MAINT: generate random positive definite matrices, not just stacks of identities

Author: ev-br

array_api_tests/hypothesis_helpers.py

@@ -314,16 +314,20 @@ def symmetric_matrices(draw, dtypes=real_floating_dtypes, finite=True, bound=10.
 
 @composite
 def positive_definite_matrices(draw, dtypes=floating_dtypes):
-    # For now just generate stacks of identity matrices
-    # TODO: Generate arbitrary positive definite matrices, for instance, by
-    # using something like
-    # https://github.com/scikit-learn/scikit-learn/blob/844b4be24/sklearn/datasets/_samples_generator.py#L1351.
     base_shape = draw(shapes())
     n = draw(integers(0, 8))  # 8 is an arbitrary small but interesting-enough value
     shape = base_shape + (n, n)
     assume(prod(i for i in shape if i) < MAX_ARRAY_SIZE)
     dtype = draw(dtypes)
-    return broadcast_to(eye(n, dtype=dtype), shape)
+
+    import numpy as np
+    rng = np.random.default_rng(1234567)
+    a = np.random.uniform(size=(n, n))
+    q, r = np.linalg.qr(a)
+    arr = q.T @ (np.diag(3 + np.random.uniform(size=n))) @ q
+    arr = xp.asarray(arr, dtype=dtype)
+
+    return broadcast_to(arr, shape)
 
 @composite
 def invertible_matrices(draw, dtypes=floating_dtypes, stack_shapes=shapes()):