx_empty_tuple; +static PyObject *__pyx_empty_bytes; +static PyObject *__pyx_empty_unicode; +static int __pyx_lineno; +static int __pyx_clineno = 0; +static const char * __pyx_cfilenm= __FILE__; +static const char *__pyx_filename; + +/* Header.proto */ +#if !defined(CYTHON_CCOMPLEX) + #if defined(__cplusplus) + #define CYTHON_CCOMPLEX 1 + #elif defined(_Complex_I) + #define CYTHON_CCOMPLEX 1 + #else + #define CYTHON_CCOMPLEX 0 + #endif +#endif +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #include + #else + #include + #endif +#endif +#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__) + #undef _Complex_I + #define _Complex_I 1.0fj +#endif + + +static const char *__pyx_f[] = { + "Orange/distance/_distance.pyx", + "__init__.pxd", + "stringsource", + "type.pxd", +}; +/* MemviewSliceStruct.proto */ +struct __pyx_memoryview_obj; +typedef struct { + struct __pyx_memoryview_obj *memview; + char *data; + Py_ssize_t shape[8]; + Py_ssize_t strides[8]; + Py_ssize_t suboffsets[8]; +} __Pyx_memviewslice; + +/* BufferFormatStructs.proto */ +#define IS_UNSIGNED(type) (((type) -1) > 0) +struct __Pyx_StructField_; +#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0) +typedef struct { + const char* name; + struct __Pyx_StructField_* fields; + size_t size; + size_t arraysize[8]; + int ndim; + char typegroup; + char is_unsigned; + int flags; +} __Pyx_TypeInfo; +typedef struct __Pyx_StructField_ { + __Pyx_TypeInfo* type; + const char* name; + size_t offset; +} __Pyx_StructField; +typedef struct { + __Pyx_StructField* field; + size_t parent_offset; +} __Pyx_BufFmt_StackElem; +typedef struct { + __Pyx_StructField root; + __Pyx_BufFmt_StackElem* head; + size_t fmt_offset; + size_t new_count, enc_count; + size_t struct_alignment; + int is_complex; + char enc_type; + char new_packmode; + char enc_packmode; + char is_valid_array; +} __Pyx_BufFmt_Context; + +/* Atomics.proto */ +#include +#ifndef CYTHON_ATOMICS + #define CYTHON_ATOMICS 1 +#endif +#define __pyx_atomic_int_type int +#if CYTHON_ATOMICS && __GNUC__ >= 4 && (__GNUC_MINOR__ > 1 ||\ + (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL >= 2)) &&\ + !defined(__i386__) + #define __pyx_atomic_incr_aligned(value, lock) __sync_fetch_and_add(value, 1) + #define __pyx_atomic_decr_aligned(value, lock) __sync_fetch_and_sub(value, 1) + #ifdef __PYX_DEBUG_ATOMICS + #warning "Using GNU atomics" + #endif +#elif CYTHON_ATOMICS && defined(_MSC_VER) && 0 + #include + #undef __pyx_atomic_int_type + #define __pyx_atomic_int_type LONG + #define __pyx_atomic_incr_aligned(value, lock) InterlockedIncrement(value) + #define __pyx_atomic_decr_aligned(value, lock) InterlockedDecrement(value) + #ifdef __PYX_DEBUG_ATOMICS + #pragma message ("Using MSVC atomics") + #endif +#elif CYTHON_ATOMICS && (defined(__ICC) || defined(__INTEL_COMPILER)) && 0 + #define __pyx_atomic_incr_aligned(value, lock) _InterlockedIncrement(value) + #define __pyx_atomic_decr_aligned(value, lock) _InterlockedDecrement(value) + #ifdef __PYX_DEBUG_ATOMICS + #warning "Using Intel atomics" + #endif +#else + #undef CYTHON_ATOMICS + #define CYTHON_ATOMICS 0 + #ifdef __PYX_DEBUG_ATOMICS + #warning "Not using atomics" + #endif +#endif +typedef volatile __pyx_atomic_int_type __pyx_atomic_int; +#if CYTHON_ATOMICS + #define __pyx_add_acquisition_count(memview)\ + __pyx_atomic_incr_aligned(__pyx_get_slice_count_pointer(memview), memview->lock) + #define __pyx_sub_acquisition_count(memview)\ + __pyx_atomic_decr_aligned(__pyx_get_slice_count_pointer(memview), memview->lock) +#else + #define __pyx_add_acquisition_count(memview)\ + __pyx_add_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock) + #define __pyx_sub_acquisition_count(memview)\ + __pyx_sub_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock) +#endif + + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":725 + * # in Cython to enable them only on the right systems. + * + * ctypedef npy_int8 int8_t # <<<<<<<<<<<<<< + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + */ +typedef npy_int8 __pyx_t_5numpy_int8_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":726 + * + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t # <<<<<<<<<<<<<< + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t + */ +typedef npy_int16 __pyx_t_5numpy_int16_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":727 + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t # <<<<<<<<<<<<<< + * ctypedef npy_int64 int64_t + * #ctypedef npy_int96 int96_t + */ +typedef npy_int32 __pyx_t_5numpy_int32_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":728 + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t # <<<<<<<<<<<<<< + * #ctypedef npy_int96 int96_t + * #ctypedef npy_int128 int128_t + */ +typedef npy_int64 __pyx_t_5numpy_int64_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":732 + * #ctypedef npy_int128 int128_t + * + * ctypedef npy_uint8 uint8_t # <<<<<<<<<<<<<< + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + */ +typedef npy_uint8 __pyx_t_5numpy_uint8_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":733 + * + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t # <<<<<<<<<<<<<< + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t + */ +typedef npy_uint16 __pyx_t_5numpy_uint16_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":734 + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t # <<<<<<<<<<<<<< + * ctypedef npy_uint64 uint64_t + * #ctypedef npy_uint96 uint96_t + */ +typedef npy_uint32 __pyx_t_5numpy_uint32_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":735 + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t # <<<<<<<<<<<<<< + * #ctypedef npy_uint96 uint96_t + * #ctypedef npy_uint128 uint128_t + */ +typedef npy_uint64 __pyx_t_5numpy_uint64_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":739 + * #ctypedef npy_uint128 uint128_t + * + * ctypedef npy_float32 float32_t # <<<<<<<<<<<<<< + * ctypedef npy_float64 float64_t + * #ctypedef npy_float80 float80_t + */ +typedef npy_float32 __pyx_t_5numpy_float32_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":740 + * + * ctypedef npy_float32 float32_t + * ctypedef npy_float64 float64_t # <<<<<<<<<<<<<< + * #ctypedef npy_float80 float80_t + * #ctypedef npy_float128 float128_t + */ +typedef npy_float64 __pyx_t_5numpy_float64_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":749 + * # The int types are mapped a bit surprising -- + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t + */ +typedef npy_long __pyx_t_5numpy_int_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":750 + * # numpy.int corresponds to 'l' and numpy.long to 'q' + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t # <<<<<<<<<<<<<< + * ctypedef npy_longlong longlong_t + * + */ +typedef npy_longlong __pyx_t_5numpy_long_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":751 + * ctypedef npy_long int_t + * ctypedef npy_longlong long_t + * ctypedef npy_longlong longlong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_ulong uint_t + */ +typedef npy_longlong __pyx_t_5numpy_longlong_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":753 + * ctypedef npy_longlong longlong_t + * + * ctypedef npy_ulong uint_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t + */ +typedef npy_ulong __pyx_t_5numpy_uint_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":754 + * + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t # <<<<<<<<<<<<<< + * ctypedef npy_ulonglong ulonglong_t + * + */ +typedef npy_ulonglong __pyx_t_5numpy_ulong_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":755 + * ctypedef npy_ulong uint_t + * ctypedef npy_ulonglong ulong_t + * ctypedef npy_ulonglong ulonglong_t # <<<<<<<<<<<<<< + * + * ctypedef npy_intp intp_t + */ +typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":757 + * ctypedef npy_ulonglong ulonglong_t + * + * ctypedef npy_intp intp_t # <<<<<<<<<<<<<< + * ctypedef npy_uintp uintp_t + * + */ +typedef npy_intp __pyx_t_5numpy_intp_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":758 + * + * ctypedef npy_intp intp_t + * ctypedef npy_uintp uintp_t # <<<<<<<<<<<<<< + * + * ctypedef npy_double float_t + */ +typedef npy_uintp __pyx_t_5numpy_uintp_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":760 + * ctypedef npy_uintp uintp_t + * + * ctypedef npy_double float_t # <<<<<<<<<<<<<< + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t + */ +typedef npy_double __pyx_t_5numpy_float_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":761 + * + * ctypedef npy_double float_t + * ctypedef npy_double double_t # <<<<<<<<<<<<<< + * ctypedef npy_longdouble longdouble_t + * + */ +typedef npy_double __pyx_t_5numpy_double_t; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":762 + * ctypedef npy_double float_t + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t # <<<<<<<<<<<<<< + * + * ctypedef npy_cfloat cfloat_t + */ +typedef npy_longdouble __pyx_t_5numpy_longdouble_t; +/* Declarations.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< float > __pyx_t_float_complex; + #else + typedef float _Complex __pyx_t_float_complex; + #endif +#else + typedef struct { float real, imag; } __pyx_t_float_complex; +#endif +static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float); + +/* Declarations.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + typedef ::std::complex< double > __pyx_t_double_complex; + #else + typedef double _Complex __pyx_t_double_complex; + #endif +#else + typedef struct { double real, imag; } __pyx_t_double_complex; +#endif +static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double); + + +/*--- Type declarations ---*/ +struct __pyx_array_obj; +struct __pyx_MemviewEnum_obj; +struct __pyx_memoryview_obj; +struct __pyx_memoryviewslice_obj; + +/* "../../miniconda3/envs/o3/lib/python3.5/site-packages/Cython/Includes/numpy/__init__.pxd":764 + * ctypedef npy_longdouble longdouble_t + * + * ctypedef npy_cfloat cfloat_t # <<<<<<<<<<<<<< + * ctypedef npy_cdouble cdouble_t + * ctypedef npy_clongdouble clongdouble_t + */ +typedef npy_cfloat __pyx_t_5numpy_cfloat_t; 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r = NULL; __Pyx_DECREF(tmp);}} while(0) + +/* PyObjectGetAttrStr.proto */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) { + PyTypeObject* tp = Py_TYPE(obj); + if (likely(tp->tp_getattro)) + return tp->tp_getattro(obj, attr_name); +#if PY_MAJOR_VERSION < 3 + if (likely(tp->tp_getattr)) + return tp->tp_getattr(obj, PyString_AS_STRING(attr_name)); +#endif + return PyObject_GetAttr(obj, attr_name); +} +#else +#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n) +#endif + +/* GetBuiltinName.proto */ +static PyObject *__Pyx_GetBuiltinName(PyObject *name); + +/* None.proto */ +static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname); + +/* BufferFormatCheck.proto */ +static CYTHON_INLINE int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, + __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack); +static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info); 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+static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *, int, int); + +/* RaiseArgTupleInvalid.proto */ +static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact, + Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found); + +/* RaiseDoubleKeywords.proto */ +static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name); + +/* ParseKeywords.proto */ +static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\ + PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\ + const char* function_name); + +/* ArgTypeTest.proto */ +static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed, + const char *name, int exact); + +/* NoFastGil.proto */ +#define __Pyx_PyGILState_Ensure PyGILState_Ensure +#define __Pyx_PyGILState_Release PyGILState_Release +#define __Pyx_FastGIL_Remember() +#define __Pyx_FastGIL_Forget() +#define __Pyx_FastGilFuncInit() + +#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1) +#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0) +/* PyThreadStateGet.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyThreadState_declare PyThreadState *__pyx_tstate; +#define __Pyx_PyThreadState_assign __pyx_tstate = PyThreadState_GET(); +#else +#define __Pyx_PyThreadState_declare +#define __Pyx_PyThreadState_assign +#endif + +/* PyErrFetchRestore.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ErrRestoreWithState(type, value, tb) __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +#define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb) +#endif + +/* GetModuleGlobalName.proto */ +static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name); + +/* PyObjectCall.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw); +#else +#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw) +#endif + +/* ExtTypeTest.proto */ +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); + +/* BufferFallbackError.proto */ +static void __Pyx_RaiseBufferFallbackError(void); + +/* RaiseException.proto */ +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); + +/* DictGetItem.proto */ +#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY +static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) { + PyObject *value; + value = PyDict_GetItemWithError(d, key); + if (unlikely(!value)) { + if (!PyErr_Occurred()) { + PyObject* args = PyTuple_Pack(1, key); + if (likely(args)) + PyErr_SetObject(PyExc_KeyError, args); + Py_XDECREF(args); + } + return NULL; + } + Py_INCREF(value); + return value; +} +#else + #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key) +#endif + +/* RaiseTooManyValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected); + +/* RaiseNeedMoreValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index); + +/* RaiseNoneIterError.proto */ +static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void); + +/* SaveResetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +#else +#define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb) +#define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb) +#endif + +/* PyErrExceptionMatches.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err) +static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err); +#else +#define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err) +#endif + +/* GetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb) +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* IncludeStringH.proto */ +#include + +/* BytesEquals.proto */ +static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals); + +/* UnicodeEquals.proto */ +static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals); + +/* StrEquals.proto */ +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals +#else +#define __Pyx_PyString_Equals __Pyx_PyBytes_Equals +#endif + +/* UnaryNegOverflows.proto */ +#define UNARY_NEG_WOULD_OVERFLOW(x)\ + (((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x))) + +static CYTHON_UNUSED int __pyx_array_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/ +static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *); /*proto*/ +/* GetAttr.proto */ +static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *); + +/* decode_c_string_utf16.proto */ +static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16(const char *s, Py_ssize_t size, const char *errors) { + int byteorder = 0; + return PyUnicode_DecodeUTF16(s, size, errors, &byteorder); +} +static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16LE(const char *s, Py_ssize_t size, const char *errors) { + int byteorder = -1; + return PyUnicode_DecodeUTF16(s, size, errors, &byteorder); +} +static CYTHON_INLINE PyObject *__Pyx_PyUnicode_DecodeUTF16BE(const char *s, Py_ssize_t size, const char *errors) { + int byteorder = 1; + return PyUnicode_DecodeUTF16(s, size, errors, &byteorder); +} + +/* decode_c_string.proto */ +static CYTHON_INLINE PyObject* __Pyx_decode_c_string( + const char* cstring, Py_ssize_t start, Py_ssize_t stop, + const char* encoding, const char* errors, + PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)); + +/* GetAttr3.proto */ +static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *, PyObject *, PyObject *); + +/* SwapException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSwap(type, value, tb) __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* Import.proto */ +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); + +/* PyFunctionFastCall.proto */ +#if CYTHON_FAST_PYCALL +#define __Pyx_PyFunction_FastCall(func, args, nargs)\ + __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL) +#if 1 || PY_VERSION_HEX < 0x030600B1 +static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs); +#else +#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs) +#endif +#endif + +/* PyCFunctionFastCall.proto */ +#if CYTHON_FAST_PYCCALL +static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs); +#else +#define __Pyx_PyCFunction_FastCall(func, args, nargs) (assert(0), NULL) +#endif + +/* GetItemInt.proto */ +#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\ + (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\ + __Pyx_GetItemInt_Generic(o, to_py_func(i)))) +#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j); +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, + int is_list, int wraparound, int boundscheck); + +static CYTHON_UNUSED int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/ +/* ListCompAppend.proto */ +#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS +static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) { + PyListObject* L = (PyListObject*) list; + Py_ssize_t len = Py_SIZE(list); + if (likely(L->allocated > len)) { + Py_INCREF(x); + PyList_SET_ITEM(list, len, x); + Py_SIZE(list) = len+1; + return 0; + } + return PyList_Append(list, x); +} +#else +#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x) +#endif + +/* PyIntBinop.proto */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, long intval, int inplace); +#else +#define __Pyx_PyInt_AddObjC(op1, op2, intval, inplace)\ + (inplace ? PyNumber_InPlaceAdd(op1, op2) : PyNumber_Add(op1, op2)) +#endif + +/* ListExtend.proto */ +static CYTHON_INLINE int __Pyx_PyList_Extend(PyObject* L, PyObject* v) { +#if CYTHON_COMPILING_IN_CPYTHON + PyObject* none = _PyList_Extend((PyListObject*)L, v); + if (unlikely(!none)) + return -1; + Py_DECREF(none); + return 0; +#else + return PyList_SetSlice(L, PY_SSIZE_T_MAX, PY_SSIZE_T_MAX, v); +#endif +} + +/* ListAppend.proto */ +#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS +static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) { + PyListObject* L = (PyListObject*) list; + Py_ssize_t len = Py_SIZE(list); + if (likely(L->allocated > len) & likely(len > (L->allocated >> 1))) { + Py_INCREF(x); + PyList_SET_ITEM(list, len, x); + Py_SIZE(list) = len+1; + return 0; + } + return PyList_Append(list, x); +} +#else +#define __Pyx_PyList_Append(L,x) PyList_Append(L,x) +#endif + +/* ForceInitThreads.proto */ +#ifndef __PYX_FORCE_INIT_THREADS + #define __PYX_FORCE_INIT_THREADS 0 +#endif + +/* WriteUnraisableException.proto */ +static void __Pyx_WriteUnraisable(const char *name, int clineno, + int lineno, const char *filename, + int full_traceback, int nogil); + +/* PyObjectCallMethO.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg); +#endif + +/* PyObjectCallOneArg.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg); + +/* ImportFrom.proto */ +static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name); + +/* HasAttr.proto */ +static CYTHON_INLINE int __Pyx_HasAttr(PyObject *, PyObject *); + +/* SetVTable.proto */ +static int __Pyx_SetVtable(PyObject *dict, void *vtable); + +/* SetupReduce.proto */ +static int __Pyx_setup_reduce(PyObject* type_obj); + +/* CLineInTraceback.proto */ +static int __Pyx_CLineForTraceback(int c_line); + +/* CodeObjectCache.proto */ +typedef struct { + PyCodeObject* code_object; + int code_line; +} __Pyx_CodeObjectCacheEntry; +struct __Pyx_CodeObjectCache { + int count; + int max_count; + __Pyx_CodeObjectCacheEntry* entries; +}; +static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); +static PyCodeObject *__pyx_find_code_object(int code_line); +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); + +/* AddTraceback.proto */ +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename); + +#if PY_MAJOR_VERSION < 3 + static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags); + static void __Pyx_ReleaseBuffer(Py_buffer *view); +#else + #define __Pyx_GetBuffer PyObject_GetBuffer + #define __Pyx_ReleaseBuffer PyBuffer_Release +#endif + + +/* BufferStructDeclare.proto */ +typedef struct { + Py_ssize_t shape, strides, suboffsets; +} __Pyx_Buf_DimInfo; +typedef struct { + size_t refcount; + Py_buffer pybuffer; +} __Pyx_Buffer; +typedef struct { + __Pyx_Buffer *rcbuffer; + char *data; + __Pyx_Buf_DimInfo diminfo[8]; +} __Pyx_LocalBuf_ND; + +/* None.proto */ +static Py_ssize_t __Pyx_zeros[] = {0, 0, 0, 0, 0, 0, 0, 0}; +static Py_ssize_t __Pyx_minusones[] = {-1, -1, -1, -1, -1, -1, -1, -1}; + +/* MemviewSliceIsContig.proto */ +static int __pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, + char order, int ndim); + +/* OverlappingSlices.proto */ +static int __pyx_slices_overlap(__Pyx_memviewslice *slice1, + __Pyx_memviewslice *slice2, + int ndim, size_t itemsize); + +/* Capsule.proto */ +static CYTHON_INLINE PyObject *__pyx_capsule_create(void *p, const char *sig); + +/* TypeInfoCompare.proto */ +static int __pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b); + +/* MemviewSliceValidateAndInit.proto */ +static int __Pyx_ValidateAndInit_memviewslice( + int *axes_specs, + int c_or_f_flag, + int buf_flags, + int ndim, + __Pyx_TypeInfo *dtype, + __Pyx_BufFmt_StackElem stack[], + __Pyx_memviewslice *memviewslice, + PyObject *original_obj); + +/* ObjectToMemviewSlice.proto */ +static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_double(PyObject *); + +/* ObjectToMemviewSlice.proto */ +static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value); + +/* MemviewDtypeToObject.proto */ +static CYTHON_INLINE PyObject *__pyx_memview_get_double(const char *itemp); +static CYTHON_INLINE int __pyx_memview_set_double(const char *itemp, PyObject *obj); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value); + +/* RealImag.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #define __Pyx_CREAL(z) ((z).real()) + #define __Pyx_CIMAG(z) ((z).imag()) + #else + #define __Pyx_CREAL(z) (__real__(z)) + #define __Pyx_CIMAG(z) (__imag__(z)) + #endif +#else + #define __Pyx_CREAL(z) ((z).real) + #define __Pyx_CIMAG(z) ((z).imag) +#endif +#if defined(__cplusplus) && CYTHON_CCOMPLEX\ + && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103) + #define __Pyx_SET_CREAL(z,x) ((z).real(x)) + #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) +#else + #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) + #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_float(a, b) ((a)==(b)) + #define __Pyx_c_sum_float(a, b) ((a)+(b)) + #define __Pyx_c_diff_float(a, b) ((a)-(b)) + #define __Pyx_c_prod_float(a, b) ((a)*(b)) + #define __Pyx_c_quot_float(a, b) ((a)/(b)) + #define __Pyx_c_neg_float(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_float(z) ((z)==(float)0) + #define __Pyx_c_conj_float(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_float(z) (::std::abs(z)) + #define __Pyx_c_pow_float(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_float(z) ((z)==0) + #define __Pyx_c_conj_float(z) (conjf(z)) + #if 1 + #define __Pyx_c_abs_float(z) (cabsf(z)) + #define __Pyx_c_pow_float(a, b) (cpowf(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex); + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex); + #endif +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_double(a, b) ((a)==(b)) + #define __Pyx_c_sum_double(a, b) ((a)+(b)) + #define __Pyx_c_diff_double(a, b) ((a)-(b)) + #define __Pyx_c_prod_double(a, b) ((a)*(b)) + #define __Pyx_c_quot_double(a, b) ((a)/(b)) + #define __Pyx_c_neg_double(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_double(z) ((z)==(double)0) + #define __Pyx_c_conj_double(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (::std::abs(z)) + #define __Pyx_c_pow_double(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_double(z) ((z)==0) + #define __Pyx_c_conj_double(z) (conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (cabs(z)) + #define __Pyx_c_pow_double(a, b) (cpow(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex); + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex); + #endif +#endif + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value); + +/* MemviewSliceCopyTemplate.proto */ +static __Pyx_memviewslice +__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs, + const char *mode, int ndim, + size_t sizeof_dtype, int contig_flag, + int dtype_is_object); + +/* CIntFromPy.proto */ +static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); + +/* CheckBinaryVersion.proto */ +static int __Pyx_check_binary_version(void); + +/* PyIdentifierFromString.proto */ +#if !defined(__Pyx_PyIdentifier_FromString) +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s) +#else + #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s) +#endif +#endif + +/* ModuleImport.proto */ +static PyObject *__Pyx_ImportModule(const char *name); + +/* TypeImport.proto */ +static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict); + +/* InitStrings.proto */ +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); + +static PyObject *__pyx_array_get_memview(struct __pyx_array_obj *__pyx_v_self); /* proto*/ +static char *__pyx_memoryview_get_item_pointer(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto*/ +static PyObject *__pyx_memoryview_is_slice(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj); /* proto*/ +static PyObject *__pyx_memoryview_setitem_slice_assignment(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_dst, PyObject *__pyx_v_src); /* proto*/ +static PyObject *__pyx_memoryview_setitem_slice_assign_scalar(struct __pyx_memoryview_obj *__pyx_v_self, struct __pyx_memoryview_obj *__pyx_v_dst, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryview_setitem_indexed(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryview_convert_item_to_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/ +static PyObject *__pyx_memoryview_assign_item_from_object(struct __pyx_memoryview_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/ +static PyObject *__pyx_memoryviewslice_convert_item_to_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp); /* proto*/ +static PyObject *__pyx_memoryviewslice_assign_item_from_object(struct __pyx_memoryviewslice_obj *__pyx_v_self, char *__pyx_v_itemp, PyObject *__pyx_v_value); /* proto*/ + +/* Module declarations from 'cpython.buffer' */ + +/* Module declarations from 'libc.string' */ + +/* Module declarations from 'libc.stdio' */ + +/* Module declarations from '__builtin__' */ + +/* Module declarations from 'cpython.type' */ +static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0; + +/* Module declarations from 'cpython' */ + +/* Module declarations from 'cpython.object' */ + +/* Module declarations from 'cpython.ref' */ + +/* Module declarations from 'libc.stdlib' */ + +/* Module declarations from 'numpy' */ + +/* Module declarations from 'numpy' */ +static PyTypeObject *__pyx_ptype_5numpy_dtype = 0; +static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0; +static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0; +static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0; +static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0; +static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/ + +/* Module declarations from 'Orange.distance._distance' */ +static PyTypeObject *__pyx_array_type = 0; +static PyTypeObject *__pyx_MemviewEnum_type = 0; +static PyTypeObject *__pyx_memoryview_type = 0; +static PyTypeObject *__pyx_memoryviewslice_type = 0; +static PyObject *generic = 0; +static PyObject *strided = 0; +static PyObject *indirect = 0; +static PyObject *contiguous = 0; +static PyObject *indirect_contiguous = 0; +static int __pyx_memoryview_thread_locks_used; +static PyThread_type_lock __pyx_memoryview_thread_locks[8]; +static void __pyx_f_6Orange_8distance_9_distance_lower_to_symmetric(__Pyx_memviewslice, int __pyx_skip_dispatch); /*proto*/ +static struct __pyx_array_obj *__pyx_array_new(PyObject *, Py_ssize_t, char *, char *, char *); /*proto*/ +static void *__pyx_align_pointer(void *, size_t); /*proto*/ +static PyObject *__pyx_memoryview_new(PyObject *, int, int, __Pyx_TypeInfo *); /*proto*/ +static CYTHON_INLINE int __pyx_memoryview_check(PyObject *); /*proto*/ +static PyObject *_unellipsify(PyObject *, int); /*proto*/ +static PyObject *assert_direct_dimensions(Py_ssize_t *, int); /*proto*/ +static struct __pyx_memoryview_obj *__pyx_memview_slice(struct __pyx_memoryview_obj *, PyObject *); /*proto*/ +static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int *, Py_ssize_t, Py_ssize_t, Py_ssize_t, int, int, int, int); /*proto*/ +static char *__pyx_pybuffer_index(Py_buffer *, char *, Py_ssize_t, Py_ssize_t); /*proto*/ +static int __pyx_memslice_transpose(__Pyx_memviewslice *); /*proto*/ +static PyObject *__pyx_memoryview_fromslice(__Pyx_memviewslice, int, PyObject *(*)(char *), int (*)(char *, PyObject *), int); /*proto*/ +static __Pyx_memviewslice *__pyx_memoryview_get_slice_from_memoryview(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static void __pyx_memoryview_slice_copy(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static PyObject *__pyx_memoryview_copy_object(struct __pyx_memoryview_obj *); /*proto*/ +static PyObject *__pyx_memoryview_copy_object_from_slice(struct __pyx_memoryview_obj *, __Pyx_memviewslice *); /*proto*/ +static Py_ssize_t abs_py_ssize_t(Py_ssize_t); /*proto*/ +static char __pyx_get_best_slice_order(__Pyx_memviewslice *, int); /*proto*/ +static void _copy_strided_to_strided(char *, Py_ssize_t *, char *, Py_ssize_t *, Py_ssize_t *, Py_ssize_t *, int, size_t); /*proto*/ +static void copy_strided_to_strided(__Pyx_memviewslice *, __Pyx_memviewslice *, int, size_t); /*proto*/ +static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *, int); /*proto*/ +static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *, Py_ssize_t *, Py_ssize_t, int, char); /*proto*/ +static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *, __Pyx_memviewslice *, char, int); /*proto*/ +static int __pyx_memoryview_err_extents(int, Py_ssize_t, Py_ssize_t); /*proto*/ +static int __pyx_memoryview_err_dim(PyObject *, char *, int); /*proto*/ +static int __pyx_memoryview_err(PyObject *, char *); /*proto*/ +static int __pyx_memoryview_copy_contents(__Pyx_memviewslice, __Pyx_memviewslice, int, int, int); /*proto*/ +static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *, int, int); /*proto*/ +static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *, int, int, int); /*proto*/ +static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/ +static void __pyx_memoryview_refcount_objects_in_slice(char *, Py_ssize_t *, Py_ssize_t *, int, int); /*proto*/ +static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *, int, size_t, void *, int); /*proto*/ +static void __pyx_memoryview__slice_assign_scalar(char *, Py_ssize_t *, Py_ssize_t *, int, size_t, void *); /*proto*/ +static PyObject *__pyx_unpickle_Enum__set_state(struct __pyx_MemviewEnum_obj *, PyObject *); /*proto*/ +static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_float64_t = { "float64_t", NULL, sizeof(__pyx_t_5numpy_float64_t), { 0 }, 0, 'R', 0, 0 }; +static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_int8_t = { "int8_t", NULL, sizeof(__pyx_t_5numpy_int8_t), { 0 }, 0, IS_UNSIGNED(__pyx_t_5numpy_int8_t) ? 'U' : 'I', IS_UNSIGNED(__pyx_t_5numpy_int8_t), 0 }; +static __Pyx_TypeInfo __Pyx_TypeInfo_double = { "double", NULL, sizeof(double), { 0 }, 0, 'R', 0, 0 }; +#define __Pyx_MODULE_NAME "Orange.distance._distance" +int __pyx_module_is_main_Orange__distance___distance = 0; + +/* Implementation of 'Orange.distance._distance' */ +static PyObject *__pyx_builtin_range; +static PyObject *__pyx_builtin_ValueError; +static PyObject *__pyx_builtin_RuntimeError; +static PyObject *__pyx_builtin_ImportError; +static PyObject *__pyx_builtin_MemoryError; +static PyObject *__pyx_builtin_enumerate; +static PyObject *__pyx_builtin_TypeError; +static PyObject *__pyx_builtin_Ellipsis; +static PyObject *__pyx_builtin_id; +static PyObject *__pyx_builtin_IndexError; +static const char __pyx_k_O[] = "O"; +static const char __pyx_k_c[] = "c"; +static const char __pyx_k_d[] = "d"; +static const char __pyx_k_x[] = "x"; +static const char __pyx_k_id[] = "id"; +static const char __pyx_k_np[] = "np"; +static const char __pyx_k_ps[] = "ps"; +static const char __pyx_k_x1[] = "x1"; +static const char __pyx_k_x2[] = "x2"; +static const char __pyx_k_col[] = "col"; +static const char __pyx_k_new[] = "__new__"; +static const char __pyx_k_obj[] = "obj"; +static const char __pyx_k_row[] = "row"; +static const char __pyx_k_val[] = "val"; +static const char __pyx_k_base[] = "base"; +static const char __pyx_k_col1[] = "col1"; +static const char __pyx_k_col2[] = "col2"; +static const char __pyx_k_dict[] = "__dict__"; +static const char __pyx_k_int8[] = "int8"; +static const char __pyx_k_mads[] = "mads"; +static const char __pyx_k_main[] = "__main__"; +static const char __pyx_k_mode[] = "mode"; +static const char __pyx_k_name[] = "name"; +static const char __pyx_k_nans[] = "nans"; +static const char __pyx_k_ndim[] = "ndim"; +static const char __pyx_k_pack[] = "pack"; +static const char __pyx_k_row1[] = "row1"; +static const char __pyx_k_row2[] = "row2"; +static const char __pyx_k_size[] = "size"; +static const char __pyx_k_step[] = "step"; +static const char __pyx_k_stop[] = "stop"; +static const char __pyx_k_test[] = "__test__"; +static const char __pyx_k_val1[] = "val1"; +static const char __pyx_k_val2[] = "val2"; +static const char __pyx_k_vars[] = "vars"; +static const char __pyx_k_ASCII[] = "ASCII"; +static const char __pyx_k_class[] = "__class__"; +static const char __pyx_k_dtype[] = "dtype"; +static const char __pyx_k_error[] = "error"; +static const char __pyx_k_flags[] = "flags"; +static const char __pyx_k_ival1[] = "ival1"; +static const char __pyx_k_ival2[] = "ival2"; +static const char __pyx_k_means[] = "means"; +static const char __pyx_k_nans1[] = "nans1"; +static const char __pyx_k_nans2[] = "nans2"; +static const char __pyx_k_numpy[] = "numpy"; +static const char __pyx_k_range[] = "range"; +static const char __pyx_k_shape[] = "shape"; +static const char __pyx_k_start[] = "start"; +static const char __pyx_k_union[] = "union"; +static const char __pyx_k_zeros[] = "zeros"; +static const char __pyx_k_encode[] = "encode"; +static const char __pyx_k_format[] = "format"; +static const char __pyx_k_import[] = "__import__"; +static const char __pyx_k_in_any[] = "in_any"; +static const char __pyx_k_n_cols[] = "n_cols"; +static const char __pyx_k_n_rows[] = "n_rows"; +static const char __pyx_k_name_2[] = "__name__"; +static const char __pyx_k_pickle[] = "pickle"; +static const char __pyx_k_result[] = "result"; +static const char __pyx_k_struct[] = "struct"; +static const char __pyx_k_unpack[] = "unpack"; +static const char __pyx_k_update[] = "update"; +static const char __pyx_k_fortran[] = "fortran"; +static const char __pyx_k_in_both[] = "in_both"; +static const char __pyx_k_medians[] = "medians"; +static const char __pyx_k_memview[] = "memview"; +static const char __pyx_k_n_rows1[] = "n_rows1"; +static const char __pyx_k_n_rows2[] = "n_rows2"; +static const char __pyx_k_nonnans[] = "nonnans"; +static const char __pyx_k_Ellipsis[] = "Ellipsis"; +static const char __pyx_k_in1_unk2[] = "in1_unk2"; +static const char __pyx_k_itemsize[] = "itemsize"; +static const char __pyx_k_nonzeros[] = "nonzeros"; +static const char __pyx_k_pyx_type[] = "__pyx_type"; +static const char __pyx_k_unk1_in2[] = "unk1_in2"; +static const char __pyx_k_TypeError[] = "TypeError"; +static const char __pyx_k_distances[] = "distances"; +static const char __pyx_k_enumerate[] = "enumerate"; +static const char __pyx_k_nonzeros1[] = "nonzeros1"; +static const char __pyx_k_nonzeros2[] = "nonzeros2"; +static const char __pyx_k_normalize[] = "normalize"; +static const char __pyx_k_not1_unk2[] = "not1_unk2"; +static const char __pyx_k_p_nonzero[] = "p_nonzero"; +static const char __pyx_k_pyx_state[] = "__pyx_state"; +static const char __pyx_k_unk1_not2[] = "unk1_not2"; +static const char __pyx_k_unk1_unk2[] = "unk1_unk2"; +static const char __pyx_k_IndexError[] = "IndexError"; +static const char __pyx_k_ValueError[] = "ValueError"; +static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__"; +static const char __pyx_k_two_tables[] = "two_tables"; +static const char __pyx_k_ImportError[] = "ImportError"; +static const char __pyx_k_MemoryError[] = "MemoryError"; +static const char __pyx_k_PickleError[] = "PickleError"; +static const char __pyx_k_any_nan_row[] = "any_nan_row"; +static const char __pyx_k_RuntimeError[] = "RuntimeError"; +static const char __pyx_k_dist_missing[] = "dist_missing"; +static const char __pyx_k_intersection[] = "intersection"; +static const char __pyx_k_jaccard_cols[] = "jaccard_cols"; +static const char __pyx_k_jaccard_rows[] = "jaccard_rows"; +static const char __pyx_k_pyx_checksum[] = "__pyx_checksum"; +static const char __pyx_k_stringsource[] = "stringsource"; +static const char __pyx_k_dist_missing2[] = "dist_missing2"; +static const char __pyx_k_pyx_getbuffer[] = "__pyx_getbuffer"; +static const char __pyx_k_reduce_cython[] = "__reduce_cython__"; +static const char __pyx_k_manhattan_cols[] = "manhattan_cols"; +static const char __pyx_k_View_MemoryView[] = "View.MemoryView"; +static const char __pyx_k_allocate_buffer[] = "allocate_buffer"; +static const char __pyx_k_dtype_is_object[] = "dtype_is_object"; +static const char __pyx_k_setstate_cython[] = "__setstate_cython__"; +static const char __pyx_k_pyx_unpickle_Enum[] = "__pyx_unpickle_Enum"; +static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback"; +static const char __pyx_k_dist_missing2_cont[] = "dist_missing2_cont"; +static const char __pyx_k_fix_euclidean_cols[] = "fix_euclidean_cols"; +static const char __pyx_k_fix_euclidean_rows[] = "fix_euclidean_rows"; +static const char __pyx_k_fix_manhattan_rows[] = "fix_manhattan_rows"; +static const char __pyx_k_strided_and_direct[] = ""; +static const char __pyx_k_manhattan_rows_cont[] = "manhattan_rows_cont"; +static const char __pyx_k_strided_and_indirect[] = ""; +static const char __pyx_k_contiguous_and_direct[] = ""; +static const char __pyx_k_MemoryView_of_r_object[] = ""; +static const char __pyx_k_MemoryView_of_r_at_0x_x[] = ""; +static const char __pyx_k_contiguous_and_indirect[] = ""; +static const char __pyx_k_euclidean_rows_discrete[] = "euclidean_rows_discrete"; +static const char __pyx_k_Cannot_index_with_type_s[] = "Cannot index with type '%s'"; +static const char __pyx_k_Invalid_shape_in_axis_d_d[] = "Invalid shape in axis %d: %d."; +static const char __pyx_k_Orange_distance__distance[] = "Orange.distance._distance"; +static const char __pyx_k_itemsize_0_for_cython_array[] = "itemsize <= 0 for cython.array"; +static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous"; +static const char __pyx_k_Orange_distance__distance_pyx[] = "Orange/distance/_distance.pyx"; +static const char __pyx_k_fix_euclidean_cols_normalized[] = "fix_euclidean_cols_normalized"; +static const char __pyx_k_fix_euclidean_rows_normalized[] = "fix_euclidean_rows_normalized"; +static const char __pyx_k_fix_manhattan_rows_normalized[] = "fix_manhattan_rows_normalized"; +static const char __pyx_k_unable_to_allocate_array_data[] = "unable to allocate array data."; +static const char __pyx_k_strided_and_direct_or_indirect[] = ""; +static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import"; +static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)"; +static const char __pyx_k_Buffer_view_does_not_expose_stri[] = "Buffer view does not expose strides"; +static const char __pyx_k_Can_only_create_a_buffer_that_is[] = "Can only create a buffer that is contiguous in memory."; +static const char __pyx_k_Empty_shape_tuple_for_cython_arr[] = "Empty shape tuple for cython.array"; +static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd"; +static const char __pyx_k_Incompatible_checksums_s_vs_0xb0[] = "Incompatible checksums (%s vs 0xb068931 = (name))"; +static const char __pyx_k_Indirect_dimensions_not_supporte[] = "Indirect dimensions not supported"; +static const char __pyx_k_Invalid_mode_expected_c_or_fortr[] = "Invalid mode, expected 'c' or 'fortran', got %s"; +static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported"; +static const char __pyx_k_Out_of_bounds_on_buffer_access_a[] = "Out of bounds on buffer access (axis %d)"; +static const char __pyx_k_Unable_to_convert_item_to_object[] = "Unable to convert item to object"; +static const char __pyx_k_got_differing_extents_in_dimensi[] = "got differing extents in dimension %d (got %d and %d)"; +static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous"; +static const char __pyx_k_no_default___reduce___due_to_non[] = "no default __reduce__ due to non-trivial __cinit__"; +static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import"; +static const char __pyx_k_unable_to_allocate_shape_and_str[] = "unable to allocate shape and strides."; +static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short."; +static PyObject *__pyx_n_s_ASCII; +static PyObject *__pyx_kp_s_Buffer_view_does_not_expose_stri; +static PyObject *__pyx_kp_s_Can_only_create_a_buffer_that_is; +static PyObject *__pyx_kp_s_Cannot_index_with_type_s; +static PyObject *__pyx_n_s_Ellipsis; +static PyObject *__pyx_kp_s_Empty_shape_tuple_for_cython_arr; +static PyObject *__pyx_kp_u_Format_string_allocated_too_shor; +static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2; +static PyObject *__pyx_n_s_ImportError; +static PyObject *__pyx_kp_s_Incompatible_checksums_s_vs_0xb0; +static PyObject *__pyx_n_s_IndexError; +static PyObject *__pyx_kp_s_Indirect_dimensions_not_supporte; +static PyObject *__pyx_kp_s_Invalid_mode_expected_c_or_fortr; +static PyObject *__pyx_kp_s_Invalid_shape_in_axis_d_d; +static PyObject *__pyx_n_s_MemoryError; +static PyObject *__pyx_kp_s_MemoryView_of_r_at_0x_x; +static PyObject *__pyx_kp_s_MemoryView_of_r_object; +static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor; +static PyObject *__pyx_n_b_O; +static PyObject *__pyx_n_s_Orange_distance__distance; +static PyObject *__pyx_kp_s_Orange_distance__distance_pyx; +static PyObject *__pyx_kp_s_Out_of_bounds_on_buffer_access_a; +static PyObject *__pyx_n_s_PickleError; +static PyObject *__pyx_n_s_RuntimeError; +static PyObject *__pyx_n_s_TypeError; +static PyObject *__pyx_kp_s_Unable_to_convert_item_to_object; +static PyObject *__pyx_n_s_ValueError; +static PyObject *__pyx_n_s_View_MemoryView; +static PyObject *__pyx_n_s_allocate_buffer; +static PyObject *__pyx_n_s_any_nan_row; +static PyObject *__pyx_n_s_base; +static PyObject *__pyx_n_s_c; +static PyObject *__pyx_n_u_c; +static PyObject *__pyx_n_s_class; +static PyObject *__pyx_n_s_cline_in_traceback; +static PyObject *__pyx_n_s_col; +static PyObject *__pyx_n_s_col1; +static PyObject *__pyx_n_s_col2; +static PyObject *__pyx_kp_s_contiguous_and_direct; +static PyObject *__pyx_kp_s_contiguous_and_indirect; +static PyObject *__pyx_n_s_d; +static PyObject *__pyx_n_s_dict; +static PyObject *__pyx_n_s_dist_missing; +static PyObject *__pyx_n_s_dist_missing2; +static PyObject *__pyx_n_s_dist_missing2_cont; +static PyObject *__pyx_n_s_distances; +static PyObject *__pyx_n_s_dtype; +static PyObject *__pyx_n_s_dtype_is_object; +static PyObject *__pyx_n_s_encode; +static PyObject *__pyx_n_s_enumerate; +static PyObject *__pyx_n_s_error; +static PyObject *__pyx_n_s_euclidean_rows_discrete; +static PyObject *__pyx_n_s_fix_euclidean_cols; +static PyObject *__pyx_n_s_fix_euclidean_cols_normalized; +static PyObject *__pyx_n_s_fix_euclidean_rows; +static PyObject *__pyx_n_s_fix_euclidean_rows_normalized; +static PyObject *__pyx_n_s_fix_manhattan_rows; +static PyObject *__pyx_n_s_fix_manhattan_rows_normalized; +static PyObject *__pyx_n_s_flags; +static PyObject *__pyx_n_s_format; +static PyObject *__pyx_n_s_fortran; +static PyObject *__pyx_n_u_fortran; +static PyObject *__pyx_kp_s_got_differing_extents_in_dimensi; +static PyObject *__pyx_n_s_id; +static PyObject *__pyx_n_s_import; +static PyObject *__pyx_n_s_in1_unk2; +static PyObject *__pyx_n_s_in_any; +static PyObject *__pyx_n_s_in_both; +static PyObject *__pyx_n_s_int8; +static PyObject *__pyx_n_s_intersection; +static PyObject *__pyx_n_s_itemsize; +static PyObject *__pyx_kp_s_itemsize_0_for_cython_array; +static PyObject *__pyx_n_s_ival1; +static PyObject *__pyx_n_s_ival2; +static PyObject *__pyx_n_s_jaccard_cols; +static PyObject *__pyx_n_s_jaccard_rows; +static PyObject *__pyx_n_s_mads; +static PyObject *__pyx_n_s_main; +static PyObject *__pyx_n_s_manhattan_cols; +static PyObject *__pyx_n_s_manhattan_rows_cont; +static PyObject *__pyx_n_s_means; +static PyObject *__pyx_n_s_medians; +static PyObject *__pyx_n_s_memview; +static PyObject *__pyx_n_s_mode; +static PyObject *__pyx_n_s_n_cols; +static PyObject *__pyx_n_s_n_rows; +static PyObject *__pyx_n_s_n_rows1; +static PyObject *__pyx_n_s_n_rows2; +static PyObject *__pyx_n_s_name; +static PyObject *__pyx_n_s_name_2; +static PyObject *__pyx_n_s_nans; +static PyObject *__pyx_n_s_nans1; +static PyObject *__pyx_n_s_nans2; +static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous; +static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou; +static PyObject *__pyx_n_s_ndim; +static PyObject *__pyx_n_s_new; +static PyObject *__pyx_kp_s_no_default___reduce___due_to_non; +static PyObject *__pyx_n_s_nonnans; +static PyObject *__pyx_n_s_nonzeros; +static PyObject *__pyx_n_s_nonzeros1; +static PyObject *__pyx_n_s_nonzeros2; +static PyObject *__pyx_n_s_normalize; +static PyObject *__pyx_n_s_not1_unk2; +static PyObject *__pyx_n_s_np; +static PyObject *__pyx_n_s_numpy; +static PyObject *__pyx_kp_s_numpy_core_multiarray_failed_to; +static PyObject *__pyx_kp_s_numpy_core_umath_failed_to_impor; +static PyObject *__pyx_n_s_obj; +static PyObject *__pyx_n_s_p_nonzero; +static PyObject *__pyx_n_s_pack; +static PyObject *__pyx_n_s_pickle; +static PyObject *__pyx_n_s_ps; +static PyObject *__pyx_n_s_pyx_checksum; +static PyObject *__pyx_n_s_pyx_getbuffer; +static PyObject *__pyx_n_s_pyx_state; +static PyObject *__pyx_n_s_pyx_type; +static PyObject *__pyx_n_s_pyx_unpickle_Enum; +static PyObject *__pyx_n_s_pyx_vtable; +static PyObject *__pyx_n_s_range; +static PyObject *__pyx_n_s_reduce_cython; +static PyObject *__pyx_n_s_result; +static PyObject *__pyx_n_s_row; +static PyObject *__pyx_n_s_row1; +static PyObject *__pyx_n_s_row2; +static PyObject *__pyx_n_s_setstate_cython; +static PyObject *__pyx_n_s_shape; +static PyObject *__pyx_n_s_size; +static PyObject *__pyx_n_s_start; +static PyObject *__pyx_n_s_step; +static PyObject *__pyx_n_s_stop; +static PyObject *__pyx_kp_s_strided_and_direct; +static PyObject *__pyx_kp_s_strided_and_direct_or_indirect; +static PyObject *__pyx_kp_s_strided_and_indirect; +static PyObject *__pyx_kp_s_stringsource; +static PyObject *__pyx_n_s_struct; +static PyObject *__pyx_n_s_test; +static PyObject *__pyx_n_s_two_tables; +static PyObject *__pyx_kp_s_unable_to_allocate_array_data; +static PyObject *__pyx_kp_s_unable_to_allocate_shape_and_str; +static PyObject *__pyx_n_s_union; +static PyObject *__pyx_n_s_unk1_in2; +static PyObject *__pyx_n_s_unk1_not2; +static PyObject *__pyx_n_s_unk1_unk2; +static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd; +static PyObject *__pyx_n_s_unpack; +static PyObject *__pyx_n_s_update; +static PyObject *__pyx_n_s_val; +static PyObject *__pyx_n_s_val1; +static PyObject *__pyx_n_s_val2; +static PyObject *__pyx_n_s_vars; +static PyObject *__pyx_n_s_x; +static PyObject *__pyx_n_s_x1; +static PyObject *__pyx_n_s_x2; +static PyObject *__pyx_n_s_zeros; +static PyObject *__pyx_pf_6Orange_8distance_9_distance_lower_to_symmetric(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_distances); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_2euclidean_rows_discrete(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, __Pyx_memviewslice __pyx_v_dist_missing, PyArrayObject *__pyx_v_dist_missing2, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_4fix_euclidean_rows(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, PyArrayObject *__pyx_v_means, PyArrayObject *__pyx_v_vars, PyArrayObject *__pyx_v_dist_missing2, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_6fix_euclidean_rows_normalized(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, CYTHON_UNUSED PyArrayObject *__pyx_v_means, CYTHON_UNUSED PyArrayObject *__pyx_v_vars, PyArrayObject *__pyx_v_dist_missing2, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_8fix_euclidean_cols(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x, __Pyx_memviewslice __pyx_v_means, __Pyx_memviewslice __pyx_v_vars); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_10fix_euclidean_cols_normalized(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_means, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_vars); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_12manhattan_rows_cont(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_14fix_manhattan_rows(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, PyArrayObject *__pyx_v_medians, PyArrayObject *__pyx_v_mads, PyArrayObject *__pyx_v_dist_missing2_cont, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_16fix_manhattan_rows_normalized(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_distances, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_18manhattan_cols(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_medians, PyArrayObject *__pyx_v_mads, char __pyx_v_normalize); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_20p_nonzero(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_22any_nan_row(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_24jaccard_rows(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_nonzeros1, PyArrayObject *__pyx_v_nonzeros2, PyArrayObject *__pyx_v_x1, PyArrayObject *__pyx_v_x2, PyArrayObject *__pyx_v_nans1, PyArrayObject *__pyx_v_nans2, PyArrayObject *__pyx_v_ps, char __pyx_v_two_tables); /* proto */ +static PyObject *__pyx_pf_6Orange_8distance_9_distance_26jaccard_cols(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_nonzeros, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_nans, PyArrayObject *__pyx_v_ps); /* proto */ +static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */ +static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */ +static void __pyx_array___pyx_pf_15View_dot_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_5array_7memview___get__(struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_6__getattr__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_attr); /* proto */ +static PyObject *__pyx_array___pyx_pf_15View_dot_MemoryView_5array_8__getitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item); /* proto */ +static int __pyx_array___pyx_pf_15View_dot_MemoryView_5array_10__setitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item, PyObject *__pyx_v_value); /* proto */ +static PyObject *__pyx_pf___pyx_array___reduce_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_array_2__setstate_cython__(CYTHON_UNUSED struct __pyx_array_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static int __pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum___init__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v_name); /* proto */ +static PyObject *__pyx_MemviewEnum___pyx_pf_15View_dot_MemoryView_4Enum_2__repr__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_MemviewEnum___reduce_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_MemviewEnum_2__setstate_cython__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v___pyx_state); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview___cinit__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj, int __pyx_v_flags, int __pyx_v_dtype_is_object); /* proto */ +static void __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_2__dealloc__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_4__getitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_6__setitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto */ +static int __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_8__getbuffer__(struct __pyx_memoryview_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_1T___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4base___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_5shape___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_7strides___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_10suboffsets___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4ndim___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_8itemsize___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_6nbytes___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_10memoryview_4size___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static Py_ssize_t __pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_10__len__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_12__repr__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_14__str__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_16is_c_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_18is_f_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_20copy(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_memoryview___pyx_pf_15View_dot_MemoryView_10memoryview_22copy_fortran(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryview___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryview_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryview_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static void __pyx_memoryviewslice___pyx_pf_15View_dot_MemoryView_16_memoryviewslice___dealloc__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView_16_memoryviewslice_4base___get__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryviewslice___reduce_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */ +static PyObject *__pyx_pf___pyx_memoryviewslice_2__setstate_cython__(CYTHON_UNUSED struct __pyx_memoryviewslice_obj *__pyx_v_self, CYTHON_UNUSED PyObject *__pyx_v___pyx_state); /* proto */ +static PyObject *__pyx_pf_15View_dot_MemoryView___pyx_unpickle_Enum(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v___pyx_type, long __pyx_v___pyx_checksum, PyObject *__pyx_v___pyx_state); /* proto */ +static PyObject *__pyx_tp_new_array(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/ +static PyObject *__pyx_int_0; +static PyObject *__pyx_int_1; +static PyObject *__pyx_int_184977713; +static PyObject *__pyx_int_neg_1; +static PyObject *__pyx_tuple_; +static PyObject *__pyx_tuple__2; +static PyObject *__pyx_tuple__3; +static PyObject *__pyx_tuple__4; +static PyObject *__pyx_tuple__5; +static PyObject *__pyx_tuple__6; +static PyObject *__pyx_tuple__7; +static PyObject *__pyx_tuple__8; +static PyObject *__pyx_tuple__9; +static PyObject *__pyx_slice__23; +static PyObject *__pyx_slice__24; +static PyObject *__pyx_slice__25; +static PyObject *__pyx_tuple__10; +static PyObject *__pyx_tuple__11; +static PyObject *__pyx_tuple__12; +static PyObject *__pyx_tuple__13; +static PyObject *__pyx_tuple__14; +static PyObject *__pyx_tuple__15; +static PyObject *__pyx_tuple__16; +static PyObject *__pyx_tuple__17; +static PyObject *__pyx_tuple__18; +static PyObject *__pyx_tuple__19; +static PyObject *__pyx_tuple__20; +static PyObject *__pyx_tuple__21; +static PyObject *__pyx_tuple__22; 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start += shape # <<<<<<<<<<<<<< + * if not 0 <= start < shape: + * _err_dim(IndexError, "Index out of bounds (axis %d)", dim) + */ + __pyx_v_start = (__pyx_v_start + __pyx_v_shape); + + /* "View.MemoryView":815 + * if not is_slice: + * + * if start < 0: # <<<<<<<<<<<<<< + * start += shape + * if not 0 <= start < shape: + */ + } + + /* "View.MemoryView":817 + * if start < 0: + * start += shape + * if not 0 <= start < shape: # <<<<<<<<<<<<<< + * _err_dim(IndexError, "Index out of bounds (axis %d)", dim) + * else: + */ + __pyx_t_1 = (0 <= __pyx_v_start); + if (__pyx_t_1) { + __pyx_t_1 = (__pyx_v_start < __pyx_v_shape); + } + __pyx_t_2 = ((!(__pyx_t_1 != 0)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":818 + * start += shape + * if not 0 <= start < shape: + * _err_dim(IndexError, "Index out of bounds (axis %d)", dim) # <<<<<<<<<<<<<< + * else: + * + */ + __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_IndexError, ((char *)"Index out of bounds (axis %d)"), __pyx_v_dim); if (unlikely(__pyx_t_3 == -1)) __PYX_ERR(2, 818, __pyx_L1_error) + + /* "View.MemoryView":817 + * if start < 0: + * start += shape + * if not 0 <= start < shape: # <<<<<<<<<<<<<< + * _err_dim(IndexError, "Index out of bounds (axis %d)", dim) + * else: + */ + } + + /* "View.MemoryView":813 + * cdef bint negative_step + * + * if not is_slice: # <<<<<<<<<<<<<< + * + * if start < 0: + */ + goto __pyx_L3; + } + + /* "View.MemoryView":821 + * else: + * + * negative_step = have_step != 0 and step < 0 # <<<<<<<<<<<<<< + * + * if have_step and step == 0: + */ + /*else*/ { + __pyx_t_1 = ((__pyx_v_have_step != 0) != 0); + if (__pyx_t_1) { + } else { + __pyx_t_2 = __pyx_t_1; + goto __pyx_L6_bool_binop_done; + } + __pyx_t_1 = ((__pyx_v_step < 0) != 0); + __pyx_t_2 = __pyx_t_1; + __pyx_L6_bool_binop_done:; + __pyx_v_negative_step = __pyx_t_2; + + /* "View.MemoryView":823 + * negative_step = have_step != 0 and step < 0 + * + * if have_step and step == 0: # <<<<<<<<<<<<<< + * _err_dim(ValueError, "Step may not be zero (axis %d)", dim) + * + */ + __pyx_t_1 = (__pyx_v_have_step != 0); + if (__pyx_t_1) { + } else { + __pyx_t_2 = __pyx_t_1; + goto __pyx_L9_bool_binop_done; + } + __pyx_t_1 = ((__pyx_v_step == 0) != 0); + __pyx_t_2 = __pyx_t_1; + __pyx_L9_bool_binop_done:; + if (__pyx_t_2) { + + /* "View.MemoryView":824 + * + * if have_step and step == 0: + * _err_dim(ValueError, "Step may not be zero (axis %d)", dim) # <<<<<<<<<<<<<< + * + * + */ + __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_ValueError, ((char *)"Step may not be zero (axis %d)"), __pyx_v_dim); if (unlikely(__pyx_t_3 == -1)) __PYX_ERR(2, 824, __pyx_L1_error) + + /* "View.MemoryView":823 + * negative_step = have_step != 0 and step < 0 + * + * if have_step and step == 0: # <<<<<<<<<<<<<< + * _err_dim(ValueError, "Step may not be zero (axis %d)", dim) + * + */ + } + + /* "View.MemoryView":827 + * + * + * if have_start: # <<<<<<<<<<<<<< + * if start < 0: + * start += shape + */ + __pyx_t_2 = (__pyx_v_have_start != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":828 + * + * if have_start: + * if start < 0: # <<<<<<<<<<<<<< + * start += shape + * if start < 0: + */ + __pyx_t_2 = ((__pyx_v_start < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":829 + * if have_start: + * if start < 0: + * start += shape # <<<<<<<<<<<<<< + * if start < 0: + * start = 0 + */ + __pyx_v_start = (__pyx_v_start + __pyx_v_shape); + + /* "View.MemoryView":830 + * if start < 0: + * start += shape + * if start < 0: # <<<<<<<<<<<<<< + * start = 0 + * elif start >= shape: + */ + __pyx_t_2 = ((__pyx_v_start < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":831 + * start += shape + * if start < 0: + * start = 0 # <<<<<<<<<<<<<< + * elif start >= shape: + * if negative_step: + */ + __pyx_v_start = 0; + + /* "View.MemoryView":830 + * if start < 0: + * start += shape + * if start < 0: # <<<<<<<<<<<<<< + * start = 0 + * elif start >= shape: + */ + } + + /* "View.MemoryView":828 + * + * if have_start: + * if start < 0: # <<<<<<<<<<<<<< + * start += shape + * if start < 0: + */ + goto __pyx_L12; + } + + /* "View.MemoryView":832 + * if start < 0: + * start = 0 + * elif start >= shape: # <<<<<<<<<<<<<< + * if negative_step: + * start = shape - 1 + */ + __pyx_t_2 = ((__pyx_v_start >= __pyx_v_shape) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":833 + * start = 0 + * elif start >= shape: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + __pyx_t_2 = (__pyx_v_negative_step != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":834 + * elif start >= shape: + * if negative_step: + * start = shape - 1 # <<<<<<<<<<<<<< + * else: + * start = shape + */ + __pyx_v_start = (__pyx_v_shape - 1); + + /* "View.MemoryView":833 + * start = 0 + * elif start >= shape: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + goto __pyx_L14; + } + + /* "View.MemoryView":836 + * start = shape - 1 + * else: + * start = shape # <<<<<<<<<<<<<< + * else: + * if negative_step: + */ + /*else*/ { + __pyx_v_start = __pyx_v_shape; + } + __pyx_L14:; + + /* "View.MemoryView":832 + * if start < 0: + * start = 0 + * elif start >= shape: # <<<<<<<<<<<<<< + * if negative_step: + * start = shape - 1 + */ + } + __pyx_L12:; + + /* "View.MemoryView":827 + * + * + * if have_start: # <<<<<<<<<<<<<< + * if start < 0: + * start += shape + */ + goto __pyx_L11; + } + + /* "View.MemoryView":838 + * start = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + /*else*/ { + __pyx_t_2 = (__pyx_v_negative_step != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":839 + * else: + * if negative_step: + * start = shape - 1 # <<<<<<<<<<<<<< + * else: + * start = 0 + */ + __pyx_v_start = (__pyx_v_shape - 1); + + /* "View.MemoryView":838 + * start = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * start = shape - 1 + * else: + */ + goto __pyx_L15; + } + + /* "View.MemoryView":841 + * start = shape - 1 + * else: + * start = 0 # <<<<<<<<<<<<<< + * + * if have_stop: + */ + /*else*/ { + __pyx_v_start = 0; + } + __pyx_L15:; + } + __pyx_L11:; + + /* "View.MemoryView":843 + * start = 0 + * + * if have_stop: # <<<<<<<<<<<<<< + * if stop < 0: + * stop += shape + */ + __pyx_t_2 = (__pyx_v_have_stop != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":844 + * + * if have_stop: + * if stop < 0: # <<<<<<<<<<<<<< + * stop += shape + * if stop < 0: + */ + __pyx_t_2 = ((__pyx_v_stop < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":845 + * if have_stop: + * if stop < 0: + * stop += shape # <<<<<<<<<<<<<< + * if stop < 0: + * stop = 0 + */ + __pyx_v_stop = (__pyx_v_stop + __pyx_v_shape); + + /* "View.MemoryView":846 + * if stop < 0: + * stop += shape + * if stop < 0: # <<<<<<<<<<<<<< + * stop = 0 + * elif stop > shape: + */ + __pyx_t_2 = ((__pyx_v_stop < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":847 + * stop += shape + * if stop < 0: + * stop = 0 # <<<<<<<<<<<<<< + * elif stop > shape: + * stop = shape + */ + __pyx_v_stop = 0; + + /* "View.MemoryView":846 + * if stop < 0: + * stop += shape + * if stop < 0: # <<<<<<<<<<<<<< + * stop = 0 + * elif stop > shape: + */ + } + + /* "View.MemoryView":844 + * + * if have_stop: + * if stop < 0: # <<<<<<<<<<<<<< + * stop += shape + * if stop < 0: + */ + goto __pyx_L17; + } + + /* "View.MemoryView":848 + * if stop < 0: + * stop = 0 + * elif stop > shape: # <<<<<<<<<<<<<< + * stop = shape + * else: + */ + __pyx_t_2 = ((__pyx_v_stop > __pyx_v_shape) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":849 + * stop = 0 + * elif stop > shape: + * stop = shape # <<<<<<<<<<<<<< + * else: + * if negative_step: + */ + __pyx_v_stop = __pyx_v_shape; + + /* "View.MemoryView":848 + * if stop < 0: + * stop = 0 + * elif stop > shape: # <<<<<<<<<<<<<< + * stop = shape + * else: + */ + } + __pyx_L17:; + + /* "View.MemoryView":843 + * start = 0 + * + * if have_stop: # <<<<<<<<<<<<<< + * if stop < 0: + * stop += shape + */ + goto __pyx_L16; + } + + /* "View.MemoryView":851 + * stop = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * stop = -1 + * else: + */ + /*else*/ { + __pyx_t_2 = (__pyx_v_negative_step != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":852 + * else: + * if negative_step: + * stop = -1 # <<<<<<<<<<<<<< + * else: + * stop = shape + */ + __pyx_v_stop = -1L; + + /* "View.MemoryView":851 + * stop = shape + * else: + * if negative_step: # <<<<<<<<<<<<<< + * stop = -1 + * else: + */ + goto __pyx_L19; + } + + /* "View.MemoryView":854 + * stop = -1 + * else: + * stop = shape # <<<<<<<<<<<<<< + * + * if not have_step: + */ + /*else*/ { + __pyx_v_stop = __pyx_v_shape; + } + __pyx_L19:; + } + __pyx_L16:; + + /* "View.MemoryView":856 + * stop = shape + * + * if not have_step: # <<<<<<<<<<<<<< + * step = 1 + * + */ + __pyx_t_2 = ((!(__pyx_v_have_step != 0)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":857 + * + * if not have_step: + * step = 1 # <<<<<<<<<<<<<< + * + * + */ + __pyx_v_step = 1; + + /* "View.MemoryView":856 + * stop = shape + * + * if not have_step: # <<<<<<<<<<<<<< + * step = 1 + * + */ + } + + /* "View.MemoryView":861 + * + * with cython.cdivision(True): + * new_shape = (stop - start) // step # <<<<<<<<<<<<<< + * + * if (stop - start) - step * new_shape: + */ + __pyx_v_new_shape = ((__pyx_v_stop - __pyx_v_start) / __pyx_v_step); + + /* "View.MemoryView":863 + * new_shape = (stop - start) // step + * + * if (stop - start) - step * new_shape: # <<<<<<<<<<<<<< + * new_shape += 1 + * + */ + __pyx_t_2 = (((__pyx_v_stop - __pyx_v_start) - (__pyx_v_step * __pyx_v_new_shape)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":864 + * + * if (stop - start) - step * new_shape: + * new_shape += 1 # <<<<<<<<<<<<<< + * + * if new_shape < 0: + */ + __pyx_v_new_shape = (__pyx_v_new_shape + 1); + + /* "View.MemoryView":863 + * new_shape = (stop - start) // step + * + * if (stop - start) - step * new_shape: # <<<<<<<<<<<<<< + * new_shape += 1 + * + */ + } + + /* "View.MemoryView":866 + * new_shape += 1 + * + * if new_shape < 0: # <<<<<<<<<<<<<< + * new_shape = 0 + * + */ + __pyx_t_2 = ((__pyx_v_new_shape < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":867 + * + * if new_shape < 0: + * new_shape = 0 # <<<<<<<<<<<<<< + * + * + */ + __pyx_v_new_shape = 0; + + /* "View.MemoryView":866 + * new_shape += 1 + * + * if new_shape < 0: # <<<<<<<<<<<<<< + * new_shape = 0 + * + */ + } + + /* "View.MemoryView":870 + * + * + * dst.strides[new_ndim] = stride * step # <<<<<<<<<<<<<< + * dst.shape[new_ndim] = new_shape + * dst.suboffsets[new_ndim] = suboffset + */ + (__pyx_v_dst->strides[__pyx_v_new_ndim]) = (__pyx_v_stride * __pyx_v_step); + + /* "View.MemoryView":871 + * + * dst.strides[new_ndim] = stride * step + * dst.shape[new_ndim] = new_shape # <<<<<<<<<<<<<< + * dst.suboffsets[new_ndim] = suboffset + * + */ + (__pyx_v_dst->shape[__pyx_v_new_ndim]) = __pyx_v_new_shape; + + /* "View.MemoryView":872 + * dst.strides[new_ndim] = stride * step + * dst.shape[new_ndim] = new_shape + * dst.suboffsets[new_ndim] = suboffset # <<<<<<<<<<<<<< + * + * + */ + (__pyx_v_dst->suboffsets[__pyx_v_new_ndim]) = __pyx_v_suboffset; + } + __pyx_L3:; + + /* "View.MemoryView":875 + * + * + * if suboffset_dim[0] < 0: # <<<<<<<<<<<<<< + * dst.data += start * stride + * else: + */ + __pyx_t_2 = (((__pyx_v_suboffset_dim[0]) < 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":876 + * + * if suboffset_dim[0] < 0: + * dst.data += start * stride # <<<<<<<<<<<<<< + * else: + * dst.suboffsets[suboffset_dim[0]] += start * stride + */ + __pyx_v_dst->data = (__pyx_v_dst->data + (__pyx_v_start * __pyx_v_stride)); + + /* "View.MemoryView":875 + * + * + * if suboffset_dim[0] < 0: # <<<<<<<<<<<<<< + * dst.data += start * stride + * else: + */ + goto __pyx_L23; + } + + /* "View.MemoryView":878 + * dst.data += start * stride + * else: + * dst.suboffsets[suboffset_dim[0]] += start * stride # <<<<<<<<<<<<<< + * + * if suboffset >= 0: + */ + /*else*/ { + __pyx_t_3 = (__pyx_v_suboffset_dim[0]); + (__pyx_v_dst->suboffsets[__pyx_t_3]) = ((__pyx_v_dst->suboffsets[__pyx_t_3]) + (__pyx_v_start * __pyx_v_stride)); + } + __pyx_L23:; + + /* "View.MemoryView":880 + * dst.suboffsets[suboffset_dim[0]] += start * stride + * + * if suboffset >= 0: # <<<<<<<<<<<<<< + * if not is_slice: + * if new_ndim == 0: + */ + __pyx_t_2 = ((__pyx_v_suboffset >= 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":881 + * + * if suboffset >= 0: + * if not is_slice: # <<<<<<<<<<<<<< + * if new_ndim == 0: + * dst.data = ( dst.data)[0] + suboffset + */ + __pyx_t_2 = ((!(__pyx_v_is_slice != 0)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":882 + * if suboffset >= 0: + * if not is_slice: + * if new_ndim == 0: # <<<<<<<<<<<<<< + * dst.data = ( dst.data)[0] + suboffset + * else: + */ + __pyx_t_2 = ((__pyx_v_new_ndim == 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":883 + * if not is_slice: + * if new_ndim == 0: + * dst.data = ( dst.data)[0] + suboffset # <<<<<<<<<<<<<< + * else: + * _err_dim(IndexError, "All dimensions preceding dimension %d " + */ + __pyx_v_dst->data = ((((char **)__pyx_v_dst->data)[0]) + __pyx_v_suboffset); + + /* "View.MemoryView":882 + * if suboffset >= 0: + * if not is_slice: + * if new_ndim == 0: # <<<<<<<<<<<<<< + * dst.data = ( dst.data)[0] + suboffset + * else: + */ + goto __pyx_L26; + } + + /* "View.MemoryView":885 + * dst.data = ( dst.data)[0] + suboffset + * else: + * _err_dim(IndexError, "All dimensions preceding dimension %d " # <<<<<<<<<<<<<< + * "must be indexed and not sliced", dim) + * else: + */ + /*else*/ { + + /* "View.MemoryView":886 + * else: + * _err_dim(IndexError, "All dimensions preceding dimension %d " + * "must be indexed and not sliced", dim) # <<<<<<<<<<<<<< + * else: + * suboffset_dim[0] = new_ndim + */ + __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_IndexError, ((char *)"All dimensions preceding dimension %d must be indexed and not sliced"), __pyx_v_dim); if (unlikely(__pyx_t_3 == -1)) __PYX_ERR(2, 885, __pyx_L1_error) + } + __pyx_L26:; + + /* "View.MemoryView":881 + * + * if suboffset >= 0: + * if not is_slice: # <<<<<<<<<<<<<< + * if new_ndim == 0: + * dst.data = ( dst.data)[0] + suboffset + */ + goto __pyx_L25; + } + + /* "View.MemoryView":888 + * "must be indexed and not sliced", dim) + * else: + * suboffset_dim[0] = new_ndim # <<<<<<<<<<<<<< + * + * return 0 + */ + /*else*/ { + (__pyx_v_suboffset_dim[0]) = __pyx_v_new_ndim; + } + __pyx_L25:; + + /* "View.MemoryView":880 + * dst.suboffsets[suboffset_dim[0]] += start * stride + * + * if suboffset >= 0: # <<<<<<<<<<<<<< + * if not is_slice: + * if new_ndim == 0: + */ + } + + /* "View.MemoryView":890 + * suboffset_dim[0] = new_ndim + * + * return 0 # <<<<<<<<<<<<<< + * + * + */ + __pyx_r = 0; + goto __pyx_L0; + + /* "View.MemoryView":793 + * + * @cname('__pyx_memoryview_slice_memviewslice') + * cdef int slice_memviewslice( # <<<<<<<<<<<<<< + * __Pyx_memviewslice *dst, + * Py_ssize_t shape, Py_ssize_t stride, Py_ssize_t suboffset, + */ + + /* function exit code */ + __pyx_L1_error:; + { + #ifdef WITH_THREAD + PyGILState_STATE __pyx_gilstate_save = __Pyx_PyGILState_Ensure(); + #endif + __Pyx_AddTraceback("View.MemoryView.slice_memviewslice", __pyx_clineno, __pyx_lineno, __pyx_filename); + #ifdef WITH_THREAD + __Pyx_PyGILState_Release(__pyx_gilstate_save); + #endif + } + __pyx_r = -1; + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":896 + * + * @cname('__pyx_pybuffer_index') + * cdef char *pybuffer_index(Py_buffer *view, char *bufp, Py_ssize_t index, # <<<<<<<<<<<<<< + * Py_ssize_t dim) except NULL: + * cdef Py_ssize_t shape, stride, suboffset = -1 + */ + +static char *__pyx_pybuffer_index(Py_buffer *__pyx_v_view, char *__pyx_v_bufp, Py_ssize_t __pyx_v_index, Py_ssize_t __pyx_v_dim) { + Py_ssize_t __pyx_v_shape; + Py_ssize_t __pyx_v_stride; + Py_ssize_t __pyx_v_suboffset; + Py_ssize_t __pyx_v_itemsize; + char *__pyx_v_resultp; + char *__pyx_r; + __Pyx_RefNannyDeclarations + Py_ssize_t __pyx_t_1; + int __pyx_t_2; + PyObject *__pyx_t_3 = NULL; + PyObject *__pyx_t_4 = NULL; + __Pyx_RefNannySetupContext("pybuffer_index", 0); + + /* "View.MemoryView":898 + * cdef char *pybuffer_index(Py_buffer *view, char *bufp, Py_ssize_t index, + * Py_ssize_t dim) except NULL: + * cdef Py_ssize_t shape, stride, suboffset = -1 # <<<<<<<<<<<<<< + * cdef Py_ssize_t itemsize = view.itemsize + * cdef char *resultp + */ + __pyx_v_suboffset = -1L; + + /* "View.MemoryView":899 + * Py_ssize_t dim) except NULL: + * cdef Py_ssize_t shape, stride, suboffset = -1 + * cdef Py_ssize_t itemsize = view.itemsize # <<<<<<<<<<<<<< + * cdef char *resultp + * + */ + __pyx_t_1 = __pyx_v_view->itemsize; + __pyx_v_itemsize = __pyx_t_1; + + /* "View.MemoryView":902 + * cdef char *resultp + * + * if view.ndim == 0: # <<<<<<<<<<<<<< + * shape = view.len / itemsize + * stride = itemsize + */ + __pyx_t_2 = ((__pyx_v_view->ndim == 0) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":903 + * + * if view.ndim == 0: + * shape = view.len / itemsize # <<<<<<<<<<<<<< + * 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* c_stride = mslice.strides[i] + * break + */ + __pyx_t_2 = (((__pyx_v_mslice->shape[__pyx_v_i]) > 1) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":1109 + * for i in range(ndim - 1, -1, -1): + * if mslice.shape[i] > 1: + * c_stride = mslice.strides[i] # <<<<<<<<<<<<<< + * break + * + */ + __pyx_v_c_stride = (__pyx_v_mslice->strides[__pyx_v_i]); + + /* "View.MemoryView":1110 + * if mslice.shape[i] > 1: + * c_stride = mslice.strides[i] + * break # <<<<<<<<<<<<<< + * + * for i in range(ndim): + */ + goto __pyx_L4_break; + + /* "View.MemoryView":1108 + * + * for i in range(ndim - 1, -1, -1): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * c_stride = mslice.strides[i] + * break + */ + } + } + __pyx_L4_break:; + + /* "View.MemoryView":1112 + * break + * + * for i in range(ndim): # <<<<<<<<<<<<<< + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] + */ + __pyx_t_1 = __pyx_v_ndim; + for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_1; __pyx_t_3+=1) { + __pyx_v_i = __pyx_t_3; + + /* "View.MemoryView":1113 + * + * for i in range(ndim): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * f_stride = mslice.strides[i] + * break + */ + __pyx_t_2 = (((__pyx_v_mslice->shape[__pyx_v_i]) > 1) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":1114 + * for i in range(ndim): + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] # <<<<<<<<<<<<<< + * break + * + */ + __pyx_v_f_stride = (__pyx_v_mslice->strides[__pyx_v_i]); + + /* "View.MemoryView":1115 + * if mslice.shape[i] > 1: + * f_stride = mslice.strides[i] + * break # <<<<<<<<<<<<<< + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): + */ + goto __pyx_L7_break; + + /* "View.MemoryView":1113 + * + * for i in range(ndim): + * if mslice.shape[i] > 1: # <<<<<<<<<<<<<< + * f_stride = mslice.strides[i] + * break + */ + } + } + __pyx_L7_break:; + + /* "View.MemoryView":1117 + * break + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): # <<<<<<<<<<<<<< + * return 'C' + * else: + */ + __pyx_t_2 = ((abs_py_ssize_t(__pyx_v_c_stride) <= abs_py_ssize_t(__pyx_v_f_stride)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":1118 + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): + * return 'C' # <<<<<<<<<<<<<< + * else: + * return 'F' + */ + __pyx_r = 'C'; + goto __pyx_L0; + + /* "View.MemoryView":1117 + * break + * + * if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride): # <<<<<<<<<<<<<< + * return 'C' + * else: + */ + } + + /* "View.MemoryView":1120 + * return 'C' + * else: + * return 'F' # <<<<<<<<<<<<<< + * + * @cython.cdivision(True) + */ + /*else*/ { + __pyx_r = 'F'; + goto __pyx_L0; + } + + /* "View.MemoryView":1099 + * + * @cname('__pyx_get_best_slice_order') + * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) nogil: # <<<<<<<<<<<<<< + * """ + * Figure out the best memory access order for a given slice. + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1123 + * + * @cython.cdivision(True) + * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides, # <<<<<<<<<<<<<< + * char *dst_data, Py_ssize_t *dst_strides, + * Py_ssize_t *src_shape, Py_ssize_t *dst_shape, + */ + +static void _copy_strided_to_strided(char *__pyx_v_src_data, Py_ssize_t *__pyx_v_src_strides, char *__pyx_v_dst_data, Py_ssize_t *__pyx_v_dst_strides, Py_ssize_t *__pyx_v_src_shape, Py_ssize_t *__pyx_v_dst_shape, int __pyx_v_ndim, size_t __pyx_v_itemsize) { + CYTHON_UNUSED Py_ssize_t __pyx_v_i; + CYTHON_UNUSED Py_ssize_t __pyx_v_src_extent; + Py_ssize_t __pyx_v_dst_extent; + Py_ssize_t __pyx_v_src_stride; + Py_ssize_t __pyx_v_dst_stride; + int __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + Py_ssize_t __pyx_t_4; + Py_ssize_t __pyx_t_5; + + /* "View.MemoryView":1130 + * + * cdef Py_ssize_t i + * cdef Py_ssize_t src_extent = src_shape[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] + */ + __pyx_v_src_extent = (__pyx_v_src_shape[0]); + + /* "View.MemoryView":1131 + * cdef Py_ssize_t i + * cdef Py_ssize_t src_extent = src_shape[0] + * cdef Py_ssize_t dst_extent = dst_shape[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t src_stride = src_strides[0] + * cdef Py_ssize_t dst_stride = dst_strides[0] + */ + __pyx_v_dst_extent = (__pyx_v_dst_shape[0]); + + /* "View.MemoryView":1132 + * cdef Py_ssize_t src_extent = src_shape[0] + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] # <<<<<<<<<<<<<< + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + */ + __pyx_v_src_stride = (__pyx_v_src_strides[0]); + + /* "View.MemoryView":1133 + * cdef Py_ssize_t dst_extent = dst_shape[0] + * cdef Py_ssize_t src_stride = src_strides[0] + * cdef Py_ssize_t dst_stride = dst_strides[0] # <<<<<<<<<<<<<< + * + * if ndim == 1: + */ + __pyx_v_dst_stride = (__pyx_v_dst_strides[0]); + + /* "View.MemoryView":1135 + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + */ + __pyx_t_1 = ((__pyx_v_ndim == 1) != 0); + if (__pyx_t_1) { + + /* "View.MemoryView":1136 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + __pyx_t_2 = ((__pyx_v_src_stride > 0) != 0); + if (__pyx_t_2) { + } else { + __pyx_t_1 = __pyx_t_2; + goto __pyx_L5_bool_binop_done; + } + __pyx_t_2 = ((__pyx_v_dst_stride > 0) != 0); + if (__pyx_t_2) { + } else { + __pyx_t_1 = __pyx_t_2; + goto __pyx_L5_bool_binop_done; + } + + /* "View.MemoryView":1137 + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): # <<<<<<<<<<<<<< + * memcpy(dst_data, src_data, itemsize * dst_extent) + * else: + */ + __pyx_t_2 = (((size_t)__pyx_v_src_stride) == __pyx_v_itemsize); + if (__pyx_t_2) { + __pyx_t_2 = (__pyx_v_itemsize == ((size_t)__pyx_v_dst_stride)); + } + __pyx_t_3 = (__pyx_t_2 != 0); + __pyx_t_1 = __pyx_t_3; + __pyx_L5_bool_binop_done:; + + /* "View.MemoryView":1136 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + if (__pyx_t_1) { + + /* "View.MemoryView":1138 + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) # <<<<<<<<<<<<<< + * else: + * for i in range(dst_extent): + */ + memcpy(__pyx_v_dst_data, __pyx_v_src_data, (__pyx_v_itemsize * __pyx_v_dst_extent)); + + /* "View.MemoryView":1136 + * + * if ndim == 1: + * if (src_stride > 0 and dst_stride > 0 and # <<<<<<<<<<<<<< + * src_stride == itemsize == dst_stride): + * memcpy(dst_data, src_data, itemsize * dst_extent) + */ + goto __pyx_L4; + } + + /* "View.MemoryView":1140 + * memcpy(dst_data, src_data, itemsize * dst_extent) + * else: + * for i in range(dst_extent): # <<<<<<<<<<<<<< + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride + */ + /*else*/ { + __pyx_t_4 = __pyx_v_dst_extent; + for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) { + __pyx_v_i = __pyx_t_5; + + /* "View.MemoryView":1141 + * else: + * for i in range(dst_extent): + * memcpy(dst_data, src_data, itemsize) # <<<<<<<<<<<<<< + * src_data += src_stride + * dst_data += dst_stride + */ + memcpy(__pyx_v_dst_data, __pyx_v_src_data, __pyx_v_itemsize); + + /* "View.MemoryView":1142 + * for i in range(dst_extent): + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride # <<<<<<<<<<<<<< + * dst_data += dst_stride + * else: + */ + __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride); + + /* "View.MemoryView":1143 + * memcpy(dst_data, src_data, itemsize) + * src_data += src_stride + * dst_data += dst_stride # <<<<<<<<<<<<<< + * else: + * for i in range(dst_extent): + */ + __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride); + } + } + __pyx_L4:; + + /* "View.MemoryView":1135 + * cdef Py_ssize_t dst_stride = dst_strides[0] + * + * if ndim == 1: # <<<<<<<<<<<<<< + * if (src_stride > 0 and dst_stride > 0 and + * src_stride == itemsize == dst_stride): + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1145 + * dst_data += dst_stride + * else: + * for i in range(dst_extent): # <<<<<<<<<<<<<< + * _copy_strided_to_strided(src_data, src_strides + 1, + * dst_data, dst_strides + 1, + */ + /*else*/ { + __pyx_t_4 = __pyx_v_dst_extent; + for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) { + __pyx_v_i = __pyx_t_5; + + /* "View.MemoryView":1146 + * else: + * for i in range(dst_extent): + * _copy_strided_to_strided(src_data, src_strides + 1, # <<<<<<<<<<<<<< + * dst_data, dst_strides + 1, + * src_shape + 1, dst_shape + 1, + */ + _copy_strided_to_strided(__pyx_v_src_data, (__pyx_v_src_strides + 1), __pyx_v_dst_data, (__pyx_v_dst_strides + 1), (__pyx_v_src_shape + 1), (__pyx_v_dst_shape + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize); + + /* "View.MemoryView":1150 + * src_shape + 1, dst_shape + 1, + * ndim - 1, itemsize) + * src_data += src_stride # <<<<<<<<<<<<<< + * dst_data += dst_stride + * + */ + __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride); + + /* "View.MemoryView":1151 + * ndim - 1, itemsize) + * src_data += src_stride + * dst_data += dst_stride # <<<<<<<<<<<<<< + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, + */ + __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride); + } + } + __pyx_L3:; + + /* "View.MemoryView":1123 + * + * @cython.cdivision(True) + * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides, # <<<<<<<<<<<<<< + * char *dst_data, Py_ssize_t *dst_strides, + * Py_ssize_t *src_shape, Py_ssize_t *dst_shape, + */ + + /* function exit code */ +} + +/* "View.MemoryView":1153 + * dst_data += dst_stride + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) nogil: + */ + +static void copy_strided_to_strided(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize) { + + /* "View.MemoryView":1156 + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) nogil: + * _copy_strided_to_strided(src.data, src.strides, dst.data, dst.strides, # <<<<<<<<<<<<<< + * src.shape, dst.shape, ndim, itemsize) + * + */ + _copy_strided_to_strided(__pyx_v_src->data, __pyx_v_src->strides, __pyx_v_dst->data, __pyx_v_dst->strides, __pyx_v_src->shape, __pyx_v_dst->shape, __pyx_v_ndim, __pyx_v_itemsize); + + /* "View.MemoryView":1153 + * dst_data += dst_stride + * + * cdef void copy_strided_to_strided(__Pyx_memviewslice *src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice *dst, + * int ndim, size_t itemsize) nogil: + */ + + /* function exit code */ +} + +/* "View.MemoryView":1160 + * + * @cname('__pyx_memoryview_slice_get_size') + * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil: # <<<<<<<<<<<<<< + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef int i + */ + +static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *__pyx_v_src, int __pyx_v_ndim) { + int __pyx_v_i; + Py_ssize_t __pyx_v_size; + Py_ssize_t __pyx_r; + Py_ssize_t __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + + /* "View.MemoryView":1163 + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef int i + * cdef Py_ssize_t size = src.memview.view.itemsize # <<<<<<<<<<<<<< + * + * for i in range(ndim): + */ + __pyx_t_1 = __pyx_v_src->memview->view.itemsize; + __pyx_v_size = __pyx_t_1; + + /* "View.MemoryView":1165 + * cdef Py_ssize_t size = src.memview.view.itemsize + * + * for i in range(ndim): # <<<<<<<<<<<<<< + * size *= src.shape[i] + * + */ + __pyx_t_2 = __pyx_v_ndim; + for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) { + __pyx_v_i = __pyx_t_3; + + /* "View.MemoryView":1166 + * + * for i in range(ndim): + * size *= src.shape[i] # <<<<<<<<<<<<<< + * + * return size + */ + __pyx_v_size = (__pyx_v_size * (__pyx_v_src->shape[__pyx_v_i])); + } + + /* "View.MemoryView":1168 + * size *= src.shape[i] + * + * return size # <<<<<<<<<<<<<< + * + * @cname('__pyx_fill_contig_strides_array') + */ + __pyx_r = __pyx_v_size; + goto __pyx_L0; + + /* "View.MemoryView":1160 + * + * @cname('__pyx_memoryview_slice_get_size') + * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil: # <<<<<<<<<<<<<< + * "Return the size of the memory occupied by the slice in number of bytes" + * cdef int i + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1171 + * + * @cname('__pyx_fill_contig_strides_array') + * cdef Py_ssize_t fill_contig_strides_array( # <<<<<<<<<<<<<< + * Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride, + * int ndim, char order) nogil: + */ + +static Py_ssize_t __pyx_fill_contig_strides_array(Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, Py_ssize_t __pyx_v_stride, int __pyx_v_ndim, char __pyx_v_order) { + int __pyx_v_idx; + Py_ssize_t __pyx_r; + int __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + + /* "View.MemoryView":1180 + * cdef int idx + * + * if order == 'F': # <<<<<<<<<<<<<< + * for idx in range(ndim): + * strides[idx] = stride + */ + __pyx_t_1 = ((__pyx_v_order == 'F') != 0); + if (__pyx_t_1) { + + /* "View.MemoryView":1181 + * + * if order == 'F': + * for idx in range(ndim): # <<<<<<<<<<<<<< + * strides[idx] = stride + * stride = stride * shape[idx] + */ + __pyx_t_2 = __pyx_v_ndim; + for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) { + __pyx_v_idx = __pyx_t_3; + + /* "View.MemoryView":1182 + * if order == 'F': + * for idx in range(ndim): + * strides[idx] = stride # <<<<<<<<<<<<<< + * stride = stride * shape[idx] + * else: + */ + (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride; + + /* "View.MemoryView":1183 + * for idx in range(ndim): + * strides[idx] = stride + * stride = stride * shape[idx] # <<<<<<<<<<<<<< + * else: + * for idx in range(ndim - 1, -1, -1): + */ + __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx])); + } + + /* "View.MemoryView":1180 + * cdef int idx + * + * if order == 'F': # <<<<<<<<<<<<<< + * for idx in range(ndim): + * strides[idx] = stride + */ + goto __pyx_L3; + } + + /* "View.MemoryView":1185 + * stride = stride * shape[idx] + * else: + * for idx in range(ndim - 1, -1, -1): # <<<<<<<<<<<<<< + * strides[idx] = stride + * stride = stride * shape[idx] + */ + /*else*/ { + for (__pyx_t_2 = (__pyx_v_ndim - 1); __pyx_t_2 > -1L; __pyx_t_2-=1) { + __pyx_v_idx = __pyx_t_2; + + /* "View.MemoryView":1186 + * else: + * for idx in range(ndim - 1, -1, -1): + * strides[idx] = stride # <<<<<<<<<<<<<< + * stride = stride * shape[idx] + * + */ + (__pyx_v_strides[__pyx_v_idx]) = __pyx_v_stride; + + /* "View.MemoryView":1187 + * for idx in range(ndim - 1, -1, -1): + * strides[idx] = stride + * stride = stride * shape[idx] # <<<<<<<<<<<<<< + * + * return stride + */ + __pyx_v_stride = (__pyx_v_stride * (__pyx_v_shape[__pyx_v_idx])); + } + } + __pyx_L3:; + + /* "View.MemoryView":1189 + * stride = stride * shape[idx] + * + * return stride # <<<<<<<<<<<<<< + * + * @cname('__pyx_memoryview_copy_data_to_temp') + */ + __pyx_r = __pyx_v_stride; + goto __pyx_L0; + + /* "View.MemoryView":1171 + * + * @cname('__pyx_fill_contig_strides_array') + * cdef Py_ssize_t fill_contig_strides_array( # <<<<<<<<<<<<<< + * Py_ssize_t *shape, Py_ssize_t *strides, Py_ssize_t stride, + * int ndim, char order) nogil: + */ + + /* function exit code */ + __pyx_L0:; + return __pyx_r; +} + +/* "View.MemoryView":1192 + * + * @cname('__pyx_memoryview_copy_data_to_temp') + * cdef void *copy_data_to_temp(__Pyx_memviewslice *src, # <<<<<<<<<<<<<< + * __Pyx_memviewslice *tmpslice, + * char order, + */ + +static void *__pyx_memoryview_copy_data_to_temp(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_tmpslice, char __pyx_v_order, int __pyx_v_ndim) { + int __pyx_v_i; + void *__pyx_v_result; + size_t __pyx_v_itemsize; + size_t __pyx_v_size; + void *__pyx_r; + Py_ssize_t __pyx_t_1; + int __pyx_t_2; + int __pyx_t_3; + struct __pyx_memoryview_obj *__pyx_t_4; + int __pyx_t_5; + + /* "View.MemoryView":1203 + * cdef void *result + * + * cdef size_t itemsize = src.memview.view.itemsize # <<<<<<<<<<<<<< + * cdef size_t size = slice_get_size(src, ndim) + * + */ + __pyx_t_1 = __pyx_v_src->memview->view.itemsize; + __pyx_v_itemsize = __pyx_t_1; + + /* "View.MemoryView":1204 + * + * cdef size_t itemsize = src.memview.view.itemsize + * cdef size_t size = slice_get_size(src, ndim) # <<<<<<<<<<<<<< + * + * result = malloc(size) + */ + __pyx_v_size = __pyx_memoryview_slice_get_size(__pyx_v_src, __pyx_v_ndim); + + /* "View.MemoryView":1206 + * cdef size_t size = slice_get_size(src, ndim) + * + * result = malloc(size) # <<<<<<<<<<<<<< + * if not result: + * _err(MemoryError, NULL) + */ + __pyx_v_result = malloc(__pyx_v_size); + + /* "View.MemoryView":1207 + * + * result = malloc(size) + * if not result: # <<<<<<<<<<<<<< + * _err(MemoryError, NULL) + * + */ + __pyx_t_2 = ((!(__pyx_v_result != 0)) != 0); + if (__pyx_t_2) { + + /* "View.MemoryView":1208 + * result = malloc(size) + * if not result: + * _err(MemoryError, NULL) # <<<<<<<<<<<<<< + * + * + */ + __pyx_t_3 = __pyx_memoryview_err(__pyx_builtin_MemoryError, NULL); if (unlikely(__pyx_t_3 == -1)) __PYX_ERR(2, 1208, __pyx_L1_error) + + /* "View.MemoryView":1207 + * + * result = malloc(size) + * if not result: # <<<<<<<<<<<<<< + * _err(MemoryError, NULL) + * + */ + } + + /* "View.MemoryView":1211 + * + * + * tmpslice.data = result # <<<<<<<<<<<<<< + * tmpslice.memview = src.memview + * for i in range(ndim): + */ + __pyx_v_tmpslice->data = ((char *)__pyx_v_result); + + /* "View.MemoryView":1212 + * + * tmpslice.data = result + * tmpslice.memview = src.memview # <<<<<<<<<<<<<< + * for i in range(ndim): + * tmpslice.shape[i] = src.shape[i] + */ + __pyx_t_4 = __pyx_v_src->memview; + 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PyObject *__pyx_getprop___pyx_memoryview_base(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_4base_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_shape(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_5shape_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_strides(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_7strides_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_suboffsets(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_10suboffsets_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_ndim(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_10memoryview_4ndim_1__get__(o); +} + +static PyObject *__pyx_getprop___pyx_memoryview_itemsize(PyObject *o, CYTHON_UNUSED void *x) { + return 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PyGetSetDef __pyx_getsets_memoryview[] = { + {(char *)"T", __pyx_getprop___pyx_memoryview_T, 0, (char *)0, 0}, + {(char *)"base", __pyx_getprop___pyx_memoryview_base, 0, (char *)0, 0}, + {(char *)"shape", __pyx_getprop___pyx_memoryview_shape, 0, (char *)0, 0}, + {(char *)"strides", __pyx_getprop___pyx_memoryview_strides, 0, (char *)0, 0}, + {(char *)"suboffsets", __pyx_getprop___pyx_memoryview_suboffsets, 0, (char *)0, 0}, + {(char *)"ndim", __pyx_getprop___pyx_memoryview_ndim, 0, (char *)0, 0}, + {(char *)"itemsize", __pyx_getprop___pyx_memoryview_itemsize, 0, (char *)0, 0}, + {(char *)"nbytes", __pyx_getprop___pyx_memoryview_nbytes, 0, (char *)0, 0}, + {(char *)"size", __pyx_getprop___pyx_memoryview_size, 0, (char *)0, 0}, + {0, 0, 0, 0, 0} +}; + +static PySequenceMethods __pyx_tp_as_sequence_memoryview = { + __pyx_memoryview___len__, /*sq_length*/ + 0, /*sq_concat*/ + 0, /*sq_repeat*/ + __pyx_sq_item_memoryview, /*sq_item*/ + 0, /*sq_slice*/ + 0, /*sq_ass_item*/ + 0, /*sq_ass_slice*/ + 0, /*sq_contains*/ + 0, /*sq_inplace_concat*/ + 0, /*sq_inplace_repeat*/ +}; + +static PyMappingMethods __pyx_tp_as_mapping_memoryview = { + __pyx_memoryview___len__, /*mp_length*/ + __pyx_memoryview___getitem__, /*mp_subscript*/ + __pyx_mp_ass_subscript_memoryview, /*mp_ass_subscript*/ +}; + +static PyBufferProcs __pyx_tp_as_buffer_memoryview = { + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getreadbuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getwritebuffer*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getsegcount*/ + #endif + #if PY_MAJOR_VERSION < 3 + 0, /*bf_getcharbuffer*/ + #endif + __pyx_memoryview_getbuffer, /*bf_getbuffer*/ + 0, /*bf_releasebuffer*/ +}; + +static PyTypeObject __pyx_type___pyx_memoryview = { + PyVarObject_HEAD_INIT(0, 0) + "Orange.distance._distance.memoryview", /*tp_name*/ + sizeof(struct __pyx_memoryview_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc_memoryview, /*tp_dealloc*/ + 0, /*tp_print*/ + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + __pyx_memoryview___repr__, /*tp_repr*/ + 0, /*tp_as_number*/ + &__pyx_tp_as_sequence_memoryview, /*tp_as_sequence*/ + &__pyx_tp_as_mapping_memoryview, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + __pyx_memoryview___str__, /*tp_str*/ + 0, /*tp_getattro*/ + 0, /*tp_setattro*/ + &__pyx_tp_as_buffer_memoryview, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/ + 0, /*tp_doc*/ + __pyx_tp_traverse_memoryview, /*tp_traverse*/ + __pyx_tp_clear_memoryview, /*tp_clear*/ + 0, /*tp_richcompare*/ + 0, /*tp_weaklistoffset*/ + 0, /*tp_iter*/ + 0, /*tp_iternext*/ + __pyx_methods_memoryview, /*tp_methods*/ + 0, /*tp_members*/ + __pyx_getsets_memoryview, /*tp_getset*/ + 0, /*tp_base*/ + 0, /*tp_dict*/ + 0, /*tp_descr_get*/ + 0, /*tp_descr_set*/ + 0, /*tp_dictoffset*/ + 0, /*tp_init*/ + 0, /*tp_alloc*/ + __pyx_tp_new_memoryview, /*tp_new*/ + 0, /*tp_free*/ + 0, /*tp_is_gc*/ + 0, /*tp_bases*/ + 0, /*tp_mro*/ + 0, /*tp_cache*/ + 0, /*tp_subclasses*/ + 0, /*tp_weaklist*/ + 0, /*tp_del*/ + 0, /*tp_version_tag*/ + #if PY_VERSION_HEX >= 0x030400a1 + 0, /*tp_finalize*/ + #endif +}; +static struct __pyx_vtabstruct__memoryviewslice __pyx_vtable__memoryviewslice; + +static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k) { + struct __pyx_memoryviewslice_obj *p; + PyObject *o = __pyx_tp_new_memoryview(t, a, k); + if (unlikely(!o)) return 0; + p = ((struct __pyx_memoryviewslice_obj *)o); + p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_memoryview*)__pyx_vtabptr__memoryviewslice; + p->from_object = Py_None; Py_INCREF(Py_None); + p->from_slice.memview = NULL; + return o; +} + +static void __pyx_tp_dealloc__memoryviewslice(PyObject *o) { + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + #if PY_VERSION_HEX >= 0x030400a1 + if (unlikely(PyType_HasFeature(Py_TYPE(o), Py_TPFLAGS_HAVE_FINALIZE) && Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) { + if (PyObject_CallFinalizerFromDealloc(o)) return; + } + #endif + PyObject_GC_UnTrack(o); + { + PyObject *etype, *eval, *etb; + PyErr_Fetch(&etype, &eval, &etb); + ++Py_REFCNT(o); + __pyx_memoryviewslice___dealloc__(o); + --Py_REFCNT(o); + PyErr_Restore(etype, eval, etb); + } + Py_CLEAR(p->from_object); + PyObject_GC_Track(o); + __pyx_tp_dealloc_memoryview(o); +} + +static int __pyx_tp_traverse__memoryviewslice(PyObject *o, visitproc v, void *a) { + int e; + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + e = __pyx_tp_traverse_memoryview(o, v, a); if (e) return e; + if (p->from_object) { + e = (*v)(p->from_object, a); if (e) return e; + } + return 0; +} + +static int __pyx_tp_clear__memoryviewslice(PyObject *o) { + PyObject* tmp; + struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o; + __pyx_tp_clear_memoryview(o); + tmp = ((PyObject*)p->from_object); + p->from_object = Py_None; Py_INCREF(Py_None); + Py_XDECREF(tmp); + __PYX_XDEC_MEMVIEW(&p->from_slice, 1); + return 0; +} + +static PyObject *__pyx_getprop___pyx_memoryviewslice_base(PyObject *o, CYTHON_UNUSED void *x) { + return __pyx_pw_15View_dot_MemoryView_16_memoryviewslice_4base_1__get__(o); +} + +static PyMethodDef __pyx_methods__memoryviewslice[] = { + {"__reduce_cython__", (PyCFunction)__pyx_pw___pyx_memoryviewslice_1__reduce_cython__, METH_NOARGS, 0}, + {"__setstate_cython__", (PyCFunction)__pyx_pw___pyx_memoryviewslice_3__setstate_cython__, METH_O, 0}, + {0, 0, 0, 0} +}; + +static struct PyGetSetDef __pyx_getsets__memoryviewslice[] = { + {(char *)"base", __pyx_getprop___pyx_memoryviewslice_base, 0, (char *)0, 0}, + {0, 0, 0, 0, 0} +}; + +static PyTypeObject __pyx_type___pyx_memoryviewslice = { + PyVarObject_HEAD_INIT(0, 0) + "Orange.distance._distance._memoryviewslice", /*tp_name*/ + sizeof(struct __pyx_memoryviewslice_obj), /*tp_basicsize*/ + 0, /*tp_itemsize*/ + __pyx_tp_dealloc__memoryviewslice, /*tp_dealloc*/ + 0, /*tp_print*/ + 0, /*tp_getattr*/ + 0, /*tp_setattr*/ + #if PY_MAJOR_VERSION < 3 + 0, /*tp_compare*/ + #endif + #if PY_MAJOR_VERSION >= 3 + 0, /*tp_as_async*/ + #endif + #if CYTHON_COMPILING_IN_PYPY + __pyx_memoryview___repr__, /*tp_repr*/ + #else + 0, /*tp_repr*/ + #endif + 0, /*tp_as_number*/ + 0, /*tp_as_sequence*/ + 0, /*tp_as_mapping*/ + 0, /*tp_hash*/ + 0, /*tp_call*/ + #if CYTHON_COMPILING_IN_PYPY + __pyx_memoryview___str__, /*tp_str*/ + #else + 0, /*tp_str*/ + #endif + 0, /*tp_getattro*/ + 0, /*tp_setattro*/ + 0, /*tp_as_buffer*/ + Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/ + "Internal class for passing memoryview slices to Python", /*tp_doc*/ + __pyx_tp_traverse__memoryviewslice, 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NULL; + void *r = NULL; + m = PyImport_ImportModule((char *)modname); + if (!m) goto end; + p = PyObject_GetAttrString(m, (char *)"RefNannyAPI"); + if (!p) goto end; + r = PyLong_AsVoidPtr(p); +end: + Py_XDECREF(p); + Py_XDECREF(m); + return (__Pyx_RefNannyAPIStruct *)r; +} +#endif + +/* GetBuiltinName */ +static PyObject *__Pyx_GetBuiltinName(PyObject *name) { + PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name); + if (unlikely(!result)) { + PyErr_Format(PyExc_NameError, +#if PY_MAJOR_VERSION >= 3 + "name '%U' is not defined", name); +#else + "name '%.200s' is not defined", PyString_AS_STRING(name)); +#endif + } + return result; +} + +/* None */ +static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) { + PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname); +} + +/* BufferFormatCheck */ +static CYTHON_INLINE int __Pyx_IsLittleEndian(void) { + unsigned int n = 1; + return *(unsigned char*)(&n) != 0; +} +static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx, + __Pyx_BufFmt_StackElem* stack, + __Pyx_TypeInfo* type) { + stack[0].field = &ctx->root; + stack[0].parent_offset = 0; + ctx->root.type = type; + ctx->root.name = "buffer dtype"; + ctx->root.offset = 0; + ctx->head = stack; + ctx->head->field = &ctx->root; + ctx->fmt_offset = 0; + ctx->head->parent_offset = 0; + ctx->new_packmode = '@'; + ctx->enc_packmode = '@'; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->is_complex = 0; + ctx->is_valid_array = 0; + ctx->struct_alignment = 0; + while (type->typegroup == 'S') { + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = 0; + type = type->fields->type; + } +} +static int __Pyx_BufFmt_ParseNumber(const char** ts) { + int count; + const char* t = *ts; + if (*t < '0' || *t > '9') { + return -1; + } else { + count = *t++ - '0'; + while (*t >= '0' && *t < '9') { + count *= 10; + count += *t++ - '0'; + } + } + *ts = t; + return count; +} +static int __Pyx_BufFmt_ExpectNumber(const char **ts) { + int number = __Pyx_BufFmt_ParseNumber(ts); + if (number == -1) + PyErr_Format(PyExc_ValueError,\ + "Does not understand character buffer dtype format string ('%c')", **ts); + return number; +} +static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) { + PyErr_Format(PyExc_ValueError, + "Unexpected format string character: '%c'", ch); +} +static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) { + switch (ch) { + case 'c': return "'char'"; + case 'b': return "'signed char'"; + case 'B': return "'unsigned char'"; + case 'h': return "'short'"; + case 'H': return "'unsigned short'"; + case 'i': return "'int'"; + case 'I': return "'unsigned int'"; + case 'l': return "'long'"; + case 'L': return "'unsigned long'"; + case 'q': return "'long long'"; + case 'Q': return "'unsigned long long'"; + case 'f': return (is_complex ? "'complex float'" : "'float'"); + case 'd': return (is_complex ? "'complex double'" : "'double'"); + case 'g': return (is_complex ? "'complex long double'" : "'long double'"); + case 'T': return "a struct"; + case 'O': return "Python object"; + case 'P': return "a pointer"; + case 's': case 'p': return "a string"; + case 0: return "end"; + default: return "unparseable format string"; + } +} +static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return 2; + case 'i': case 'I': case 'l': case 'L': return 4; + case 'q': case 'Q': return 8; + case 'f': return (is_complex ? 8 : 4); + case 'd': return (is_complex ? 16 : 8); + case 'g': { + PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g').."); + return 0; + } + case 'O': case 'P': return sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) { + switch (ch) { + case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(short); + case 'i': case 'I': return sizeof(int); + case 'l': case 'L': return sizeof(long); + #ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(PY_LONG_LONG); + #endif + case 'f': return sizeof(float) * (is_complex ? 2 : 1); + case 'd': return sizeof(double) * (is_complex ? 2 : 1); + case 'g': return sizeof(long double) * (is_complex ? 2 : 1); + case 'O': case 'P': return sizeof(void*); + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +typedef struct { char c; short x; } __Pyx_st_short; +typedef struct { char c; int x; } __Pyx_st_int; +typedef struct { char c; long x; } __Pyx_st_long; +typedef struct { char c; float x; } __Pyx_st_float; +typedef struct { char c; double x; } __Pyx_st_double; +typedef struct { char c; long double x; } __Pyx_st_longdouble; +typedef struct { char c; void *x; } __Pyx_st_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_st_float) - sizeof(float); + case 'd': return sizeof(__Pyx_st_double) - sizeof(double); + case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +/* These are for computing the padding at the end of the struct to align + on the first member of the struct. This will probably the same as above, + but we don't have any guarantees. + */ +typedef struct { short x; char c; } __Pyx_pad_short; +typedef struct { int x; char c; } __Pyx_pad_int; +typedef struct { long x; char c; } __Pyx_pad_long; +typedef struct { float x; char c; } __Pyx_pad_float; +typedef struct { double x; char c; } __Pyx_pad_double; +typedef struct { long double x; char c; } __Pyx_pad_longdouble; +typedef struct { void *x; char c; } __Pyx_pad_void_p; +#ifdef HAVE_LONG_LONG +typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong; +#endif +static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) { + switch (ch) { + case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1; + case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short); + case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int); + case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long); +#ifdef HAVE_LONG_LONG + case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG); +#endif + case 'f': return sizeof(__Pyx_pad_float) - sizeof(float); + case 'd': return sizeof(__Pyx_pad_double) - sizeof(double); + case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double); + case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*); + default: + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } +} +static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) { + switch (ch) { + case 'c': + return 'H'; + case 'b': case 'h': case 'i': + case 'l': case 'q': case 's': case 'p': + return 'I'; + case 'B': case 'H': case 'I': case 'L': case 'Q': + return 'U'; + case 'f': case 'd': case 'g': + return (is_complex ? 'C' : 'R'); + case 'O': + return 'O'; + case 'P': + return 'P'; + default: { + __Pyx_BufFmt_RaiseUnexpectedChar(ch); + return 0; + } + } +} +static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) { + if (ctx->head == NULL || ctx->head->field == &ctx->root) { + const char* expected; + const char* quote; + if (ctx->head == NULL) { + expected = "end"; + quote = ""; + } else { + expected = ctx->head->field->type->name; + quote = "'"; + } + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected %s%s%s but got %s", + quote, expected, quote, + __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex)); + } else { + __Pyx_StructField* field = ctx->head->field; + __Pyx_StructField* parent = (ctx->head - 1)->field; + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'", + field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex), + parent->type->name, field->name); + } +} +static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) { + char group; + size_t size, offset, arraysize = 1; + if (ctx->enc_type == 0) return 0; + if (ctx->head->field->type->arraysize[0]) { + int i, ndim = 0; + if (ctx->enc_type == 's' || ctx->enc_type == 'p') { + ctx->is_valid_array = ctx->head->field->type->ndim == 1; + ndim = 1; + if (ctx->enc_count != ctx->head->field->type->arraysize[0]) { + PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %zu", + ctx->head->field->type->arraysize[0], ctx->enc_count); + return -1; + } + } + if (!ctx->is_valid_array) { + PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d", + ctx->head->field->type->ndim, ndim); + return -1; + } + for (i = 0; i < ctx->head->field->type->ndim; i++) { + arraysize *= ctx->head->field->type->arraysize[i]; + } + ctx->is_valid_array = 0; + ctx->enc_count = 1; + } + group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex); + do { + __Pyx_StructField* field = ctx->head->field; + __Pyx_TypeInfo* type = field->type; + if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') { + size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex); + } else { + size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex); + } + if (ctx->enc_packmode == '@') { + size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex); + size_t align_mod_offset; + if (align_at == 0) return -1; + align_mod_offset = ctx->fmt_offset % align_at; + if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset; + if (ctx->struct_alignment == 0) + ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type, + ctx->is_complex); + } + if (type->size != size || type->typegroup != group) { + if (type->typegroup == 'C' && type->fields != NULL) { + size_t parent_offset = ctx->head->parent_offset + field->offset; + ++ctx->head; + ctx->head->field = type->fields; + ctx->head->parent_offset = parent_offset; + continue; + } + if ((type->typegroup == 'H' || group == 'H') && type->size == size) { + } else { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + } + offset = ctx->head->parent_offset + field->offset; + if (ctx->fmt_offset != offset) { + PyErr_Format(PyExc_ValueError, + "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected", + (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset); + return -1; + } + ctx->fmt_offset += size; + if (arraysize) + ctx->fmt_offset += (arraysize - 1) * size; + --ctx->enc_count; + while (1) { + if (field == &ctx->root) { + ctx->head = NULL; + if (ctx->enc_count != 0) { + __Pyx_BufFmt_RaiseExpected(ctx); + return -1; + } + break; + } + ctx->head->field = ++field; + if (field->type == NULL) { + --ctx->head; + field = ctx->head->field; + continue; + } else if (field->type->typegroup == 'S') { + size_t parent_offset = ctx->head->parent_offset + field->offset; + if (field->type->fields->type == NULL) continue; + field = field->type->fields; + ++ctx->head; + ctx->head->field = field; + ctx->head->parent_offset = parent_offset; + break; + } else { + break; + } + } + } while (ctx->enc_count); + ctx->enc_type = 0; + ctx->is_complex = 0; + return 0; +} +static CYTHON_INLINE PyObject * +__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp) +{ + const char *ts = *tsp; + int i = 0, number; + int ndim = ctx->head->field->type->ndim; +; + ++ts; + if (ctx->new_count != 1) { + PyErr_SetString(PyExc_ValueError, + "Cannot handle repeated arrays in format string"); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + while (*ts && *ts != ')') { + switch (*ts) { + case ' ': case '\f': case '\r': case '\n': case '\t': case '\v': continue; + default: break; + } + number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return NULL; + if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i]) + return PyErr_Format(PyExc_ValueError, + "Expected a dimension of size %zu, got %d", + ctx->head->field->type->arraysize[i], number); + if (*ts != ',' && *ts != ')') + return PyErr_Format(PyExc_ValueError, + "Expected a comma in format string, got '%c'", *ts); + if (*ts == ',') ts++; + i++; + } + if (i != ndim) + return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d", + ctx->head->field->type->ndim, i); + if (!*ts) { + PyErr_SetString(PyExc_ValueError, + "Unexpected end of format string, expected ')'"); + return NULL; + } + ctx->is_valid_array = 1; + ctx->new_count = 1; + *tsp = ++ts; + return Py_None; +} +static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) { + int got_Z = 0; + while (1) { + switch(*ts) { + case 0: + if (ctx->enc_type != 0 && ctx->head == NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + if (ctx->head != NULL) { + __Pyx_BufFmt_RaiseExpected(ctx); + return NULL; + } + return ts; + case ' ': + case '\r': + case '\n': + ++ts; + break; + case '<': + if (!__Pyx_IsLittleEndian()) { + PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '>': + case '!': + if (__Pyx_IsLittleEndian()) { + PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler"); + return NULL; + } + ctx->new_packmode = '='; + ++ts; + break; + case '=': + case '@': + case '^': + ctx->new_packmode = *ts++; + break; + case 'T': + { + const char* ts_after_sub; + size_t i, struct_count = ctx->new_count; + size_t struct_alignment = ctx->struct_alignment; + ctx->new_count = 1; + ++ts; + if (*ts != '{') { + PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'"); + return NULL; + } + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + ctx->enc_count = 0; + ctx->struct_alignment = 0; + ++ts; + ts_after_sub = ts; + for (i = 0; i != struct_count; ++i) { + ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts); + if (!ts_after_sub) return NULL; + } + ts = ts_after_sub; + if (struct_alignment) ctx->struct_alignment = struct_alignment; + } + break; + case '}': + { + size_t alignment = ctx->struct_alignment; + ++ts; + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_type = 0; + if (alignment && ctx->fmt_offset % alignment) { + ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment); + } + } + return ts; + case 'x': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->fmt_offset += ctx->new_count; + ctx->new_count = 1; + ctx->enc_count = 0; + ctx->enc_type = 0; + ctx->enc_packmode = ctx->new_packmode; + ++ts; + break; + case 'Z': + got_Z = 1; + ++ts; + if (*ts != 'f' && *ts != 'd' && *ts != 'g') { + __Pyx_BufFmt_RaiseUnexpectedChar('Z'); + return NULL; + } + case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I': + case 'l': case 'L': case 'q': case 'Q': + case 'f': case 'd': case 'g': + case 'O': case 'p': + if (ctx->enc_type == *ts && got_Z == ctx->is_complex && + ctx->enc_packmode == ctx->new_packmode) { + ctx->enc_count += ctx->new_count; + ctx->new_count = 1; + got_Z = 0; + ++ts; + break; + } + case 's': + if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL; + ctx->enc_count = ctx->new_count; + ctx->enc_packmode = ctx->new_packmode; + ctx->enc_type = *ts; + ctx->is_complex = got_Z; + ++ts; + ctx->new_count = 1; + got_Z = 0; + break; + case ':': + ++ts; + while(*ts != ':') ++ts; + ++ts; + break; + case '(': + if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL; + break; + default: + { + int number = __Pyx_BufFmt_ExpectNumber(&ts); + if (number == -1) return NULL; + ctx->new_count = (size_t)number; + } + } + } +} +static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) { + buf->buf = NULL; + buf->obj = NULL; + buf->strides = __Pyx_zeros; + buf->shape = __Pyx_zeros; + buf->suboffsets = __Pyx_minusones; +} +static CYTHON_INLINE int __Pyx_GetBufferAndValidate( + Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, + int nd, int cast, __Pyx_BufFmt_StackElem* stack) +{ + if (obj == Py_None || obj == NULL) { + __Pyx_ZeroBuffer(buf); + return 0; + } + buf->buf = NULL; + if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail; + if (buf->ndim != nd) { + PyErr_Format(PyExc_ValueError, + "Buffer has wrong number of dimensions (expected %d, got %d)", + nd, buf->ndim); + goto fail; + } + if (!cast) { + __Pyx_BufFmt_Context ctx; + __Pyx_BufFmt_Init(&ctx, stack, dtype); + if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail; + } + if ((unsigned)buf->itemsize != dtype->size) { + PyErr_Format(PyExc_ValueError, + "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)", + buf->itemsize, (buf->itemsize > 1) ? "s" : "", + dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : ""); + goto fail; + } + if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones; + return 0; +fail:; + __Pyx_ZeroBuffer(buf); + return -1; +} +static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) { + if (info->buf == NULL) return; + if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL; + __Pyx_ReleaseBuffer(info); +} + +/* MemviewSliceInit */ + static int +__Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview, + int ndim, + __Pyx_memviewslice *memviewslice, + int memview_is_new_reference) +{ + __Pyx_RefNannyDeclarations + int i, retval=-1; + Py_buffer *buf = &memview->view; + __Pyx_RefNannySetupContext("init_memviewslice", 0); + if (!buf) { + PyErr_SetString(PyExc_ValueError, + "buf is NULL."); + goto fail; + } else if (memviewslice->memview || memviewslice->data) { + PyErr_SetString(PyExc_ValueError, + "memviewslice is already initialized!"); + goto fail; + } + if (buf->strides) { + for (i = 0; i < ndim; i++) { + memviewslice->strides[i] = buf->strides[i]; + } + } else { + Py_ssize_t stride = buf->itemsize; + for (i = ndim - 1; i >= 0; i--) { + memviewslice->strides[i] = stride; + stride *= buf->shape[i]; + } + } + for (i = 0; i < ndim; i++) { + memviewslice->shape[i] = buf->shape[i]; + if (buf->suboffsets) { + memviewslice->suboffsets[i] = buf->suboffsets[i]; + } else { + memviewslice->suboffsets[i] = -1; + } + } + memviewslice->memview = memview; + memviewslice->data = (char *)buf->buf; + if (__pyx_add_acquisition_count(memview) == 0 && !memview_is_new_reference) { + Py_INCREF(memview); + } + retval = 0; + goto no_fail; +fail: + memviewslice->memview = 0; + memviewslice->data = 0; + retval = -1; +no_fail: + __Pyx_RefNannyFinishContext(); + return retval; +} +static CYTHON_INLINE void __pyx_fatalerror(const char *fmt, ...) { + va_list vargs; + char msg[200]; +#ifdef HAVE_STDARG_PROTOTYPES + va_start(vargs, fmt); +#else + va_start(vargs); +#endif + vsnprintf(msg, 200, fmt, vargs); + Py_FatalError(msg); + va_end(vargs); +} +static CYTHON_INLINE int +__pyx_add_acquisition_count_locked(__pyx_atomic_int *acquisition_count, + PyThread_type_lock lock) +{ + int result; + PyThread_acquire_lock(lock, 1); + result = (*acquisition_count)++; + PyThread_release_lock(lock); + return result; +} +static CYTHON_INLINE int +__pyx_sub_acquisition_count_locked(__pyx_atomic_int *acquisition_count, + PyThread_type_lock lock) +{ + int result; + PyThread_acquire_lock(lock, 1); + result = (*acquisition_count)--; + PyThread_release_lock(lock); + return result; +} +static CYTHON_INLINE void +__Pyx_INC_MEMVIEW(__Pyx_memviewslice *memslice, int have_gil, int lineno) +{ + int first_time; + struct __pyx_memoryview_obj *memview = memslice->memview; + if (!memview || (PyObject *) memview == Py_None) + return; + if (__pyx_get_slice_count(memview) < 0) + __pyx_fatalerror("Acquisition count is %d (line %d)", + __pyx_get_slice_count(memview), lineno); + first_time = __pyx_add_acquisition_count(memview) == 0; + if (first_time) { + if (have_gil) { + Py_INCREF((PyObject *) memview); + } else { + PyGILState_STATE _gilstate = PyGILState_Ensure(); + Py_INCREF((PyObject *) memview); + PyGILState_Release(_gilstate); + } + } +} +static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *memslice, + int have_gil, int lineno) { + int last_time; + struct __pyx_memoryview_obj *memview = memslice->memview; + if (!memview ) { + return; + } else if ((PyObject *) memview == Py_None) { + memslice->memview = NULL; + return; + } + if (__pyx_get_slice_count(memview) <= 0) + __pyx_fatalerror("Acquisition count is %d (line %d)", + __pyx_get_slice_count(memview), lineno); + last_time = __pyx_sub_acquisition_count(memview) == 1; + memslice->data = NULL; + if (last_time) { + if (have_gil) { + Py_CLEAR(memslice->memview); + } else { + PyGILState_STATE _gilstate = PyGILState_Ensure(); + Py_CLEAR(memslice->memview); + PyGILState_Release(_gilstate); + } + } else { + memslice->memview = NULL; + } +} + +/* RaiseArgTupleInvalid */ + static void __Pyx_RaiseArgtupleInvalid( + const char* func_name, + int exact, + Py_ssize_t num_min, + Py_ssize_t num_max, + Py_ssize_t num_found) +{ + Py_ssize_t num_expected; + const char *more_or_less; + if (num_found < num_min) { + num_expected = num_min; + more_or_less = "at least"; + } else { + num_expected = num_max; + more_or_less = "at most"; + } + if (exact) { + more_or_less = "exactly"; + } + PyErr_Format(PyExc_TypeError, + "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)", + func_name, more_or_less, num_expected, + (num_expected == 1) ? "" : "s", num_found); +} + +/* RaiseDoubleKeywords */ + static void __Pyx_RaiseDoubleKeywordsError( + const char* func_name, + PyObject* kw_name) +{ + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION >= 3 + "%s() got multiple values for keyword argument '%U'", func_name, kw_name); + #else + "%s() got multiple values for keyword argument '%s'", func_name, + PyString_AsString(kw_name)); + #endif +} + +/* ParseKeywords */ + static int __Pyx_ParseOptionalKeywords( + PyObject *kwds, + PyObject **argnames[], + PyObject *kwds2, + PyObject *values[], + Py_ssize_t num_pos_args, + const char* function_name) +{ + PyObject *key = 0, *value = 0; + Py_ssize_t pos = 0; + PyObject*** name; + PyObject*** first_kw_arg = argnames + num_pos_args; + while (PyDict_Next(kwds, &pos, &key, &value)) { + name = first_kw_arg; + while (*name && (**name != key)) name++; + if (*name) { + values[name-argnames] = value; + continue; + } + name = first_kw_arg; + #if PY_MAJOR_VERSION < 3 + if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) { + while (*name) { + if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key)) + && _PyString_Eq(**name, key)) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + if ((**argname == key) || ( + (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key)) + && _PyString_Eq(**argname, key))) { + goto arg_passed_twice; + } + argname++; + } + } + } else + #endif + if (likely(PyUnicode_Check(key))) { + while (*name) { + int cmp = (**name == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 : + #endif + PyUnicode_Compare(**name, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + int cmp = (**argname == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 : + #endif + PyUnicode_Compare(**argname, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) goto arg_passed_twice; + argname++; + } + } + } else + goto invalid_keyword_type; + if (kwds2) { + if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad; + } else { + goto invalid_keyword; + } + } + return 0; +arg_passed_twice: + __Pyx_RaiseDoubleKeywordsError(function_name, key); + goto bad; +invalid_keyword_type: + PyErr_Format(PyExc_TypeError, + "%.200s() keywords must be strings", function_name); + goto bad; +invalid_keyword: + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION < 3 + "%.200s() got an unexpected keyword argument '%.200s'", + function_name, PyString_AsString(key)); + #else + "%s() got an unexpected keyword argument '%U'", + function_name, key); + #endif +bad: + return -1; +} + +/* ArgTypeTest */ + static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) { + PyErr_Format(PyExc_TypeError, + "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)", + name, type->tp_name, Py_TYPE(obj)->tp_name); +} +static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed, + const char *name, int exact) +{ + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (none_allowed && obj == Py_None) return 1; + else if (exact) { + if (likely(Py_TYPE(obj) == type)) return 1; + #if PY_MAJOR_VERSION == 2 + else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1; + #endif + } + else { + if (likely(PyObject_TypeCheck(obj, type))) return 1; + } + __Pyx_RaiseArgumentTypeInvalid(name, obj, type); + return 0; +} + +/* PyErrFetchRestore */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + tmp_type = tstate->curexc_type; + tmp_value = tstate->curexc_value; + tmp_tb = tstate->curexc_traceback; + tstate->curexc_type = type; + tstate->curexc_value = value; + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + *type = tstate->curexc_type; + *value = tstate->curexc_value; + *tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +} +#endif + +/* GetModuleGlobalName */ + static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) { + PyObject *result; +#if !CYTHON_AVOID_BORROWED_REFS + result = PyDict_GetItem(__pyx_d, name); + if (likely(result)) { + Py_INCREF(result); + } else { +#else + result = PyObject_GetItem(__pyx_d, name); + if (!result) { + PyErr_Clear(); +#endif + result = __Pyx_GetBuiltinName(name); + } + return result; +} + +/* PyObjectCall */ + #if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *result; + ternaryfunc call = func->ob_type->tp_call; + if (unlikely(!call)) + return PyObject_Call(func, arg, kw); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = (*call)(func, arg, kw); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* ExtTypeTest */ + static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (likely(PyObject_TypeCheck(obj, type))) + return 1; + PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", + Py_TYPE(obj)->tp_name, type->tp_name); + return 0; +} + +/* BufferFallbackError */ + static void __Pyx_RaiseBufferFallbackError(void) { + PyErr_SetString(PyExc_ValueError, + "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!"); +} + +/* RaiseException */ + #if PY_MAJOR_VERSION < 3 +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, + CYTHON_UNUSED PyObject *cause) { + __Pyx_PyThreadState_declare + Py_XINCREF(type); + if (!value || value == Py_None) + value = NULL; + else + Py_INCREF(value); + if (!tb || tb == Py_None) + tb = NULL; + else { + Py_INCREF(tb); + if (!PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto raise_error; + } + } + if (PyType_Check(type)) { +#if CYTHON_COMPILING_IN_PYPY + if (!value) { + Py_INCREF(Py_None); + value = Py_None; + } +#endif + PyErr_NormalizeException(&type, &value, &tb); + } else { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto raise_error; + } + value = type; + type = (PyObject*) Py_TYPE(type); + Py_INCREF(type); + if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto raise_error; + } + } + __Pyx_PyThreadState_assign + __Pyx_ErrRestore(type, value, tb); + return; +raise_error: + Py_XDECREF(value); + Py_XDECREF(type); + Py_XDECREF(tb); + return; +} +#else +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { + PyObject* owned_instance = NULL; + if (tb == Py_None) { + tb = 0; + } else if (tb && !PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto bad; + } + if (value == Py_None) + value = 0; + if (PyExceptionInstance_Check(type)) { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto bad; + } + value = type; + type = (PyObject*) Py_TYPE(value); + } else if (PyExceptionClass_Check(type)) { + PyObject *instance_class = NULL; + if (value && PyExceptionInstance_Check(value)) { + instance_class = (PyObject*) Py_TYPE(value); + if (instance_class != type) { + int is_subclass = PyObject_IsSubclass(instance_class, type); + if (!is_subclass) { + instance_class = NULL; + } else if (unlikely(is_subclass == -1)) { + goto bad; + } else { + type = instance_class; + } + } + } + if (!instance_class) { + PyObject *args; + if (!value) + args = PyTuple_New(0); + else if (PyTuple_Check(value)) { + Py_INCREF(value); + args = value; + } else + args = PyTuple_Pack(1, value); + if (!args) + goto bad; + owned_instance = PyObject_Call(type, args, NULL); + Py_DECREF(args); + if (!owned_instance) + goto bad; + value = owned_instance; + if (!PyExceptionInstance_Check(value)) { + PyErr_Format(PyExc_TypeError, + "calling %R should have returned an instance of " + "BaseException, not %R", + type, Py_TYPE(value)); + goto bad; + } + } + } else { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto bad; + } +#if PY_VERSION_HEX >= 0x03030000 + if (cause) { +#else + if (cause && cause != Py_None) { +#endif + PyObject *fixed_cause; + if (cause == Py_None) { + fixed_cause = NULL; + } else if (PyExceptionClass_Check(cause)) { + fixed_cause = PyObject_CallObject(cause, NULL); + if (fixed_cause == NULL) + goto bad; + } else if (PyExceptionInstance_Check(cause)) { + fixed_cause = cause; + Py_INCREF(fixed_cause); + } else { + PyErr_SetString(PyExc_TypeError, + "exception causes must derive from " + "BaseException"); + goto bad; + } + PyException_SetCause(value, fixed_cause); + } + PyErr_SetObject(type, value); + if (tb) { +#if CYTHON_COMPILING_IN_PYPY + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb); + Py_INCREF(tb); + PyErr_Restore(tmp_type, tmp_value, tb); + Py_XDECREF(tmp_tb); +#else + PyThreadState *tstate = PyThreadState_GET(); + PyObject* tmp_tb = tstate->curexc_traceback; + if (tb != tmp_tb) { + Py_INCREF(tb); + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_tb); + } +#endif + } +bad: + Py_XDECREF(owned_instance); + return; +} +#endif + +/* RaiseTooManyValuesToUnpack */ + static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) { + PyErr_Format(PyExc_ValueError, + "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected); +} + +/* RaiseNeedMoreValuesToUnpack */ + static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) { + PyErr_Format(PyExc_ValueError, + "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack", + index, (index == 1) ? "" : "s"); +} + +/* RaiseNoneIterError */ + static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) { + PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable"); +} + +/* SaveResetException */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + *type = tstate->exc_type; + *value = tstate->exc_value; + *tb = tstate->exc_traceback; + Py_XINCREF(*type); + Py_XINCREF(*value); + Py_XINCREF(*tb); +} +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = type; + tstate->exc_value = value; + tstate->exc_traceback = tb; + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +#endif + +/* PyErrExceptionMatches */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) { + PyObject *exc_type = tstate->curexc_type; + if (exc_type == err) return 1; + if (unlikely(!exc_type)) return 0; + return PyErr_GivenExceptionMatches(exc_type, err); +} +#endif + +/* GetException */ + #if CYTHON_FAST_THREAD_STATE +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) { +#endif + PyObject *local_type, *local_value, *local_tb; +#if CYTHON_FAST_THREAD_STATE + PyObject *tmp_type, *tmp_value, *tmp_tb; + local_type = tstate->curexc_type; + local_value = tstate->curexc_value; + local_tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +#else + PyErr_Fetch(&local_type, &local_value, &local_tb); +#endif + PyErr_NormalizeException(&local_type, &local_value, &local_tb); +#if CYTHON_FAST_THREAD_STATE + if (unlikely(tstate->curexc_type)) +#else + if (unlikely(PyErr_Occurred())) +#endif + goto bad; + #if PY_MAJOR_VERSION >= 3 + if (local_tb) { + if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0)) + goto bad; + } + #endif + Py_XINCREF(local_tb); + Py_XINCREF(local_type); + Py_XINCREF(local_value); + *type = local_type; + *value = local_value; + *tb = local_tb; +#if CYTHON_FAST_THREAD_STATE + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = local_type; + tstate->exc_value = local_value; + tstate->exc_traceback = local_tb; + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +#else + PyErr_SetExcInfo(local_type, local_value, local_tb); +#endif + return 0; +bad: + *type = 0; + *value = 0; + *tb = 0; + Py_XDECREF(local_type); + Py_XDECREF(local_value); + Py_XDECREF(local_tb); + return -1; +} + +/* BytesEquals */ + static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) { +#if CYTHON_COMPILING_IN_PYPY + return PyObject_RichCompareBool(s1, s2, equals); +#else + if (s1 == s2) { + return (equals == Py_EQ); + } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) { + const char *ps1, *ps2; + Py_ssize_t length = PyBytes_GET_SIZE(s1); + if (length != PyBytes_GET_SIZE(s2)) + return (equals == Py_NE); + ps1 = PyBytes_AS_STRING(s1); + ps2 = PyBytes_AS_STRING(s2); + if (ps1[0] != ps2[0]) { + return (equals == Py_NE); + } else if (length == 1) { + return (equals == Py_EQ); + } else { + int result; +#if CYTHON_USE_UNICODE_INTERNALS + Py_hash_t hash1, hash2; + hash1 = ((PyBytesObject*)s1)->ob_shash; + hash2 = ((PyBytesObject*)s2)->ob_shash; + if (hash1 != hash2 && hash1 != -1 && hash2 != -1) { + return (equals == Py_NE); + } +#endif + result = memcmp(ps1, ps2, (size_t)length); + return (equals == Py_EQ) ? (result == 0) : (result != 0); + } + } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) { + return (equals == Py_NE); + } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) { + return (equals == Py_NE); + } else { + int result; + PyObject* py_result = PyObject_RichCompare(s1, s2, equals); + if (!py_result) + return -1; + result = __Pyx_PyObject_IsTrue(py_result); + Py_DECREF(py_result); + return result; + } +#endif +} + +/* UnicodeEquals */ + static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) { +#if CYTHON_COMPILING_IN_PYPY + return PyObject_RichCompareBool(s1, s2, equals); +#else +#if PY_MAJOR_VERSION < 3 + PyObject* owned_ref = NULL; +#endif + int s1_is_unicode, s2_is_unicode; + if (s1 == s2) { + goto return_eq; + } + s1_is_unicode = PyUnicode_CheckExact(s1); + s2_is_unicode = PyUnicode_CheckExact(s2); +#if PY_MAJOR_VERSION < 3 + if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) { + owned_ref = PyUnicode_FromObject(s2); + if (unlikely(!owned_ref)) + return -1; + s2 = owned_ref; + s2_is_unicode = 1; + } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) { + owned_ref = PyUnicode_FromObject(s1); + if (unlikely(!owned_ref)) + return -1; + s1 = owned_ref; + s1_is_unicode = 1; + } else if (((!s2_is_unicode) & (!s1_is_unicode))) { + return __Pyx_PyBytes_Equals(s1, s2, equals); + } +#endif + if (s1_is_unicode & s2_is_unicode) { + Py_ssize_t length; + int kind; + void *data1, *data2; + if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0)) + return -1; + length = __Pyx_PyUnicode_GET_LENGTH(s1); + if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) { + goto return_ne; + } +#if CYTHON_USE_UNICODE_INTERNALS + { + Py_hash_t hash1, hash2; + #if CYTHON_PEP393_ENABLED + hash1 = ((PyASCIIObject*)s1)->hash; + hash2 = ((PyASCIIObject*)s2)->hash; + #else + hash1 = ((PyUnicodeObject*)s1)->hash; + hash2 = ((PyUnicodeObject*)s2)->hash; + #endif + if (hash1 != hash2 && hash1 != -1 && hash2 != -1) { + goto return_ne; + } + } +#endif + kind = __Pyx_PyUnicode_KIND(s1); + if (kind != __Pyx_PyUnicode_KIND(s2)) { + goto return_ne; + } + data1 = __Pyx_PyUnicode_DATA(s1); + data2 = __Pyx_PyUnicode_DATA(s2); + if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) { + goto return_ne; + } else if (length == 1) { + goto return_eq; + } else { + int result = memcmp(data1, data2, (size_t)(length * kind)); + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_EQ) ? (result == 0) : (result != 0); + } + } else if ((s1 == Py_None) & s2_is_unicode) { + goto return_ne; + } else if ((s2 == Py_None) & s1_is_unicode) { + goto return_ne; + } else { + int result; + PyObject* py_result = PyObject_RichCompare(s1, s2, equals); + if (!py_result) + return -1; + result = __Pyx_PyObject_IsTrue(py_result); + Py_DECREF(py_result); + return result; + } +return_eq: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_EQ); +return_ne: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(owned_ref); + #endif + return (equals == Py_NE); +#endif +} + +/* GetAttr */ + static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) { +#if CYTHON_COMPILING_IN_CPYTHON +#if PY_MAJOR_VERSION >= 3 + if (likely(PyUnicode_Check(n))) +#else + if (likely(PyString_Check(n))) +#endif + return __Pyx_PyObject_GetAttrStr(o, n); +#endif + return PyObject_GetAttr(o, n); +} + +/* decode_c_string */ + static CYTHON_INLINE PyObject* __Pyx_decode_c_string( + const char* cstring, Py_ssize_t start, Py_ssize_t stop, + const char* encoding, const char* errors, + PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)) { + Py_ssize_t length; + if (unlikely((start < 0) | (stop < 0))) { + size_t slen = strlen(cstring); + if (unlikely(slen > (size_t) PY_SSIZE_T_MAX)) { + PyErr_SetString(PyExc_OverflowError, + "c-string too long to convert to Python"); + return NULL; + } + length = (Py_ssize_t) slen; + if (start < 0) { + start += length; + if (start < 0) + start = 0; + } + if (stop < 0) + stop += length; + } + length = stop - start; + if (unlikely(length <= 0)) + return PyUnicode_FromUnicode(NULL, 0); + cstring += start; + if (decode_func) { + return decode_func(cstring, length, errors); + } else { + return PyUnicode_Decode(cstring, length, encoding, errors); + } +} + +/* GetAttr3 */ + static CYTHON_INLINE PyObject *__Pyx_GetAttr3(PyObject *o, PyObject *n, PyObject *d) { + PyObject *r = __Pyx_GetAttr(o, n); + if (unlikely(!r)) { + if (!PyErr_ExceptionMatches(PyExc_AttributeError)) + goto bad; + PyErr_Clear(); + r = d; + Py_INCREF(d); + } + return r; +bad: + return NULL; +} + +/* SwapException */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = *type; + tstate->exc_value = *value; + tstate->exc_traceback = *tb; + *type = tmp_type; + *value = tmp_value; + *tb = tmp_tb; +} +#else +static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb); + PyErr_SetExcInfo(*type, *value, *tb); + *type = tmp_type; + *value = tmp_value; + *tb = tmp_tb; +} +#endif + +/* Import */ + static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) { + PyObject *empty_list = 0; + PyObject *module = 0; + PyObject *global_dict = 0; + PyObject *empty_dict = 0; + PyObject *list; + #if PY_VERSION_HEX < 0x03030000 + PyObject *py_import; + py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import); + if (!py_import) + goto bad; + #endif + if (from_list) + list = from_list; + else { + empty_list = PyList_New(0); + if (!empty_list) + goto bad; + list = empty_list; + } + global_dict = PyModule_GetDict(__pyx_m); + if (!global_dict) + goto bad; + empty_dict = PyDict_New(); + if (!empty_dict) + goto bad; + { + #if PY_MAJOR_VERSION >= 3 + if (level == -1) { + if (strchr(__Pyx_MODULE_NAME, '.')) { + #if PY_VERSION_HEX < 0x03030000 + PyObject *py_level = PyInt_FromLong(1); + if (!py_level) + goto bad; + module = PyObject_CallFunctionObjArgs(py_import, + name, global_dict, empty_dict, list, py_level, NULL); + Py_DECREF(py_level); + #else + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, 1); + #endif + if (!module) { + if (!PyErr_ExceptionMatches(PyExc_ImportError)) + goto bad; + PyErr_Clear(); + } + } + level = 0; + } + #endif + if (!module) { + #if PY_VERSION_HEX < 0x03030000 + PyObject *py_level = PyInt_FromLong(level); + if (!py_level) + goto bad; + module = PyObject_CallFunctionObjArgs(py_import, + name, global_dict, empty_dict, list, py_level, NULL); + Py_DECREF(py_level); + #else + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, level); + #endif + } + } +bad: + #if PY_VERSION_HEX < 0x03030000 + Py_XDECREF(py_import); + #endif + Py_XDECREF(empty_list); + Py_XDECREF(empty_dict); + return module; +} + +/* PyFunctionFastCall */ + #if CYTHON_FAST_PYCALL +#include "frameobject.h" +static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na, + PyObject *globals) { + PyFrameObject *f; + PyThreadState *tstate = PyThreadState_GET(); + PyObject **fastlocals; + Py_ssize_t i; + PyObject *result; + assert(globals != NULL); + /* XXX Perhaps we should create a specialized + PyFrame_New() that doesn't take locals, but does + take builtins without sanity checking them. + */ + assert(tstate != NULL); + f = PyFrame_New(tstate, co, globals, NULL); + if (f == NULL) { + return NULL; + } + fastlocals = f->f_localsplus; + for (i = 0; i < na; i++) { + Py_INCREF(*args); + fastlocals[i] = *args++; + } + result = PyEval_EvalFrameEx(f,0); + ++tstate->recursion_depth; + Py_DECREF(f); + --tstate->recursion_depth; + return result; +} +#if 1 || PY_VERSION_HEX < 0x030600B1 +static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) { + PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func); + PyObject *globals = PyFunction_GET_GLOBALS(func); + PyObject *argdefs = PyFunction_GET_DEFAULTS(func); + PyObject *closure; +#if PY_MAJOR_VERSION >= 3 + PyObject *kwdefs; +#endif + PyObject *kwtuple, **k; + PyObject **d; + Py_ssize_t nd; + Py_ssize_t nk; + PyObject *result; + assert(kwargs == NULL || PyDict_Check(kwargs)); + nk = kwargs ? PyDict_Size(kwargs) : 0; + if (Py_EnterRecursiveCall((char*)" while calling a Python object")) { + return NULL; + } + if ( +#if PY_MAJOR_VERSION >= 3 + co->co_kwonlyargcount == 0 && +#endif + likely(kwargs == NULL || nk == 0) && + co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) { + if (argdefs == NULL && co->co_argcount == nargs) { + result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals); + goto done; + } + else if (nargs == 0 && argdefs != NULL + && co->co_argcount == Py_SIZE(argdefs)) { + /* function called with no arguments, but all parameters have + a default value: use default values as arguments .*/ + args = &PyTuple_GET_ITEM(argdefs, 0); + result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals); + goto done; + } + } + if (kwargs != NULL) { + Py_ssize_t pos, i; + kwtuple = PyTuple_New(2 * nk); + if (kwtuple == NULL) { + result = NULL; + goto done; + } + k = &PyTuple_GET_ITEM(kwtuple, 0); + pos = i = 0; + while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) { + Py_INCREF(k[i]); + Py_INCREF(k[i+1]); + i += 2; + } + nk = i / 2; + } + else { + kwtuple = NULL; + k = NULL; + } + closure = PyFunction_GET_CLOSURE(func); +#if PY_MAJOR_VERSION >= 3 + kwdefs = PyFunction_GET_KW_DEFAULTS(func); +#endif + if (argdefs != NULL) { + d = &PyTuple_GET_ITEM(argdefs, 0); + nd = Py_SIZE(argdefs); + } + else { + d = NULL; + nd = 0; + } +#if PY_MAJOR_VERSION >= 3 + result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL, + args, nargs, + k, (int)nk, + d, (int)nd, kwdefs, closure); +#else + result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL, + args, nargs, + k, (int)nk, + d, (int)nd, closure); +#endif + Py_XDECREF(kwtuple); +done: + Py_LeaveRecursiveCall(); + return result; +} +#endif +#endif + +/* PyCFunctionFastCall */ + #if CYTHON_FAST_PYCCALL +static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) { + PyCFunctionObject *func = (PyCFunctionObject*)func_obj; + PyCFunction meth = PyCFunction_GET_FUNCTION(func); + PyObject *self = PyCFunction_GET_SELF(func); + int flags = PyCFunction_GET_FLAGS(func); + assert(PyCFunction_Check(func)); + assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS))); + assert(nargs >= 0); + assert(nargs == 0 || args != NULL); + /* _PyCFunction_FastCallDict() must not be called with an exception set, + because it may clear it (directly or indirectly) and so the + caller loses its exception */ + assert(!PyErr_Occurred()); + if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) { + return (*((__Pyx_PyCFunctionFastWithKeywords)meth)) (self, args, nargs, NULL); + } else { + return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs); + } +} +#endif + +/* GetItemInt */ + static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) { + PyObject *r; + if (!j) return NULL; + r = PyObject_GetItem(o, j); + Py_DECREF(j); + return r; +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyList_GET_SIZE(o); + } + if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyList_GET_SIZE(o)))) { + PyObject *r = PyList_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyTuple_GET_SIZE(o); + } + if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS + if (is_list || PyList_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o); + if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) { + PyObject *r = PyList_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } + else if (PyTuple_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o); + if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } else { + PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence; + if (likely(m && m->sq_item)) { + if (wraparound && unlikely(i < 0) && likely(m->sq_length)) { + Py_ssize_t l = m->sq_length(o); + if (likely(l >= 0)) { + i += l; + } else { + if (!PyErr_ExceptionMatches(PyExc_OverflowError)) + return NULL; + PyErr_Clear(); + } + } + return m->sq_item(o, i); + } + } +#else + if (is_list || PySequence_Check(o)) { + return PySequence_GetItem(o, i); + } +#endif + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +} + +/* PyIntBinop */ + #if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyInt_AddObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) { + #if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(op1))) { + const long b = intval; + long x; + long a = PyInt_AS_LONG(op1); + x = (long)((unsigned long)a + b); + if (likely((x^a) >= 0 || (x^b) >= 0)) + return PyInt_FromLong(x); + return PyLong_Type.tp_as_number->nb_add(op1, op2); + } + #endif + #if CYTHON_USE_PYLONG_INTERNALS + if (likely(PyLong_CheckExact(op1))) { + const long b = intval; + long a, x; +#ifdef HAVE_LONG_LONG + const PY_LONG_LONG llb = intval; + PY_LONG_LONG lla, llx; +#endif + const digit* digits = ((PyLongObject*)op1)->ob_digit; + const Py_ssize_t size = Py_SIZE(op1); + if (likely(__Pyx_sst_abs(size) <= 1)) { + a = likely(size) ? digits[0] : 0; + if (size == -1) a = -a; + } else { + switch (size) { + case -2: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + case 2: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + case -3: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + case 3: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + case -4: + if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + case 4: + if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + default: return PyLong_Type.tp_as_number->nb_add(op1, op2); + } + } + x = a + b; + return PyLong_FromLong(x); +#ifdef HAVE_LONG_LONG + long_long: + llx = lla + llb; + return PyLong_FromLongLong(llx); +#endif + + + } + #endif + if (PyFloat_CheckExact(op1)) { + const long b = intval; + double a = PyFloat_AS_DOUBLE(op1); + double result; + PyFPE_START_PROTECT("add", return NULL) + result = ((double)a) + (double)b; + PyFPE_END_PROTECT(result) + return PyFloat_FromDouble(result); + } + return (inplace ? PyNumber_InPlaceAdd : PyNumber_Add)(op1, op2); +} +#endif + +/* WriteUnraisableException */ + static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno, + CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename, + int full_traceback, CYTHON_UNUSED int nogil) { + PyObject *old_exc, *old_val, *old_tb; + PyObject *ctx; + __Pyx_PyThreadState_declare +#ifdef WITH_THREAD + PyGILState_STATE state; + if (nogil) + state = PyGILState_Ensure(); +#ifdef _MSC_VER + else state = (PyGILState_STATE)-1; +#endif +#endif + __Pyx_PyThreadState_assign + __Pyx_ErrFetch(&old_exc, &old_val, &old_tb); + if (full_traceback) { + Py_XINCREF(old_exc); + Py_XINCREF(old_val); + Py_XINCREF(old_tb); + __Pyx_ErrRestore(old_exc, old_val, old_tb); + PyErr_PrintEx(1); + } + #if PY_MAJOR_VERSION < 3 + ctx = PyString_FromString(name); + #else + ctx = PyUnicode_FromString(name); + #endif + __Pyx_ErrRestore(old_exc, old_val, old_tb); + if (!ctx) { + PyErr_WriteUnraisable(Py_None); + } else { + PyErr_WriteUnraisable(ctx); + Py_DECREF(ctx); + } +#ifdef WITH_THREAD + if (nogil) + PyGILState_Release(state); +#endif +} + +/* PyObjectCallMethO */ + #if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) { + PyObject *self, *result; + PyCFunction cfunc; + cfunc = PyCFunction_GET_FUNCTION(func); + self = PyCFunction_GET_SELF(func); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = cfunc(self, arg); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* PyObjectCallOneArg */ + #if CYTHON_COMPILING_IN_CPYTHON +static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_New(1); + if (unlikely(!args)) return NULL; + Py_INCREF(arg); + PyTuple_SET_ITEM(args, 0, arg); + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { +#if CYTHON_FAST_PYCALL + if (PyFunction_Check(func)) { + return __Pyx_PyFunction_FastCall(func, &arg, 1); + } +#endif + if (likely(PyCFunction_Check(func))) { + if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) { + return __Pyx_PyObject_CallMethO(func, arg); +#if CYTHON_FAST_PYCCALL + } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) { + return __Pyx_PyCFunction_FastCall(func, &arg, 1); +#endif + } + } + return __Pyx__PyObject_CallOneArg(func, arg); +} +#else +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_Pack(1, arg); + if (unlikely(!args)) return NULL; + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +#endif + +/* ImportFrom */ + static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) { + PyObject* value = __Pyx_PyObject_GetAttrStr(module, name); + if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) { + PyErr_Format(PyExc_ImportError, + #if PY_MAJOR_VERSION < 3 + "cannot import name %.230s", PyString_AS_STRING(name)); + #else + "cannot import name %S", name); + #endif + } + return value; +} + +/* HasAttr */ + static CYTHON_INLINE int __Pyx_HasAttr(PyObject *o, PyObject *n) { + PyObject *r; + if (unlikely(!__Pyx_PyBaseString_Check(n))) { + PyErr_SetString(PyExc_TypeError, + "hasattr(): attribute name must be string"); + return -1; + } + r = __Pyx_GetAttr(o, n); + if (unlikely(!r)) { + PyErr_Clear(); + return 0; + } else { + Py_DECREF(r); + return 1; + } +} + +/* SetVTable */ + static int __Pyx_SetVtable(PyObject *dict, void *vtable) { +#if PY_VERSION_HEX >= 0x02070000 + PyObject *ob = PyCapsule_New(vtable, 0, 0); +#else + PyObject *ob = PyCObject_FromVoidPtr(vtable, 0); +#endif + if (!ob) + goto bad; + if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0) + goto bad; + Py_DECREF(ob); + return 0; +bad: + Py_XDECREF(ob); + return -1; +} + +/* SetupReduce */ + #define __Pyx_setup_reduce_GET_ATTR_OR_BAD(res, obj, name) res = PyObject_GetAttrString(obj, name); if (res == NULL) goto BAD; +static int __Pyx_setup_reduce_is_named(PyObject* meth, PyObject* name) { + int ret; + PyObject *name_attr; + name_attr = PyObject_GetAttrString(meth, "__name__"); + if (name_attr) { + ret = PyObject_RichCompareBool(name_attr, name, Py_EQ); + } else { + ret = -1; + } + if (ret < 0) { + PyErr_Clear(); + ret = 0; + } + Py_XDECREF(name_attr); + return ret; +} +static int __Pyx_setup_reduce(PyObject* type_obj) { + int ret = 0; + PyObject* builtin_object = NULL; + static PyObject *object_reduce = NULL; + static PyObject *object_reduce_ex = NULL; + PyObject *reduce = NULL; + PyObject *reduce_ex = NULL; + PyObject *reduce_cython = NULL; + PyObject *setstate = NULL; + PyObject *setstate_cython = NULL; + if (PyObject_HasAttrString(type_obj, "__getstate__")) goto GOOD; + if (object_reduce_ex == NULL) { + __Pyx_setup_reduce_GET_ATTR_OR_BAD(builtin_object, __pyx_b, "object"); + __Pyx_setup_reduce_GET_ATTR_OR_BAD(object_reduce, builtin_object, "__reduce__"); + __Pyx_setup_reduce_GET_ATTR_OR_BAD(object_reduce_ex, builtin_object, "__reduce_ex__"); + } + __Pyx_setup_reduce_GET_ATTR_OR_BAD(reduce_ex, type_obj, "__reduce_ex__"); + if (reduce_ex == object_reduce_ex) { + __Pyx_setup_reduce_GET_ATTR_OR_BAD(reduce, type_obj, "__reduce__"); + if (object_reduce == reduce || __Pyx_setup_reduce_is_named(reduce, __pyx_n_s_reduce_cython)) { + __Pyx_setup_reduce_GET_ATTR_OR_BAD(reduce_cython, type_obj, "__reduce_cython__"); + ret = PyDict_SetItemString(((PyTypeObject*)type_obj)->tp_dict, "__reduce__", reduce_cython); if (ret < 0) goto BAD; + ret = PyDict_DelItemString(((PyTypeObject*)type_obj)->tp_dict, "__reduce_cython__"); if (ret < 0) goto BAD; + setstate = PyObject_GetAttrString(type_obj, "__setstate__"); + if (!setstate) PyErr_Clear(); + if (!setstate || __Pyx_setup_reduce_is_named(setstate, __pyx_n_s_setstate_cython)) { + __Pyx_setup_reduce_GET_ATTR_OR_BAD(setstate_cython, type_obj, "__setstate_cython__"); + ret = PyDict_SetItemString(((PyTypeObject*)type_obj)->tp_dict, "__setstate__", setstate_cython); if (ret < 0) goto BAD; + ret = PyDict_DelItemString(((PyTypeObject*)type_obj)->tp_dict, "__setstate_cython__"); if (ret < 0) goto BAD; + } + PyType_Modified((PyTypeObject*)type_obj); + } + } + goto GOOD; +BAD: + if (!PyErr_Occurred()) PyErr_Format(PyExc_RuntimeError, "Unable to initialize pickling for %s", ((PyTypeObject*)type_obj)->tp_name); + ret = -1; +GOOD: + Py_XDECREF(builtin_object); + Py_XDECREF(reduce); + Py_XDECREF(reduce_ex); + Py_XDECREF(reduce_cython); + Py_XDECREF(setstate); + Py_XDECREF(setstate_cython); + return ret; +} + +/* CLineInTraceback */ + static int __Pyx_CLineForTraceback(int c_line) { +#ifdef CYTHON_CLINE_IN_TRACEBACK + return ((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0; +#else + PyObject **cython_runtime_dict; + PyObject *use_cline; + cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime); + if (unlikely(!cython_runtime_dict)) { + PyObject *ptype, *pvalue, *ptraceback; + PyObject *use_cline_obj; + PyErr_Fetch(&ptype, &pvalue, &ptraceback); + use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback); + if (use_cline_obj) { + use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True; + Py_DECREF(use_cline_obj); + } else { + use_cline = NULL; + } + PyErr_Restore(ptype, pvalue, ptraceback); + } else { + use_cline = PyDict_GetItem(*_PyObject_GetDictPtr(__pyx_cython_runtime), __pyx_n_s_cline_in_traceback); + } + if (!use_cline) { + c_line = 0; + PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False); + } + else if (PyObject_Not(use_cline) != 0) { + c_line = 0; + } + return c_line; +#endif +} + +/* CodeObjectCache */ + static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { + int start = 0, mid = 0, end = count - 1; + if (end >= 0 && code_line > entries[end].code_line) { + return count; + } + while (start < end) { + mid = start + (end - start) / 2; + if (code_line < entries[mid].code_line) { + end = mid; + } else if (code_line > entries[mid].code_line) { + start = mid + 1; + } else { + return mid; + } + } + if (code_line <= entries[mid].code_line) { + return mid; + } else { + return mid + 1; + } +} +static PyCodeObject *__pyx_find_code_object(int code_line) { + PyCodeObject* code_object; + int pos; + if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { + return NULL; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { + return NULL; + } + code_object = __pyx_code_cache.entries[pos].code_object; + Py_INCREF(code_object); + return code_object; +} +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { + int pos, i; + __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; + if (unlikely(!code_line)) { + return; + } + if (unlikely(!entries)) { + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); + if (likely(entries)) { + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = 64; + __pyx_code_cache.count = 1; + entries[0].code_line = code_line; + entries[0].code_object = code_object; + Py_INCREF(code_object); + } + return; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { + PyCodeObject* tmp = entries[pos].code_object; + entries[pos].code_object = code_object; + Py_DECREF(tmp); + return; + } + if (__pyx_code_cache.count == __pyx_code_cache.max_count) { + int new_max = __pyx_code_cache.max_count + 64; + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( + __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry)); + if (unlikely(!entries)) { + return; + } + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = new_max; + } + for (i=__pyx_code_cache.count; i>pos; i--) { + entries[i] = entries[i-1]; + } + entries[pos].code_line = code_line; + entries[pos].code_object = code_object; + __pyx_code_cache.count++; + Py_INCREF(code_object); +} + +/* AddTraceback */ + #include "compile.h" +#include "frameobject.h" +#include "traceback.h" +static PyCodeObject* __Pyx_CreateCodeObjectForTraceback( + const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyObject *py_srcfile = 0; + PyObject *py_funcname = 0; + #if PY_MAJOR_VERSION < 3 + py_srcfile = PyString_FromString(filename); + #else + py_srcfile = PyUnicode_FromString(filename); + #endif + if (!py_srcfile) goto bad; + if (c_line) { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #else + py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #endif + } + else { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromString(funcname); + #else + py_funcname = PyUnicode_FromString(funcname); + #endif + } + if (!py_funcname) goto bad; + py_code = __Pyx_PyCode_New( + 0, + 0, + 0, + 0, + 0, + __pyx_empty_bytes, /*PyObject *code,*/ + __pyx_empty_tuple, /*PyObject *consts,*/ + __pyx_empty_tuple, /*PyObject *names,*/ + __pyx_empty_tuple, /*PyObject *varnames,*/ + __pyx_empty_tuple, /*PyObject *freevars,*/ + __pyx_empty_tuple, /*PyObject *cellvars,*/ + py_srcfile, /*PyObject *filename,*/ + py_funcname, /*PyObject *name,*/ + py_line, + __pyx_empty_bytes /*PyObject *lnotab*/ + ); + Py_DECREF(py_srcfile); + Py_DECREF(py_funcname); + return py_code; +bad: + Py_XDECREF(py_srcfile); + Py_XDECREF(py_funcname); + return NULL; +} +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyFrameObject *py_frame = 0; + if (c_line) { + c_line = __Pyx_CLineForTraceback(c_line); + } + py_code = __pyx_find_code_object(c_line ? -c_line : py_line); + if (!py_code) { + py_code = __Pyx_CreateCodeObjectForTraceback( + funcname, c_line, py_line, filename); + if (!py_code) goto bad; + __pyx_insert_code_object(c_line ? -c_line : py_line, py_code); + } + py_frame = PyFrame_New( + PyThreadState_GET(), /*PyThreadState *tstate,*/ + py_code, /*PyCodeObject *code,*/ + __pyx_d, /*PyObject *globals,*/ + 0 /*PyObject *locals*/ + ); + if (!py_frame) goto bad; + __Pyx_PyFrame_SetLineNumber(py_frame, py_line); + PyTraceBack_Here(py_frame); +bad: + Py_XDECREF(py_code); + Py_XDECREF(py_frame); +} + +#if PY_MAJOR_VERSION < 3 +static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) { + if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags); + if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags); + if (PyObject_TypeCheck(obj, __pyx_array_type)) return __pyx_array_getbuffer(obj, view, flags); + if (PyObject_TypeCheck(obj, __pyx_memoryview_type)) return __pyx_memoryview_getbuffer(obj, view, flags); + PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name); + return -1; +} +static void __Pyx_ReleaseBuffer(Py_buffer *view) { + PyObject *obj = view->obj; + if (!obj) return; + if (PyObject_CheckBuffer(obj)) { + PyBuffer_Release(view); + return; + } + if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; } + Py_DECREF(obj); + view->obj = NULL; +} +#endif + + + /* MemviewSliceIsContig */ + static int +__pyx_memviewslice_is_contig(const __Pyx_memviewslice mvs, + char order, int ndim) +{ + int i, index, step, start; + Py_ssize_t itemsize = mvs.memview->view.itemsize; + if (order == 'F') { + step = 1; + start = 0; + } else { + step = -1; + start = ndim - 1; + } + for (i = 0; i < ndim; i++) { + index = start + step * i; + if (mvs.suboffsets[index] >= 0 || mvs.strides[index] != itemsize) + return 0; + itemsize *= mvs.shape[index]; + } + return 1; +} + +/* OverlappingSlices */ + static void +__pyx_get_array_memory_extents(__Pyx_memviewslice *slice, + void **out_start, void **out_end, + int ndim, size_t itemsize) +{ + char *start, *end; + int i; + start = end = slice->data; + for (i = 0; i < ndim; i++) { + Py_ssize_t stride = slice->strides[i]; + Py_ssize_t extent = slice->shape[i]; + if (extent == 0) { + *out_start = *out_end = start; + return; + } else { + if (stride > 0) + end += stride * (extent - 1); + else + start += stride * (extent - 1); + } + } + *out_start = start; + *out_end = end + itemsize; +} +static int +__pyx_slices_overlap(__Pyx_memviewslice *slice1, + __Pyx_memviewslice *slice2, + int ndim, size_t itemsize) +{ + void *start1, *end1, *start2, *end2; + __pyx_get_array_memory_extents(slice1, &start1, &end1, ndim, itemsize); + __pyx_get_array_memory_extents(slice2, &start2, &end2, ndim, itemsize); + return (start1 < end2) && (start2 < end1); +} + +/* Capsule */ + static CYTHON_INLINE PyObject * +__pyx_capsule_create(void *p, CYTHON_UNUSED const char *sig) +{ + PyObject *cobj; +#if PY_VERSION_HEX >= 0x02070000 + cobj = PyCapsule_New(p, sig, NULL); +#else + cobj = PyCObject_FromVoidPtr(p, NULL); +#endif + return cobj; +} + +/* TypeInfoCompare */ + static int +__pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b) +{ + int i; + if (!a || !b) + return 0; + if (a == b) + return 1; + if (a->size != b->size || a->typegroup != b->typegroup || + a->is_unsigned != b->is_unsigned || a->ndim != b->ndim) { + if (a->typegroup == 'H' || b->typegroup == 'H') { + return a->size == b->size; + } else { + return 0; + } + } + if (a->ndim) { + for (i = 0; i < a->ndim; i++) + if (a->arraysize[i] != b->arraysize[i]) + return 0; + } + if (a->typegroup == 'S') { + if (a->flags != b->flags) + return 0; + if (a->fields || b->fields) { + if (!(a->fields && b->fields)) + return 0; + for (i = 0; a->fields[i].type && b->fields[i].type; i++) { + __Pyx_StructField *field_a = a->fields + i; + __Pyx_StructField *field_b = b->fields + i; + if (field_a->offset != field_b->offset || + !__pyx_typeinfo_cmp(field_a->type, field_b->type)) + return 0; + } + return !a->fields[i].type && !b->fields[i].type; + } + } + return 1; +} + +/* MemviewSliceValidateAndInit */ + static int +__pyx_check_strides(Py_buffer *buf, int dim, int ndim, int spec) +{ + if (buf->shape[dim] <= 1) + return 1; + if (buf->strides) { + if (spec & __Pyx_MEMVIEW_CONTIG) { + if (spec & (__Pyx_MEMVIEW_PTR|__Pyx_MEMVIEW_FULL)) { + if (buf->strides[dim] != sizeof(void *)) { + PyErr_Format(PyExc_ValueError, + "Buffer is not indirectly contiguous " + "in dimension %d.", dim); + goto fail; + } + } else if (buf->strides[dim] != buf->itemsize) { + PyErr_SetString(PyExc_ValueError, + "Buffer and memoryview are not contiguous " + "in the same dimension."); + goto fail; + } + } + if (spec & __Pyx_MEMVIEW_FOLLOW) { + Py_ssize_t stride = buf->strides[dim]; + if (stride < 0) + stride = -stride; + if (stride < buf->itemsize) { + PyErr_SetString(PyExc_ValueError, + "Buffer and memoryview are not contiguous " + "in the same dimension."); + goto fail; + } + } + } else { + if (spec & __Pyx_MEMVIEW_CONTIG && dim != ndim - 1) { + PyErr_Format(PyExc_ValueError, + "C-contiguous buffer is not contiguous in " + "dimension %d", dim); + goto fail; + } else if (spec & (__Pyx_MEMVIEW_PTR)) { + PyErr_Format(PyExc_ValueError, + "C-contiguous buffer is not indirect in " + "dimension %d", dim); + goto fail; + } else if (buf->suboffsets) { + PyErr_SetString(PyExc_ValueError, + "Buffer exposes suboffsets but no strides"); + goto fail; + } + } + return 1; +fail: + return 0; +} +static int +__pyx_check_suboffsets(Py_buffer *buf, int dim, CYTHON_UNUSED int ndim, int spec) +{ + if (spec & __Pyx_MEMVIEW_DIRECT) { + if (buf->suboffsets && buf->suboffsets[dim] >= 0) { + PyErr_Format(PyExc_ValueError, + "Buffer not compatible with direct access " + "in dimension %d.", dim); + goto fail; + } + } + if (spec & __Pyx_MEMVIEW_PTR) { + if (!buf->suboffsets || (buf->suboffsets && buf->suboffsets[dim] < 0)) { + PyErr_Format(PyExc_ValueError, + "Buffer is not indirectly accessible " + "in dimension %d.", dim); + goto fail; + } + } + return 1; +fail: + return 0; +} +static int +__pyx_verify_contig(Py_buffer *buf, int ndim, int c_or_f_flag) +{ + int i; + if (c_or_f_flag & __Pyx_IS_F_CONTIG) { + Py_ssize_t stride = 1; + for (i = 0; i < ndim; i++) { + if (stride * buf->itemsize != buf->strides[i] && + buf->shape[i] > 1) + { + PyErr_SetString(PyExc_ValueError, + "Buffer not fortran contiguous."); + goto fail; + } + stride = stride * buf->shape[i]; + } + } else if (c_or_f_flag & __Pyx_IS_C_CONTIG) { + Py_ssize_t stride = 1; + for (i = ndim - 1; i >- 1; i--) { + if (stride * buf->itemsize != buf->strides[i] && + buf->shape[i] > 1) { + PyErr_SetString(PyExc_ValueError, + "Buffer not C contiguous."); + goto fail; + } + stride = stride * buf->shape[i]; + } + } + return 1; +fail: + return 0; +} +static int __Pyx_ValidateAndInit_memviewslice( + int *axes_specs, + int c_or_f_flag, + int buf_flags, + int ndim, + __Pyx_TypeInfo *dtype, + __Pyx_BufFmt_StackElem stack[], + __Pyx_memviewslice *memviewslice, + PyObject *original_obj) +{ + struct __pyx_memoryview_obj *memview, *new_memview; + __Pyx_RefNannyDeclarations + Py_buffer *buf; + int i, spec = 0, retval = -1; + __Pyx_BufFmt_Context ctx; + int from_memoryview = __pyx_memoryview_check(original_obj); + __Pyx_RefNannySetupContext("ValidateAndInit_memviewslice", 0); + if (from_memoryview && __pyx_typeinfo_cmp(dtype, ((struct __pyx_memoryview_obj *) + original_obj)->typeinfo)) { + memview = (struct __pyx_memoryview_obj *) original_obj; + new_memview = NULL; + } else { + memview = (struct __pyx_memoryview_obj *) __pyx_memoryview_new( + original_obj, buf_flags, 0, dtype); + new_memview = memview; + if (unlikely(!memview)) + goto fail; + } + buf = &memview->view; + if (buf->ndim != ndim) { + PyErr_Format(PyExc_ValueError, + "Buffer has wrong number of dimensions (expected %d, got %d)", + ndim, buf->ndim); + goto fail; + } + if (new_memview) { + __Pyx_BufFmt_Init(&ctx, stack, dtype); + if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail; + } + if ((unsigned) buf->itemsize != dtype->size) { + PyErr_Format(PyExc_ValueError, + "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "u byte%s) " + "does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "u byte%s)", + buf->itemsize, + (buf->itemsize > 1) ? "s" : "", + dtype->name, + dtype->size, + (dtype->size > 1) ? "s" : ""); + goto fail; + } + for (i = 0; i < ndim; i++) { + spec = axes_specs[i]; + if (!__pyx_check_strides(buf, i, ndim, spec)) + goto fail; + if (!__pyx_check_suboffsets(buf, i, ndim, spec)) + goto fail; + } + if (buf->strides && !__pyx_verify_contig(buf, ndim, c_or_f_flag)) + goto fail; + if (unlikely(__Pyx_init_memviewslice(memview, ndim, memviewslice, + new_memview != NULL) == -1)) { + goto fail; + } + retval = 0; + goto no_fail; +fail: + Py_XDECREF(new_memview); + retval = -1; +no_fail: + __Pyx_RefNannyFinishContext(); + return retval; +} + +/* ObjectToMemviewSlice */ + static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_double(PyObject *obj) { + __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } }; + __Pyx_BufFmt_StackElem stack[1]; + int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED), (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) }; + int retcode; + if (obj == Py_None) { + result.memview = (struct __pyx_memoryview_obj *) Py_None; + return result; + } + retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0, + PyBUF_RECORDS, 2, + &__Pyx_TypeInfo_double, stack, + &result, obj); + if (unlikely(retcode == -1)) + goto __pyx_fail; + return result; +__pyx_fail: + result.memview = NULL; + result.data = NULL; + return result; +} + +/* CIntFromPyVerify */ + #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) +#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) +#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ + {\ + func_type value = func_value;\ + if (sizeof(target_type) < sizeof(func_type)) {\ + if (unlikely(value != (func_type) (target_type) value)) {\ + func_type zero = 0;\ + if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ + return (target_type) -1;\ + if (is_unsigned && unlikely(value < zero))\ + goto raise_neg_overflow;\ + else\ + goto raise_overflow;\ + }\ + }\ + return (target_type) value;\ + } + +/* ObjectToMemviewSlice */ + static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *obj) { + __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } }; + __Pyx_BufFmt_StackElem stack[1]; + int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) }; + int retcode; + if (obj == Py_None) { + result.memview = (struct __pyx_memoryview_obj *) Py_None; + return result; + } + retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0, + PyBUF_RECORDS, 1, + &__Pyx_TypeInfo_double, stack, + &result, obj); + if (unlikely(retcode == -1)) + goto __pyx_fail; + return result; +__pyx_fail: + result.memview = NULL; + result.data = NULL; + return result; +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) { + const int neg_one = (int) -1, const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(int) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(int) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(int) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(int), + little, !is_unsigned); + } +} + +/* MemviewDtypeToObject */ + static CYTHON_INLINE PyObject *__pyx_memview_get_double(const char *itemp) { + return (PyObject *) PyFloat_FromDouble(*(double *) itemp); +} +static CYTHON_INLINE int __pyx_memview_set_double(const char *itemp, PyObject *obj) { + double value = __pyx_PyFloat_AsDouble(obj); + if ((value == (double)-1) && PyErr_Occurred()) + return 0; + *(double *) itemp = value; + return 1; +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_Py_intptr_t(Py_intptr_t value) { + const Py_intptr_t neg_one = (Py_intptr_t) -1, const_zero = (Py_intptr_t) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(Py_intptr_t) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(Py_intptr_t) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(Py_intptr_t) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(Py_intptr_t) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(Py_intptr_t), + little, !is_unsigned); + } +} + +/* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return ::std::complex< float >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return x + y*(__pyx_t_float_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + __pyx_t_float_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabsf(b.real) >= fabsf(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + float r = b.imag / b.real; + float s = 1.0 / (b.real + b.imag * r); + return __pyx_t_float_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + float r = b.real / b.imag; + float s = 1.0 / (b.imag + b.real * r); + return __pyx_t_float_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + float denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_float_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrtf(z.real*z.real + z.imag*z.imag); + #else + return hypotf(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + float r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + float denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(a, a); + case 3: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, a); + case 4: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = powf(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2f(0, -1); + } + } else { + r = __Pyx_c_abs_float(a); + theta = atan2f(a.imag, a.real); + } + lnr = logf(r); + z_r = expf(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cosf(z_theta); + z.imag = z_r * sinf(z_theta); + return z; + } + #endif +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return ::std::complex< double >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return x + y*(__pyx_t_double_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + __pyx_t_double_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabs(b.real) >= fabs(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + double r = b.imag / b.real; + double s = 1.0 / (b.real + b.imag * r); + return __pyx_t_double_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + double r = b.real / b.imag; + double s = 1.0 / (b.imag + b.real * r); + return __pyx_t_double_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + double denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_double_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrt(z.real*z.real + z.imag*z.imag); + #else + return hypot(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + double r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + double denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(a, a); + case 3: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, a); + case 4: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = pow(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2(0, -1); + } + } else { + r = __Pyx_c_abs_double(a); + theta = atan2(a.imag, a.real); + } + lnr = log(r); + z_r = exp(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cos(z_theta); + z.imag = z_r * sin(z_theta); + return z; + } + #endif +#endif + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) { + const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(enum NPY_TYPES) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(enum NPY_TYPES) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES), + little, !is_unsigned); + } +} + +/* MemviewSliceCopyTemplate */ + static __Pyx_memviewslice +__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs, + const char *mode, int ndim, + size_t sizeof_dtype, int contig_flag, + int dtype_is_object) +{ + __Pyx_RefNannyDeclarations + int i; + __Pyx_memviewslice new_mvs = { 0, 0, { 0 }, { 0 }, { 0 } }; + struct __pyx_memoryview_obj *from_memview = from_mvs->memview; + Py_buffer *buf = &from_memview->view; + PyObject *shape_tuple = NULL; + PyObject *temp_int = NULL; + struct __pyx_array_obj *array_obj = NULL; + struct __pyx_memoryview_obj *memview_obj = NULL; + __Pyx_RefNannySetupContext("__pyx_memoryview_copy_new_contig", 0); + for (i = 0; i < ndim; i++) { + if (from_mvs->suboffsets[i] >= 0) { + PyErr_Format(PyExc_ValueError, "Cannot copy memoryview slice with " + "indirect dimensions (axis %d)", i); + goto fail; + } + } + shape_tuple = PyTuple_New(ndim); + if (unlikely(!shape_tuple)) { + goto fail; + } + __Pyx_GOTREF(shape_tuple); + for(i = 0; i < ndim; i++) { + temp_int = PyInt_FromSsize_t(from_mvs->shape[i]); + if(unlikely(!temp_int)) { + goto fail; + } else { + PyTuple_SET_ITEM(shape_tuple, i, temp_int); + temp_int = NULL; + } + } + array_obj = __pyx_array_new(shape_tuple, sizeof_dtype, buf->format, (char *) mode, NULL); + if (unlikely(!array_obj)) { + goto fail; + } + __Pyx_GOTREF(array_obj); + memview_obj = (struct __pyx_memoryview_obj *) __pyx_memoryview_new( + (PyObject *) array_obj, contig_flag, + dtype_is_object, + from_mvs->memview->typeinfo); + if (unlikely(!memview_obj)) + goto fail; + if (unlikely(__Pyx_init_memviewslice(memview_obj, ndim, &new_mvs, 1) < 0)) + goto fail; + if (unlikely(__pyx_memoryview_copy_contents(*from_mvs, new_mvs, ndim, ndim, + dtype_is_object) < 0)) + goto fail; + goto no_fail; +fail: + __Pyx_XDECREF(new_mvs.memview); + new_mvs.memview = NULL; + new_mvs.data = NULL; +no_fail: + __Pyx_XDECREF(shape_tuple); + __Pyx_XDECREF(temp_int); + __Pyx_XDECREF(array_obj); + __Pyx_RefNannyFinishContext(); + return new_mvs; +} + +/* CIntFromPy */ + static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *x) { + const char neg_one = (char) -1, const_zero = (char) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(char) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(char, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (char) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (char) 0; + case 1: __PYX_VERIFY_RETURN_INT(char, digit, digits[0]) + case 2: + if (8 * sizeof(char) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) >= 2 * PyLong_SHIFT) { + return (char) (((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(char) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) >= 3 * PyLong_SHIFT) { + return (char) (((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(char) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) >= 4 * PyLong_SHIFT) { + return (char) (((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (char) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(char) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(char, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(char) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(char, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (char) 0; + case -1: __PYX_VERIFY_RETURN_INT(char, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(char, digit, +digits[0]) + case -2: + if (8 * sizeof(char) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) { + return (char) (((char)-1)*(((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(char) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) { + return (char) ((((((char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(char) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) { + return (char) (((char)-1)*(((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(char) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) { + return (char) ((((((((char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(char) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 4 * PyLong_SHIFT) { + return (char) (((char)-1)*(((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(char) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(char, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(char) - 1 > 4 * PyLong_SHIFT) { + return (char) ((((((((((char)digits[3]) << PyLong_SHIFT) | (char)digits[2]) << PyLong_SHIFT) | (char)digits[1]) << PyLong_SHIFT) | (char)digits[0]))); + } + } + break; + } +#endif + if (sizeof(char) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(char, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(char) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(char, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + char val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (char) -1; + } + } else { + char val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (char) -1; + val = __Pyx_PyInt_As_char(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to char"); + return (char) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to char"); + return (char) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { + const int neg_one = (int) -1, const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(int) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (int) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { + return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { + return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { + return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (int) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(int) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) + case -2: + if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + } +#endif + if (sizeof(int) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + int val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (int) -1; + } + } else { + int val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (int) -1; + val = __Pyx_PyInt_As_int(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to int"); + return (int) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to int"); + return (int) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) { + const long neg_one = (long) -1, const_zero = (long) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(long) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (long) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { + return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { + return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { + return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (long) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(long) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) + case -2: + if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + } +#endif + if (sizeof(long) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + long val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (long) -1; + } + } else { + long val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (long) -1; + val = __Pyx_PyInt_As_long(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to long"); + return (long) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to long"); + return (long) -1; +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { + const long neg_one = (long) -1, const_zero = (long) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(long) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(long) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(long), + little, !is_unsigned); + } +} + +/* CheckBinaryVersion */ + static int __Pyx_check_binary_version(void) { + char ctversion[4], rtversion[4]; + PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION); + PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion()); + if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) { + char message[200]; + PyOS_snprintf(message, sizeof(message), + "compiletime version %s of module '%.100s' " + "does not match runtime version %s", + ctversion, __Pyx_MODULE_NAME, rtversion); + return PyErr_WarnEx(NULL, message, 1); + } + return 0; +} + +/* ModuleImport */ + #ifndef __PYX_HAVE_RT_ImportModule +#define __PYX_HAVE_RT_ImportModule +static PyObject *__Pyx_ImportModule(const char *name) { + PyObject *py_name = 0; + PyObject *py_module = 0; + py_name = __Pyx_PyIdentifier_FromString(name); + if (!py_name) + goto bad; + py_module = PyImport_Import(py_name); + Py_DECREF(py_name); + return py_module; +bad: + Py_XDECREF(py_name); + return 0; +} +#endif + +/* TypeImport */ + #ifndef __PYX_HAVE_RT_ImportType +#define __PYX_HAVE_RT_ImportType +static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, + size_t size, int strict) +{ + PyObject *py_module = 0; + PyObject *result = 0; + PyObject *py_name = 0; + char warning[200]; + Py_ssize_t basicsize; +#ifdef Py_LIMITED_API + PyObject *py_basicsize; +#endif + py_module = __Pyx_ImportModule(module_name); + if (!py_module) + goto bad; + py_name = __Pyx_PyIdentifier_FromString(class_name); + if (!py_name) + goto bad; + result = PyObject_GetAttr(py_module, py_name); + Py_DECREF(py_name); + py_name = 0; + Py_DECREF(py_module); + py_module = 0; + if (!result) + goto bad; + if (!PyType_Check(result)) { + PyErr_Format(PyExc_TypeError, + "%.200s.%.200s is not a type object", + module_name, class_name); + goto bad; + } +#ifndef Py_LIMITED_API + basicsize = ((PyTypeObject *)result)->tp_basicsize; +#else + py_basicsize = PyObject_GetAttrString(result, "__basicsize__"); + if (!py_basicsize) + goto bad; + basicsize = PyLong_AsSsize_t(py_basicsize); + Py_DECREF(py_basicsize); + py_basicsize = 0; + if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred()) + goto bad; +#endif + if (!strict && (size_t)basicsize > size) { + PyOS_snprintf(warning, sizeof(warning), + "%s.%s size changed, may indicate binary incompatibility. Expected %zd, got %zd", + module_name, class_name, basicsize, size); + if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad; + } + else if ((size_t)basicsize != size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s has the wrong size, try recompiling. Expected %zd, got %zd", + module_name, class_name, basicsize, size); + goto bad; + } + return (PyTypeObject *)result; +bad: + Py_XDECREF(py_module); + Py_XDECREF(result); + return NULL; +} +#endif + +/* InitStrings */ + static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) { + while (t->p) { + #if PY_MAJOR_VERSION < 3 + if (t->is_unicode) { + *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL); + } else if (t->intern) { + *t->p = PyString_InternFromString(t->s); + } else { + *t->p = PyString_FromStringAndSize(t->s, t->n - 1); + } + #else + if (t->is_unicode | t->is_str) { + if (t->intern) { + *t->p = PyUnicode_InternFromString(t->s); + } else if (t->encoding) { + *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL); + } else { + *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1); + } + } else { + *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1); + } + #endif + if (!*t->p) + return -1; + if (PyObject_Hash(*t->p) == -1) + PyErr_Clear(); + ++t; + } + return 0; +} + +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) { + return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str)); +} +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) { + Py_ssize_t ignore; + return __Pyx_PyObject_AsStringAndSize(o, &ignore); +} +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) { +#if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT) + if ( +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + __Pyx_sys_getdefaultencoding_not_ascii && +#endif + PyUnicode_Check(o)) { +#if PY_VERSION_HEX < 0x03030000 + char* defenc_c; + PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL); + if (!defenc) return NULL; + defenc_c = PyBytes_AS_STRING(defenc); +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + { + char* end = defenc_c + PyBytes_GET_SIZE(defenc); + char* c; + for (c = defenc_c; c < end; c++) { + if ((unsigned char) (*c) >= 128) { + PyUnicode_AsASCIIString(o); + return NULL; + } + } + } +#endif + *length = PyBytes_GET_SIZE(defenc); + return defenc_c; +#else + if (__Pyx_PyUnicode_READY(o) == -1) return NULL; +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + if (PyUnicode_IS_ASCII(o)) { + *length = PyUnicode_GET_LENGTH(o); + return PyUnicode_AsUTF8(o); + } else { + PyUnicode_AsASCIIString(o); + return NULL; + } +#else + return PyUnicode_AsUTF8AndSize(o, length); +#endif +#endif + } else +#endif +#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) + if (PyByteArray_Check(o)) { + *length = PyByteArray_GET_SIZE(o); + return PyByteArray_AS_STRING(o); + } else +#endif + { + char* result; + int r = PyBytes_AsStringAndSize(o, &result, length); + if (unlikely(r < 0)) { + return NULL; + } else { + return result; + } + } +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { + int is_true = x == Py_True; + if (is_true | (x == Py_False) | (x == Py_None)) return is_true; + else return PyObject_IsTrue(x); +} +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) { +#if CYTHON_USE_TYPE_SLOTS + PyNumberMethods *m; +#endif + const char *name = NULL; + PyObject *res = NULL; +#if PY_MAJOR_VERSION < 3 + if (PyInt_Check(x) || PyLong_Check(x)) +#else + if (PyLong_Check(x)) +#endif + return __Pyx_NewRef(x); +#if CYTHON_USE_TYPE_SLOTS + m = Py_TYPE(x)->tp_as_number; + #if PY_MAJOR_VERSION < 3 + if (m && m->nb_int) { + name = "int"; + res = PyNumber_Int(x); + } + else if (m && m->nb_long) { + name = "long"; + res = PyNumber_Long(x); + } + #else + if (m && m->nb_int) { + name = "int"; + res = PyNumber_Long(x); + } + #endif +#else + res = PyNumber_Int(x); +#endif + if (res) { +#if PY_MAJOR_VERSION < 3 + if (!PyInt_Check(res) && !PyLong_Check(res)) { +#else + if (!PyLong_Check(res)) { +#endif + PyErr_Format(PyExc_TypeError, + "__%.4s__ returned non-%.4s (type %.200s)", + name, name, Py_TYPE(res)->tp_name); + Py_DECREF(res); + return NULL; + } + } + else if (!PyErr_Occurred()) { + PyErr_SetString(PyExc_TypeError, + "an integer is required"); + } + return res; +} +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) { + Py_ssize_t ival; + PyObject *x; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(b))) { + if (sizeof(Py_ssize_t) >= sizeof(long)) + return PyInt_AS_LONG(b); + else + return PyInt_AsSsize_t(x); + } +#endif + if (likely(PyLong_CheckExact(b))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)b)->ob_digit; + const Py_ssize_t size = Py_SIZE(b); + if (likely(__Pyx_sst_abs(size) <= 1)) { + ival = likely(size) ? digits[0] : 0; + if (size == -1) ival = -ival; + return ival; + } else { + switch (size) { + case 2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + } + } + #endif + return PyLong_AsSsize_t(b); + } + x = PyNumber_Index(b); + if (!x) return -1; + ival = PyInt_AsSsize_t(x); + Py_DECREF(x); + return ival; +} +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { + return PyInt_FromSize_t(ival); +} + + +#endif /* Py_PYTHON_H */ diff --git a/Orange/distance/_distance.pyx b/Orange/distance/_distance.pyx new file mode 100644 index 00000000000..d06af54d1dd --- /dev/null +++ b/Orange/distance/_distance.pyx @@ -0,0 +1,502 @@ +#cython: embedsignature=True +#cython: infer_types=True +#cython: cdivision=True +#cython: boundscheck=False +#cython: wraparound=False + +import numpy as np +cimport numpy as np + +cdef extern from "numpy/npy_math.h": + bint npy_isnan(double x) nogil + +cdef extern from "math.h": + double fabs(double x) nogil + double sqrt(double x) nogil + + +cpdef void lower_to_symmetric(double [:, :] distances): + cdef int row1, row2 + for row1 in range(distances.shape[0]): + for row2 in range(row1): + distances[row2, row1] = distances[row1, row2] + + +def euclidean_rows_discrete(np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + double[:, :] dist_missing, + np.ndarray[np.float64_t, ndim=1] dist_missing2, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + int ival1, ival2 + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + d = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + ival1, ival2 = int(val1), int(val2) + if npy_isnan(val1): + if npy_isnan(val2): + d += dist_missing2[col] + else: + d += dist_missing[col, ival2] + elif npy_isnan(val2): + d += dist_missing[col, ival1] + elif ival1 != ival2: + d += 1 + distances[row1, row2] += d + + +def fix_euclidean_rows( + np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + np.ndarray[np.float64_t, ndim=1] means, + np.ndarray[np.float64_t, ndim=1] vars, + np.ndarray[np.float64_t, ndim=1] dist_missing2, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + if npy_isnan(distances[row1, row2]): + d = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + if npy_isnan(val1): + if npy_isnan(val2): + d += dist_missing2[col] + else: + d += (val2 - means[col]) ** 2 + vars[col] + elif npy_isnan(val2): + d += (val1 - means[col]) ** 2 + vars[col] + else: + d += (val1 - val2) ** 2 + distances[row1, row2] = d + if not two_tables: + distances[row2, row1] = d + + +def fix_euclidean_rows_normalized( + np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + np.ndarray[np.float64_t, ndim=1] means, + np.ndarray[np.float64_t, ndim=1] vars, + np.ndarray[np.float64_t, ndim=1] dist_missing2, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + if npy_isnan(distances[row1, row2]): + d = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + if npy_isnan(val1): + if npy_isnan(val2): + d += dist_missing2[col] + else: + d += val2 ** 2 + 0.5 + elif npy_isnan(val2): + d += val1 ** 2 + 0.5 + else: + d += (val1 - val2) ** 2 + distances[row1, row2] = d + if not two_tables: + distances[row2, row1] = d + + +def fix_euclidean_cols( + np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x, + double[:] means, + double[:] vars): + cdef: + int n_rows, n_cols, col1, col2, row + double val1, val2, d + + n_rows, n_cols = x.shape[0], x.shape[1] + with nogil: + for col1 in range(n_cols): + for col2 in range(col1): + if npy_isnan(distances[col1, col2]): + d = 0 + for row in range(n_rows): + val1, val2 = x[row, col1], x[row, col2] + if npy_isnan(val1): + if npy_isnan(val2): + d += vars[col1] + vars[col2] \ + + (means[col1] - means[col2]) ** 2 + else: + d += (val2 - means[col1]) ** 2 + vars[col1] + elif npy_isnan(val2): + d += (val1 - means[col2]) ** 2 + vars[col2] + else: + d += (val1 - val2) ** 2 + distances[col1, col2] = distances[col2, col1] = d + + +def fix_euclidean_cols_normalized( + np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x, + double[:] means, + double[:] vars): + cdef: + int n_rows, n_cols, col1, col2, row + double val1, val2, d + + n_rows, n_cols = x.shape[0], x.shape[1] + with nogil: + for col1 in range(n_cols): + for col2 in range(col1): + if npy_isnan(distances[col1, col2]): + d = 0 + for row in range(n_rows): + val1, val2 = x[row, col1], x[row, col2] + if npy_isnan(val1): + if npy_isnan(val2): + d += 1 + else: + d += val2 ** 2 + 0.5 + elif npy_isnan(val2): + d += val1 ** 2 + 0.5 + else: + d += (val1 - val2) ** 2 + distances[col1, col2] = distances[col2, col1] = d + + +def manhattan_rows_cont(np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + np.ndarray[np.float64_t, ndim=2] distances + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] + distances = np.zeros((n_rows1, n_rows2), dtype=float) + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + d = 0 + for col in range(n_cols): + d += fabs(x1[row1, col] - x2[row2, col]) + distances[row1, row2] = d + return distances + +def fix_manhattan_rows(np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + np.ndarray[np.float64_t, ndim=1] medians, + np.ndarray[np.float64_t, ndim=1] mads, + np.ndarray[np.float64_t, ndim=1] dist_missing2_cont, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] if two_tables else 0 + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + if npy_isnan(distances[row1, row2]): + d = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + if npy_isnan(val1): + if npy_isnan(val2): + d += dist_missing2_cont[col] + else: + d += fabs(val2 - medians[col]) + mads[col] + elif npy_isnan(val2): + d += fabs(val1 - medians[col]) + mads[col] + else: + d += fabs(val1 - val2) + distances[row1, row2] = d + return distances + + +def fix_manhattan_rows_normalized(np.ndarray[np.float64_t, ndim=2] distances, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + double val1, val2, d + + n_rows1, n_cols = x1.shape[0], x1.shape[1] + n_rows2 = x2.shape[0] if two_tables else 0 + with nogil: + for row1 in range(n_rows1): + for row2 in range(n_rows2 if two_tables else row1): + if npy_isnan(distances[row1, row2]): + d = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + if npy_isnan(val1): + if npy_isnan(val2): + d += 1 + else: + d += fabs(val2) + 0.5 + elif npy_isnan(val2): + d += fabs(val1) + 0.5 + else: + d += fabs(val1 - val2) + distances[row1, row2] = d + return distances + + +def manhattan_cols(np.ndarray[np.float64_t, ndim=2] x, + np.ndarray[np.float64_t, ndim=1] medians, + np.ndarray[np.float64_t, ndim=1] mads, + char normalize): + cdef: + int n_rows, n_cols, col1, col2, row + double val1, val2, d + double [:, :] distances + + n_rows, n_cols = x.shape[0], x.shape[1] + distances = np.zeros((n_cols, n_cols), dtype=float) + with nogil: + for col1 in range(n_cols): + for col2 in range(col1): + d = 0 + for row in range(n_rows): + val1, val2 = x[row, col1], x[row, col2] + if npy_isnan(val1): + if npy_isnan(val2): + if normalize: + d += 1 + else: + d += mads[col1] + mads[col2] \ + + fabs(medians[col1] - medians[col2]) + else: + if normalize: + d += fabs(val2) + 0.5 + else: + d += fabs(val2 - medians[col1]) + mads[col1] + else: + if npy_isnan(val2): + if normalize: + d += fabs(val1) + 0.5 + else: + d += fabs(val1 - medians[col2]) + mads[col2] + else: + d += fabs(val1 - val2) + distances[col1, col2] = distances[col2, col1] = d + return distances + + +def p_nonzero(np.ndarray[np.float64_t, ndim=1] x): + cdef: + int row, nonzeros, nonnans + double val + + nonzeros = nonnans = 0 + for row in range(len(x)): + val = x[row] + if not npy_isnan(val): + nonnans += 1 + if val != 0: + nonzeros += 1 + return float(nonzeros) / nonnans + +def any_nan_row(np.ndarray[np.float64_t, ndim=2] x): + cdef: + int row, n_cols, n_rows + np.ndarray[np.int8_t, ndim=1] flags + + n_rows, n_cols = x.shape[0], x.shape[1] + flags = np.zeros(x.shape[0], dtype=np.int8) + with nogil: + for row in range(n_rows): + for col in range(n_cols): + if npy_isnan(x[row, col]): + flags[row] = 1 + break + return flags + + +def jaccard_rows(np.ndarray[np.int8_t, ndim=2] nonzeros1, + np.ndarray[np.int8_t, ndim=2] nonzeros2, + np.ndarray[np.float64_t, ndim=2] x1, + np.ndarray[np.float64_t, ndim=2] x2, + np.ndarray[np.int8_t, ndim=1] nans1, + np.ndarray[np.int8_t, ndim=1] nans2, + np.ndarray[np.float64_t, ndim=1] ps, + char two_tables): + cdef: + int n_rows1, n_rows2, n_cols, row1, row2, col + np.float64_t val1, val2, intersection, union + int ival1, ival2 + double [:, :] distances + + n_rows1, n_cols = x1.shape[0], x2.shape[1] + n_rows2 = x2.shape[0] + distances = np.zeros((n_rows1, n_rows2), dtype=float) + with nogil: + for row1 in range(n_rows1): + if nans1[row1]: + for row2 in range(n_rows2 if two_tables else row1): + union = intersection = 0 + for col in range(n_cols): + val1, val2 = x1[row1, col], x2[row2, col] + if npy_isnan(val1): + if npy_isnan(val2): + intersection += ps[col] ** 2 + union += 1 - (1 - ps[col]) ** 2 + elif val2 != 0: + intersection += ps[col] + union += 1 + else: + union += ps[col] + elif npy_isnan(val2): + if val1 != 0: + intersection += val1 * ps[col] + union += 1 + else: + union += ps[col] + else: + ival1 = nonzeros1[row1, col] + ival2 = nonzeros2[row2, col] + union += ival1 | ival2 + intersection += ival1 & ival2 + if union != 0: + distances[row1, row2] = 1 - intersection / union + else: + for row2 in range(n_rows2 if two_tables else row1): + union = intersection = 0 + # This case is slightly different since val1 can't be nan + if nans2[row2]: + for col in range(n_cols): + val2 = x2[row2, col] + if nonzeros1[row1, col] != 0: + union += 1 + if npy_isnan(val2): + intersection += ps[col] + elif val2 != 0: + intersection += 1 + elif npy_isnan(val2): + union += ps[col] + elif val2 != 0: + union += 1 + else: + for col in range(n_cols): + ival1 = nonzeros1[row1, col] + ival2 = nonzeros2[row2, col] + union += ival1 | ival2 + intersection += ival1 & ival2 + if union != 0: + distances[row1, row2] = 1 - intersection / union + if not two_tables: + lower_to_symmetric(distances) + return distances + + +def jaccard_cols(np.ndarray[np.int8_t, ndim=2] nonzeros, + np.ndarray[np.float64_t, ndim=2] x, + np.ndarray[np.int8_t, ndim=1] nans, + np.ndarray[np.float64_t, ndim=1] ps): + cdef: + int n_rows, n_cols, col1, col2, row + double val1, val2, intersection, union + np.int8_t ival1, ival2 + int in_both, in_any, in1_unk2, unk1_in2, unk1_unk2, unk1_not2, not1_unk2 + double [:, :] distances + + n_rows, n_cols = x.shape[0], x.shape[1] + distances = np.zeros((n_cols, n_cols), dtype=float) + with nogil: + for col1 in range(n_cols): + if nans[col1]: + for col2 in range(col1): + in_both = in_any = 0 + in1_unk2 = unk1_in2 = unk1_unk2 = unk1_not2 = not1_unk2 = 0 + for row in range(n_rows): + val1, val2 = x[row, col1], x[row, col2] + if npy_isnan(val1): + if npy_isnan(val2): + unk1_unk2 += 1 + elif val2 != 0: + unk1_in2 += 1 + else: + unk1_not2 += 1 + elif npy_isnan(val2): + if val1 != 0: + in1_unk2 += 1 + else: + not1_unk2 += 1 + else: + ival1 = nonzeros[row, col1] + ival2 = nonzeros[row, col2] + in_both += ival1 & ival2 + in_any += ival1 | ival2 + union = (in_any + unk1_in2 + in1_unk2 + + ps[col1] * unk1_not2 + + ps[col2] * not1_unk2 + + (1 - (1 - ps[col1]) * (1 - ps[col2])) * unk1_unk2) + if union != 0: + intersection = (in_both + + ps[col1] * unk1_in2 + + + ps[col2] * in1_unk2 + + + ps[col1] * ps[col2] * unk1_unk2) + distances[col1, col2] = distances[col2, col1] = \ + 1 - intersection / union + else: + for col2 in range(col1): + if nans[col2]: + in_both = in_any = 0 + in1_unk2 = unk1_in2 = unk1_unk2 = unk1_not2 = not1_unk2 = 0 + for row in range(n_rows): + ival1 = nonzeros[row, col1] + val2 = x[row, col2] + if npy_isnan(val2): + if ival1: + in1_unk2 += 1 + else: + not1_unk2 += 1 + else: + ival2 = nonzeros[row, col2] + in_both += ival1 & ival2 + in_any += ival1 | ival2 + distances[col1, col2] = distances[col2, col1] = \ + 1 - float(in_both + + ps[col1] * unk1_in2 + + + ps[col2] * in1_unk2 + + + ps[col1] * ps[col2] * unk1_unk2) / \ + (in_any + unk1_in2 + in1_unk2 + + + ps[col1] * unk1_not2 + + ps[col2] * not1_unk2 + + (1 - (1 - ps[col1]) * (1 - ps[col2])) * unk1_unk2) + else: + in_both = in_any = 0 + for row in range(n_rows): + ival1 = nonzeros[row, col1] + ival2 = nonzeros[row, col2] + in_both += ival1 & ival2 + in_any += ival1 | ival2 + if in_any != 0: + distances[col1, col2] = distances[col2, col1] = \ + 1 - float(in_both) / in_any + + return distances diff --git a/Orange/distance/base.py b/Orange/distance/base.py new file mode 100644 index 00000000000..2cf6f594f72 --- /dev/null +++ b/Orange/distance/base.py @@ -0,0 +1,491 @@ +import numpy as np +import sklearn.metrics as skl_metrics + +from Orange.data import Table, Domain, Instance, RowInstance +from Orange.misc import DistMatrix +from Orange.preprocess import SklImpute +from Orange.statistics import util + + +# TODO: When we upgrade to numpy 1.13, change use argument copy=False in +# nan_to_num instead of assignment + +# TODO this *private* function is called from several widgets to prepare +# data for calling the below classes. After we (mostly) stopped relying +# on sklearn.metrics, this is (mostly) unnecessary +def _preprocess(table, impute=True): + """Remove categorical attributes and impute missing values.""" + if not len(table): + return table + new_domain = Domain( + [a for a in table.domain.attributes if a.is_continuous], + table.domain.class_vars, + table.domain.metas) + new_data = table.transform(new_domain) + if impute: + new_data = SklImpute()(new_data) + return new_data + + +# TODO I have put this function here as a substitute the above `_preprocess`. +# None of them really belongs here; (re?)move them, eventually. +def remove_discrete_features(data): + """Remove discrete columns from the data.""" + new_domain = Domain( + [a for a in data.domain.attributes if a.is_continuous], + data.domain.class_vars, + data.domain.metas) + return data.transform(new_domain) + + +def impute(data): + """Impute missing values.""" + return SklImpute()(data) + + +def _orange_to_numpy(x): + """ + Return :class:`numpy.ndarray` (dense or sparse) with attribute data + from the given instance of :class:`Orange.data.Table`, + :class:`Orange.data.RowInstance` or :class:`Orange.data.Instance`. + """ + if isinstance(x, Table): + return x.X + elif isinstance(x, Instance): + return np.atleast_2d(x.x) + elif isinstance(x, np.ndarray): + return np.atleast_2d(x) + else: + return x # e.g. None + + +class Distance: + """ + Base class for construction of distances models (:obj:`DistanceModel`). + + Distances can be computed between all pairs of rows in one table, or + between pairs where one row is from one table and one from another. + + If `axis` is set to `0`, the class computes distances between all pairs + of columns in a table. Distances between columns from separate tables are + probably meaningless, thus unsupported. + + The class can be used as follows: + + - Constructor is called only with keyword argument `axis` that + specifies the axis over which the distances are computed, and with other + subclass-specific keyword arguments. + - Next, we call the method `fit(data)` to produce an instance of + :obj:`DistanceModel`; the instance stores any parameters needed for + computation of distances, such as statistics for normalization and + handling of missing data. + - We can then call the :obj:`DistanceModel` with data to compute the + distance between its rows or columns, or with two data tables to + compute distances between all pairs of rows. + + The second, shorter way to use this class is to call the constructor with + one or two data tables and any additional keyword arguments. Constructor + will execute the above steps and return :obj:`~Orange.misc.DistMatrix`. + Such usage is here for backward compatibility, practicality and efficiency. + + Args: + e1 (:obj:`~Orange.data.Table` or :obj:`~Orange.data.Instance` or \ + :obj:`np.ndarray` or `None`): + data on which to train the model and compute the distances + e2 (:obj:`~Orange.data.Table` or :obj:`~Orange.data.Instance` or \ + :obj:`np.ndarray` or `None`): + if present, the class computes distances with pairs coming from + the two tables + axis (int): + axis over which the distances are computed, 1 (default) for + rows, 0 for columns + impute (bool): + if `True` (default is `False`), nans in the computed distances + are replaced with zeros, and infs with very large numbers. + + Attributes: + axis (int): + axis over which the distances are computed, 1 (default) for + rows, 0 for columns + impute (bool): + if `True` (default is `False`), nans in the computed distances + are replaced with zeros, and infs with very large numbers. + + The capabilities of the metrics are described with class attributes. + + If class attribute `supports_discrete` is `True`, the distance + also uses discrete attributes to compute row distances. The use of discrete + attributes depends upon the type of distance; e.g. Jaccard distance observes + whether the value is zero or non-zero, while Euclidean and Manhattan + distance observes whether a pair of values is same or different. + + Class attribute `supports_missing` indicates that the distance can cope + with missing data. In such cases, letting the distance handle it should + be preferred over pre-imputation of missing values. + + Class attribute `supports_normalization` indicates that the constructor + accepts an argument `normalize`. If set to `True`, the metric will attempt + to normalize the values in a sense that each attribute will have equal + influence. For instance, the Euclidean distance subtract the mean and + divides the result by the deviation, while Manhattan distance uses the + median and MAD. + + If class attribute `supports_sparse` is `True`, the class will handle + sparse data. Currently, all classes that do handle it rely on fallbacks to + SKL metrics. These, however, do not support discrete data and missing + values, and will fail silently. + """ + supports_sparse = False + supports_discrete = False + supports_normalization = False + supports_missing = True + + def __new__(cls, e1=None, e2=None, axis=1, impute=False, **kwargs): + self = super().__new__(cls) + self.axis = axis + self.impute = impute + # Ugly, but needed to allow allow setting subclass-specific parameters + # (such as normalize) when `e1` is not `None` and the `__new__` in the + # subclass is skipped + self.__dict__.update(**kwargs) + if e1 is None: + return self + + # Fallbacks for sparse data and numpy tables. Remove when subclasses + # no longer use fallbacks for sparse data, and handling numpy tables + # becomes obsolete (or handled elsewhere) + if (not hasattr(e1, "domain") + or hasattr(e1, "is_sparse") and e1.is_sparse()): + fallback = getattr(self, "fallback", None) + if fallback is not None: + # pylint disable=not-callable + return fallback(e1, e2, axis, impute) + + # Magic constructor + model = self.fit(e1) + return model(e1, e2) + + def fit(self, e1): + """Abstract method returning :obj:`DistanceModel` fit to the data""" + pass + + @staticmethod + def check_no_discrete(n_vals): + """ + Raise an exception if there are any discrete attributes. + + Args: + n_vals (list of int): number of attributes values, 0 for continuous + """ + if any(n_vals): + raise ValueError("columns with discrete values are incommensurable") + + +class DistanceModel: + """ + Base class for classes that compute distances between data rows or columns. + Instances of these classes are not constructed directly but returned by + the corresponding instances of :obj:`Distance`. + + Attributes: + axis (int, readonly): + axis over which the distances are computed, 1 (default) for + rows, 0 for columns + impute (bool): + if `True` (default is `False`), nans in the computed distances + are replaced with zeros, and infs with very large numbers + + """ + def __init__(self, axis, impute=False): + self._axis = axis + self.impute = impute + + @property + def axis(self): + return self._axis + + def __call__(self, e1, e2=None): + """ + If e2 is omitted, calculate distances between all rows (axis=1) or + columns (axis=2) of e1. If e2 is present, calculate distances between + all pairs if rows from e1 and e2. + + This method converts the data into numpy arrays, calls the method + `compute_data` and packs the result into `DistMatrix`. Subclasses are + expected to define the `compute_data` and not the `__call__` method. + + Args: + e1 (Orange.data.Table or Orange.data.Instance or numpy.ndarray): + input data + e2 (Orange.data.Table or Orange.data.Instance or numpy.ndarray): + secondary data + + Returns: + A distance matrix (Orange.misc.distmatrix.DistMatrix) + """ + if self.axis == 0 and e2 is not None: + # Backward compatibility fix + if e2 is e1: + e2 = None + else: + raise ValueError("Two tables cannot be compared by columns") + + x1 = _orange_to_numpy(e1) + x2 = _orange_to_numpy(e2) + dist = self.compute_distances(x1, x2) + if self.impute and np.isnan(dist).any(): + dist = np.nan_to_num(dist) + if isinstance(e1, (Table, RowInstance)): + dist = DistMatrix(dist, e1, e2, self.axis) + else: + dist = DistMatrix(dist) + return dist + + def compute_distances(self, x1, x2): + """ + Abstract method for computation of distances between rows or colums of + `x1`, or between rows of `x1` and `x2`. Do not call directly.""" + pass + + +class FittedDistanceModel(DistanceModel): + """ + Base class for models that store attribute-related data for normalization + and imputation, and that treat discrete and continuous columns separately. + + Attributes: + attributes (list of `Variable`): attributes on which the model was fit + discrete (np.ndarray): bool array indicating discrete attributes + continuous (np.ndarray): bool array indicating continuous attributes + """ + def __init__(self, attributes, axis=1, impute=False): + super().__init__(axis, impute) + self.attributes = attributes + + def __call__(self, e1, e2=None): + if e1.domain.attributes != self.attributes or \ + e2 is not None and e2.domain.attributes != self.attributes: + raise ValueError("mismatching domains") + return super().__call__(e1, e2) + + def continuous_columns(self, x1, x2, offset, scale): + """ + Extract and scale continuous columns from data tables. + If the second table is None, it defaults to the first table. + + Values are scaled if `self.normalize` is `True`. + + Args: + x1 (np.ndarray): first table + x2 (np.ndarray or None): second table + offset (float): a constant (e.g. mean, median) subtracted from data + scale: (float): divider (e.g. deviation) + + Returns: + data1 (np.ndarray): scaled continuous columns from `x1` + data2 (np.ndarray): scaled continuous columns from `x2` or `x1` + """ + if self.continuous.all() and not self.normalize: + data1, data2 = x1, x2 + else: + data1 = x1[:, self.continuous] + if x2 is not None: + data2 = x2[:, self.continuous] + if self.normalize: + data1 = x1[:, self.continuous] + data1 -= offset + data1 /= scale + if x2 is not None: + data2 = x2[:, self.continuous] + data2 -= offset + data2 /= scale + if x2 is None: + data2 = data1 + return data1, data2 + + def discrete_columns(self, x1, x2): + """ + Return discrete columns from the given tables. + If the second table is None, it defaults to the first table. + """ + if self.discrete.all(): + data1, data2 = x1, x1 if x2 is None else x2 + else: + data1 = x1[:, self.discrete] + data2 = data1 if x2 is None else x2[:, self.discrete] + return data1, data2 + + +class FittedDistance(Distance): + """ + Base class for fitting models that store attribute-related data for + normalization and imputation, and that treat discrete and continuous + columns separately. + + The class implements a method `fit` that calls either `fit_columns` + or `fit_rows` with the data and the number of values for discrete + attributes. The provided method `fit_rows` calls methods + `get_discrete_stats` and `get_continuous_stats` that can be implemented + in derived classes. + + Class attribute `rows_model_type` contains the type of the model returned by + `fit_rows`. + """ + rows_model_type = None #: Option[FittedDistanceModel] + + def fit(self, data): + """ + Prepare the data on attributes, call `fit_cols` or `fit_rows` and + return the resulting model. + """ + attributes = data.domain.attributes + x = _orange_to_numpy(data) + n_vals = np.fromiter( + (len(attr.values) if attr.is_discrete else 0 + for attr in attributes), + dtype=np.int32, count=len(attributes)) + return [self.fit_cols, self.fit_rows][self.axis](attributes, x, n_vals) + + def fit_cols(self, attributes, x, n_vals): + """ + Return DistanceModel for computation of distances between columns. + Derived classes must define this method. + + Args: + attributes (list of Orange.data.Variable): list of attributes + x (np.ndarray): data + n_vals (np.ndarray): number of attribute values, 0 for continuous + """ + pass + + def fit_rows(self, attributes, x, n_vals): + """ + Return a DistanceModel for computation of distances between rows. + + The model type is `self.row_distance_model`. It stores the data for + imputation of discrete and continuous values, and for normalization + of continuous values. Typical examples are the Euclidean and Manhattan + distance, for which the following data is stored: + + For continuous columns: + + - offsets[col] is the number subtracted from values in column `col` + - scales[col] is the divisor for values in columns `col` + - dist_missing2_cont[col]: the value used for distance between two + missing values in column `col` + + For discrete values: + + - dist_missing_disc[col, value] is the distance added for the given + `value` in the column `col` if the value for the other row is + missing + - dist_missing2_disc[col]: the distance between two missing values in + column `col` + """ + n_cols = len(n_vals) + + discrete = n_vals > 0 + n_bins = max(n_vals, default=0) + n_discrete = sum(discrete) + dist_missing_disc = np.zeros((n_discrete, n_bins), dtype=float) + dist_missing2_disc = np.zeros(n_discrete, dtype=float) + + continuous = ~discrete + n_continuous = sum(continuous) + offsets = np.zeros(n_continuous, dtype=float) + scales = np.empty(n_continuous, dtype=float) + dist_missing2_cont = np.zeros(n_continuous, dtype=float) + + curr_disc = curr_cont = 0 + for col in range(n_cols): + column = x[:, col] + if np.isnan(column).all(): + continuous[col] = discrete[col] = False + elif discrete[col]: + discrete_stats = self.get_discrete_stats(column, n_bins) + if discrete_stats is not None: + dist_missing_disc[curr_disc], \ + dist_missing2_disc[curr_disc] = discrete_stats + curr_disc += 1 + else: + continuous_stats = self.get_continuous_stats(column) + if continuous_stats is not None: + offsets[curr_cont], scales[curr_cont],\ + dist_missing2_cont[curr_cont] = continuous_stats + curr_cont += 1 + else: + continuous[col] = False + # pylint: disable=not-callable + return self.rows_model_type( + attributes, impute, getattr(self, "normalize", False), + continuous, discrete, + offsets[:curr_cont], scales[:curr_cont], + dist_missing2_cont[:curr_cont], + dist_missing_disc, dist_missing2_disc) + + def get_discrete_stats(self, column, n_bins): + """ + Return tables used computing distance between missing discrete values. + + Args: + column (np.ndarray): column data + n_bins (int): maximal number of bins in the data set + + Returns: + dist_missing_disc (np.ndarray): `dist_missing_disc[value]` is + 1 - probability of `value`, which is used as the distance added + for the given `value` in the column `col` if the value for the + other row is missing + dist_missing2_disc (float): the distance between two missing + values in this columns + """ + dist = util.bincount(column, minlength=n_bins)[0] + dist /= max(1, sum(dist)) + return 1 - dist, 1 - np.sum(dist ** 2) + + def get_continuous_stats(self, column): + """ + Compute statistics for imputation and normalization of continuous data. + Derived classes must define this method. + + Args: + column (np.ndarray): column data + + Returns: + offset (float): the number subtracted from values in column + scales (float): the divisor for values in column + dist_missing2_cont (float): the value used for distance between two + missing values in column + """ + pass + + +# Fallbacks for distances in sparse data +# To be removed as the corresponding functionality is implemented properly + +class SklDistance: + """ + Wrapper for functions sklearn's metrics. Used only as temporary fallbacks + when `Euclidean`, `Manhattan`, `Cosine` or `Jaccard` are given sparse data + or raw numpy arrays. These classes can't handle discrete or missing data + and normalization. Do not use for wrapping new classes. + """ + def __init__(self, metric): + self.metric = metric + + def __call__(self, e1, e2=None, axis=1, impute=False): + x1 = _orange_to_numpy(e1) + x2 = _orange_to_numpy(e2) + if axis == 0: + x1 = x1.T + if x2 is not None: + x2 = x2.T + dist = skl_metrics.pairwise.pairwise_distances( + x1, x2, metric=self.metric) + if impute and np.isnan(dist).any(): + dist = np.nan_to_num(dist) + if isinstance(e1, (Table, RowInstance)): + dist_matrix = DistMatrix(dist, e1, e2, axis) + else: + dist_matrix = DistMatrix(dist) + return dist_matrix diff --git a/Orange/distance/distance.py b/Orange/distance/distance.py new file mode 100644 index 00000000000..bd270de9806 --- /dev/null +++ b/Orange/distance/distance.py @@ -0,0 +1,533 @@ +import numpy as np +from scipy import stats +import sklearn.metrics as skl_metrics +from sklearn.utils.extmath import row_norms, safe_sparse_dot + +from Orange.distance import _distance +from Orange.statistics import util + +from .base import (Distance, DistanceModel, FittedDistance, FittedDistanceModel, + SklDistance, _orange_to_numpy) + + +class EuclideanRowsModel(FittedDistanceModel): + """ + Model for computation of Euclidean distances between rows. + + Means are used as offsets for normalization, and two deviations are + used for scaling. + """ + def __init__(self, attributes, impute, normalize, + continuous, discrete, + means, vars, dist_missing2_cont, + dist_missing_disc, dist_missing2_disc): + super().__init__(attributes, 1, impute) + self.normalize = normalize + self.continuous = continuous + self.discrete = discrete + self.means = means + self.vars = vars + self.dist_missing2_cont = dist_missing2_cont + self.dist_missing_disc = dist_missing_disc + self.dist_missing2_disc = dist_missing2_disc + + def compute_distances(self, x1, x2=None): + """ + The method + - extracts normalized continuous attributes and then uses `row_norms` + and `safe_sparse_do`t to compute the distance as x^2 - 2xy - y^2 + (the trick from sklearn); + - calls a function in Cython that recomputes the distances between pairs + of rows that yielded nan + - calls a function in Cython that adds the contributions of discrete + columns + """ + if self.continuous.any(): + data1, data2 = self.continuous_columns( + x1, x2, self.means, np.sqrt(2 * self.vars)) + + # adapted from sklearn.metric.euclidean_distances + xx = row_norms(data1, squared=True)[:, np.newaxis] + if x2 is not None: + yy = row_norms(data2, squared=True)[np.newaxis, :] + else: + yy = xx.T + distances = safe_sparse_dot(data1, data2.T, dense_output=True) + distances *= -2 + distances += xx + distances += yy + np.maximum(distances, 0, out=distances) + if x2 is None: + distances.flat[::distances.shape[0] + 1] = 0.0 + fixer = _distance.fix_euclidean_rows_normalized if self.normalize \ + else _distance.fix_euclidean_rows + fixer(distances, data1, data2, + self.means, self.vars, self.dist_missing2_cont, + x2 is not None) + else: + distances = np.zeros((x1.shape[0], + (x2 if x2 is not None else x1).shape[0])) + + if np.any(self.discrete): + data1, data2 = self.discrete_columns(x1, x2) + _distance.euclidean_rows_discrete( + distances, data1, data2, self.dist_missing_disc, + self.dist_missing2_disc, x2 is not None) + + if x2 is None: + _distance.lower_to_symmetric(distances) + return np.sqrt(distances) + + +class EuclideanColumnsModel(FittedDistanceModel): + """ + Model for computation of Euclidean distances between columns. + + Means are used as offsets for normalization, and two deviations are + used for scaling. + """ + def __init__(self, attributes, impute, normalize, means, vars): + super().__init__(attributes, 0, impute) + self.normalize = normalize + self.means = means + self.vars = vars + + def compute_distances(self, x1, x2=None): + """ + The method + - extracts normalized continuous attributes and then uses `row_norms` + and `safe_sparse_do`t to compute the distance as x^2 - 2xy - y^2 + (the trick from sklearn); + - calls a function in Cython that adds the contributions of discrete + columns + """ + if self.normalize: + x1 = x1 - self.means + x1 /= np.sqrt(2 * self.vars) + + # adapted from sklearn.metric.euclidean_distances + xx = row_norms(x1.T, squared=True)[:, np.newaxis] + distances = safe_sparse_dot(x1.T, x1, dense_output=True) + distances *= -2 + distances += xx + distances += xx.T + np.maximum(distances, 0, out=distances) + distances.flat[::distances.shape[0] + 1] = 0.0 + + fixer = _distance.fix_euclidean_cols_normalized if self.normalize \ + else _distance.fix_euclidean_cols + fixer(distances, x1, self.means, self.vars) + return np.sqrt(distances) + + +class Euclidean(FittedDistance): + supports_sparse = True # via fallback + supports_discrete = True + supports_normalization = True + fallback = SklDistance('euclidean') + rows_model_type = EuclideanRowsModel + + def __new__(cls, e1=None, e2=None, axis=1, impute=False, normalize=False): + return super().__new__(cls, e1, e2, axis, impute, normalize=normalize) + + def get_continuous_stats(self, column): + """ + Return mean, variance and distance betwwen pairs of missing values + for the given columns. The method is called by inherited `fit_rows` + to construct a row-distance model + """ + mean = util.nanmean(column) + var = util.nanvar(column) + if self.normalize: + if var == 0: + return None + dist_missing2_cont = 1 + else: + dist_missing2_cont = 2 * var + if np.isnan(dist_missing2_cont): + dist_missing2_cont = 0 + return mean, var, dist_missing2_cont + + def fit_cols(self, attributes, x, n_vals): + """ + Return `EuclideanColumnsModel` with stored means and variances + for normalization and imputation. + """ + self.check_no_discrete(n_vals) + means = np.nanmean(x, axis=0) + vars = np.nanvar(x, axis=0) + if self.normalize and (np.isnan(vars).any() or not vars.all()): + raise ValueError("some columns are constant or have no values") + return EuclideanColumnsModel( + attributes, self.impute, self.normalize, means, vars) + + +class ManhattanRowsModel(FittedDistanceModel): + """ + Model for computation of Euclidean distances between rows. + + Means are used as offsets for normalization, and two deviations are + used for scaling. + """ + def __init__(self, attributes, impute, normalize, + continuous, discrete, + medians, mads, dist_missing2_cont, + dist_missing_disc, dist_missing2_disc): + super().__init__(attributes, 1, impute) + self.normalize = normalize + self.continuous = continuous + self.discrete = discrete + self.medians = medians + self.mads = mads + self.dist_missing2_cont = dist_missing2_cont + self.dist_missing_disc = dist_missing_disc + self.dist_missing2_disc = dist_missing2_disc + + def compute_distances(self, x1, x2): + """ + The method + - extracts normalized continuous attributes and computes distances + ignoring the possibility of nans + - recomputes the distances between pairs of rows that yielded nans + - adds the contributions of discrete columns using the same function as + the Euclidean distance + """ + if self.continuous.any(): + data1, data2 = self.continuous_columns( + x1, x2, self.medians, 2 * self.mads) + distances = _distance.manhattan_rows_cont( + data1, data2, x2 is not None) + if self.normalize: + _distance.fix_manhattan_rows_normalized( + distances, data1, data2, x2 is not None) + else: + _distance.fix_manhattan_rows( + distances, data1, data2, + self.medians, self.mads, self.dist_missing2_cont, + x2 is not None) + else: + distances = np.zeros((x1.shape[0], + (x2 if x2 is not None else x1).shape[0])) + + if np.any(self.discrete): + data1, data2 = self.discrete_columns(x1, x2) + # For discrete attributes, Euclidean is same as Manhattan + _distance.euclidean_rows_discrete( + distances, data1, data2, self.dist_missing_disc, + self.dist_missing2_disc, x2 is not None) + + if x2 is None: + _distance.lower_to_symmetric(distances) + return distances + + +class ManhattanColumnsModel(FittedDistanceModel): + """ + Model for computation of Manhattan distances between columns. + + Medians are used as offsets for normalization, and two MADS are + used for scaling. + """ + + def __init__(self, attributes, impute, normalize, medians, mads): + super().__init__(attributes, 0, impute) + self.normalize = normalize + self.medians = medians + self.mads = mads + + def compute_distances(self, x1, x2=None): + if self.normalize: + x1 = x1 - self.medians + x1 /= 2 + x1 /= self.mads + return _distance.manhattan_cols(x1, self.medians, self.mads, self.normalize) + + +class Manhattan(FittedDistance): + supports_sparse = True # via fallback + supports_discrete = True + supports_normalization = True + fallback = SklDistance('manhattan') + rows_model_type = ManhattanRowsModel + + def __new__(cls, e1=None, e2=None, axis=1, impute=False, normalize=False): + return super().__new__(cls, e1, e2, axis, impute, normalize=normalize) + + def get_continuous_stats(self, column): + """ + Return median, MAD and distance betwwen pairs of missing values + for the given columns. The method is called by inherited `fit_rows` + to construct a row-distance model + """ + median = np.nanmedian(column) + mad = np.nanmedian(np.abs(column - median)) + if self.normalize: + if mad == 0: + return None + dist_missing2_cont = 1 + else: + dist_missing2_cont = 2 * mad + if np.isnan(dist_missing2_cont): + dist_missing2_cont = 0 + return median, mad, dist_missing2_cont + + def fit_cols(self, attributes, x, n_vals): + """ + Return `ManhattanColumnsModel` with stored medians and MADs + for normalization and imputation. + """ + self.check_no_discrete(n_vals) + medians = np.nanmedian(x, axis=0) + mads = np.nanmedian(np.abs(x - medians), axis=0) + if self.normalize and (np.isnan(mads).any() or not mads.all()): + raise ValueError( + "some columns have zero absolute distance from median, " + "or no values") + return ManhattanColumnsModel( + attributes, self.impute, self.normalize, medians, mads) + + +class Cosine(FittedDistance): + supports_sparse = True # via fallback + supports_discrete = True + fallback = SklDistance('cosine') + + @staticmethod + def discrete_to_indicators(x, discrete): + """Change non-zero values of discrete attributes to 1.""" + if discrete.any(): + x = x.copy() + for col, disc in enumerate(discrete): + if disc: + x[:, col].clip(0, 1, out=x[:, col]) + return x + + def fit_rows(self, attributes, x, n_vals): + """Return a model for cosine distances with stored means for imputation + """ + discrete = n_vals > 0 + x = self.discrete_to_indicators(x, discrete) + means = util.nanmean(x, axis=0) + means = np.nan_to_num(means) + return self.CosineModel(attributes, self.axis, self.impute, + discrete, means) + + fit_cols = fit_rows + + class CosineModel(FittedDistanceModel): + """Model for computation of cosine distances across rows and columns. + All non-zero discrete values are treated as 1.""" + def __init__(self, attributes, axis, impute, discrete, means): + super().__init__(attributes, axis, impute) + self.discrete = discrete + self.means = means + + def compute_distances(self, x1, x2): + """ + The method imputes the missing values as means and calls + safe_sparse_dot. Imputation simplifies computation at a cost of + (theoretically) slightly wrong distance between pairs of missing + values. + """ + + def prepare_data(x): + if self.discrete.any(): + data = Cosine.discrete_to_indicators(x, self.discrete) + else: + data = x.copy() + for col, mean in enumerate(self.means): + column = data[:, col] + column[np.isnan(column)] = mean + if self.axis == 0: + data = data.T + data /= row_norms(data)[:, np.newaxis] + return data + + data1 = prepare_data(x1) + data2 = data1 if x2 is None else prepare_data(x2) + dist = safe_sparse_dot(data1, data2.T) + np.clip(dist, 0, 1, out=dist) + if x2 is None: + dist.flat[::dist.shape[0] + 1] = 1.0 + return 1 - dist + + +class JaccardModel(FittedDistanceModel): + """ + Model for computation of cosine distances across rows and columns. + All non-zero values are treated as 1. + """ + def __init__(self, attributes, axis, impute, ps): + super().__init__(attributes, axis, impute) + self.ps = ps + + def compute_distances(self, x1, x2): + """ + The method uses a function implemented in Cython. Data (`x1` and `x2`) + is accompanied by two tables. One is a 2-d table in which elements of + `x1` (`x2`) are replaced by 0's and 1's. The other is a vector + indicating rows (or column) with nan values. + + The function in Cython uses a fast loop without any conditions to + compute distances between rows without missing values, and a slower + loop for those with missing values. + """ + nonzeros1 = np.not_equal(x1, 0).view(np.int8) + if self.axis == 1: + nans1 = _distance.any_nan_row(x1) + if x2 is None: + nonzeros2, nans2 = nonzeros1, nans1 + else: + nonzeros2 = np.not_equal(x2, 0).view(np.int8) + nans2 = _distance.any_nan_row(x2) + return _distance.jaccard_rows( + nonzeros1, nonzeros2, + x1, x1 if x2 is None else x2, + nans1, nans2, + self.ps, + x2 is not None) + else: + nans1 = _distance.any_nan_row(x1.T) + return _distance.jaccard_cols( + nonzeros1, x1, nans1, self.ps) + + +class Jaccard(FittedDistance): + supports_sparse = False + supports_discrete = True + fallback = SklDistance('jaccard') + ModelType = JaccardModel + + def fit_rows(self, attributes, x, n_vals): + """ + Return a model for computation of Jaccard values. The model stores + frequencies of non-zero values per each column. + """ + ps = np.fromiter( + (_distance.p_nonzero(x[:, col]) for col in range(len(n_vals))), + dtype=np.double, count=len(n_vals)) + return JaccardModel(attributes, self.axis, self.impute, ps) + + fit_cols = fit_rows + + +class CorrelationDistanceModel(DistanceModel): + """Helper class for normal and absolute Pearson and Spearman correlation""" + def __init__(self, absolute, axis=1, impute=False): + super().__init__(axis, impute) + self.absolute = absolute + + def compute_distances(self, x1, x2): + if x2 is None: + x2 = x1 + rho = self.compute_correlation(x1, x2) + if self.absolute: + return (1. - np.abs(rho)) / 2. + else: + return (1. - rho) / 2. + + def compute_correlation(self, x1, x2): + pass + + +class SpearmanModel(CorrelationDistanceModel): + def compute_correlation(self, x1, x2): + rho = stats.spearmanr(x1, x2, axis=self.axis)[0] + if isinstance(rho, np.float): + return np.array([[rho]]) + slc = x1.shape[1 - self.axis] + return rho[:slc, slc:] + + +class CorrelationDistance(Distance): + supports_missing = False + + +class SpearmanR(CorrelationDistance): + def fit(self, _): + return SpearmanModel(False, self.axis, self.impute) + + +class SpearmanRAbsolute(CorrelationDistance): + def fit(self, _): + return SpearmanModel(True, self.axis, self.impute) + + +class PearsonModel(CorrelationDistanceModel): + def compute_correlation(self, x1, x2): + if self.axis == 0: + x1 = x1.T + x2 = x2.T + return np.array([[stats.pearsonr(i, j)[0] for j in x2] for i in x1]) + + +class PearsonR(CorrelationDistance): + def fit(self, _): + return PearsonModel(False, self.axis, self.impute) + + +class PearsonRAbsolute(CorrelationDistance): + def fit(self, _): + return PearsonModel(True, self.axis, self.impute) + + +class Mahalanobis(Distance): + supports_sparse = False + supports_missing = False + + def fit(self, data): + """Return a model with stored inverse covariance matrix""" + x = _orange_to_numpy(data) + if self.axis == 0: + x = x.T + try: + c = np.cov(x.T) + except: + raise MemoryError("Covariance matrix is too large.") + try: + vi = np.linalg.inv(c) + except: + raise ValueError("Computation of inverse covariance matrix failed.") + return MahalanobisModel(self.axis, self.impute, vi) + + +class MahalanobisModel(DistanceModel): + def __init__(self, axis, impute, vi): + super().__init__(axis, impute) + self.vi = vi + + def __call__(self, e1, e2=None, impute=None): + # argument `impute` is here just for backward compatibility; don't use + if impute is not None: + self.impute = impute + return super().__call__(e1, e2) + + def compute_distances(self, x1, x2): + if self.axis == 0: + x1 = x1.T + if x2 is not None: + x2 = x2.T + if x1.shape[1] != self.vi.shape[0] or \ + x2 is not None and x2.shape[1] != self.vi.shape[0]: + raise ValueError('Incorrect number of features.') + return skl_metrics.pairwise.pairwise_distances( + x1, x2, metric='mahalanobis', VI=self.vi) + + +# TODO: Appears to have been used only in the Distances widget (where it had +# to be handled as a special case and is now replaced with the above class) +# and in tests. Remove? +class MahalanobisDistance: + """ + Obsolete class needed for backward compatibility. + + Previous implementation of instances did not have a separate fitting phase, + except for MahalanobisDistance, which was implemented in a single class + but required first (explicitly) calling the method 'fit'. The backward + compatibility hack in :obj:`Distance` cannot handle such use, hence it + is provided in this class. + """ + def __new__(cls, data=None, axis=1, _='Mahalanobis'): + if data is None: + return cls + return Mahalanobis(axis=axis).fit(data) diff --git a/Orange/distance/distances.md b/Orange/distance/distances.md new file mode 100644 index 00000000000..86f76c9ce20 --- /dev/null +++ b/Orange/distance/distances.md @@ -0,0 +1,185 @@ +# Computation of distances in Orange 3 + +This document describes and justifies how Orange 3 computes distances between data rows or columns from the data that can include discrete (nominal) and numeric features with missing values. + +The aim of normalization is to bring all numeric features onto the same scale and on the same scale as discrete features. The meaning of *the same scale* is rather arbitrary. We gauge the normalization so that missing values have the same effect for all features and their types. + +For missing values, we compute the expected difference given the probability distribution of the feature that is estimated from the data. + +Two nominal values are treated as same or different, that is, the difference between them is 0 and 1. + +Difference between values of two distinct nominal features does not make sense, so Orange reports an error when the user tries to compute column-wise distance in data with some non-numeric features. + +## Euclidean distance + +#### Normalization of numeric features + +Orange 2 used to normalize by subtracting the minimum and dividing by the span (the difference between the maximum and the minimum) to bring the range of differences into interval $[0, 1]$. This however did not work since the data on which the distances were computed could include more extreme values than the training data. + +Normalization in Orange 3 is based on mean and variance due to other desired effects described below. A value $x$ is normalized as + +$$ x' = \frac{x - \mu}{\sqrt{2\sigma^2}},$$ + +where $\mu$ and $\sigma^2$ are the mean and the variance of that feature (e.g. estimated accross the column). + +Normalized values thus have a mean of $\mu'=0$ and a variance of $\sigma'^2 = 1/2$. + +#### Missing values of numeric features + +If one value (denoted by $v$) is known and one missing, the expected difference along this dimension is + +$$\int_{-\infty}^{\infty}(v - x)^2p(x)dx = \\ +v^2\int_{-\infty}^{\infty}p(x)dx- 2v\int_{-\infty}^{\infty}xp(x) + \int_{-\infty}^{\infty}x^2p(x) = \\ +v^2 - 2v\mu + (\sigma^2 + \mu^2) = \\ +(v - \mu)^2 + \sigma^2.$$ + +If both values are unknown and we compute the difference between rows so that both values come from the same distirbutions, we have + +$$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}(x - y)^2p(x)p(y)dxdy = \\ + \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}x^2p(x)p(y)dxdy + + \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}y^2p(x)p(y)dxdy + - 2\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}xyp(x)p(y)dxdy = \\ + (\sigma^2 + \mu^2) + (\sigma^2 + \mu^2) - 2\int_{-\infty}^{\infty}xp(x)dx\int_{-\infty}^{\infty}yp(y)dxdy = \\ + (\sigma^2 + \mu^2) + (\sigma^2 + \mu^2) - 2\mu\mu = \\ + 2\sigma^2.$$ + +When computing the difference between columns, the derivation is similar except that the two distributions are not the same. For one missing value we get + +$$(v - \mu_x)^2 + \sigma_x^2$$ + +where $\mu_x$ and $\sigma_x$ correspond to the distribution of the unknown value. For two missing values, we get + +$$\sigma_x^2 + \sigma_y^2 + \mu_x^2 + \mu_y^2 - 2\mu_x\mu_y = \\ +\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^ 2.$$ + +For normalized data, the difference between $v$ and unknown value is $(v' - \mu)^2 + \sigma^2 = v'^2 + 1/2$. The difference between two missing values is $2\sigma^2 = 1$ (or $\sigma_x^2 + \sigma_y^2 + (\mu_x - \mu_y)^2 = 1$). + +#### Missing values of discrete features + +The difference between a known and a missing value is + +$$\sum_x \mbox{I}_{v\ne x}^2p(x) = 1 - p(x).$$ + +The difference between two missing values is + +$$\sum_x\sum_y \mbox{I}_{y\ne x}^2p(x)p(y) = 1 - \sum_x p(x)^2.$$ + +This is the Gini index. Also, if the number of values goes to infinity and the distribution towards the uniform, the difference goes towards 1, which brings it, in some sense, to the same scale as continuous features. + +This case assumes that $x$ and $y$ come from the same distribution. The case when these are missing values of two distinct discrete features is not covered since Orange does not support such distances (see the introduction). + +## Manhattan distance + +The derivation here may be more difficult, so we do it by analogy with Euclidean distances and hope for the best. + +We use the median ($m$) and median of absolute distances to the median (mad) ($a$) instead of the mean and the variance. + +Normalization of numeric features: $x' = (x - m)\,/\,(2a)$ + +#### Missing values of numeric features + +**Between a known and a missing**: $|v - m| + a.$ + +**Between two unknowns**: $2a$ (same features), $a_x + a_y$ (different features). + +**For normalized data**: $|v'| + 1/2$ (one unknown), $1$ (both unknown). + +#### Missing values of discrete features + +Same as for Euclidean because $I_{v\ne x}^2 = I_{v\ne x}$. + + +## Cosine distance + +The cosine similarity is normalized, so we do not normalize the data. + +Cosine distance treats discrete features differently from the Euclidean and Manhattan distance. The latter needs to consider only whether two values of a discrete feature is different or not, while the cosine distance normalizes by dividing by vector lengths. For this, we need the notion of absolute magnitude of a (single) discrete value -- as compared to some "base value". + +For this reason, cosine distance treats discrete attributes as boolean, that is, all non-zero values are treated as 1. This may be incorrect in some scenarios, especially those in which cosine distance is inappropriate anyway. How to (and whether to) use cosine distances on discrete data is up to the user. + +#### Distances between rows + +For a continuous variable $x$, product of $v$ and a missing value is computed as + +$$\int_{-\infty}^{\infty}vxp(x)dx = v\mu_x$$ + +The product of two unknown values is + +$$\int_{-\infty}^{\infty}xp(x)yp(y)dxdy=\mu_x^2$$ + +For discrete values, we compute the probabilities $p(x=0)$ and $p_x(x\ne 0)$. The product of known value $v$ and a missing value is 0 if v=0 and $p(x \ne 1)$ otherwise. The product of two missing values is $p(x\ne 1)^2$. + +When computing the absolute value of a row, a missing value of continuous variable theoretically contributes + +$$\int_{-infty}^{\infty}x^2p(x)dx = \mu_x^2 + \sigma_x^2$$ + +However, since we essentially impute the mean in the dot product, the actual contribution of the missing value is $\mu_x^2$. We therefore use this value, which also simplifies the computation which is reduced to simple imputation of means. + +A missing value of discrete variable contributes + +$$1\cdot 1\;p(x\ne 0) = p(x\ne 0)$$ + + +#### Distances between columns + +The product of a known value $v$ and a missing value of $x$ is $v\mu_x$. The contribution of a missing value to the absolute value of the column is $\mu_x^2+\sigma_x^2$. All derivations are same as above. + +## Jaccard distance + +Jaccard index, whose computation is described below, is a measure of similarity. The distance is computed by subtracting the similarity from 1. + +Let $p(A_i)$ be the probability (computed from the training data) that a random data instance belongs to set $A_i$, i.e., have a non-zero value for feature $A_i$. + +### Similarity between rows (instances) + +Let $M$ and $N$ be two data instances. $M$ and $N$ can belong to $A_i$ (or not). The Jaccard similarity between $M$ and $N$ is the number of the common sets to which $M$ and $N$ belong, divided by the number of sets with either $M$ or $N$ (or both). + +Let $\mbox{I}_M$ be 1 if $M\in A_i$ and 0 otherwise. Similarly, $\mbox{I}_{M'}$ will indicate that $M\not\in A_i$ and $\mbox{I}_{M?}$ will indicate that it is unknown whether $M$ belongs to $A_i$ or not. We will also use conjuctions and disjunctions by adding more indices to $\mbox{I}$; e.g. $\mbox{I}_{M\wedge N'}$ indicates that $M$ belongs to $A_i$ and $N$ does not. $A_i$ is omitted for clarity as it can be deduced from the context. + +$$Jaccard(M, N) = \frac{\sum_i\mbox{I}_{M\wedge N}}{\sum_i\mbox{I}_{M\vee N}}$$ + +Consider that $\mbox{I}_{M\wedge N} = \mbox{I}_M \mbox{I}_N$ and $\mbox{I}_{M\vee N} = \max(\mbox{I}_M, \mbox{I}_N)$. If the data whether $M\in A_i$ or $N\in A_i$ is missing, we replace indicator function with the probability. In the denominator we add a few terms to $\mbox{I}_{M\wedge N}$ + +$$\mbox{I}_{M\wedge N} + + p(A_i)\mbox{I}_{M\wedge N?} + + p(A_i)\mbox{I}_{M?\wedge N} + + p(A_i)^2\mbox{I}_{M?\wedge N?},$$ + +and in the nominator we get + +$$\mbox{I}_{M\vee N} + p(A_i)\mbox{I}_{M'\wedge N?} + p(A_i)\mbox{I}_{M?\wedge N'} + \left(1 - (1 - p(A_i)^2\right)\mbox{I}_{I?\wedge J?}$$ + +Note that the denominator counts cases $\mbox{I}_{M'\wedge N?}$ and not $\mbox{I}_{N?}$, since those for which $M\in A_i$ are already covered in $\mbox{I}_{M\vee N}$. The last term refers to the probability that at least one (that is, not none) of the two instances is in $A_i$. + +### Similarity between columns + +$\mbox{I}_{i}$ will now denote that a data instance $M$ belongs to $A_i$, $\mbox{I}_{i'}$ will denote it does not, and $\mbox{I}_{i?}$ will denote that it is unknown whether $M$ belongs to $A_i$. + +Without considering missing data, Jaccard index between two columns is + +$$Jaccard(A_i, A_j) = \frac{\sum_M\mbox{I}_{i\wedge j}}{\sum_M\mbox{I}_{i\vee j}}$$ + +By the same reasoning as above, the denominator becomes + +$$\mbox{I}_{i\wedge j} + + p(A_j)\mbox{I}_{i\wedge j?} + + p(A_i)\mbox{I}_{i?\wedge j} + + p(A_i)p(A_j)\mbox{I}_{i?\wedge j?},$$ + +and the nominator is + +$$\mbox{I}_{i\vee j} + p(A_j)\mbox{I}_{i'\wedge j?} + p(A_i)\mbox{I}_{i?\wedge j'} + \left(1 - [1 - p(A_i)][1 - p(A_j)]\right)\mbox{I}_{I?\wedge J?}.$$ + +The sums runs over instances, $M$, so the actual implementation can work by counting the cases and multipying by probabilities at the end. Let $N_c$ represent the number of cases that match condition $c$, i.e. $N_c = \sum_M\mbox{I}_c$. Then + +$$Jaccard(A_i, A_j) = \frac{ + N_{i\wedge j} + + p(A_j)N_{i\wedge j?} + + p(A_i)N_{i?\wedge j} + + p(A_i) p(A_j)N_{i?\wedge j?} + }{ + N_{i\vee j} + + p(A_j)N_{i'\wedge j?} + + p(A_i)N_{i?\wedge j'} + + \left(1 - [1 - p(A_i)][1 - p(A_j]\right)N_{i?\wedge j?} + }$$ diff --git a/Orange/distance/setup.py b/Orange/distance/setup.py new file mode 100644 index 00000000000..7ea061bd6b7 --- /dev/null +++ b/Orange/distance/setup.py @@ -0,0 +1,22 @@ +import os + +import numpy + + +def configuration(parent_package='', top_path=None): + from numpy.distutils.misc_util import Configuration + + libraries = [] + if os.name == 'posix': + libraries.append('m') + + config = Configuration('distance', parent_package, top_path) + config.add_extension('_distance', + sources=['_distance.c'], + include_dirs=[numpy.get_include()], + libraries=libraries) + return config + +if __name__ == '__main__': + from numpy.distutils.core import setup + setup(**configuration(top_path='').todict()) diff --git a/Orange/distance/tests/__init__.py b/Orange/distance/tests/__init__.py new file mode 100644 index 00000000000..8b137891791 --- /dev/null +++ b/Orange/distance/tests/__init__.py @@ -0,0 +1 @@ + diff --git a/Orange/distance/tests/calculation.xlsx b/Orange/distance/tests/calculation.xlsx new file mode 100644 index 00000000000..c75b6f215d6 Binary files /dev/null and b/Orange/distance/tests/calculation.xlsx differ diff --git a/Orange/distance/tests/test_distance.py b/Orange/distance/tests/test_distance.py new file mode 100644 index 00000000000..7fdfb564756 --- /dev/null +++ b/Orange/distance/tests/test_distance.py @@ -0,0 +1,874 @@ +import unittest +from math import sqrt + +import numpy as np + +from Orange.data import ContinuousVariable, DiscreteVariable, Domain, Table +from Orange import distance + + +class CommonTests: + """Tests applicable to all distance measures""" + + def test_no_data(self): + """distances return zero-dimensional matrices when no data""" + n = len(self.data) + np.testing.assert_almost_equal( + self.Distance(Table(self.domain)), + np.zeros((0, 0))) + np.testing.assert_almost_equal( + self.Distance(self.data, Table(self.domain)), + np.zeros((n, 0))) + np.testing.assert_almost_equal( + self.Distance(Table(self.domain), self.data), + np.zeros((0, n))) + + +class CommonFittedTests(CommonTests): + """Tests applicable to all distances with fitting""" + def test_mismatching_attributes(self): + """distances can't be computed if fit from other attributes""" + def new_table(): + return Table.from_list(Domain([ContinuousVariable("a")]), [[1]]) + + table1 = new_table() + model = self.Distance().fit(table1) + self.assertRaises(ValueError, model, new_table()) + self.assertRaises(ValueError, model, table1, new_table()) + self.assertRaises(ValueError, model, new_table(), table1) + + +class CommonNormalizedTests(CommonFittedTests): + """Tests applicable to distances the have normalization""" + + def test_zero_variance(self): + """zero-variance columns have no effect on row distance""" + assert_almost_equal = np.testing.assert_almost_equal + normalized = self.Distance(axis=1, normalize=True) + nonnormalized = self.Distance(axis=1, normalize=False) + + def is_same(d1, d2, fit1=None, fit2=None): + if fit1 is None: + fit1 = d1 + if fit2 is None: + fit2 = d2 + assert_almost_equal(normalized.fit(fit1)(d1), + normalized.fit(fit2)(d2)) + assert_almost_equal(nonnormalized.fit(fit1)(d1), + nonnormalized.fit(fit2)(d2)) + + data = self.cont_data + n = len(data) + X = data.X + domain = Domain(data.domain.attributes + (ContinuousVariable("d"),)) + data_const = Table(domain, np.hstack((X, np.ones((n, 1))))) + data_nan = Table(domain, np.hstack((X, np.full((n, 1), np.nan)))) + data_nan_1 = Table(domain, np.hstack((X, np.full((n, 1), np.nan)))) + data_nan_1.X[0, -1] = 1 + is_same(data, data_const) + is_same(data, data_nan) + is_same(data, data_nan_1) + + # Test whether it's possible to fit with singular data and use the + # parameters on data where the same column is defined + is_same(data_nan, data_const, data_const) + is_same(data_const, data_const, data_nan) + + self.assertRaises(ValueError, self.Distance, + data_const, axis=0, normalize=True) + self.assertRaises(ValueError, self.Distance, + data_nan, axis=0, normalize=True) + self.assertRaises(ValueError, self.Distance, + data_nan_1, axis=0, normalize=True) + + def test_mixed_cols(self): + """distance over columns raises exception for discrete columns""" + self.assertRaises(ValueError, self.Distance, self.mixed_data, axis=0) + self.assertRaises(ValueError, + self.Distance(axis=0).fit, self.mixed_data) + + +class FittedDistanceTest(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.attributes = ( + ContinuousVariable("c1"), + ContinuousVariable("c2"), + ContinuousVariable("c3"), + DiscreteVariable("d1", values=["a", "b"]), + DiscreteVariable("d2", values=["a", "b", "c", "d"]), + DiscreteVariable("d3", values=["a", "b", "c"])) + cls.domain = Domain(cls.attributes) + cls.cont_domain = Domain(cls.attributes[:3]) + cls.disc_domain = Domain(cls.attributes[3:]) + + def setUp(self): + self.cont_data = Table.from_list( + self.cont_domain, + [[1, 3, 2], + [-1, 5, 0], + [1, 1, 1], + [7, 2, 3]]) + + self.cont_data2 = Table.from_list( + self.cont_domain, + [[2, 1, 3], + [1, 2, 2]] + ) + + self.disc_data = Table.from_list( + self.disc_domain, + [[0, 0, 0], + [0, 1, 1], + [1, 3, 1]] + ) + + self.disc_data4 = Table.from_list( + self.disc_domain, + [[0, 0, 0], + [0, 1, 1], + [0, 1, 1], + [1, 3, 1]] + ) + + self.mixed_data = self.data = Table.from_numpy( + self.domain, np.hstack((self.cont_data.X[:3], self.disc_data.X))) + + + +# Correct results in these tests were computed manually or with Excel; +# these are not regression tests +class EuclideanDistanceTest(FittedDistanceTest, CommonNormalizedTests): + Distance = distance.Euclidean + + def test_euclidean_disc(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.disc_data + + model = distance.Euclidean().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1/3, 2/3, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 5/9, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal(dist, + np.sqrt(np.array([[0, 2, 3], + [2, 0, 2], + [3, 2, 0]]))) + + data.X[1, 0] = np.nan + model = distance.Euclidean().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1/2, 1/2, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1] + ]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 2/4, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal(dist, + np.sqrt(np.array([[0, 2.5, 3], + [2.5, 0, 1.5], + [3, 1.5, 0]]))) + + data.X[0, 0] = np.nan + model = distance.Euclidean().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1, 0, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 1, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal(dist, + np.sqrt(np.array([[0, 2, 2], + [2, 0, 1], + [2, 1, 0]]))) + + data = self.disc_data4 + data.X[:2, 0] = np.nan + model = distance.Euclidean().fit(data) + + assert_almost_equal(model.dist_missing_disc, + [[1/2, 1/2, 1, 1], + [3/4, 2/4, 1, 3/4], + [3/4, 1/4, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 2/4, 1 - 6/16, 1 - 10/16]) + + dist = model(data) + assert_almost_equal(dist, + np.sqrt(np.array([[0, 2.5, 2.5, 2.5], + [2.5, 0, 0.5, 1.5], + [2.5, 0.5, 0, 2], + [2.5, 1.5, 2, 0]]))) + + def test_euclidean_cont(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Euclidean(data, axis=1, normalize=False) + assert_almost_equal( + dist, + np.sqrt(np.array([[0, 12, 5, 38], + [12, 0, 21, 82], + [5, 21, 0, 41], + [38, 82, 41, 0]]))) + + data.X[1, 0] = np.nan + dist = distance.Euclidean(data, axis=1, normalize=False) + assert_almost_equal( + dist, + [[0, 4.472135955, 2.236067977, 6.164414003], + [4.472135955, 0, 5.385164807, 6.480740698], + [2.236067977, 5.385164807, 0, 6.403124237], + [6.164414003, 6.480740698, 6.403124237, 0]]) + + data.X[0, 0] = np.nan + dist = distance.Euclidean(data, axis=1, normalize=False) + assert_almost_equal( + dist, + [[0, 5.099019514, 4.795831523, 4.472135955], + [5.099019514, 0, 5.916079783, 6], + [4.795831523, 5.916079783, 0, 6.403124237], + [4.472135955, 6, 6.403124237, 0]]) + + def test_euclidean_cont_normalized(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + model = distance.Euclidean(axis=1, normalize=True).fit(data) + assert_almost_equal(model.means, [2, 2.75, 1.5]) + assert_almost_equal(model.vars, [9, 2.1875, 1.25]) + assert_almost_equal(model.dist_missing2_cont, [1, 1, 1]) + + dist = model(data) + assert_almost_equal( + dist, + [[0, 1.654239383, 1.146423008, 1.621286967], + [1.654239383, 0, 2.068662631, 3.035242727], + [1.146423008, 2.068662631, 0, 1.956673562], + [1.621286967, 3.035242727, 1.956673562, 0]]) + + dist = distance.Euclidean(data, axis=1, normalize=True) + assert_almost_equal( + dist, + [[0, 1.654239383, 1.146423008, 1.621286967], + [1.654239383, 0, 2.068662631, 3.035242727], + [1.146423008, 2.068662631, 0, 1.956673562], + [1.621286967, 3.035242727, 1.956673562, 0]]) + + data.X[1, 0] = np.nan + model = distance.Euclidean(axis=1, normalize=True).fit(data) + assert_almost_equal(model.means, [3, 2.75, 1.5]) + assert_almost_equal(model.vars, [8, 2.1875, 1.25]) + dist = model(data) + assert_almost_equal( + dist, + [[0, 1.806733438, 1.146423008, 1.696635326], + [1.806733438, 0, 2.192519751, 2.675283697], + [1.146423008, 2.192519751, 0, 2.019547333], + [1.696635326, 2.675283697, 2.019547333, 0]]) + + data.X[0, 0] = np.nan + model = distance.Euclidean(axis=1, normalize=True).fit(data) + assert_almost_equal(model.means, [4, 2.75, 1.5]) + assert_almost_equal(model.vars, [9, 2.1875, 1.25]) + dist = model(data) + assert_almost_equal( + dist, + [[0, 1.874642823, 1.521277659, 1.276154939], + [1.874642823, 0, 2.248809209, 2.580143961], + [1.521277659, 2.248809209, 0, 1.956673562], + [1.276154939, 2.580143961, 1.956673562, 0]]) + + def test_euclidean_cols(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Euclidean(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 8.062257748, 4.242640687], + [8.062257748, 0, 5.196152423], + [4.242640687, 5.196152423, 0]]) + + data.X[1, 1] = np.nan + dist = distance.Euclidean(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 6.218252702, 4.242640687], + [6.218252702, 0, 2.581988897], + [4.242640687, 2.581988897, 0]]) + + data.X[1, 0] = np.nan + dist = distance.Euclidean(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 6.218252702, 5.830951895], + [6.218252702, 0, 2.581988897], + [5.830951895, 2.581988897, 0]]) + + def test_euclidean_cols_normalized(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Euclidean(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 2.455273959, 0.649839392], + [2.455273959, 0, 2.473176308], + [0.649839392, 2.473176308, 0]]) + + data.X[1, 1] = np.nan + dist = distance.Euclidean(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 2, 0.649839392], + [2, 0, 1.704275472], + [0.649839392, 1.704275472, 0]]) + + data.X[1, 0] = np.nan + dist = distance.Euclidean(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 2, 1.450046001], + [2, 0, 1.704275472], + [1.450046001, 1.704275472, 0]]) + + def test_euclidean_mixed(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.mixed_data + + model = distance.Euclidean(axis=1, normalize=True).fit(data) + + assert_almost_equal(model.means, [1/3, 3, 1]) + assert_almost_equal(model.vars, [8/9, 8/3, 2/3]) + assert_almost_equal(model.dist_missing_disc, + [[1/3, 2/3, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_cont, [1, 1, 1]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 5/9, 1 - 3/9, 1 - 5/9]) + dist = model(data) + assert_almost_equal( + dist, + [[0, 2.828427125, 2.121320344], + [2.828427125, 0, 2.828427125], + [2.121320344, 2.828427125, 0]]) + + def test_two_tables(self): + assert_almost_equal = np.testing.assert_almost_equal + + dist = distance.Euclidean(self.cont_data, self.cont_data2, + normalize=True) + assert_almost_equal( + dist, + [[1.17040218, 0.47809144], + [2.78516478, 1.96961039], + [1.28668394, 0.79282497], + [1.27179413, 1.54919334]]) + + model = distance.Euclidean(normalize=True).fit(self.cont_data) + dist = model(self.cont_data, self.cont_data2) + assert_almost_equal( + dist, + [[1.17040218, 0.47809144], + [2.78516478, 1.96961039], + [1.28668394, 0.79282497], + [1.27179413, 1.54919334]]) + + dist = model(self.cont_data2) + assert_almost_equal(dist, [[0, 0.827119692], [0.827119692, 0]]) + + +class ManhattanDistanceTest(FittedDistanceTest, CommonNormalizedTests): + Distance = distance.Euclidean + + # The data used for testing Euclidean distances unfortunately yields + # mads = 1, so we change it a bit + def setUp(self): + super().setUp() + self.cont_data = Table.from_list( + self.cont_domain, + [[1, 3, 2], + [-1, 6, 0], + [2, 7, 1], + [7, 1, 3]]) + + def test_manhattan_no_data(self): + np.testing.assert_almost_equal( + distance.Manhattan(Table(self.domain)), + np.zeros((0, 0))) + np.testing.assert_almost_equal( + distance.Manhattan(self.mixed_data, Table(self.domain)), + np.zeros((3, 0))) + np.testing.assert_almost_equal( + distance.Manhattan(Table(self.domain), self.mixed_data), + np.zeros((0, 3))) + self.assertRaises( + ValueError, + distance.Manhattan, Table(self.cont_domain), axis=0, normalize=True) + + def test_manhattan_disc(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.disc_data + + model = distance.Manhattan().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1/3, 2/3, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 5/9, 1 - 3/9, 1 - 5/9]) + dist = model(data) + assert_almost_equal(dist, + [[0, 2, 3], + [2, 0, 2], + [3, 2, 0]]) + + data.X[1, 0] = np.nan + model = distance.Manhattan().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1/2, 1/2, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 2/4, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal(dist, + [[0, 2.5, 3], + [2.5, 0, 1.5], + [3, 1.5, 0]]) + + data.X[0, 0] = np.nan + model = distance.Manhattan().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1, 0, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 1, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal(dist, + [[0, 2, 2], + [2, 0, 1], + [2, 1, 0]]) + + data = self.disc_data4 + data.X[:2, 0] = np.nan + model = distance.Manhattan().fit(data) + assert_almost_equal(model.dist_missing_disc, + [[1/2, 1/2, 1, 1], + [3/4, 2/4, 1, 3/4], + [3/4, 1/4, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 2/4, 1 - 6/16, 1 - 10/16]) + + dist = model(data) + assert_almost_equal(dist, + [[0, 2.5, 2.5, 2.5], + [2.5, 0, 0.5, 1.5], + [2.5, 0.5, 0, 2], + [2.5, 1.5, 2, 0]]) + + def test_manhattan_cont(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Manhattan(data, axis=1, normalize=False) + assert_almost_equal( + dist, + [[0, 7, 6, 9], + [7, 0, 5, 16], + [6, 5, 0, 13], + [9, 16, 13, 0]]) + + data.X[1, 0] = np.nan + dist = distance.Manhattan(data, axis=1, normalize=False) + assert_almost_equal( + dist, + [[0, 7, 6, 9], + [7, 0, 3, 14], + [6, 3, 0, 13], + [9, 14, 13, 0]]) + + data.X[0, 0] = np.nan + dist = distance.Manhattan(data, axis=1, normalize=False) + assert_almost_equal( + dist, + [[0, 10, 10, 8], + [10, 0, 7, 13], + [10, 7, 0, 13], + [8, 13, 13, 0]]) + + def test_manhattan_cont_normalized(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + model = distance.Manhattan(axis=1, normalize=True).fit(data) + assert_almost_equal(model.medians, [1.5, 4.5, 1.5]) + assert_almost_equal(model.mads, [1.5, 2, 1]) + assert_almost_equal(model.dist_missing2_cont, np.ones(3)) + + dist = model(data) + assert_almost_equal( + dist, + [[0, 2.416666667, 1.833333333, 3], + [2.416666667, 0, 1.75, 5.416666667], + [1.833333333, 1.75, 0, 4.166666667], + [3, 5.416666667, 4.166666667, 0]]) + + dist = distance.Manhattan(data, axis=1, normalize=True) + assert_almost_equal( + dist, + [[0, 2.416666667, 1.833333333, 3], + [2.416666667, 0, 1.75, 5.416666667], + [1.833333333, 1.75, 0, 4.166666667], + [3, 5.416666667, 4.166666667, 0]]) + + data.X[1, 0] = np.nan + model = distance.Manhattan(axis=1, normalize=True).fit(data) + assert_almost_equal(model.medians, [2, 4.5, 1.5]) + assert_almost_equal(model.mads, [1, 2, 1]) + + dist = model(data) + assert_almost_equal( + dist, + [[0, 2.75, 2, 4], + [2.75, 0, 1.25, 5.75], + [2, 1.25, 0, 5], + [4, 5.75, 5, 0]]) + + data.X[0, 0] = np.nan + model = distance.Manhattan(axis=1, normalize=True).fit(data) + assert_almost_equal(model.medians, [4.5, 4.5, 1.5]) + assert_almost_equal(model.mads, [2.5, 2, 1]) + + dist = model(data) + assert_almost_equal( + dist, + [[0, 2.75, 2.5, 2], + [2.75, 0, 1.75, 3.75], + [2.5, 1.75, 0, 3.5], + [2, 3.75, 3.5, 0]]) + + def test_manhattan_cols(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Manhattan(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 20, 7], + [20, 0, 15], + [7, 15, 0]]) + + data.X[1, 1] = np.nan + dist = distance.Manhattan(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 19, 7], + [19, 0, 14], + [7, 14, 0]]) + + data.X[1, 0] = np.nan + dist = distance.Manhattan(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 17, 9], + [17, 0, 14], + [9, 14, 0]]) + + + def test_manhattan_cols_normalized(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Manhattan(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 4.5833333, 2], + [4.5833333, 0, 4.25], + [2, 4.25, 0]]) + + data.X[1, 1] = np.nan + dist = distance.Manhattan(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 4.6666667, 2], + [4.6666667, 0, 4], + [2, 4, 0]]) + + data.X[1, 0] = np.nan + dist = distance.Manhattan(data, axis=0, normalize=True) + assert_almost_equal( + dist, + [[0, 5.5, 4], + [5.5, 0, 4], + [4, 4, 0]]) + + def test_manhattan_mixed(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.mixed_data + + data.X[2, 0] = 2 # prevent mads[0] = 0 + model = distance.Manhattan(axis=1, normalize=True).fit(data) + assert_almost_equal(model.medians, [1, 3, 1]) + assert_almost_equal(model.mads, [1, 2, 1]) + assert_almost_equal(model.dist_missing_disc, + [[1/3, 2/3, 1, 1], + [2/3, 2/3, 1, 2/3], + [2/3, 1/3, 1, 1]]) + assert_almost_equal(model.dist_missing2_disc, + [1 - 5/9, 1 - 3/9, 1 - 5/9]) + + dist = model(data) + assert_almost_equal( + dist, + [[0, 4.5, 4.5], + [4.5, 0, 5], + [4.5, 5, 0]]) + + def test_two_tables(self): + assert_almost_equal = np.testing.assert_almost_equal + + dist = distance.Manhattan(self.cont_data, self.cont_data2, + normalize=True) + assert_almost_equal( + dist, + [[1.3333333, 0.25], + [3.75, 2.6666667], + [2.5, 2.0833333], + [1.6666667, 2.75]]) + + model = distance.Manhattan(normalize=True).fit(self.cont_data) + dist = model(self.cont_data, self.cont_data2) + assert_almost_equal( + dist, + [[1.3333333, 0.25], + [3.75, 2.6666667], + [2.5, 2.0833333], + [1.6666667, 2.75]]) + + dist = model(self.cont_data2) + assert_almost_equal(dist, [[0, 1.083333333], [1.083333333, 0]]) + + def test_manhattan_mixed_cols(self): + self.assertRaises(ValueError, + distance.Manhattan, self.mixed_data, axis=0) + self.assertRaises(ValueError, + distance.Manhattan(axis=0).fit, self.mixed_data) + + +class CosineDistanceTest(FittedDistanceTest, CommonFittedTests): + Distance = distance.Cosine + + def test_cosine_disc(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.disc_data + data.X = np.array([[1, 0, 0], + [0, 1, 1], + [1, 3, 0]], dtype=float) + + model = distance.Cosine().fit(data) + assert_almost_equal(model.means, [2 / 3, 2 / 3, 1 / 3]) + + dist = model(data) + assert_almost_equal(dist, 1 - np.array([[1, 0, 1 / sqrt(2)], + [0, 1, 0.5], + [1 / sqrt(2), 0.5, 1]])) + + data.X[1, 1] = np.nan + model = distance.Cosine().fit(data) + assert_almost_equal(model.means, [2 / 3, 1 / 2, 1 / 3]) + dist = model(data) + assert_almost_equal( + dist, + 1 - np.array([[1, 0, 1 / sqrt(2)], + [0, 1, 0.5 / sqrt(1.25) / sqrt(2)], + [1 / sqrt(2), 0.5 / sqrt(1.25) / sqrt(2), 1]])) + + data.X = np.array([[1, 0, 0], + [0, np.nan, 1], + [1, np.nan, 1], + [1, 3, 1]]) + model = distance.Cosine().fit(data) + dist = model(data) + assert_almost_equal(model.means, [0.75, 0.5, 0.75]) + assert_almost_equal(dist, [[0, 1, 0.333333333, 0.422649731], + [1, 0, 0.254644008, 0.225403331], + [0.333333333, 0.254644008, 0, 0.037749551], + [0.422649731, 0.225403331, 0.037749551, 0]]) + + def test_cosine_cont(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Cosine(data, axis=1) + assert_almost_equal( + dist, + [[0, 0.266200614, 0.0741799, 0.355097978], + [0.266200614, 0, 0.547089186, 0.925279678], + [0.0741799, 0.547089186, 0, 0.12011731], + [0.355097978, 0.925279678, 0.12011731, 0]] + ) + + data.X[1, 0] = np.nan + dist = distance.Cosine(data, axis=1) + assert_almost_equal( + dist, + [[0, 0.174971353, 0.0741799, 0.355097978], + [0.174971353, 0, 0.207881966, 0.324809395], + [0.0741799, 0.207881966, 0, 0.12011731], + [0.355097978, 0.324809395, 0.12011731, 0]]) + + data.X[0, 0] = np.nan + dist = distance.Cosine(data, axis=1) + assert_almost_equal( + dist, + [[0, 0.100977075, 0.035098719, 0.056666739], + [0.100977075, 0, 0.188497329, 0.246304671], + [0.035098719, 0.188497329, 0, 0.12011731], + [0.056666739, 0.246304671, 0.12011731, 0]]) + + def test_cosine_mixed(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.mixed_data + data.X = np.array([[1, 3, 2, 1, 0, 0], + [-1, 5, 0, 0, 1, 1], + [1, 1, 1, 1, 3, 0]], dtype=float) + + model = distance.Cosine(axis=1).fit(data) + assert_almost_equal(model.means, [1/3, 3, 1, 2/3, 2/3, 1/3]) + dist = model(data) + assert_almost_equal( + dist, + [[0, 0.316869949, 0.191709623], + [0.316869949, 0, 0.577422873], + [0.191709623, 0.577422873, 0]]) + + def test_two_tables(self): + assert_almost_equal = np.testing.assert_almost_equal + self.cont_data.X[1, 0] = np.nan + self.cont_data2.X[1, 0] = np.nan + + dist = distance.Cosine(self.cont_data, self.cont_data2) + assert_almost_equal( + dist, + [[0.2142857, 0.1573352], + [0.4958158, 0.2097042], + [0.0741799, 0.0198039], + [0.1514447, 0.0451363]]) + + model = distance.Cosine().fit(self.cont_data) + dist = model(self.cont_data, self.cont_data2) + assert_almost_equal( + dist, + [[0.2142857, 0.1573352], + [0.4958158, 0.2097042], + [0.0741799, 0.0198039], + [0.1514447, 0.0451363]]) + + dist = model(self.cont_data2) + assert_almost_equal(dist, [[0, 0.092514787], [0.092514787, 0]]) + + def test_cosine_cols(self): + assert_almost_equal = np.testing.assert_almost_equal + data = self.cont_data + + dist = distance.Cosine(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 0.711324865, 0.11050082], + [0.711324865, 0, 0.44365136], + [0.11050082, 0.44365136, 0]]) + + data.X[1, 1] = np.nan + dist = distance.Cosine(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 0.47702364, 0.11050082], + [0.47702364, 0, 0.181076975], + [0.11050082, 0.181076975, 0]]) + + data.X[1, 0] = np.nan + data.X[1, 2] = 2 + dist = distance.Cosine(data, axis=0, normalize=False) + assert_almost_equal( + dist, + [[0, 0.269703257, 0.087129071], + [0.269703257, 0, 0.055555556], + [0.087129071, 0.055555556, 0]]) + + +class JaccardDistanceTest(unittest.TestCase, CommonFittedTests): + Distance = distance.Jaccard + + def setUp(self): + self.domain = Domain([DiscreteVariable(c) for c in "abc"]) + self.data = Table( + self.domain, + [[0, 1, 1], + [1, 1, 1], + [1, 0, 1], + [1, 0, 0]]) + + def test_jaccard_rows(self): + assert_almost_equal = np.testing.assert_almost_equal + + model = distance.Jaccard().fit(self.data) + assert_almost_equal(model.ps, [0.75, 0.5, 0.75]) + assert_almost_equal( + model(self.data), + 1 - np.array([[1, 2/3, 1/3, 0], + [2/3, 1, 2/3, 1/3], + [1/3, 2/3, 1, 1/2], + [0, 1/3, 1/2, 1]])) + + X = self.data.X + X[1, 0] = X[2, 0] = X[3, 1] = np.nan + model = distance.Jaccard().fit(self.data) + assert_almost_equal(model.ps, np.array([0.5, 2/3, 0.75])) + + # pylint: disable=bad-whitespace + assert_almost_equal( + model(self.data), + 1 - np.array([[ 1, 2 / 2.5, 1 / 2.5, 2/3 / 3], + [2 / 2.5, 1, 1.25 / 2.75, (1/2+2/3) / 3], + [1 / 2.5, 1.25 / 2.75, 1, 0.5 / (2+2/3)], + [2/3 / 3, (1/2+2/3) / 3, 0.5 / (2+2/3), 1]])) + + def test_jaccard_cols(self): + assert_almost_equal = np.testing.assert_almost_equal + model = distance.Jaccard(axis=0).fit(self.data) + assert_almost_equal(model.ps, [0.75, 0.5, 0.75]) + assert_almost_equal( + model(self.data), + 1 - np.array([[1, 1/4, 1/2], + [1/4, 1, 2/3], + [1/2, 2/3, 1]])) + + self.data.X = np.array([[0, 1, 1], + [np.nan, np.nan, 1], + [np.nan, 0, 1], + [1, 1, 0]]) + model = distance.Jaccard(axis=0).fit(self.data) + assert_almost_equal(model.ps, [0.5, 2/3, 0.75]) + assert_almost_equal( + model(self.data), + 1 - np.array([[1, 0.4, 0.25], + [0.4, 1, 5/12], + [0.25, 5/12, 1]])) + + +if __name__ == "__main__": + unittest.main() diff --git a/Orange/projection/manifold.py b/Orange/projection/manifold.py index 0aa36f2f3c5..e55248aed8d 100644 --- a/Orange/projection/manifold.py +++ b/Orange/projection/manifold.py @@ -1,8 +1,7 @@ import numpy as np import sklearn.manifold as skl_manifold -from Orange.distance import (SklDistance, SpearmanDistance, PearsonDistance, - Euclidean) +from Orange.distance import Distance, DistanceModel, Euclidean from Orange.projection import SklProjector __all__ = ["MDS", "Isomap", "LocallyLinearEmbedding", "SpectralEmbedding", @@ -60,8 +59,9 @@ def __init__(self, n_components=2, metric=True, n_init=4, max_iter=300, def __call__(self, data): params = self.params.copy() dissimilarity = params['dissimilarity'] - distances = SklDistance, SpearmanDistance, PearsonDistance - if isinstance(self._metric, distances): + if isinstance(self._metric, DistanceModel) \ + or (isinstance(self._metric, type) + and issubclass(self._metric, Distance)): data = self.preprocess(data) _X, Y, domain = data.X, data.Y, data.domain X = dist_matrix = self._metric(_X) @@ -147,8 +147,7 @@ def __call__(self, data): else: data = self.preprocess(data) X, Y, domain = data.X, data.Y, data.domain - distances = SklDistance, SpearmanDistance, PearsonDistance - if isinstance(metric, distances): + if isinstance(metric, Distance): X = metric(X) params['metric'] = 'precomputed' diff --git a/Orange/setup.py b/Orange/setup.py index 0fc1084134f..df7faf01a73 100644 --- a/Orange/setup.py +++ b/Orange/setup.py @@ -11,6 +11,7 @@ def configuration(parent_package='', top_path=None): config = Configuration('Orange', parent_package, top_path) config.add_subpackage('classification') config.add_subpackage('data') + config.add_subpackage('distance') config.add_subpackage('evaluation') config.add_subpackage('ensembles') config.add_subpackage('misc') diff --git a/Orange/statistics/util.py b/Orange/statistics/util.py index 24a47815ce0..478128a2f26 100644 --- a/Orange/statistics/util.py +++ b/Orange/statistics/util.py @@ -284,24 +284,40 @@ def mean(x): return m -def nanmean(x, axis=None): +def _apply_func(x, dense_func, sparse_func, axis=None): """ Equivalent of np.nanmean that supports sparse or dense matrices. """ - def nanmean_sparse(x): - n_values = np.prod(x.shape) - np.sum(np.isnan(x.data)) - return np.nansum(x.data) / n_values - if not sp.issparse(x): - return np.nanmean(x, axis=axis) + return dense_func(x, axis=axis) if axis is None: - return nanmean_sparse(x) + return sparse_func(x) if axis in [0, 1]: arr = x if axis == 1 else x.T arr = arr.tocsr() - return np.array([nanmean_sparse(row) for row in arr]) + return np.fromiter((sparse_func(row) for row in arr), + dtype=np.double, count=arr.shape[0]) else: raise NotImplementedError +def nanmean(x, axis=None): + """ Equivalent of np.nanmean that supports sparse or dense matrices. """ + def nanmean_sparse(x): + n_values = np.prod(x.shape) - np.sum(np.isnan(x.data)) + return np.nansum(x.data) / n_values + + return _apply_func(x, np.nanmean, nanmean_sparse, axis=axis) + + +def nanvar(x, axis=None): + """ Equivalent of np.nanvar that supports sparse or dense matrices. """ + def nanvar_sparse(x): + n_values = np.prod(x.shape) - np.sum(np.isnan(x.data)) + mean = np.nansum(x.data) / n_values + return np.nansum((x.data - mean) ** 2) / n_values + + return _apply_func(x, np.nanvar, nanvar_sparse, axis=axis) + + def unique(x, return_counts=False): """ Equivalent of np.unique that supports sparse or dense matrices. """ if not sp.issparse(x): diff --git a/Orange/tests/test_distances.py b/Orange/tests/test_distances.py index fb3796652fe..46693b2aafc 100644 --- a/Orange/tests/test_distances.py +++ b/Orange/tests/test_distances.py @@ -2,7 +2,6 @@ # pylint: disable=missing-docstring from unittest import TestCase -import os import pickle import numpy as np @@ -31,6 +30,7 @@ def setUpClass(cls): cls.iris = Table('iris') cls.dist = Euclidean(cls.iris) + # pylint: disable=unsubscriptable-object def test_submatrix(self): sub = self.dist.submatrix([2, 3, 4]) np.testing.assert_equal(sub, self.dist[2:5, 2:5]) @@ -39,8 +39,10 @@ def test_submatrix(self): def test_pickling(self): unpickled_dist = pickle.loads(pickle.dumps(self.dist)) np.testing.assert_equal(unpickled_dist, self.dist) - self.assertTrue(tables_equal(unpickled_dist.row_items, self.dist.row_items)) - self.assertTrue(tables_equal(unpickled_dist.col_items, self.dist.col_items)) + self.assertTrue(tables_equal(unpickled_dist.row_items, + self.dist.row_items)) + self.assertTrue(tables_equal(unpickled_dist.col_items, + self.dist.col_items)) self.assertEqual(unpickled_dist.axis, self.dist.axis) def test_deprecated(self): @@ -182,6 +184,7 @@ def test_save(self): self.assertEqual(m.axis, 0) +# noinspection PyTypeChecker class TestEuclidean(TestCase): @classmethod def setUpClass(cls): @@ -190,65 +193,83 @@ def setUpClass(cls): cls.dist = Euclidean def test_euclidean_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1]), np.array([[0.53851648071346281]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1], axis=1), np.array([[0.53851648071346281]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1]), + np.array([[0.53851648071346281]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1], axis=1), + np.array([[0.53851648071346281]])) def test_euclidean_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.iris[:2]), - np.array([[0., 0.53851648], - [0.53851648, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], axis=0), - np.array([[0., 2.48394847, 5.09313263, 6.78969808], - [2.48394847, 0., 2.64007576, 4.327817], - [5.09313263, 2.64007576, 0., 1.69705627], - [6.78969808, 4.327817, 1.69705627, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[2], self.iris[:3]), - np. array([[0.50990195, 0.3, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[3]), - np.array([[0.64807407], - [0.33166248]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:3]), - np.array([[0., 0.53851648, 0.50990195], - [0.53851648, 0., 0.3]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:2], axis=0), - np.array([[0., 2.48394847, 5.09313263, 6.78969808], - [2.48394847, 0., 2.64007576, 4.327817], - [5.09313263, 2.64007576, 0., 1.69705627], - [6.78969808, 4.327817, 1.69705627, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2]), + np.array([[0., 0.53851648], + [0.53851648, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], axis=0), + np.array([[0., 2.48394847, 5.09313263, 6.78969808], + [2.48394847, 0., 2.64007576, 4.327817], + [5.09313263, 2.64007576, 0., 1.69705627], + [6.78969808, 4.327817, 1.69705627, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2], self.iris[:3]), + np. array([[0.50990195, 0.3, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[3]), + np.array([[0.64807407], + [0.33166248]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[:3]), + np.array([[0., 0.53851648, 0.50990195], + [0.53851648, 0., 0.3]])) def test_euclidean_distance_sparse(self): - np.testing.assert_almost_equal(self.dist(self.sparse), - np.array([[0., 3.74165739, 6.164414], - [3.74165739, 0., 4.47213595], - [6.164414, 4.47213595, 0.]])) - np.testing.assert_almost_equal(self.dist(self.sparse, axis=0), - np.array([[0., 4.12310563, 3.31662479], - [4.12310563, 0., 6.164414], - [3.31662479, 6.164414, 0.]])) - np.testing.assert_almost_equal(self.dist(self.sparse[:2]), - np.array([[0., 3.74165739], - [3.74165739, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse), + np.array([[0., 3.74165739, 6.164414], + [3.74165739, 0., 4.47213595], + [6.164414, 4.47213595, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse, axis=0), + np.array([[0., 4.12310563, 3.31662479], + [4.12310563, 0., 6.164414], + [3.31662479, 6.164414, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse[:2]), + np.array([[0., 3.74165739], + [3.74165739, 0.]])) def test_euclidean_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.iris[0].x, self.iris[1].x, axis=1), - np.array([[0.53851648071346281]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X), - np.array([[0., 0.53851648], - [0.53851648, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[2].x, self.iris[:3].X), - np. array([[0.50990195, 0.3, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[3].x), - np.array([[0.64807407], - [0.33166248]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[:3].X), - np.array([[0., 0.53851648, 0.50990195], - [0.53851648, 0., 0.3]])) - - + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X), + np.array([[0., 0.53851648], + [0.53851648, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2].x, self.iris[:3].X), + np. array([[0.50990195, 0.3, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[3].x), + np.array([[0.64807407], + [0.33166248]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[:3].X), + np.array([[0., 0.53851648, 0.50990195], + [0.53851648, 0., 0.3]])) + + +# noinspection PyTypeChecker class TestManhattan(TestCase): @classmethod def setUpClass(cls): @@ -257,64 +278,86 @@ def setUpClass(cls): cls.dist = Manhattan def test_manhattan_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1]), np.array([[0.7]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1], axis=1), np.array([[0.7]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1]), + np.array([[0.7]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1], axis=1), + np.array([[0.7]])) def test_manhattan_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.iris[:2]), - np.array([[0., 0.7], - [0.7, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], axis=0), - np.array([[0., 3.5, 7.2, 9.6], - [3.5, 0., 3.7, 6.1], - [7.2, 3.7, 0., 2.4], - [9.6, 6.1, 2.4, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[2], self.iris[:3]), - np.array([[0.8, 0.5, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[3]), - np.array([[1.], - [0.5]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:3]), - np.array([[0., 0.7, 0.8], - [0.7, 0., 0.5]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:2], axis=0), - np.array([[0., 3.5, 7.2, 9.6], - [3.5, 0., 3.7, 6.1], - [7.2, 3.7, 0., 2.4], - [9.6, 6.1, 2.4, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2]), + np.array([[0., 0.7], + [0.7, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], axis=0), + np.array([[0., 3.5, 7.2, 9.6], + [3.5, 0., 3.7, 6.1], + [7.2, 3.7, 0., 2.4], + [9.6, 6.1, 2.4, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2], self.iris[:3]), + np.array([[0.8, 0.5, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[3]), + np.array([[1.], + [0.5]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[:3]), + np.array([[0., 0.7, 0.8], + [0.7, 0., 0.5]])) def test_manhattan_distance_sparse(self): - np.testing.assert_almost_equal(self.dist(self.sparse), - np.array([[0., 6., 10.], - [6., 0., 6.], - [10., 6., 0.]])) - np.testing.assert_almost_equal(self.dist(self.sparse, axis=0), - np.array([[0., 5., 5.], - [5., 0., 10.], - [5., 10., 0.]])) - np.testing.assert_almost_equal(self.dist(self.sparse[:2]), - np.array([[0., 6.], - [6., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse), + np.array([[0., 6., 10.], + [6., 0., 6.], + [10., 6., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse, axis=0), + np.array([[0., 5., 5.], + [5., 0., 10.], + [5., 10., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.sparse[:2]), + np.array([[0., 6.], + [6., 0.]])) def test_manhattan_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.iris[0].x, self.iris[1].x, axis=1), np.array([[0.7]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X), - np.array([[0., 0.7], - [0.7, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[2].x, self.iris[:3].X), - np.array([[0.8, 0.5, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[3].x), - np.array([[1.], - [0.5]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[:3].X), - np.array([[0., 0.7, 0.8], - [0.7, 0., 0.5]])) - - + np.testing.assert_almost_equal( + self.dist(self.iris[0].x, self.iris[1].x, axis=1), + np.array([[0.7]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X), + np.array([[0., 0.7], + [0.7, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2].x, self.iris[:3].X), + np.array([[0.8, 0.5, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[3].x), + np.array([[1.], + [0.5]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[:3].X), + np.array([[0., 0.7, 0.8], + [0.7, 0., 0.5]])) + + +# noinspection PyTypeChecker class TestCosine(TestCase): @classmethod def setUpClass(cls): @@ -323,64 +366,85 @@ def setUpClass(cls): cls.dist = Cosine def test_cosine_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1]), np.array([[0.00142084]])) - np.testing.assert_almost_equal(self.dist(self.iris[0], self.iris[1], axis=1), np.array([[0.00142084]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0]), np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1]), + np.array([[0.00142084]])) + np.testing.assert_almost_equal( + self.dist(self.iris[0], self.iris[1], axis=1), + np.array([[0.00142084]])) def test_cosine_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.iris[:2]), - np.array([[0., 1.42083650e-03], - [1.42083650e-03, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], axis=0), - np.array([[0.0, 1.61124231e-03, 1.99940020e-04, 1.99940020e-04], - [1.61124231e-03, 0.0, 2.94551450e-03, 2.94551450e-03], - [1.99940020e-04, 2.94551450e-03, 0.0, 0.0], - [1.99940020e-04, 2.94551450e-03, 0.0, 0.0]])) - np.testing.assert_almost_equal(self.dist(self.iris[2], self.iris[:3]), - np.array([[1.26527175e-05, 1.20854727e-03, 0.0]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[3]), - np.array([[0.00089939], - [0.00120607]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:3]), - np.array([[0.0, 1.42083650e-03, 1.26527175e-05], - [1.42083650e-03, 0.0, 1.20854727e-03]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2], self.iris[:2], axis=0), - np.array([[0.0, 1.61124231e-03, 1.99940020e-04, 1.99940020e-04], - [1.61124231e-03, 0.0, 2.94551450e-03, 2.94551450e-03], - [1.99940020e-04, 2.94551450e-03, 0.0, 0.0], - [1.99940020e-04, 2.94551450e-03, 0.0, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2]), + np.array([[0., 1.42083650e-03], + [1.42083650e-03, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], axis=0), + np.array([[0.0, 1.61124231e-03, 1.99940020e-04, 1.99940020e-04], + [1.61124231e-03, 0.0, 2.94551450e-03, 2.94551450e-03], + [1.99940020e-04, 2.94551450e-03, 0.0, 0.0], + [1.99940020e-04, 2.94551450e-03, 0.0, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2], self.iris[:3]), + np.array([[1.26527175e-05, 1.20854727e-03, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[3]), + np.array([[0.00089939], + [0.00120607]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2], self.iris[:3]), + np.array([[0.0, 1.42083650e-03, 1.26527175e-05], + [1.42083650e-03, 0.0, 1.20854727e-03]])) def test_cosine_distance_sparse(self): - np.testing.assert_almost_equal(self.dist(self.sparse), - np.array([[0.0, 1.00000000e+00, 7.20627882e-01], - [1.00000000e+00, 0.0, 2.19131191e-01], - [7.20627882e-01, 2.19131191e-01, 0.0]])) - np.testing.assert_almost_equal(self.dist(self.sparse, axis=0), - np.array([[0.0, 7.57464375e-01, 1.68109669e-01], - [7.57464375e-01, 0.0, 1.00000000e+00], - [1.68109669e-01, 1.00000000e+00, 0.0]])) - np.testing.assert_almost_equal(self.dist(self.sparse[:2]), - np.array([[0.0, 1.00000000e+00], - [1.00000000e+00, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.sparse), + np.array([[0.0, 1.00000000e+00, 7.20627882e-01], + [1.00000000e+00, 0.0, 2.19131191e-01], + [7.20627882e-01, 2.19131191e-01, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.sparse, axis=0), + np.array([[0.0, 7.57464375e-01, 1.68109669e-01], + [7.57464375e-01, 0.0, 1.00000000e+00], + [1.68109669e-01, 1.00000000e+00, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.sparse[:2]), + np.array([[0.0, 1.00000000e+00], + [1.00000000e+00, 0.0]])) def test_cosine_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.iris[0].x, self.iris[1].x, axis=1), np.array([[0.00142084]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X), - np.array([[0., 1.42083650e-03], - [1.42083650e-03, 0.]])) - np.testing.assert_almost_equal(self.dist(self.iris[2].x, self.iris[:3].X), - np.array([[1.26527175e-05, 1.20854727e-03, 0.0]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[3].x), - np.array([[0.00089939], - [0.00120607]])) - np.testing.assert_almost_equal(self.dist(self.iris[:2].X, self.iris[:3].X), - np.array([[0.0, 1.42083650e-03, 1.26527175e-05], - [1.42083650e-03, 0.0, 1.20854727e-03]])) - - + np.testing.assert_almost_equal( + self.dist(self.iris[0].x, self.iris[1].x, axis=1), + np.array([[0.00142084]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X), + np.array([[0., 1.42083650e-03], + [1.42083650e-03, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.iris[2].x, self.iris[:3].X), + np.array([[1.26527175e-05, 1.20854727e-03, 0.0]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[3].x), + np.array([[0.00089939], + [0.00120607]])) + np.testing.assert_almost_equal( + self.dist(self.iris[:2].X, self.iris[:3].X), + np.array([[0.0, 1.42083650e-03, 1.26527175e-05], + [1.42083650e-03, 0.0, 1.20854727e-03]])) + + +# noinspection PyTypeChecker class TestJaccard(TestCase): @classmethod def setUpClass(cls): @@ -388,53 +452,73 @@ def setUpClass(cls): cls.dist = Jaccard def test_jaccard_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.titanic[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.titanic[0], self.titanic[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.titanic[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.titanic[0], self.titanic[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.titanic[0], self.titanic[2]), np.array([[0.5]])) - np.testing.assert_almost_equal(self.dist(self.titanic[0], self.titanic[2], axis=1), np.array([[0.5]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0], self.titanic[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0], self.titanic[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0], self.titanic[2]), + np.array([[0.5]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[0], self.titanic[2], axis=1), + np.array([[0.5]])) def test_jaccard_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.titanic), - np.array([[0., 0., 0.5, 0.5], - [0., 0., 0.5, 0.5], - [0.5, 0.5, 0., 0.], - [0.5, 0.5, 0., 0.]])) - np.testing.assert_almost_equal(self.dist(self.titanic, axis=0), - np.array([[0., 1., 0.5], - [1., 0., 1.], - [0.5, 1., 0.]])) - np.testing.assert_almost_equal(self.dist(self.titanic[2], self.titanic[:3]), - np.array([[0.5, 0.5, 0.]])) - np.testing.assert_almost_equal(self.dist(self.titanic[:2], self.titanic[3]), - np.array([[0.5], - [0.5]])) - np.testing.assert_almost_equal(self.dist(self.titanic[:2], self.titanic[:3]), - np.array([[0., 0., 0.5], - [0., 0., 0.5]])) - np.testing.assert_almost_equal(self.dist(self.titanic, self.titanic, axis=0), - np.array([[0., 1., 0.5], - [1., np.nan, 1.], - [0.5, 1., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic), + np.array([[0., 0., 0.5, 0.5], + [0., 0., 0.5, 0.5], + [0.5, 0.5, 0., 0.], + [0.5, 0.5, 0., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic, axis=0), + np.array([[0., 1., 0.5], + [1., 0., 1.], + [0.5, 1., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[2], self.titanic[:3]), + np.array([[0.5, 0.5, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[:2], self.titanic[3]), + np.array([[0.5], + [0.5]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[:2], self.titanic[:3]), + np.array([[0., 0., 0.5], + [0., 0., 0.5]])) def test_jaccard_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.titanic[0].x, self.titanic[2].x, axis=1), np.array([[0.5]])) - np.testing.assert_almost_equal(self.dist(self.titanic.X), - np.array([[0., 0., 0.5, 0.5], - [0., 0., 0.5, 0.5], - [0.5, 0.5, 0., 0.], - [0.5, 0.5, 0., 0.]])) - np.testing.assert_almost_equal(self.dist(self.titanic[2].x, self.titanic[:3].X), - np.array([[0.5, 0.5, 0.]])) - np.testing.assert_almost_equal(self.dist(self.titanic[:2].X, self.titanic[3].x), - np.array([[0.5], - [0.5]])) - np.testing.assert_almost_equal(self.dist(self.titanic[:2].X, self.titanic[:3].X), - np.array([[0., 0., 0.5], - [0., 0., 0.5]])) - - + np.testing.assert_almost_equal( + self.dist(self.titanic[0].x, self.titanic[2].x, axis=1), + np.array([[0.5]])) + np.testing.assert_almost_equal( + self.dist(self.titanic.X), + np.array([[0., 0., 0.5, 0.5], + [0., 0., 0.5, 0.5], + [0.5, 0.5, 0., 0.], + [0.5, 0.5, 0., 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[2].x, self.titanic[:3].X), + np.array([[0.5, 0.5, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[:2].X, self.titanic[3].x), + np.array([[0.5], + [0.5]])) + np.testing.assert_almost_equal( + self.dist(self.titanic[:2].X, self.titanic[:3].X), + np.array([[0., 0., 0.5], + [0., 0., 0.5]])) + + +# noinspection PyTypeChecker class TestSpearmanR(TestCase): @classmethod def setUpClass(cls): @@ -442,78 +526,80 @@ def setUpClass(cls): cls.dist = SpearmanR def test_spearmanr_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1]), np.array([[0.5083333333333333]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1], axis=1), - np.array([[0.5083333333333333]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1]), + np.array([[0.5083333333333333]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1], axis=1), + np.array([[0.5083333333333333]])) def test_spearmanr_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.breast[:2]), - np.array([[0., 0.5083333333333333], - [0.5083333333333333, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:4]), - np.array([[0., 0.50833333, 0.075, 0.61666667], - [0.50833333, 0., 0.38333333, 0.53333333], - [0.075, 0.38333333, 0., 0.63333333], - [0.61666667, 0.53333333, 0.63333333, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.75, 0.25, 0.75, 0.25, 0.25, 0.25, 0., 0.25, 1.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0.75, 0.25, 0.75, 0.75, 0.75, 1., 0.75, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:4]), - np.array([[0., 0.50833333, 0.075, 0.61666667], - [0.50833333, 0., 0.38333333, 0.53333333], - [0.075, 0.38333333, 0., 0.63333333]])) - np.testing.assert_almost_equal(self.dist(self.breast[2], self.breast[:3]), - np. array([[0.075, 0.3833333, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[2]), - np. array([[0.075], - [0.3833333], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:3], axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.75, 0.25, 0.75, 0.25, 0.25, 0.25, 0., 0.25, 1.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0.75, 0.25, 0.75, 0.75, 0.75, 1., 0.75, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2]), + np.array([[0., 0.5083333333333333], + [0.5083333333333333, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:4]), + np.array([[0., 0.50833333, 0.075, 0.61666667], + [0.50833333, 0., 0.38333333, 0.53333333], + [0.075, 0.38333333, 0., 0.63333333], + [0.61666667, 0.53333333, 0.63333333, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], axis=0), + np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], + [0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], + [0.75, 0.25, 0.75, 0.25, 0.25, 0.25, 0., 0.25, 1.], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], + [0.25, 0.75, 0.25, 0.75, 0.75, 0.75, 1., 0.75, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[:4]), + np.array([[0., 0.50833333, 0.075, 0.61666667], + [0.50833333, 0., 0.38333333, 0.53333333], + [0.075, 0.38333333, 0., 0.63333333]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2], self.breast[:3]), + np.array([[0.075, 0.3833333, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[2]), + np.array([[0.075], + [0.3833333], + [0.]])) def test_spearmanr_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.breast[0].x, self.breast[1].x, axis=1), - np.array([[0.5083333333333333]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2].X), - np.array([[0., 0.5083333333333333], - [0.5083333333333333, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[2].x, self.breast[:3].X), - np. array([[0.075, 0.3833333, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3].X, self.breast[2].x), - np. array([[0.075], - [0.3833333], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3].X, self.breast[:3].X, axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.75, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.75, 0.25, 0.75, 0.25, 0.25, 0.25, 0., 0.25, 1.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.75], - [0.25, 0.75, 0.25, 0.75, 0.75, 0.75, 1., 0.75, 0.]])) - - + np.testing.assert_almost_equal( + self.dist(self.breast[0].x, self.breast[1].x, axis=1), + np.array([[0.5083333333333333]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2].X), + np.array([[0., 0.5083333333333333], + [0.5083333333333333, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2].x, self.breast[:3].X), + np.array([[0.075, 0.3833333, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3].X, self.breast[2].x), + np.array([[0.075], + [0.3833333], + [0.]])) + + +# noinspection PyTypeChecker class TestSpearmanRAbsolute(TestCase): @classmethod def setUpClass(cls): @@ -521,76 +607,76 @@ def setUpClass(cls): cls.dist = SpearmanRAbsolute def test_spearmanrabsolute_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1]), - np.array([[0.49166666666666664]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1], axis=1), - np.array([[0.49166666666666664]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1]), + np.array([[0.49166666666666664]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1], axis=1), + np.array([[0.49166666666666664]])) def test_spearmanrabsolute_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.breast[:2]), - np.array([[0., 0.49166667], - [0.49166667, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:4]), - np.array([[0., 0.49166667, 0.075, 0.38333333], - [0.49166667, 0., 0.38333333, 0.46666667], - [0.075, 0.38333333, 0., 0.36666667]])) - np.testing.assert_almost_equal(self.dist(self.breast[3], self.breast[:4]), - np.array([[0.3833333, 0.4666667, 0.3666667, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:4], self.breast[3]), - np.array([[0.3833333], - [0.4666667], - [0.3666667], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:3], axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2]), + np.array([[0., 0.49166667], + [0.49166667, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], axis=0), + np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], + [0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], + [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.], + [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], + [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[:4]), + np.array([[0., 0.49166667, 0.075, 0.38333333], + [0.49166667, 0., 0.38333333, 0.46666667], + [0.075, 0.38333333, 0., 0.36666667]])) + np.testing.assert_almost_equal( + self.dist(self.breast[3], self.breast[:4]), + np.array([[0.3833333, 0.4666667, 0.3666667, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:4], self.breast[3]), + np.array([[0.3833333], + [0.4666667], + [0.3666667], + [0.]])) def test_spearmanrabsolute_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.breast[0].x, self.breast[1].x, axis=1), - np.array([[0.49166666666666664]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2].X), - np.array([[0., 0.49166667], - [0.49166667, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[3].x, self.breast[:4].X), - np.array([[0.3833333, 0.4666667, 0.3666667, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:4].X, self.breast[3].x), - np.array([[0.3833333], - [0.4666667], - [0.3666667], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3].X, self.breast[:3].X, axis=0), - np.array([[0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0., 0.25, 0., 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.], - [0.25, 0., 0.25, 0., 0., 0., 0.25, 0., 0.25], - [0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0., 0.25, 0.]])) - - + np.testing.assert_almost_equal( + self.dist(self.breast[0].x, self.breast[1].x, axis=1), + np.array([[0.49166666666666664]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2].X), + np.array([[0., 0.49166667], + [0.49166667, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[3].x, self.breast[:4].X), + np.array([[0.3833333, 0.4666667, 0.3666667, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:4].X, self.breast[3].x), + np.array([[0.3833333], + [0.4666667], + [0.3666667], + [0.]])) + + +# noinspection PyTypeChecker class TestPearsonR(TestCase): @classmethod def setUpClass(cls): @@ -598,73 +684,76 @@ def setUpClass(cls): cls.dist = PearsonR def test_pearsonr_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1]), np.array([[0.48462293898088876]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1], axis=1), - np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1]), + np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1], axis=1), + np.array([[0.48462293898088876]])) def test_pearsonr_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.breast[:2]), - np.array([[0., 0.48462294], - [0.48462294, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20], axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.57976119], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.57976119, 0.45930368, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:4]), - np.array([[0., 0.48462294, 0.10133593, 0.5016744], - [0.48462294, 0., 0.32783865, 0.57317387], - [0.10133593, 0.32783865, 0., 0.63789635]])) - np.testing.assert_almost_equal(self.dist(self.breast[2], self.breast[:3]), - np.array([[0.10133593, 0.32783865, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[2]), - np.array([[0.10133593], - [0.32783865], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20], self.breast[:20], axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.57976119], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.57976119, 0.45930368, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2]), + np.array([[0., 0.48462294], + [0.48462294, 0.]])) + # pylint: disable=line-too-long + # Because it looks better + np.testing.assert_almost_equal( + self.dist(self.breast[:20], axis=0), + np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], + [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], + [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], + [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], + [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], + [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], + [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.57976119], + [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], + [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.57976119, 0.45930368, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[:4]), + np.array([[0., 0.48462294, 0.10133593, 0.5016744], + [0.48462294, 0., 0.32783865, 0.57317387], + [0.10133593, 0.32783865, 0., 0.63789635]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2], self.breast[:3]), + np.array([[0.10133593, 0.32783865, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[2]), + np.array([[0.10133593], + [0.32783865], + [0.]])) def test_pearsonr_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.breast[0].x, self.breast[1].x, axis=1), - np.array([[0.48462293898088876]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2].X), - np.array([[0., 0.48462294], - [0.48462294, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[2].x, self.breast[:3].X), - np.array([[0.10133593, 0.32783865, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3].X, self.breast[2].x), - np.array([[0.10133593], - [0.32783865], - [0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20].X, self.breast[:20].X, axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.57976119], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.57976119, 0.45930368, 0.]])) - - + np.testing.assert_almost_equal( + self.dist(self.breast[0].x, self.breast[1].x, axis=1), + np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2].X), + np.array([[0., 0.48462294], + [0.48462294, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2].x, self.breast[:3].X), + np.array([[0.10133593, 0.32783865, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3].X, self.breast[2].x), + np.array([[0.10133593], + [0.32783865], + [0.]])) + + +# noinspection PyTypeChecker class TestPearsonRAbsolute(TestCase): @classmethod def setUpClass(cls): @@ -672,71 +761,76 @@ def setUpClass(cls): cls.dist = PearsonRAbsolute def test_pearsonrabsolute_distance_one_example(self): - np.testing.assert_almost_equal(self.dist(self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0]), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[0], axis=1), np.array([[0]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1]), np.array([[0.48462293898088876]])) - np.testing.assert_almost_equal(self.dist(self.breast[0], self.breast[1], axis=1), - np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0]), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[0], axis=1), + np.array([[0]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1]), + np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[0], self.breast[1], axis=1), + np.array([[0.48462293898088876]])) def test_pearsonrabsolute_distance_many_examples(self): - np.testing.assert_almost_equal(self.dist(self.breast[:2]), - np.array([[0., 0.48462294], - [0.48462294, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20], axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.42023881], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.42023881, 0.45930368, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:3], self.breast[:4]), - np.array([[0., 0.48462294, 0.10133593, 0.4983256], - [0.48462294, 0., 0.32783865, 0.42682613], - [0.10133593, 0.32783865, 0., 0.36210365]])) - np.testing.assert_almost_equal(self.dist(self.breast[2], self.breast[:3]), - np.array([[0.10133593, 0.32783865, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2], self.breast[3]), - np.array([[0.4983256], - [0.42682613]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20], self.breast[:20], axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.42023881], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.42023881, 0.45930368, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2]), + np.array([[0., 0.48462294], + [0.48462294, 0.]])) + # pylint: disable=line-too-long + # Because it looks better + np.testing.assert_almost_equal( + self.dist(self.breast[:20], axis=0), + np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], + [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], + [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], + [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], + [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], + [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], + [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.42023881], + [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], + [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.42023881, 0.45930368, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:3], self.breast[:4]), + np.array([[0., 0.48462294, 0.10133593, 0.4983256], + [0.48462294, 0., 0.32783865, 0.42682613], + [0.10133593, 0.32783865, 0., 0.36210365]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2], self.breast[:3]), + np.array([[0.10133593, 0.32783865, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2], self.breast[3]), + np.array([[0.4983256], + [0.42682613]])) def test_pearsonrabsolute_distance_numpy(self): - np.testing.assert_almost_equal(self.dist(self.breast[0].x, self.breast[1].x, axis=1), - np.array([[0.48462293898088876]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2].X), - np.array([[0., 0.48462294], - [0.48462294, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[2].x, self.breast[:3].X), - np.array([[0.10133593, 0.32783865, 0.]])) - np.testing.assert_almost_equal(self.dist(self.breast[:2].X, self.breast[3].x), - np.array([[0.4983256], - [0.42682613]])) - np.testing.assert_almost_equal(self.dist(self.breast[:20].X, self.breast[:20].X, axis=0), - np.array([[0., 0.10239274, 0.12786763, 0.13435117, 0.15580385, 0.27429811, 0.21006195, 0.24072005, 0.42847752], - [0.10239274, 0., 0.01695375, 0.10313851, 0.1138925, 0.16978203, 0.1155948, 0.08043531, 0.43326547], - [0.12786763, 0.01695375, 0., 0.16049178, 0.13692762, 0.21784201, 0.11607395, 0.06493949, 0.46590168], - [0.13435117, 0.10313851, 0.16049178, 0., 0.07181648, 0.15585667, 0.13891172, 0.21622332, 0.37404826], - [0.15580385, 0.1138925, 0.13692762, 0.07181648, 0., 0.16301705, 0.17324382, 0.21452448, 0.42283252], - [0.27429811, 0.16978203, 0.21784201, 0.15585667, 0.16301705, 0., 0.25512861, 0.29560909, 0.42766076], - [0.21006195, 0.1155948, 0.11607395, 0.13891172, 0.17324382, 0.25512861, 0., 0.14419442, 0.42023881], - [0.24072005, 0.08043531, 0.06493949, 0.21622332, 0.21452448, 0.29560909, 0.14419442, 0., 0.45930368], - [0.42847752, 0.43326547, 0.46590168, 0.37404826, 0.42283252, 0.42766076, 0.42023881, 0.45930368, 0.]])) - - + np.testing.assert_almost_equal( + self.dist(self.breast[0].x, self.breast[1].x, axis=1), + np.array([[0.48462293898088876]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2].X), + np.array([[0., 0.48462294], + [0.48462294, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[2].x, self.breast[:3].X), + np.array([[0.10133593, 0.32783865, 0.]])) + np.testing.assert_almost_equal( + self.dist(self.breast[:2].X, self.breast[3].x), + np.array([[0.4983256], + [0.42682613]])) + + +# noinspection PyTypeChecker +# Pylint doesn't get magic __new__ operators +# pylint: disable=not-callable class TestMahalanobis(TestCase): def setUp(self): self.n, self.m = 10, 5 @@ -750,7 +844,8 @@ def test_correctness(self): d = scipy.spatial.distance.squareform(d) for i in range(self.n): for j in range(self.n): - self.assertAlmostEqual(d[i][j], mah(self.x[i], self.x[j]), delta=1e-5) + self.assertAlmostEqual(d[i][j], mah(self.x[i], self.x[j]), + delta=1e-5) def test_attributes(self): metric = MahalanobisDistance(self.x) @@ -771,14 +866,6 @@ def test_iris(self): self.assertEqual(metric(tab).shape, (150, 150)) self.assertEqual(metric(tab[0], tab[1]).shape, (1, 1)) - def test_axis(self): - mah = MahalanobisDistance(self.x, axis=1) - self.assertEqual(mah(self.x, self.x).shape, (self.n, self.n)) - x = self.x.T - mah = MahalanobisDistance(x, axis=0) - self.assertRaises(AssertionError, mah, x, axis=1) - self.assertEqual(mah(x, x).shape, (self.n, self.n)) - def test_dimensions(self): x = Table('iris')[:20].X xt = Table('iris')[:20].X.T @@ -787,17 +874,6 @@ def test_dimensions(self): mah = MahalanobisDistance(xt) mah(xt[0], xt[1]) - def test_global_is_borked(self): - """ - Test that the global state retaining non-safe Mahalanobis instance - raises RuntimeErrors on all invocations - """ - from Orange.distance import Mahalanobis - with self.assertRaises(RuntimeError): - Mahalanobis.fit(self.x) - with self.assertRaises(RuntimeError): - Mahalanobis(self.x) - class TestDistances(TestCase): @classmethod diff --git a/Orange/widgets/unsupervised/owdistances.py b/Orange/widgets/unsupervised/owdistances.py index 62b15f2d9fb..3fe41cdf105 100644 --- a/Orange/widgets/unsupervised/owdistances.py +++ b/Orange/widgets/unsupervised/owdistances.py @@ -1,6 +1,6 @@ -import bottleneck as bn from AnyQt.QtCore import Qt from scipy.sparse import issparse +import bottleneck as bn import Orange.data import Orange.misc @@ -9,21 +9,17 @@ from Orange.widgets.utils.sql import check_sql_input from Orange.widgets.widget import OWWidget, Msg, Input, Output -# A placeholder. This metric is handled specially in commit method. -__Mahalanobis = distance.MahalanobisDistance() -__Mahalanobis.fit = None - METRICS = [ - distance.Euclidean, - distance.Manhattan, - __Mahalanobis, - distance.Cosine, - distance.Jaccard, - distance.SpearmanR, - distance.SpearmanRAbsolute, - distance.PearsonR, - distance.PearsonRAbsolute, + ("Euclidean", distance.Euclidean), + ("Manhattan", distance.Manhattan), + ("Mahalanobis", distance.Mahalanobis), + ("Cosine", distance.Cosine), + ("Jaccard", distance.Jaccard), + ("Spearman", distance.SpearmanR), + ("Absolute Spearman", distance.SpearmanRAbsolute), + ("Pearson", distance.PearsonR), + ("Absolute Pearson", distance.PearsonRAbsolute), ] @@ -47,15 +43,13 @@ class Outputs: class Error(OWWidget.Error): no_continuous_features = Msg("No numeric features") - dense_metric_sparse_data = Msg("Selected metric does not support sparse data") - empty_data = Msg("Empty data set") - mahalanobis_error = Msg("{}") - distances_memory_error = Msg("Not enough memory.") - distances_value_error = Msg("Error occurred while calculating distances\n{}") + dense_metric_sparse_data = Msg("{} requires dense data.") + distances_memory_error = Msg("Not enough memory") + distances_value_error = Msg("Problem in calculation:\n{}") class Warning(OWWidget.Warning): ignoring_discrete = Msg("Ignoring categorical features") - imputing_data = Msg("Imputing missing values") + imputing_data = Msg("Missing values were imputed") def __init__(self): super().__init__() @@ -67,7 +61,7 @@ def __init__(self): ) self.metrics_combo = gui.comboBox(self.controlArea, self, "metric_idx", box="Distance Metric", - items=[m.name for m in METRICS], + items=[m[0] for m in METRICS], callback=self._invalidate ) box = gui.auto_commit(self.buttonsArea, self, "autocommit", "Apply", @@ -80,98 +74,66 @@ def __init__(self): @Inputs.data @check_sql_input def set_data(self, data): - """ - Set the input data set from which to compute the distances - """ self.data = data self.refresh_metrics() self.unconditional_commit() def refresh_metrics(self): - """ - Refresh available metrics depending on the input data's sparsenes - """ sparse = self.data is not None and issparse(self.data.X) for i, metric in enumerate(METRICS): item = self.metrics_combo.model().item(i) - item.setEnabled(not sparse or metric.supports_sparse) - - self._checksparse() - - def _checksparse(self): - # Check the current metric for input data compatibility and set/clear - # appropriate informational GUI state - self.Error.dense_metric_sparse_data( - shown=self.data is not None and issparse(self.data.X) and - not METRICS[self.metric_idx].supports_sparse) + item.setEnabled(not sparse or metric[1].supports_sparse) def commit(self): - metric = METRICS[self.metric_idx] - self.Outputs.distances.send(self.compute_distances(metric, self.data)) + # pylint: disable=invalid-sequence-index + metric = METRICS[self.metric_idx][1] + dist = self.compute_distances(metric, self.data) + self.Outputs.distances.send(dist) def compute_distances(self, metric, data): - def checks(metric, data): - if data is None: - return - + def _check_sparse(): + # pylint: disable=invalid-sequence-index if issparse(data.X) and not metric.supports_sparse: - self.Error.dense_metric_sparse_data() - return - - if not any(a.is_continuous for a in data.domain.attributes): - self.Error.no_continuous_features() - return - - needs_preprocessing = False - if any(a.is_discrete for a in self.data.domain.attributes): + self.Error.dense_metric_sparse_data(METRICS[self.metric_idx][0]) + return False + + def _fix_discrete(): + nonlocal data + if data.domain.has_discrete_attributes() and ( + issparse(data.X) and getattr(metric, "fallback", None) + or not metric.supports_discrete + or self.axis == 1): + if not data.domain.has_continuous_attributes(): + self.Error.no_continuous_features() + return False self.Warning.ignoring_discrete() - needs_preprocessing = True + data = distance.remove_discrete_features(data) - if not issparse(data.X) and bn.anynan(data.X): + def _fix_missing(): + nonlocal data + if not metric.supports_missing and bn.anynan(data.X): self.Warning.imputing_data() - needs_preprocessing = True - - if needs_preprocessing: - # removes discrete features and imputes data - data = distance._preprocess(data) - - if not data.X.size: - self.Error.empty_data() - return - - return data + data = distance.impute(data) self.clear_messages() - - data = checks(metric, data) if data is None: return - - if isinstance(metric, distance.MahalanobisDistance): - # Mahalanobis distance has to be trained before it can be used - # to compute distances - try: - metric = distance.MahalanobisDistance(data, axis=1 - self.axis) - except (ValueError, MemoryError) as e: - self.Error.mahalanobis_error(e) + for check in (_check_sparse, _fix_discrete, _fix_missing): + if check() is False: return - try: - met = metric(data, data, 1 - self.axis, impute=True) + return metric(data, axis=1 - self.axis, impute=True) except ValueError as e: self.Error.distances_value_error(e) - return except MemoryError: self.Error.distances_memory_error() - return - return met def _invalidate(self): - self._checksparse() self.commit() def send_report(self): + # pylint: disable=invalid-sequence-index self.report_items(( ("Distances Between", ["Rows", "Columns"][self.axis]), - ("Metric", METRICS[self.metric_idx].name) + ("Metric", METRICS[self.metric_idx][0]) )) diff --git a/Orange/widgets/unsupervised/tests/test_owdistances.py b/Orange/widgets/unsupervised/tests/test_owdistances.py index f5f6b7d320d..d54f9c49147 100644 --- a/Orange/widgets/unsupervised/tests/test_owdistances.py +++ b/Orange/widgets/unsupervised/tests/test_owdistances.py @@ -5,7 +5,6 @@ import numpy as np from Orange.data import Table -from Orange.distance import MahalanobisDistance from Orange.widgets.unsupervised.owdistances import OWDistances, METRICS from Orange.widgets.tests.base import WidgetTest @@ -24,9 +23,7 @@ def test_distance_combo(self): """Check distances when the metric changes""" self.assertEqual(self.widget.metrics_combo.count(), len(METRICS)) self.send_signal(self.widget.Inputs.data, self.iris) - for i, metric in enumerate(METRICS): - if isinstance(metric, MahalanobisDistance): - metric = MahalanobisDistance(self.iris) + for i, (_, metric) in enumerate(METRICS): self.widget.metrics_combo.activated.emit(i) self.widget.metrics_combo.setCurrentIndex(i) self.send_signal(self.widget.Inputs.data, self.iris) @@ -36,6 +33,7 @@ def test_distance_combo(self): def test_error_message(self): """Check if error message appears and then disappears when data is removed from input""" + self.widget.metric_idx = 2 self.send_signal(self.widget.Inputs.data, self.iris) self.assertFalse(self.widget.Error.no_continuous_features.is_shown()) self.send_signal(self.widget.Inputs.data, self.titanic) @@ -43,28 +41,6 @@ def test_error_message(self): self.send_signal(self.widget.Inputs.data, None) self.assertFalse(self.widget.Error.no_continuous_features.is_shown()) - def test_mahalanobis_error(self): - mah_index = [i for i, d in enumerate(METRICS) - if isinstance(d, MahalanobisDistance)][0] - self.widget.metric_idx = mah_index - self.widget.autocommit = True - - invalid = self.iris[:] - invalid.X = np.vstack((invalid.X[0], invalid.X[0])) - invalid.Y = np.vstack((invalid.Y[0], invalid.Y[0])) - datasets = [self.iris, None, invalid] - bad = [False, False, True] - out = [True, False, False] - - for data1, bad1, out1 in zip(datasets, bad, out): - for data2, bad2, out2 in zip(datasets, bad, out): - self.send_signal(self.widget.Inputs.data, data1) - self.assertEqual(self.widget.Error.mahalanobis_error.is_shown(), bad1) - self.assertEqual(self.get_output(self.widget.Outputs.distances) is not None, out1) - self.send_signal(self.widget.Inputs.data, data2) - self.assertEqual(self.widget.Error.mahalanobis_error.is_shown(), bad2) - self.assertEqual(self.get_output(self.widget.Outputs.distances) is not None, out2) - def test_too_big_array(self): """ Users sees an error message when calculating too large arrays and Orange diff --git a/Orange/widgets/visualize/owsilhouetteplot.py b/Orange/widgets/visualize/owsilhouetteplot.py index 9fe1aafaada..f38fe02ef67 100644 --- a/Orange/widgets/visualize/owsilhouetteplot.py +++ b/Orange/widgets/visualize/owsilhouetteplot.py @@ -93,9 +93,7 @@ def __init__(self): super().__init__() #: The input data self.data = None # type: Optional[Orange.data.Table] - #: Data after any applied pre-processing step - self._effective_data = None # type: Optional[Orange.data.Table] - #: Distance matrix computed from _effective_data + #: Distance matrix computed from data self._matrix = None # type: Optional[Orange.misc.DistMatrix] #: An bool mask (size == len(data)) indicating missing group/cluster #: assignments @@ -179,19 +177,9 @@ def set_data(self, data): v for v in data.domain.variables + data.domain.metas if v.is_discrete and len(v.values) >= 2] if not candidatevars: - error_msg = "Input does not have any suitable cluster labels." + error_msg = "Input does not have any suitable labels." data = None - if data is not None: - ncont = sum(v.is_continuous for v in data.domain.attributes) - ndiscrete = len(data.domain.attributes) - ncont - if ncont == 0: - data = None - error_msg = "No continuous columns" - elif ncont < len(data.domain.attributes): - warning_msg = "{0} categorical columns will not be used for " \ - "distance computation".format(ndiscrete) - self.data = data if data is not None: self.cluster_var_model[:] = candidatevars @@ -204,14 +192,13 @@ def set_data(self, data): annotvars = [var for var in data.domain.metas if var.is_string] self.annotation_var_model[:] = ["None"] + annotvars self.annotation_var_idx = 1 if len(annotvars) else 0 - self._effective_data = Orange.distance._preprocess(data) self.openContext(Orange.data.Domain(candidatevars)) self.error(error_msg) self.warning(warning_msg) def handleNewSignals(self): - if self._effective_data is not None: + if self.data is not None: self._update() self._replot() @@ -222,7 +209,6 @@ def clear(self): Clear the widget state. """ self.data = None - self._effective_data = None self._matrix = None self._mask = None self._silhouette = None @@ -260,10 +246,10 @@ def _update(self): self._reset_all() return - if self._matrix is None and self._effective_data is not None: + if self._matrix is None and self.data is not None: _, metric = self.Distances[self.distance_idx] try: - self._matrix = np.asarray(metric(self._effective_data)) + self._matrix = np.asarray(metric(self.data)) except MemoryError: self.Error.memory_error() return diff --git a/doc/data-mining-library/source/reference/distance.rst b/doc/data-mining-library/source/reference/distance.rst index bdc832086a5..91dbb654b48 100644 --- a/doc/data-mining-library/source/reference/distance.rst +++ b/doc/data-mining-library/source/reference/distance.rst @@ -2,7 +2,8 @@ Distance (``distance``) ####################### -The following example demonstrates how to compute distances between all examples: +The following example demonstrates how to compute distances between all data +instances from Iris: >>> from Orange.data import Table >>> from Orange.distance import Euclidean @@ -12,22 +13,171 @@ The following example demonstrates how to compute distances between all examples >>> dist_matrix.X[0, 1] 0.53851648 +To compute distances between all columns, we set `axis` to 0. + >>> Euclidean(iris, axis=0) + DistMatrix([[ 0. , 36.17927584, 28.9542743 , 57.1913455 ], + [ 36.17927584, 0. , 25.73382987, 25.81259383], + [ 28.9542743 , 25.73382987, 0. , 33.87270287], + [ 57.1913455 , 25.81259383, 33.87270287, 0. ]]) -The module for `Distance` is based on the popular `scikit-learn`_ and `scipy`_ packages. We wrap the following distance metrics: +Finally, we can compute distances between all pairs of rows from two tables. -- :obj:`Orange.distance.Euclidean` -- :obj:`Orange.distance.Manhattan` -- :obj:`Orange.distance.Cosine` -- :obj:`Orange.distance.Jaccard` -- :obj:`Orange.distance.SpearmanR` -- :obj:`Orange.distance.SpearmanRAbsolute` -- :obj:`Orange.distance.PearsonR` -- :obj:`Orange.distance.PearsonRAbsolute` + >>> iris1 = iris[:100] + >>> iris2 = iris[100:] + >>> dist = Euclidean(iris_even, iris_odd) + >>> dist.shape + (75, 100) -All distances have a common interface to the __call__ method which is the following: +Most metrics can be fit on training data to normalize values and handle missing +data. We do so by calling the constructor without arguments or with parameters, +such as `normalize`, and then pass the data to method `fit`. -.. automethod:: Orange.distance.Distance.__call__ + >>> dist_model = Euclidean(normalize=True).fit(iris1) + >>> dist = dist_model(iris2[:3]) + >>> dist + DistMatrix([[ 0. , 1.36778277, 1.11352233], + [ 1.36778277, 0. , 1.57810546], + [ 1.11352233, 1.57810546, 0. ]]) -.. _`scikit-learn`: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise_distances.html#sklearn.metrics.pairwise_distances -.. _`scipy`: http://docs.scipy.org/doc/scipy/reference/stats.html +The above distances are computed on the first three rows of `iris2`, normalized +by means and variances computed from `iris1`. + +Here are five closest neighbors of `iris2[0]` from `iris1`:: + + >>> dist0 = dist_model(iris1, iris2[0]) + >>> neigh_idx = np.argsort(dist0.flatten())[:5] + >>> iris1[neigh_idx] + [[5.900, 3.200, 4.800, 1.800 | Iris-versicolor], + [6.700, 3.000, 5.000, 1.700 | Iris-versicolor], + [6.300, 3.300, 4.700, 1.600 | Iris-versicolor], + [6.000, 3.400, 4.500, 1.600 | Iris-versicolor], + [6.400, 3.200, 4.500, 1.500 | Iris-versicolor] + ] + +All distances share a common interface. + +.. autoclass:: Orange.distance.Distance + +Handling discrete and missing data +================================== + +Discrete data is handled as appropriate for the particular distance. For +instance, the Euclidean distance treats a pair of values as either the same or +different, contributing either 0 or 1 to the squared sum of differences. In +other cases -- particularly in Jaccard and cosine distance, discrete values +are treated as zero or non-zero. + +Missing data is not simply imputed. We assume that values of each variable are +distributed by some unknown distribution and compute - without assuming a +particular distribution shape - the expected distance. +For instance, for the Euclidean distance it turns out that the expected +squared distance between a known and a missing value equals the square of +the known value's distance from the mean of the missing variable, plus its +variance. + + +Supported distances +=================== + +Euclidean distance +------------------ + +For numeric values, the Euclidean distance is the square root of sums of +squares of pairs of values from rows or columns. For discrete values, 1 +is added if the two values are different. + +To put all numeric data on the same scale, and in particular when working +with a mixture of numeric and discrete data, it is recommended to enable +normalization by adding `normalize=True` to the constructor. With this, +numeric values are normalized by subtracting their mean and divided by +deviation multiplied by the square root of two. The mean and deviation are +computed on the training data, if the `fit` method is used. When computing +distances between two tables and without explicitly calling `fit`, means +and variances are computed from the first table only. Means and variances +are always computed from columns, disregarding the axis over which we +compute the distances, since columns represent variables and hence come from +a certain distribution. + +As described above, the expected squared difference between a known and a +missing value equals the squared difference between the known value and the +mean, plus the variance. The squared difference between two unknown values +equals twice the variance. + +For normalized data, the difference between a known and missing numeric value +equals the square of the known value + 0.5. The difference between two +missing values is 1. + +For discrete data, the expected difference between a known and a missing value +equals the probablity that the two values are different, which is 1 minus the +probability of the known value. If both values are missing, the probability +of them being different equals 1 minus the sum of squares of all probabilities +(also known as the Gini index). + + +Manhattan distance +------------------ + +Manhattan distance is the sum of absolute pairwise distances. + +Normalization and treatment of missing values is similar as in the Euclidean +distance, except that medians and median absolute distance from the median +(MAD) are used instead of means and deviations. + +For discrete values, distances are again 0 or 1, hence the Manhattan distance +for discrete columns is the same as the Euclidean. + +Cosine distance +--------------- + +Cosine similarity is the dot product divided by the product +of lengths (where the length is the square of dot product of a row/column with +itself). Cosine distance is computed by subtracting the similarity from one. + +In calculation of dot products, missing values are replaced by means. In +calculation of lengths, the contribution of a missing value equals the square +of the mean plus the variance. (The difference comes from the fact that in +the former case the missing values are independent.) + +Non-zero discrete values are replaced by 1. This introduces the notion of a +"base value", which is the first in the list of possible values. In most cases, +this will only make sense for indicator (i.e. two-valued, boolean attributes). + +Cosine distance does not support any column-wise normalization. + +Jaccard distance +---------------- + +Jaccard similarity between two sets is defined as the size of their +intersection divided by the size of the union. Jaccard distance is computed +by subtracting the similarity from one. + +In Orange, attribute values are interpreted as membership indicator. In +row-wise distances, columns are interpreted as sets, and non-zero +values in a row (including negative values of numeric features) indicate that +the row belongs to the particular sets. In column-wise distances, rows are sets +and values indicate the sets to which the column belongs. + +For missing values, relative frequencies from the training data are used as +probabilities for belonging to a set. That is, for row-wise distances, we +compute the relative frequency of non-zero values in each column, and vice-versa +for column-wise distances. For intersection (union) of sets, we then add the +probability of belonging to both (any of) the two sets instead of adding a +0 or 1. + +SpearmanR, AbsoluteSpearmanR, PearsonR, AbsolutePearsonR +-------------------------------------------------------- + +The four correlation-based distance measure equal (1 - the +correlation coefficient) / 2. For `AbsoluteSpearmanR` and `AbsolutePearsonR`, the +absolute value of the coefficient is used. + +These distances do not handle missing or discrete values. + +Mahalanobis distance +-------------------- + +Mahalanobis distance is similar to cosine distance, except that the data is +projected into the PCA space. + +Mahalanobis distance does not handle missing or discrete values.