800 lines
27 KiB
Python
800 lines
27 KiB
Python
import sys
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import threading
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import numpy as np
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from numpy import array, finfo, arange, eye, all, unique, ones, dot
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import numpy.random as random
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from numpy.testing import (
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assert_array_almost_equal, assert_almost_equal,
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assert_equal, assert_array_equal, assert_, assert_allclose,
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assert_warns, suppress_warnings)
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import pytest
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from pytest import raises as assert_raises
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import scipy.linalg
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from scipy.linalg import norm, inv
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from scipy.sparse import (spdiags, SparseEfficiencyWarning, csc_matrix,
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csr_matrix, identity, isspmatrix, dok_matrix, lil_matrix, bsr_matrix)
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from scipy.sparse.linalg import SuperLU
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from scipy.sparse.linalg._dsolve import (spsolve, use_solver, splu, spilu,
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MatrixRankWarning, _superlu, spsolve_triangular, factorized)
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import scipy.sparse
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from scipy._lib._testutils import check_free_memory
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sup_sparse_efficiency = suppress_warnings()
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sup_sparse_efficiency.filter(SparseEfficiencyWarning)
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# scikits.umfpack is not a SciPy dependency but it is optionally used in
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# dsolve, so check whether it's available
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try:
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import scikits.umfpack as umfpack
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has_umfpack = True
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except ImportError:
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has_umfpack = False
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def toarray(a):
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if isspmatrix(a):
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return a.toarray()
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else:
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return a
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def setup_bug_8278():
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N = 2 ** 6
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h = 1/N
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Ah1D = scipy.sparse.diags([-1, 2, -1], [-1, 0, 1],
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shape=(N-1, N-1))/(h**2)
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eyeN = scipy.sparse.eye(N - 1)
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A = (scipy.sparse.kron(eyeN, scipy.sparse.kron(eyeN, Ah1D))
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+ scipy.sparse.kron(eyeN, scipy.sparse.kron(Ah1D, eyeN))
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+ scipy.sparse.kron(Ah1D, scipy.sparse.kron(eyeN, eyeN)))
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b = np.random.rand((N-1)**3)
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return A, b
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class TestFactorized:
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def setup_method(self):
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n = 5
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d = arange(n) + 1
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self.n = n
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self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n).tocsc()
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random.seed(1234)
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def _check_singular(self):
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A = csc_matrix((5,5), dtype='d')
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b = ones(5)
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assert_array_almost_equal(0. * b, factorized(A)(b))
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def _check_non_singular(self):
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# Make a diagonal dominant, to make sure it is not singular
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n = 5
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a = csc_matrix(random.rand(n, n))
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b = ones(n)
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expected = splu(a).solve(b)
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assert_array_almost_equal(factorized(a)(b), expected)
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def test_singular_without_umfpack(self):
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use_solver(useUmfpack=False)
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with assert_raises(RuntimeError, match="Factor is exactly singular"):
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self._check_singular()
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_singular_with_umfpack(self):
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use_solver(useUmfpack=True)
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with suppress_warnings() as sup:
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sup.filter(RuntimeWarning, "divide by zero encountered in double_scalars")
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assert_warns(umfpack.UmfpackWarning, self._check_singular)
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def test_non_singular_without_umfpack(self):
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use_solver(useUmfpack=False)
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self._check_non_singular()
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_non_singular_with_umfpack(self):
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use_solver(useUmfpack=True)
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self._check_non_singular()
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def test_cannot_factorize_nonsquare_matrix_without_umfpack(self):
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use_solver(useUmfpack=False)
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msg = "can only factor square matrices"
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with assert_raises(ValueError, match=msg):
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factorized(self.A[:, :4])
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_factorizes_nonsquare_matrix_with_umfpack(self):
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use_solver(useUmfpack=True)
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# does not raise
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factorized(self.A[:,:4])
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def test_call_with_incorrectly_sized_matrix_without_umfpack(self):
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use_solver(useUmfpack=False)
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solve = factorized(self.A)
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b = random.rand(4)
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B = random.rand(4, 3)
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BB = random.rand(self.n, 3, 9)
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with assert_raises(ValueError, match="is of incompatible size"):
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solve(b)
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with assert_raises(ValueError, match="is of incompatible size"):
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solve(B)
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with assert_raises(ValueError,
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match="object too deep for desired array"):
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solve(BB)
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_call_with_incorrectly_sized_matrix_with_umfpack(self):
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use_solver(useUmfpack=True)
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solve = factorized(self.A)
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b = random.rand(4)
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B = random.rand(4, 3)
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BB = random.rand(self.n, 3, 9)
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# does not raise
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solve(b)
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msg = "object too deep for desired array"
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with assert_raises(ValueError, match=msg):
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solve(B)
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with assert_raises(ValueError, match=msg):
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solve(BB)
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def test_call_with_cast_to_complex_without_umfpack(self):
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use_solver(useUmfpack=False)
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solve = factorized(self.A)
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b = random.rand(4)
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for t in [np.complex64, np.complex128]:
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with assert_raises(TypeError, match="Cannot cast array data"):
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solve(b.astype(t))
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_call_with_cast_to_complex_with_umfpack(self):
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use_solver(useUmfpack=True)
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solve = factorized(self.A)
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b = random.rand(4)
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for t in [np.complex64, np.complex128]:
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assert_warns(np.ComplexWarning, solve, b.astype(t))
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_assume_sorted_indices_flag(self):
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# a sparse matrix with unsorted indices
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unsorted_inds = np.array([2, 0, 1, 0])
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data = np.array([10, 16, 5, 0.4])
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indptr = np.array([0, 1, 2, 4])
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A = csc_matrix((data, unsorted_inds, indptr), (3, 3))
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b = ones(3)
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# should raise when incorrectly assuming indices are sorted
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use_solver(useUmfpack=True, assumeSortedIndices=True)
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with assert_raises(RuntimeError,
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match="UMFPACK_ERROR_invalid_matrix"):
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factorized(A)
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# should sort indices and succeed when not assuming indices are sorted
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use_solver(useUmfpack=True, assumeSortedIndices=False)
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expected = splu(A.copy()).solve(b)
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assert_equal(A.has_sorted_indices, 0)
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assert_array_almost_equal(factorized(A)(b), expected)
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@pytest.mark.slow
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_bug_8278(self):
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check_free_memory(8000)
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use_solver(useUmfpack=True)
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A, b = setup_bug_8278()
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A = A.tocsc()
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f = factorized(A)
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x = f(b)
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assert_array_almost_equal(A @ x, b)
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class TestLinsolve:
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def setup_method(self):
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use_solver(useUmfpack=False)
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def test_singular(self):
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A = csc_matrix((5,5), dtype='d')
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b = array([1, 2, 3, 4, 5],dtype='d')
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with suppress_warnings() as sup:
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sup.filter(MatrixRankWarning, "Matrix is exactly singular")
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x = spsolve(A, b)
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assert_(not np.isfinite(x).any())
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def test_singular_gh_3312(self):
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# "Bad" test case that leads SuperLU to call LAPACK with invalid
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# arguments. Check that it fails moderately gracefully.
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ij = np.array([(17, 0), (17, 6), (17, 12), (10, 13)], dtype=np.int32)
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v = np.array([0.284213, 0.94933781, 0.15767017, 0.38797296])
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A = csc_matrix((v, ij.T), shape=(20, 20))
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b = np.arange(20)
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try:
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# should either raise a runtime error or return value
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# appropriate for singular input (which yields the warning)
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with suppress_warnings() as sup:
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sup.filter(MatrixRankWarning, "Matrix is exactly singular")
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x = spsolve(A, b)
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assert not np.isfinite(x).any()
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except RuntimeError:
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pass
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def test_twodiags(self):
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A = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
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b = array([1, 2, 3, 4, 5])
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# condition number of A
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cond_A = norm(A.toarray(), 2) * norm(inv(A.toarray()), 2)
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for t in ['f','d','F','D']:
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eps = finfo(t).eps # floating point epsilon
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b = b.astype(t)
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for format in ['csc','csr']:
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Asp = A.astype(t).asformat(format)
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x = spsolve(Asp,b)
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assert_(norm(b - Asp@x) < 10 * cond_A * eps)
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def test_bvector_smoketest(self):
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Adense = array([[0., 1., 1.],
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[1., 0., 1.],
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[0., 0., 1.]])
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As = csc_matrix(Adense)
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random.seed(1234)
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x = random.randn(3)
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b = As@x
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x2 = spsolve(As, b)
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assert_array_almost_equal(x, x2)
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def test_bmatrix_smoketest(self):
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Adense = array([[0., 1., 1.],
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[1., 0., 1.],
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[0., 0., 1.]])
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As = csc_matrix(Adense)
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random.seed(1234)
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x = random.randn(3, 4)
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Bdense = As.dot(x)
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Bs = csc_matrix(Bdense)
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x2 = spsolve(As, Bs)
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assert_array_almost_equal(x, x2.toarray())
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@sup_sparse_efficiency
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def test_non_square(self):
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# A is not square.
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A = ones((3, 4))
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b = ones((4, 1))
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assert_raises(ValueError, spsolve, A, b)
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# A2 and b2 have incompatible shapes.
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A2 = csc_matrix(eye(3))
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b2 = array([1.0, 2.0])
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assert_raises(ValueError, spsolve, A2, b2)
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@sup_sparse_efficiency
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def test_example_comparison(self):
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row = array([0,0,1,2,2,2])
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col = array([0,2,2,0,1,2])
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data = array([1,2,3,-4,5,6])
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sM = csr_matrix((data,(row,col)), shape=(3,3), dtype=float)
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M = sM.toarray()
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row = array([0,0,1,1,0,0])
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col = array([0,2,1,1,0,0])
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data = array([1,1,1,1,1,1])
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sN = csr_matrix((data, (row,col)), shape=(3,3), dtype=float)
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N = sN.toarray()
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sX = spsolve(sM, sN)
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X = scipy.linalg.solve(M, N)
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assert_array_almost_equal(X, sX.toarray())
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@sup_sparse_efficiency
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_shape_compatibility(self):
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use_solver(useUmfpack=True)
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A = csc_matrix([[1., 0], [0, 2]])
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bs = [
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[1, 6],
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array([1, 6]),
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[[1], [6]],
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array([[1], [6]]),
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csc_matrix([[1], [6]]),
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csr_matrix([[1], [6]]),
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dok_matrix([[1], [6]]),
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bsr_matrix([[1], [6]]),
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array([[1., 2., 3.], [6., 8., 10.]]),
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csc_matrix([[1., 2., 3.], [6., 8., 10.]]),
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csr_matrix([[1., 2., 3.], [6., 8., 10.]]),
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dok_matrix([[1., 2., 3.], [6., 8., 10.]]),
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bsr_matrix([[1., 2., 3.], [6., 8., 10.]]),
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]
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for b in bs:
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x = np.linalg.solve(A.toarray(), toarray(b))
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for spmattype in [csc_matrix, csr_matrix, dok_matrix, lil_matrix]:
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x1 = spsolve(spmattype(A), b, use_umfpack=True)
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x2 = spsolve(spmattype(A), b, use_umfpack=False)
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# check solution
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if x.ndim == 2 and x.shape[1] == 1:
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# interprets also these as "vectors"
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x = x.ravel()
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assert_array_almost_equal(toarray(x1), x, err_msg=repr((b, spmattype, 1)))
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assert_array_almost_equal(toarray(x2), x, err_msg=repr((b, spmattype, 2)))
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# dense vs. sparse output ("vectors" are always dense)
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if isspmatrix(b) and x.ndim > 1:
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assert_(isspmatrix(x1), repr((b, spmattype, 1)))
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assert_(isspmatrix(x2), repr((b, spmattype, 2)))
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else:
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assert_(isinstance(x1, np.ndarray), repr((b, spmattype, 1)))
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assert_(isinstance(x2, np.ndarray), repr((b, spmattype, 2)))
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# check output shape
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if x.ndim == 1:
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# "vector"
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assert_equal(x1.shape, (A.shape[1],))
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assert_equal(x2.shape, (A.shape[1],))
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else:
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# "matrix"
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assert_equal(x1.shape, x.shape)
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assert_equal(x2.shape, x.shape)
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A = csc_matrix((3, 3))
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b = csc_matrix((1, 3))
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assert_raises(ValueError, spsolve, A, b)
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@sup_sparse_efficiency
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def test_ndarray_support(self):
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A = array([[1., 2.], [2., 0.]])
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x = array([[1., 1.], [0.5, -0.5]])
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b = array([[2., 0.], [2., 2.]])
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assert_array_almost_equal(x, spsolve(A, b))
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def test_gssv_badinput(self):
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N = 10
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d = arange(N) + 1.0
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A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), N, N)
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for spmatrix in (csc_matrix, csr_matrix):
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A = spmatrix(A)
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b = np.arange(N)
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def not_c_contig(x):
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return x.repeat(2)[::2]
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def not_1dim(x):
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return x[:,None]
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def bad_type(x):
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return x.astype(bool)
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def too_short(x):
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return x[:-1]
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badops = [not_c_contig, not_1dim, bad_type, too_short]
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for badop in badops:
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msg = "%r %r" % (spmatrix, badop)
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# Not C-contiguous
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assert_raises((ValueError, TypeError), _superlu.gssv,
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N, A.nnz, badop(A.data), A.indices, A.indptr,
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b, int(spmatrix == csc_matrix), err_msg=msg)
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assert_raises((ValueError, TypeError), _superlu.gssv,
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N, A.nnz, A.data, badop(A.indices), A.indptr,
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b, int(spmatrix == csc_matrix), err_msg=msg)
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assert_raises((ValueError, TypeError), _superlu.gssv,
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N, A.nnz, A.data, A.indices, badop(A.indptr),
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b, int(spmatrix == csc_matrix), err_msg=msg)
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def test_sparsity_preservation(self):
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ident = csc_matrix([
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[1, 0, 0],
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[0, 1, 0],
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[0, 0, 1]])
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b = csc_matrix([
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[0, 1],
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[1, 0],
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[0, 0]])
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x = spsolve(ident, b)
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assert_equal(ident.nnz, 3)
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assert_equal(b.nnz, 2)
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assert_equal(x.nnz, 2)
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assert_allclose(x.A, b.A, atol=1e-12, rtol=1e-12)
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def test_dtype_cast(self):
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A_real = scipy.sparse.csr_matrix([[1, 2, 0],
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[0, 0, 3],
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[4, 0, 5]])
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A_complex = scipy.sparse.csr_matrix([[1, 2, 0],
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[0, 0, 3],
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[4, 0, 5 + 1j]])
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b_real = np.array([1,1,1])
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b_complex = np.array([1,1,1]) + 1j*np.array([1,1,1])
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x = spsolve(A_real, b_real)
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assert_(np.issubdtype(x.dtype, np.floating))
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x = spsolve(A_real, b_complex)
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assert_(np.issubdtype(x.dtype, np.complexfloating))
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x = spsolve(A_complex, b_real)
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assert_(np.issubdtype(x.dtype, np.complexfloating))
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x = spsolve(A_complex, b_complex)
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assert_(np.issubdtype(x.dtype, np.complexfloating))
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@pytest.mark.slow
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@pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
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def test_bug_8278(self):
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check_free_memory(8000)
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use_solver(useUmfpack=True)
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A, b = setup_bug_8278()
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x = spsolve(A, b)
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assert_array_almost_equal(A @ x, b)
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class TestSplu:
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def setup_method(self):
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use_solver(useUmfpack=False)
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n = 40
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d = arange(n) + 1
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self.n = n
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self.A = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
|
|
random.seed(1234)
|
|
|
|
def _smoketest(self, spxlu, check, dtype):
|
|
if np.issubdtype(dtype, np.complexfloating):
|
|
A = self.A + 1j*self.A.T
|
|
else:
|
|
A = self.A
|
|
|
|
A = A.astype(dtype)
|
|
lu = spxlu(A)
|
|
|
|
rng = random.RandomState(1234)
|
|
|
|
# Input shapes
|
|
for k in [None, 1, 2, self.n, self.n+2]:
|
|
msg = "k=%r" % (k,)
|
|
|
|
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)
|
|
|
|
@sup_sparse_efficiency
|
|
def test_splu_smoketest(self):
|
|
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)
|
|
|
|
self._smoketest(splu, check, np.float32)
|
|
self._smoketest(splu, check, np.float64)
|
|
self._smoketest(splu, check, np.complex64)
|
|
self._smoketest(splu, check, np.complex128)
|
|
|
|
@sup_sparse_efficiency
|
|
def test_spilu_smoketest(self):
|
|
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)
|
|
|
|
self._smoketest(spilu, check, np.float32)
|
|
self._smoketest(spilu, check, np.float64)
|
|
self._smoketest(spilu, check, np.complex64)
|
|
self._smoketest(spilu, check, np.complex128)
|
|
|
|
assert_(max(errors) > 1e-5)
|
|
|
|
@sup_sparse_efficiency
|
|
def test_spilu_drop_rule(self):
|
|
# Test passing in the drop_rule argument to spilu.
|
|
A = identity(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_matrix((5,5), dtype='d')
|
|
assert_raises(RuntimeError, splu, A)
|
|
|
|
def test_spilu_nnz0(self):
|
|
A = csc_matrix((5,5), dtype='d')
|
|
assert_raises(RuntimeError, spilu, A)
|
|
|
|
def test_splu_basic(self):
|
|
# Test basic splu functionality.
|
|
n = 30
|
|
rng = random.RandomState(12)
|
|
a = rng.rand(n, n)
|
|
a[a < 0.95] = 0
|
|
# First test with a singular matrix
|
|
a[:, 0] = 0
|
|
a_ = csc_matrix(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_matrix(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
|
|
a = random.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_matrix(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_matrix(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
|
|
np.random.seed(42)
|
|
n = 500
|
|
p = 0.01
|
|
A = scipy.sparse.random(n, n, p)
|
|
x = np.random.rand(n)
|
|
# Make A diagonal dominant to make sure it is not singular
|
|
A += (n+1)*scipy.sparse.identity(n)
|
|
A_ = csc_matrix(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
|
|
a = random.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_matrix(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()
|
|
|
|
assert_raises(ValueError, splu, A[:,:4])
|
|
assert_raises(ValueError, spilu, A[:,:4])
|
|
|
|
for lu in [splu(A), spilu(A)]:
|
|
b = random.rand(42)
|
|
B = random.rand(42, 3)
|
|
BB = random.rand(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))
|
|
|
|
@sup_sparse_efficiency
|
|
def test_superlu_dlamch_i386_nan(self):
|
|
# 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 = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n)
|
|
A = A.astype(np.float32)
|
|
spilu(A)
|
|
A = A + 1j*A
|
|
B = A.A
|
|
assert_(not np.isnan(B).any())
|
|
|
|
@sup_sparse_efficiency
|
|
def test_lu_attr(self):
|
|
|
|
def check(dtype, complex_2=False):
|
|
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 advertized
|
|
|
|
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
|
|
@sup_sparse_efficiency
|
|
def test_threads_parallel(self):
|
|
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)
|
|
|
|
|
|
class TestSpsolveTriangular:
|
|
def setup_method(self):
|
|
use_solver(useUmfpack=False)
|
|
|
|
def test_zero_diagonal(self):
|
|
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='csr')
|
|
|
|
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 suppress_warnings() as sup:
|
|
sup.filter(SparseEfficiencyWarning, "CSR matrix format is")
|
|
spsolve_triangular(A, b, unit_diagonal=True)
|
|
|
|
def test_singular(self):
|
|
n = 5
|
|
A = csr_matrix((n, n))
|
|
b = np.arange(n)
|
|
for lower in (True, False):
|
|
assert_raises(scipy.linalg.LinAlgError, spsolve_triangular, A, b, lower=lower)
|
|
|
|
@sup_sparse_efficiency
|
|
def test_bad_shape(self):
|
|
# 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_matrix(eye(3))
|
|
b2 = array([1.0, 2.0])
|
|
assert_raises(ValueError, spsolve_triangular, A2, b2)
|
|
|
|
@sup_sparse_efficiency
|
|
def test_input_types(self):
|
|
A = array([[1., 0.], [1., 2.]])
|
|
b = array([[2., 0.], [2., 2.]])
|
|
for matrix_type in (array, csc_matrix, csr_matrix):
|
|
x = spsolve_triangular(matrix_type(A), b, lower=True)
|
|
assert_array_almost_equal(A.dot(x), b)
|
|
|
|
@pytest.mark.slow
|
|
@pytest.mark.timeout(120) # prerelease_deps_coverage_64bit_blas job
|
|
@sup_sparse_efficiency
|
|
def test_random(self):
|
|
def random_triangle_matrix(n, lower=True):
|
|
A = scipy.sparse.random(n, n, density=0.1, format='coo')
|
|
if lower:
|
|
A = scipy.sparse.tril(A)
|
|
else:
|
|
A = scipy.sparse.triu(A)
|
|
A = A.tocsr(copy=False)
|
|
for i in range(n):
|
|
A[i, i] = np.random.rand() + 1
|
|
return A
|
|
|
|
np.random.seed(1234)
|
|
for lower in (True, False):
|
|
for n in (10, 10**2, 10**3):
|
|
A = random_triangle_matrix(n, lower=lower)
|
|
for m in (1, 10):
|
|
for b in (np.random.rand(n, m),
|
|
np.random.randint(-9, 9, (n, m)),
|
|
np.random.randint(-9, 9, (n, m)) +
|
|
np.random.randint(-9, 9, (n, m)) * 1j):
|
|
x = spsolve_triangular(A, b, lower=lower)
|
|
assert_array_almost_equal(A.dot(x), b)
|
|
x = spsolve_triangular(A, b, lower=lower,
|
|
unit_diagonal=True)
|
|
A.setdiag(1)
|
|
assert_array_almost_equal(A.dot(x), b)
|