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18 changes: 16 additions & 2 deletions dpnp/linalg/dpnp_iface_linalg.py
Original file line number Diff line number Diff line change
Expand Up @@ -180,8 +180,22 @@ def cond(x, p=None):
x : {dpnp.ndarray, usm_ndarray}
The matrix whose condition number is sought.
p : {None, 1, -1, 2, -2, inf, -inf, "fro"}, optional
Order of the norm used in the condition number computation.
``inf`` means the `dpnp.inf` object, and the Frobenius norm is
Order of the norm used in the condition number computation:

===== ============================
p norm for matrices
===== ============================
None 2-norm
'fro' Frobenius norm
inf max(sum(abs(x), axis=1))
-inf min(sum(abs(x), axis=1))
1 max(sum(abs(x), axis=0))
-1 min(sum(abs(x), axis=0))
2 2-norm (largest singular value)
-2 smallest singular value
===== ============================

``inf`` means the :obj:`dpnp.inf` object, and the Frobenius norm is
the root-of-sum-of-squares norm.

Default: ``None``.
Expand Down
131 changes: 130 additions & 1 deletion dpnp/tests/third_party/cupy/linalg_tests/test_norms.py
Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,6 @@
import pytest

import dpnp as cupy
from dpnp.tests.helper import is_cpu_device
from dpnp.tests.third_party.cupy import testing


Expand Down Expand Up @@ -224,3 +223,133 @@ def test_slogdet_one_dim(self, dtype):
a = testing.shaped_arange((2,), xp, dtype)
with pytest.raises(xp.linalg.LinAlgError):
xp.linalg.slogdet(a)


@testing.parameterize(
*testing.product({"ord": [-numpy.inf, -2, -1, 1, 2, numpy.inf, "fro"]})
)
class TestCond(unittest.TestCase):
@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_singular_zeros(self, xp, dtype):
if self.ord not in [None, 2, -2]:
pytest.skip("no LinAlgError is raising on singular matrices")

A = xp.zeros(shape=(2, 2), dtype=dtype)
result = xp.linalg.cond(A, self.ord)

# singular matrices don't always hit infinity.
result = xp.asarray(result) # numpy is scalar and can't be replaced
large_number = 1.0 / (xp.finfo(dtype).eps)
result[result >= large_number] = xp.inf

return result

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_singular_ones(self, xp, dtype):
if self.ord not in [None, 2, -2]:
pytest.skip("no LinAlgError is raising on singular matrices")

A = xp.ones(shape=(2, 2), dtype=dtype)
result = xp.linalg.cond(A, self.ord)

# singular matrices don't always hit infinity.
result = xp.asarray(result) # numpy is scalar and can't be replaced
large_number = 1.0 / (xp.finfo(dtype).eps)
result[result >= large_number] = xp.inf

return result

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_stacked_singular(self, xp, dtype):
if self.ord not in [None, 2, -2]:
pytest.skip("no LinAlgError is raising on singular matrices")

# Check behavior when only some of the stacked matrices are
# singular

A = xp.arange(16, dtype=dtype).reshape((2, 2, 2, 2))
A[0, 0] = 0
A[1, 1] = 0

res = xp.linalg.cond(A, self.ord)
return res

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_default(self, xp, dtype):
A = testing.shaped_arange((2, 2), xp, dtype=dtype)
return xp.linalg.cond(A)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_basic(self, xp, dtype):
A = testing.shaped_arange((2, 2), xp, dtype=dtype)
return xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_generalized_1(self, xp, dtype):
A = testing.shaped_arange((2, 2), xp, dtype=dtype)
A = xp.array([A, 2 * A, 3 * A])
return xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_generalized_2(self, xp, dtype):
A = testing.shaped_arange((2, 2), xp, dtype=dtype)
A = xp.array([A, 2 * A, 3 * A])
A = xp.array([A] * 2 * 3).reshape((3, 2) + A.shape)

return xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
def test_0x0(self, dtype):
for xp in (numpy, cupy):
A = xp.empty((0, 0), dtype=dtype)
with pytest.raises(
xp.linalg.LinAlgError,
match="cond is not defined on empty arrays",
):
xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_1x1(self, xp, dtype):
A = xp.ones((1, 1), dtype=dtype)
return xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_8x8(self, xp, dtype):
A = testing.shaped_arange((8, 8), xp, dtype=dtype) + xp.diag(
xp.ones(8, dtype=dtype)
)
return xp.linalg.cond(A, self.ord)

@pytest.mark.skip("only ndarray input is supported")
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_nonarray(self, xp):
A = [[1.0, 2.0], [3.0, 4.0]]
return xp.linalg.cond(A, self.ord)

@testing.for_float_dtypes(no_float16=True)
@testing.numpy_cupy_allclose(rtol=1e-3, atol=1e-4)
def test_hermitian(self, xp, dtype):
A = xp.array([[1.0, 2.0], [2.0, 1.0]], dtype=dtype)
return xp.linalg.cond(A, self.ord)


class TestCondBasicNonSVD(unittest.TestCase):
def test_basic_nonsvd(self):
# Smoketest the non-svd norms
A = cupy.array([[1.0, 0, 1], [0, -2.0, 0], [0, 0, 3.0]])
testing.assert_array_almost_equal(cupy.linalg.cond(A, cupy.inf), 4)
testing.assert_array_almost_equal(cupy.linalg.cond(A, -cupy.inf), 2 / 3)
testing.assert_array_almost_equal(cupy.linalg.cond(A, 1), 4)
testing.assert_array_almost_equal(cupy.linalg.cond(A, -1), 0.5)
testing.assert_array_almost_equal(
cupy.linalg.cond(A, "fro"), numpy.sqrt(265 / 12)
)
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