import sys
import threading
import warnings
import numpy as np
from numpy import array, finfo, arange, eye, all, unique, ones, dot
from numpy.exceptions import ComplexWarning
from numpy.testing import (
assert_array_almost_equal, assert_almost_equal,
assert_equal, assert_array_equal, assert_, assert_allclose)
import pytest
from pytest import raises as assert_raises, warns as assert_warns
import scipy.linalg
from scipy.linalg import norm, inv
from scipy.sparse import (dia_array, SparseEfficiencyWarning, csc_array,
csr_array, eye_array, issparse, dok_array, lil_array, bsr_array, kron)
from scipy.sparse.linalg import SuperLU
from scipy.sparse.linalg._dsolve import (spsolve, use_solver, splu, spilu,
MatrixRankWarning, _superlu, spsolve_triangular, factorized,
is_sptriangular, spbandwidth)
import scipy.sparse
from scipy._lib._testutils import check_free_memory
# scikits.umfpack is not a SciPy dependency but it is optionally used in
# dsolve, so check whether it's available
try:
import scikits.umfpack as umfpack
has_umfpack = True
except ImportError:
has_umfpack = False
def toarray(a):
if issparse(a):
return a.toarray()
else:
return a
def setup_bug_8278():
N = 2 ** 6
h = 1/N
Ah1D = dia_array(([-1, 2, -1], [-1, 0, 1]), shape=(N-1, N-1))/(h**2)
eyeN = eye_array(N - 1)
A = (kron(eyeN, kron(eyeN, Ah1D))
+ kron(eyeN, kron(Ah1D, eyeN))
+ kron(Ah1D, kron(eyeN, eyeN)))
b = np.random.rand((N-1)**3)
return A, b
class TestFactorized:
def setup_method(self):
n = 5
d = arange(n) + 1
self.n = n
self.A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n,n)).tocsc()
def _check_singular(self):
A = csc_array((5,5), dtype='d')
b = ones(5)
assert_array_almost_equal(0. * b, factorized(A)(b))
def _check_non_singular(self):
# Make a diagonal dominant, to make sure it is not singular
n = 5
rng = np.random.default_rng(14332)
a = csc_array(rng.random((n, n)))
b = ones(n)
expected = splu(a).solve(b)
assert_array_almost_equal(factorized(a)(b), expected)
def test_singular_without_umfpack(self):
use_solver(useUmfpack=False)
with assert_raises(RuntimeError, match="Factor is exactly singular"):
self._check_singular()
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_singular_with_umfpack(self):
use_solver(useUmfpack=True)
with warnings.catch_warnings():
msg = "divide by zero encountered in double_scalars"
warnings.filterwarnings("ignore", msg, RuntimeWarning)
assert_warns(umfpack.UmfpackWarning, self._check_singular)
def test_non_singular_without_umfpack(self):
use_solver(useUmfpack=False)
self._check_non_singular()
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_non_singular_with_umfpack(self):
use_solver(useUmfpack=True)
self._check_non_singular()
def test_cannot_factorize_nonsquare_matrix_without_umfpack(self):
use_solver(useUmfpack=False)
msg = "can only factor square matrices"
with assert_raises(ValueError, match=msg):
factorized(self.A[:, :4])
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_factorizes_nonsquare_matrix_with_umfpack(self):
use_solver(useUmfpack=True)
# does not raise
factorized(self.A[:,:4])
def test_call_with_incorrectly_sized_matrix_without_umfpack(self):
use_solver(useUmfpack=False)
solve = factorized(self.A)
rng = np.random.default_rng(230498)
b = rng.random(4)
B = rng.random((4, 3))
BB = rng.random((self.n, 3, 9))
with assert_raises(ValueError, match="is of incompatible size"):
solve(b)
with assert_raises(ValueError, match="is of incompatible size"):
solve(B)
with assert_raises(ValueError,
match="object too deep for desired array"):
solve(BB)
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_call_with_incorrectly_sized_matrix_with_umfpack(self):
use_solver(useUmfpack=True)
solve = factorized(self.A)
rng = np.random.default_rng(643095823)
b = rng.random(4)
B = rng.random((4, 3))
BB = rng.random((self.n, 3, 9))
# does not raise
solve(b)
msg = "object too deep for desired array"
with assert_raises(ValueError, match=msg):
solve(B)
with assert_raises(ValueError, match=msg):
solve(BB)
def test_call_with_cast_to_complex_without_umfpack(self):
use_solver(useUmfpack=False)
solve = factorized(self.A)
rng = np.random.default_rng(23454)
b = rng.random(4)
for t in [np.complex64, np.complex128]:
with assert_raises(TypeError, match="Cannot cast array data"):
solve(b.astype(t))
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_call_with_cast_to_complex_with_umfpack(self):
use_solver(useUmfpack=True)
solve = factorized(self.A)
rng = np.random.default_rng(23454)
b = rng.random(4)
for t in [np.complex64, np.complex128]:
assert_warns(ComplexWarning, solve, b.astype(t))
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_assume_sorted_indices_flag(self):
# a sparse matrix with unsorted indices
unsorted_inds = np.array([2, 0, 1, 0])
data = np.array([10, 16, 5, 0.4])
indptr = np.array([0, 1, 2, 4])
A = csc_array((data, unsorted_inds, indptr), (3, 3))
b = ones(3)
# should raise when incorrectly assuming indices are sorted
use_solver(useUmfpack=True, assumeSortedIndices=True)
with assert_raises(RuntimeError,
match="UMFPACK_ERROR_invalid_matrix"):
factorized(A)
# should sort indices and succeed when not assuming indices are sorted
use_solver(useUmfpack=True, assumeSortedIndices=False)
expected = splu(A.copy()).solve(b)
assert_equal(A.has_sorted_indices, 0)
assert_array_almost_equal(factorized(A)(b), expected)
@pytest.mark.slow
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_bug_8278(self):
check_free_memory(8000)
use_solver(useUmfpack=True)
A, b = setup_bug_8278()
A = A.tocsc()
f = factorized(A)
x = f(b)
assert_array_almost_equal(A @ x, b)
class TestLinsolve:
def setup_method(self):
use_solver(useUmfpack=False)
def test_singular(self):
A = csc_array((5,5), dtype='d')
b = array([1, 2, 3, 4, 5],dtype='d')
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore", "Matrix is exactly singular", MatrixRankWarning)
x = spsolve(A, b)
assert_(not np.isfinite(x).any())
def test_singular_gh_3312(self):
# "Bad" test case that leads SuperLU to call LAPACK with invalid
# arguments. Check that it fails moderately gracefully.
ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32)
v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296])
A = csc_array((v, ij.T), shape=(20, 20))
b = np.arange(20)
try:
# should either raise a runtime error or return value
# appropriate for singular input (which yields the warning)
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore", "Matrix is exactly singular", MatrixRankWarning)
x = spsolve(A, b)
assert not np.isfinite(x).any()
except RuntimeError:
pass
@pytest.mark.parametrize('format', ['csc', 'csr'])
@pytest.mark.parametrize('idx_dtype', [np.int32, np.int64])
def test_twodiags(self, format: str, idx_dtype: np.dtype):
A = dia_array(([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1]),
shape=(5, 5)).asformat(format)
b = array([1, 2, 3, 4, 5])
# condition number of A
cond_A = norm(A.toarray(), 2) * norm(inv(A.toarray()), 2)
for t in ['f','d','F','D']:
eps = finfo(t).eps # floating point epsilon
b = b.astype(t)
Asp = A.astype(t)
Asp.indices = Asp.indices.astype(idx_dtype, copy=False)
Asp.indptr = Asp.indptr.astype(idx_dtype, copy=False)
x = spsolve(Asp, b)
assert_(norm(b - Asp@x) < 10 * cond_A * eps)
def test_bvector_smoketest(self):
Adense = array([[0., 1., 1.],
[1., 0., 1.],
[0., 0., 1.]])
As = csc_array(Adense)
rng = np.random.default_rng(1234)
x = rng.standard_normal(3)
b = As@x
x2 = spsolve(As, b)
assert_array_almost_equal(x, x2)
def test_bmatrix_smoketest(self):
Adense = array([[0., 1., 1.],
[1., 0., 1.],
[0., 0., 1.]])
As = csc_array(Adense)
rng = np.random.default_rng(1234)
x = rng.standard_normal((3, 4))
Bdense = As.dot(x)
Bs = csc_array(Bdense)
x2 = spsolve(As, Bs)
assert_array_almost_equal(x, x2.toarray())
def test_non_square(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', SparseEfficiencyWarning)
# A is not square.
A = ones((3, 4))
b = ones((4, 1))
assert_raises(ValueError, spsolve, A, b)
# A2 and b2 have incompatible shapes.
A2 = csc_array(eye(3))
b2 = array([1.0, 2.0])
assert_raises(ValueError, spsolve, A2, b2)
def test_example_comparison(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', SparseEfficiencyWarning)
row = array([0,0,1,2,2,2])
col = array([0,2,2,0,1,2])
data = array([1,2,3,-4,5,6])
sM = csr_array((data,(row,col)), shape=(3,3), dtype=float)
M = sM.toarray()
row = array([0,0,1,1,0,0])
col = array([0,2,1,1,0,0])
data = array([1,1,1,1,1,1])
sN = csr_array((data, (row,col)), shape=(3,3), dtype=float)
N = sN.toarray()
sX = spsolve(sM, sN)
X = scipy.linalg.solve(M, N)
assert_array_almost_equal(X, sX.toarray())
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_shape_compatibility(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', SparseEfficiencyWarning)
use_solver(useUmfpack=True)
A = csc_array([[1., 0], [0, 2]])
bs = [
[1, 6],
array([1, 6]),
[[1], [6]],
array([[1], [6]]),
csc_array([[1], [6]]),
csr_array([[1], [6]]),
dok_array([[1], [6]]),
bsr_array([[1], [6]]),
array([[1., 2., 3.], [6., 8., 10.]]),
csc_array([[1., 2., 3.], [6., 8., 10.]]),
csr_array([[1., 2., 3.], [6., 8., 10.]]),
dok_array([[1., 2., 3.], [6., 8., 10.]]),
bsr_array([[1., 2., 3.], [6., 8., 10.]]),
]
for b in bs:
x = np.linalg.solve(A.toarray(), toarray(b))
for spmattype in [csc_array, csr_array, dok_array, lil_array]:
x1 = spsolve(spmattype(A), b, use_umfpack=True)
x2 = spsolve(spmattype(A), b, use_umfpack=False)
# check solution
if x.ndim == 2 and x.shape[1] == 1:
# interprets also these as "vectors"
x = x.ravel()
assert_array_almost_equal(toarray(x1), x,
err_msg=repr((b, spmattype, 1)))
assert_array_almost_equal(toarray(x2), x,
err_msg=repr((b, spmattype, 2)))
# dense vs. sparse output ("vectors" are always dense)
if issparse(b) and x.ndim > 1:
assert_(issparse(x1), repr((b, spmattype, 1)))
assert_(issparse(x2), repr((b, spmattype, 2)))
else:
assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1)))
assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2)))
# check output shape
if x.ndim == 1:
# "vector"
assert_equal(x1.shape, (A.shape[1],))
assert_equal(x2.shape, (A.shape[1],))
else:
# "matrix"
assert_equal(x1.shape, x.shape)
assert_equal(x2.shape, x.shape)
A = csc_array((3, 3))
b = csc_array((1, 3))
assert_raises(ValueError, spsolve, A, b)
def test_ndarray_support(self):
with warnings.catch_warnings():
warnings.simplefilter('ignore', SparseEfficiencyWarning)
A = array([[1., 2.], [2., 0.]])
x = array([[1., 1.], [0.5, -0.5]])
b = array([[2., 0.], [2., 2.]])
assert_array_almost_equal(x, spsolve(A, b))
def test_gssv_badinput(self):
N = 10
d = arange(N) + 1.0
A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(N, N))
for container in (csc_array, csr_array):
A = container(A)
b = np.arange(N)
def not_c_contig(x):
return x.repeat(2)[::2]
def not_1dim(x):
return x[:,None]
def bad_type(x):
return x.astype(bool)
def too_short(x):
return x[:-1]
badops = [not_c_contig, not_1dim, bad_type, too_short]
for badop in badops:
msg = f"{container!r} {badop!r}"
# Not C-contiguous
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, badop(A.data), A.indices, A.indptr,
b, int(A.format == 'csc'), err_msg=msg)
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, A.data, badop(A.indices), A.indptr,
b, int(A.format == 'csc'), err_msg=msg)
assert_raises((ValueError, TypeError), _superlu.gssv,
N, A.nnz, A.data, A.indices, badop(A.indptr),
b, int(A.format == 'csc'), err_msg=msg)
def test_sparsity_preservation(self):
ident = csc_array([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
b = csc_array([
[0, 1],
[1, 0],
[0, 0]])
x = spsolve(ident, b)
assert_equal(ident.nnz, 3)
assert_equal(b.nnz, 2)
assert_equal(x.nnz, 2)
assert_allclose(x.toarray(), b.toarray(), atol=1e-12, rtol=1e-12)
def test_dtype_cast(self):
A_real = scipy.sparse.csr_array([[1, 2, 0],
[0, 0, 3],
[4, 0, 5]])
A_complex = scipy.sparse.csr_array([[1, 2, 0],
[0, 0, 3],
[4, 0, 5 + 1j]])
b_real = np.array([1,1,1])
b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
x = spsolve(A_real, b_real)
assert_(np.issubdtype(x.dtype, np.floating))
x = spsolve(A_real, b_complex)
assert_(np.issubdtype(x.dtype, np.complexfloating))
x = spsolve(A_complex, b_real)
assert_(np.issubdtype(x.dtype, np.complexfloating))
x = spsolve(A_complex, b_complex)
assert_(np.issubdtype(x.dtype, np.complexfloating))
@pytest.mark.slow
@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
def test_bug_8278(self):
check_free_memory(8000)
use_solver(useUmfpack=True)
A, b = setup_bug_8278()
x = spsolve(A, b)
assert_array_almost_equal(A @ x, b)
class TestSplu:
def setup_method(self):
use_solver(useUmfpack=False)
n = 40
d = arange(n) + 1
self.n = n
self.A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n, n)).tocsc()
def _smoketest(self, spxlu, check, dtype, idx_dtype):
if np.issubdtype(dtype, np.complexfloating):
A = self.A + 1j*self.A.T
else:
A = self.A
A = A.astype(dtype)
A.indices = A.indices.astype(idx_dtype, copy=False)
A.indptr = A.indptr.astype(idx_dtype, copy=False)
lu = spxlu(A)
rng = np.random.RandomState(1234)
# Input shapes
for k in [None, 1, 2, self.n, self.n+2]:
msg = f"k={k!r}"
if k is None:
b = rng.rand(self.n)
else:
b = rng.rand(self.n, k)
if np.issubdtype(dtype, np.complexfloating):
b = b + 1j*rng.rand(*b.shape)
b = b.astype(dtype)
x = lu.solve(b)
check(A, b, x, msg)
x = lu.solve(b, 'T')
check(A.T, b, x, msg)
x = lu.solve(b, 'H')
check(A.T.conj(), b, x, msg)
def test_splu_smoketest(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
self._internal_test_splu_smoketest()
def _internal_test_splu_smoketest(self):
# Check that splu works at all
def check(A, b, x, msg=""):
eps = np.finfo(A.dtype).eps
r = A @ x
assert_(abs(r - b).max() < 1e3*eps, msg)
for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
for idx_dtype in [np.int32, np.int64]:
self._smoketest(splu, check, dtype, idx_dtype)
def test_spilu_smoketest(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
self._internal_test_spilu_smoketest()
def _internal_test_spilu_smoketest(self):
errors = []
def check(A, b, x, msg=""):
r = A @ x
err = abs(r - b).max()
assert_(err < 1e-2, msg)
if b.dtype in (np.float64, np.complex128):
errors.append(err)
for dtype in [np.float32, np.float64, np.complex64, np.complex128]:
for idx_dtype in [np.int32, np.int64]:
self._smoketest(spilu, check, dtype, idx_dtype)
assert_(max(errors) > 1e-5)
def test_spilu_drop_rule(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
# Test passing in the drop_rule argument to spilu.
A = eye_array(2)
rules = [
b'basic,area'.decode('ascii'), # unicode
b'basic,area', # ascii
[b'basic', b'area'.decode('ascii')]
]
for rule in rules:
# Argument should be accepted
assert_(isinstance(spilu(A, drop_rule=rule), SuperLU))
def test_splu_nnz0(self):
A = csc_array((5,5), dtype='d')
assert_raises(RuntimeError, splu, A)
def test_spilu_nnz0(self):
A = csc_array((5,5), dtype='d')
assert_raises(RuntimeError, spilu, A)
def test_splu_basic(self):
# Test basic splu functionality.
n = 30
rng = np.random.RandomState(12)
a = rng.rand(n, n)
a[a < 0.95] = 0
# First test with a singular matrix
a[:, 0] = 0
a_ = csc_array(a)
# Matrix is exactly singular
assert_raises(RuntimeError, splu, a_)
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_array(a)
lu = splu(a_)
b = ones(n)
x = lu.solve(b)
assert_almost_equal(dot(a, x), b)
def test_splu_perm(self):
# Test the permutation vectors exposed by splu.
n = 30
rng = np.random.default_rng(1342354)
a = rng.random((n, n))
a[a < 0.95] = 0
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_array(a)
lu = splu(a_)
# Check that the permutation indices do belong to [0, n-1].
for perm in (lu.perm_r, lu.perm_c):
assert_(all(perm > -1))
assert_(all(perm < n))
assert_equal(len(unique(perm)), len(perm))
# Now make a symmetric, and test that the two permutation vectors are
# the same
# Note: a += a.T relies on undefined behavior.
a = a + a.T
a_ = csc_array(a)
lu = splu(a_)
assert_array_equal(lu.perm_r, lu.perm_c)
@pytest.mark.parametrize("splu_fun, rtol", [(splu, 1e-7), (spilu, 1e-1)])
def test_natural_permc(self, splu_fun, rtol):
# Test that the "NATURAL" permc_spec does not permute the matrix
rng = np.random.RandomState(42)
n = 500
p = 0.01
A = scipy.sparse.random(n, n, p, random_state=rng)
x = rng.rand(n)
# Make A diagonal dominant to make sure it is not singular
A += (n+1)*scipy.sparse.eye_array(n)
A_ = csc_array(A)
b = A_ @ x
# without permc_spec, permutation is not identity
lu = splu_fun(A_)
assert_(np.any(lu.perm_c != np.arange(n)))
# with permc_spec="NATURAL", permutation is identity
lu = splu_fun(A_, permc_spec="NATURAL")
assert_array_equal(lu.perm_c, np.arange(n))
# Also, lu decomposition is valid
x2 = lu.solve(b)
assert_allclose(x, x2, rtol=rtol)
@pytest.mark.skipif(not hasattr(sys, 'getrefcount'), reason="no sys.getrefcount")
def test_lu_refcount(self):
# Test that we are keeping track of the reference count with splu.
n = 30
rng = np.random.default_rng(1342354)
a = rng.random((n, n))
a[a < 0.95] = 0
# Make a diagonal dominant, to make sure it is not singular
a += 4*eye(n)
a_ = csc_array(a)
lu = splu(a_)
# And now test that we don't have a refcount bug
rc = sys.getrefcount(lu)
for attr in ('perm_r', 'perm_c'):
perm = getattr(lu, attr)
assert_equal(sys.getrefcount(lu), rc + 1)
del perm
assert_equal(sys.getrefcount(lu), rc)
def test_bad_inputs(self):
A = self.A.tocsc()
rng = np.random.default_rng(235634)
assert_raises(ValueError, splu, A[:,:4])
assert_raises(ValueError, spilu, A[:,:4])
for lu in [splu(A), spilu(A)]:
b = rng.random(42)
B = rng.random((42, 3))
BB = rng.random((self.n, 3, 9))
assert_raises(ValueError, lu.solve, b)
assert_raises(ValueError, lu.solve, B)
assert_raises(ValueError, lu.solve, BB)
assert_raises(TypeError, lu.solve,
b.astype(np.complex64))
assert_raises(TypeError, lu.solve,
b.astype(np.complex128))
def test_superlu_dlamch_i386_nan(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
# SuperLU 4.3 calls some functions returning floats without
# declaring them. On i386@linux call convention, this fails to
# clear floating point registers after call. As a result, NaN
# can appear in the next floating point operation made.
#
# Here's a test case that triggered the issue.
n = 8
d = np.arange(n) + 1
A = dia_array(((d, 2*d, d[::-1]), (-3, 0, 5)), shape=(n, n))
A = A.astype(np.float32)
spilu(A)
A = A + 1j*A
B = A.toarray()
assert_(not np.isnan(B).any())
def test_lu_attr(self):
def check(dtype, complex_2=False):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
A = self.A.astype(dtype)
if complex_2:
A = A + 1j*A.T
n = A.shape[0]
lu = splu(A)
# Check that the decomposition is as advertised
Pc = np.zeros((n, n))
Pc[np.arange(n), lu.perm_c] = 1
Pr = np.zeros((n, n))
Pr[lu.perm_r, np.arange(n)] = 1
Ad = A.toarray()
lhs = Pr.dot(Ad).dot(Pc)
rhs = (lu.L @ lu.U).toarray()
eps = np.finfo(dtype).eps
assert_allclose(lhs, rhs, atol=100*eps)
check(np.float32)
check(np.float64)
check(np.complex64)
check(np.complex128)
check(np.complex64, True)
check(np.complex128, True)
@pytest.mark.slow
def test_threads_parallel(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
oks = []
def worker():
try:
self.test_splu_basic()
self._internal_test_splu_smoketest()
self._internal_test_spilu_smoketest()
oks.append(True)
except Exception:
pass
threads = [threading.Thread(target=worker)
for k in range(20)]
for t in threads:
t.start()
for t in threads:
t.join()
assert_equal(len(oks), 20)
def test_singular_matrix(self):
# Test that SuperLU does not print to stdout when a singular matrix is
# passed. See gh-20993.
A = eye_array(10, format='csr')
A[-1, -1] = 0
b = np.zeros(10)
with pytest.warns(MatrixRankWarning):
res = spsolve(A, b)
assert np.isnan(res).all()
class TestGstrsErrors:
def setup_method(self):
self.A = array([[1.0,2.0,3.0],[4.0,5.0,6.0],[7.0,8.0,9.0]], dtype=np.float64)
self.b = np.array([[1.0],[2.0],[3.0]], dtype=np.float64)
def test_trans(self):
L = scipy.sparse.tril(self.A, format='csc')
U = scipy.sparse.triu(self.A, k=1, format='csc')
with assert_raises(ValueError, match="trans must be N, T, or H"):
_superlu.gstrs('X', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
def test_shape_LU(self):
L = scipy.sparse.tril(self.A[0:2,0:2], format='csc')
U = scipy.sparse.triu(self.A, k=1, format='csc')
with assert_raises(ValueError, match="L and U must have the same dimension"):
_superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
def test_shape_b(self):
L = scipy.sparse.tril(self.A, format='csc')
U = scipy.sparse.triu(self.A, k=1, format='csc')
with assert_raises(ValueError, match="right hand side array has invalid shape"):
_superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
U.shape[0], U.nnz, U.data, U.indices, U.indptr,
self.b[0:2])
def test_types_differ(self):
L = scipy.sparse.tril(self.A.astype(np.float32), format='csc')
U = scipy.sparse.triu(self.A, k=1, format='csc')
with assert_raises(TypeError, match="nzvals types of L and U differ"):
_superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
U.shape[0], U.nnz, U.data, U.indices, U.indptr, self.b)
def test_types_unsupported(self):
L = scipy.sparse.tril(self.A.astype(np.uint8), format='csc')
U = scipy.sparse.triu(self.A.astype(np.uint8), k=1, format='csc')
with assert_raises(TypeError, match="nzvals is not of a type supported"):
_superlu.gstrs('N', L.shape[0], L.nnz, L.data, L.indices, L.indptr,
U.shape[0], U.nnz, U.data, U.indices, U.indptr,
self.b.astype(np.uint8))
class TestSpsolveTriangular:
def setup_method(self):
use_solver(useUmfpack=False)
@pytest.mark.parametrize("fmt",["csr","csc"])
def test_zero_diagonal(self,fmt):
n = 5
rng = np.random.default_rng(43876432987)
A = rng.standard_normal((n, n))
b = np.arange(n)
A = scipy.sparse.tril(A, k=0, format=fmt)
x = spsolve_triangular(A, b, unit_diagonal=True, lower=True)
A.setdiag(1)
assert_allclose(A.dot(x), b)
# Regression test from gh-15199
A = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0]], dtype=np.float64)
b = np.array([1., 2., 3.])
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore", "CSC or CSR matrix format is", SparseEfficiencyWarning)
spsolve_triangular(A, b, unit_diagonal=True)
@pytest.mark.parametrize("fmt",["csr","csc"])
def test_singular(self,fmt):
n = 5
if fmt == "csr":
A = csr_array((n, n))
else:
A = csc_array((n, n))
b = np.arange(n)
for lower in (True, False):
assert_raises(scipy.linalg.LinAlgError,
spsolve_triangular, A, b, lower=lower)
def test_bad_shape(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
# A is not square.
A = np.zeros((3, 4))
b = ones((4, 1))
assert_raises(ValueError, spsolve_triangular, A, b)
# A2 and b2 have incompatible shapes.
A2 = csr_array(eye(3))
b2 = array([1.0, 2.0])
assert_raises(ValueError, spsolve_triangular, A2, b2)
def test_input_types(self):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
A = array([[1., 0.], [1., 2.]])
b = array([[2., 0.], [2., 2.]])
for matrix_type in (array, csc_array, csr_array):
x = spsolve_triangular(matrix_type(A), b, lower=True)
assert_array_almost_equal(A.dot(x), b)
@pytest.mark.slow
@pytest.mark.parametrize("n", [10, 10**2, 10**3])
@pytest.mark.parametrize("m", [1, 10])
@pytest.mark.parametrize("lower", [True, False])
@pytest.mark.parametrize("format", ["csr", "csc"])
@pytest.mark.parametrize("unit_diagonal", [False, True])
@pytest.mark.parametrize("choice_of_A", ["real", "complex"])
@pytest.mark.parametrize("choice_of_b", ["floats", "ints", "complexints"])
def test_random(self, n, m, lower, format, unit_diagonal, choice_of_A, choice_of_b):
with warnings.catch_warnings():
warnings.simplefilter("ignore", SparseEfficiencyWarning)
def random_triangle_matrix(n, lower=True, format="csr", choice_of_A="real"):
if choice_of_A == "real":
dtype = np.float64
elif choice_of_A == "complex":
dtype = np.complex128
else:
raise ValueError("choice_of_A must be 'real' or 'complex'.")
rng = np.random.default_rng(789002319)
rvs = rng.random
A = scipy.sparse.random(n, n, density=0.1, format='lil', dtype=dtype,
random_state=rng, data_rvs=rvs)
if lower:
A = scipy.sparse.tril(A, format="lil")
else:
A = scipy.sparse.triu(A, format="lil")
for i in range(n):
A[i, i] = np.random.rand() + 1
if format == "csc":
A = A.tocsc(copy=False)
else:
A = A.tocsr(copy=False)
return A
rng = np.random.default_rng(1234)
A = random_triangle_matrix(n, lower=lower)
if choice_of_b == "floats":
b = rng.random((n, m))
elif choice_of_b == "ints":
b = rng.integers(-9, 9, (n, m))
elif choice_of_b == "complexints":
b = rng.integers(-9, 9, (n, m)) + rng.integers(-9, 9, (n, m)) * 1j
else:
raise ValueError(
"choice_of_b must be 'floats', 'ints', or 'complexints'.")
x = spsolve_triangular(A, b, lower=lower, unit_diagonal=unit_diagonal)
if unit_diagonal:
A.setdiag(1)
assert_allclose(A.dot(x), b, atol=1.5e-6)
@pytest.mark.parametrize("nnz", [10, 10**2, 10**3])
@pytest.mark.parametrize("fmt", ["csr", "csc", "coo", "dia", "dok", "lil"])
def test_is_sptriangular_and_spbandwidth(nnz, fmt):
with warnings.catch_warnings():
warnings.simplefilter('ignore', SparseEfficiencyWarning)
rng = np.random.default_rng(42)
N = nnz // 2
dens = 0.1
A = scipy.sparse.random_array((N, N), density=dens, format="csr", rng=rng)
A[1, 3] = A[3, 1] = 22 # ensure not upper or lower
A = A.asformat(fmt)
AU = scipy.sparse.triu(A, format=fmt)
AL = scipy.sparse.tril(A, format=fmt)
D = 0.1 * scipy.sparse.eye_array(N, format=fmt)
assert is_sptriangular(A) == (False, False)
assert is_sptriangular(AL) == (True, False)
assert is_sptriangular(AU) == (False, True)
assert is_sptriangular(D) == (True, True)
assert spbandwidth(A) == scipy.linalg.bandwidth(A.toarray())
assert spbandwidth(AU) == scipy.linalg.bandwidth(AU.toarray())
assert spbandwidth(AL) == scipy.linalg.bandwidth(AL.toarray())
assert spbandwidth(D) == scipy.linalg.bandwidth(D.toarray())