def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None,
permc_spec=None, diag_pivot_thresh=None, relax=None,
panel_size=None, options={}):
"""Computes the incomplete LU decomposition of a sparse square matrix.
Args:
A (cupyx.scipy.sparse.spmatrix): Sparse matrix to factorize.
drop_tol (float): (For further augments, see
:func:`scipy.sparse.linalg.spilu`)
fill_factor (float):
drop_rule (str):
permc_spec (str):
diag_pivot_thresh (float):
relax (int):
panel_size (int):
options (dict):
Returns:
cupyx.scipy.sparse.linalg.SuperLU:
Object which has a ``solve`` method.
Note:
This function computes incomplete LU decomposition of a sparse matrix
on the CPU using `scipy.sparse.linalg.spilu` (unless you set
``fill_factor`` to ``1``). Therefore, incomplete LU decomposition is
not accelerated on the GPU. On the other hand, the computation of
solving linear equations using the ``solve`` method, which this
function returns, is performed on the GPU.
If you set ``fill_factor`` to ``1``, this function computes incomplete
LU decomposition on the GPU, but without fill-in or pivoting.
.. seealso:: :func:`scipy.sparse.linalg.spilu`
"""
if not scipy_available:
raise RuntimeError('scipy is not available')
if not sparse.isspmatrix(A):
raise TypeError('A must be cupyx.scipy.sparse.spmatrix')
if A.shape[0] != A.shape[1]:
raise ValueError('A must be a square matrix (A.shape: {})'
.format(A.shape))
if A.dtype.char not in 'fdFD':
raise TypeError('Invalid dtype (actual: {})'.format(A.dtype))
if fill_factor == 1:
# Computes ILU(0) on the GPU using cuSparse functions
if not sparse.isspmatrix_csr(A):
a = A.tocsr()
else:
a = A.copy()
cusparse.csrilu02(a)
return CusparseLU(a)
a = A.get().tocsc()
a_inv = scipy.sparse.linalg.spilu(
a, fill_factor=fill_factor, drop_tol=drop_tol, drop_rule=drop_rule,
permc_spec=permc_spec, diag_pivot_thresh=diag_pivot_thresh,
relax=relax, panel_size=panel_size, options=options)
return SuperLU(a_inv)
def test_csrilu02(self, dtype):
dtype = numpy.dtype(dtype)
a_ref = self._make_matrix(dtype)
a = sparse.csr_matrix(a_ref)
cusparse.csrilu02(a, level_info=self.level_info)
a = a.todense()
al = cupy.tril(a, k=-1)
al = al + cupy.diag(cupy.ones((self.n, ), dtype=dtype.char.lower()))
au = cupy.triu(a)
a = al @ au
tol = self._tol[dtype.char.lower()]
cupy.testing.assert_allclose(a, a_ref, atol=tol, rtol=tol)
def test_invalid_cases(self):
dtype = numpy.dtype('d')
a_ref = self._make_matrix(dtype)
# invalid format
a = sparse.csc_matrix(a_ref)
with pytest.raises(TypeError):
cusparse.csrilu02(a, level_info=self.level_info)
# invalid shape
a = cupy.ones((self.n, self.n + 1), dtype=dtype)
a = sparse.csr_matrix(a)
with pytest.raises(ValueError):
cusparse.csrilu02(a, level_info=self.level_info)
# matrix with zero diagonal element
a = a_ref
a[-1, -1] = 0
a = sparse.csr_matrix(a)
with pytest.raises(ValueError):
cusparse.csrilu02(a, level_info=self.level_info)
# singular matrix
a = a_ref
a[1:] = a[0]
a = sparse.csr_matrix(a)
with pytest.raises(ValueError):
cusparse.csrilu02(a, level_info=self.level_info)