def test_invh(self):
if not cusolver.check_availability('potrsBatched'):
pytest.skip('potrsBatched is not available')
a = self._create_symmetric_matrix(self.shape, self.dtype)
with cupyx.errstate(linalg='ignore'):
with self.assertRaises(cupy.cuda.cusolver.CUSOLVERError):
cupyx.linalg.solve._batched_invh(a)
def test_batched_decomposition(self, dtype):
if not cusolver.check_availability('potrfBatched'):
pytest.skip('potrfBatched is not available')
Ab1 = random_matrix((3, 5, 5), dtype, scale=(10, 10000), sym=True)
self.check_L(Ab1)
Ab2 = random_matrix((2, 2, 5, 5), dtype, scale=(10, 10000), sym=True)
self.check_L(Ab2)
def test_invh(self):
if not cusolver.check_availability('potrsBatched'):
pytest.skip('potrsBatched is not available')
a = self._create_symmetric_matrix(self.shape, self.dtype)
with cupyx.errstate(linalg='raise'):
with self.assertRaises(numpy.linalg.LinAlgError):
cupyx.linalg.invh(a)
def setUp(self):
if not cusolver.check_availability('syevj'):
pytest.skip('syevj is not available')
if self.dtype in (numpy.complex64, numpy.complex128):
self.a = numpy.array([[1, 2j, 3], [-2j, 5, 4j], [3, -4j, 9]],
dtype=self.dtype)
else:
self.a = numpy.array([[1, 2, 3], [2, 5, 4], [3, 4, 9]],
dtype=self.dtype)
def setUp(self):
if not cusolver.check_availability('gels'):
pytest.skip('gels is not available')
if self.compute_type is not None:
old_compute_type = _linalg.get_compute_type(self.dtype)
_linalg.set_compute_type(self.dtype, self.compute_type)
yield
_linalg.set_compute_type(self.dtype, old_compute_type)
else:
yield
def setUp(self):
if not cusolver.check_availability('gesvda'):
pytest.skip('gesvda is not available')
if self.dtype == numpy.complex64:
a_real = numpy.random.random(self.shape).astype(numpy.float32)
a_imag = numpy.random.random(self.shape).astype(numpy.float32)
self.a = a_real + 1.j * a_imag
elif self.dtype == numpy.complex128:
a_real = numpy.random.random(self.shape).astype(numpy.float64)
a_imag = numpy.random.random(self.shape).astype(numpy.float64)
self.a = a_real + 1.j * a_imag
else:
self.a = numpy.random.random(self.shape).astype(self.dtype)
def test_csrlsvqr(self, dtype):
if not cusolver.check_availability('csrlsvqr'):
unittest.SkipTest('csrlsvqr is not available')
a, b, test_tol = self._setup(dtype)
ref_x = numpy.linalg.solve(a, b)
cp_a = cupy.array(a)
sp_a = cupyx.scipy.sparse.csr_matrix(cp_a)
cp_b = cupy.array(b)
x = cupy.cusolver.csrlsvqr(sp_a,
cp_b,
tol=self.tol,
reorder=self.reorder)
cupy.testing.assert_allclose(x, ref_x, rtol=test_tol, atol=test_tol)
def _potrf_batched(a):
"""Batched Cholesky decomposition.
Decompose a given array of two-dimensional square matrices into
``L * L.T``, where ``L`` is a lower-triangular matrix and ``.T``
is a conjugate transpose operator.
Args:
a (cupy.ndarray): The input array of matrices
with dimension ``(..., N, N)``
Returns:
cupy.ndarray: The lower-triangular matrix.
"""
if not check_availability('potrfBatched'):
raise RuntimeError('potrfBatched is not available')
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
if dtype == 'f':
potrfBatched = cusolver.spotrfBatched
elif dtype == 'd':
potrfBatched = cusolver.dpotrfBatched
elif dtype == 'F':
potrfBatched = cusolver.cpotrfBatched
else: # dtype == 'D':
potrfBatched = cusolver.zpotrfBatched
x = a.astype(dtype, order='C', copy=True)
xp = cupy.core._mat_ptrs(x)
n = x.shape[-1]
ldx = x.strides[-2] // x.dtype.itemsize
handle = device.get_cusolver_handle()
batch_size = internal.prod(x.shape[:-2])
dev_info = cupy.empty(batch_size, dtype=numpy.int32)
potrfBatched(
handle, cublas.CUBLAS_FILL_MODE_UPPER, n, xp.data.ptr, ldx,
dev_info.data.ptr, batch_size)
cupy.linalg._util._check_cusolver_dev_info_if_synchronization_allowed(
potrfBatched, dev_info)
return cupy.tril(x)
def setUp(self):
if not cusolver.check_availability('gesv'):
pytest.skip('gesv is not available')
self.dtype = numpy.dtype(self.dtype)
self.r_dtype = self.dtype.char.lower()
a = self._make_well_conditioned_matrix((self.n, self.n))
if self.nrhs is None:
x_shape = (self.n, )
else:
x_shape = (self.n, self.nrhs)
self.x_ref = self._make_random_matrix(x_shape, cupy)
b = numpy.dot(a, self.x_ref)
self.tol = self._tol[self.r_dtype]
self.a = cupy.array(a)
self.b = cupy.array(b)
if self.compute_type is not None:
self.old_compute_type = _linalg.get_compute_type(self.dtype)
_linalg.set_compute_type(self.dtype, self.compute_type)
def setUp(self):
if not cusolver.check_availability('csrlsvqr'):
pytest.skip('csrlsvqr is not available')
def _batched_invh(a):
"""Compute the inverse of an array of Hermitian matrices.
This function computes an inverse of a real symmetric or complex hermitian
positive-definite matrix using Cholesky factorization. If matrix ``a[i]``
is not positive definite, Cholesky factorization fails and it raises
an error.
Args:
a (cupy.ndarray): Array of real symmetric or complex hermitian
matrices with dimension (..., N, N).
Returns:
cupy.ndarray: The array of inverses of matrices ``a[i]``.
"""
if not check_availability('potrsBatched'):
raise RuntimeError('potrsBatched is not available')
if a.dtype.char == 'f' or a.dtype.char == 'd':
dtype = a.dtype.char
else:
dtype = numpy.promote_types(a.dtype.char, 'f').char
if dtype == 'f':
potrfBatched = cusolver.spotrfBatched
potrsBatched = cusolver.spotrsBatched
elif dtype == 'd':
potrfBatched = cusolver.dpotrfBatched
potrsBatched = cusolver.dpotrsBatched
elif dtype == 'F':
potrfBatched = cusolver.cpotrfBatched
potrsBatched = cusolver.cpotrsBatched
elif dtype == 'D':
potrfBatched = cusolver.zpotrfBatched
potrsBatched = cusolver.zpotrsBatched
else:
msg = ('dtype must be float32, float64, complex64 or complex128'
' (actual: {})'.format(a.dtype))
raise ValueError(msg)
a = a.astype(dtype, order='C', copy=True)
ap = cupy.core.core._mat_ptrs(a)
n = a.shape[-1]
lda = a.strides[-2] // a.dtype.itemsize
handle = device.get_cusolver_handle()
uplo = cublas.CUBLAS_FILL_MODE_LOWER
batch_size = int(numpy.prod(a.shape[:-2]))
dev_info = cupy.empty(batch_size, dtype=numpy.int32)
# Cholesky factorization
potrfBatched(handle, uplo, n, ap.data.ptr, lda, dev_info.data.ptr,
batch_size)
cupy.linalg.util._check_cusolver_dev_info_if_synchronization_allowed(
potrfBatched, dev_info)
identity_matrix = cupy.eye(n, dtype=dtype)
b = cupy.empty(a.shape, dtype)
b[...] = identity_matrix
nrhs = b.shape[-1]
ldb = b.strides[-2] // a.dtype.itemsize
bp = cupy.core.core._mat_ptrs(b)
dev_info = cupy.empty(1, dtype=numpy.int32)
# NOTE: potrsBatched does not currently support nrhs > 1 (CUDA v10.2)
# Solve: A[i] * X[i] = B[i]
potrsBatched(handle, uplo, n, nrhs, ap.data.ptr, lda, bp.data.ptr, ldb,
dev_info.data.ptr, batch_size)
cupy.linalg.util._check_cusolver_dev_info_if_synchronization_allowed(
potrfBatched, dev_info)
return b
