Vehicle-cpp/hkpc/software/scipy/sparse/linalg/_dsolve/tests/test_linsolve.py

import sys
import threading

import numpy as np
from numpy import array, finfo, arange, eye, all, unique, ones, dot
import numpy.random as random
from numpy.testing import (
        assert_array_almost_equal, assert_almost_equal,
        assert_equal, assert_array_equal, assert_, assert_allclose,
        assert_warns, suppress_warnings)
import pytest
from pytest import raises as assert_raises

import scipy.linalg
from scipy.linalg import norm, inv
from scipy.sparse import (spdiags, SparseEfficiencyWarning, csc_matrix,
        csr_matrix, identity, isspmatrix, dok_matrix, lil_matrix, bsr_matrix)
from scipy.sparse.linalg import SuperLU
from scipy.sparse.linalg._dsolve import (spsolve, use_solver, splu, spilu,
        MatrixRankWarning, _superlu, spsolve_triangular, factorized)
import scipy.sparse

from scipy._lib._testutils import check_free_memory


sup_sparse_efficiency = suppress_warnings()
sup_sparse_efficiency.filter(SparseEfficiencyWarning)

# 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 isspmatrix(a):
        return a.toarray()
    else:
        return a


def setup_bug_8278():
    N = 2 ** 6
    h = 1/N
    Ah1D = scipy.sparse.diags([-1, 2, -1], [-1, 0, 1],
                              shape=(N-1, N-1))/(h**2)
    eyeN = scipy.sparse.eye(N - 1)
    A = (scipy.sparse.kron(eyeN, scipy.sparse.kron(eyeN, Ah1D))
         + scipy.sparse.kron(eyeN, scipy.sparse.kron(Ah1D, eyeN))
         + scipy.sparse.kron(Ah1D, scipy.sparse.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 = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), n, n).tocsc()
        random.seed(1234)

    def _check_singular(self):
        A = csc_matrix((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
        a = csc_matrix(random.rand(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 suppress_warnings() as sup:
            sup.filter(RuntimeWarning, "divide by zero encountered in double_scalars")
            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)
        b = random.rand(4)
        B = random.rand(4, 3)
        BB = random.rand(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)
        b = random.rand(4)
        B = random.rand(4, 3)
        BB = random.rand(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)
        b = random.rand(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)
        b = random.rand(4)
        for t in [np.complex64, np.complex128]:
            assert_warns(np.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_matrix((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_matrix((5,5), dtype='d')
        b = array([1, 2, 3, 4, 5],dtype='d')
        with suppress_warnings() as sup:
            sup.filter(MatrixRankWarning, "Matrix is exactly singular")
            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_matrix((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 suppress_warnings() as sup:
                sup.filter(MatrixRankWarning, "Matrix is exactly singular")
                x = spsolve(A, b)
            assert not np.isfinite(x).any()
        except RuntimeError:
            pass

    def test_twodiags(self):
        A = spdiags([[1, 2, 3, 4, 5], [6, 5, 8, 9, 10]], [0, 1], 5, 5)
        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)

            for format in ['csc','csr']:
                Asp = A.astype(t).asformat(format)

                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_matrix(Adense)
        random.seed(1234)
        x = random.randn(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_matrix(Adense)
        random.seed(1234)
        x = random.randn(3, 4)
        Bdense = As.dot(x)
        Bs = csc_matrix(Bdense)
        x2 = spsolve(As, Bs)
        assert_array_almost_equal(x, x2.toarray())

    @sup_sparse_efficiency
    def test_non_square(self):
        # 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_matrix(eye(3))
        b2 = array([1.0, 2.0])
        assert_raises(ValueError, spsolve, A2, b2)

    @sup_sparse_efficiency
    def test_example_comparison(self):
        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_matrix((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_matrix((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())

    @sup_sparse_efficiency
    @pytest.mark.skipif(not has_umfpack, reason="umfpack not available")
    def test_shape_compatibility(self):
        use_solver(useUmfpack=True)
        A = csc_matrix([[1., 0], [0, 2]])
        bs = [
            [1, 6],
            array([1, 6]),
            [[1], [6]],
            array([[1], [6]]),
            csc_matrix([[1], [6]]),
            csr_matrix([[1], [6]]),
            dok_matrix([[1], [6]]),
            bsr_matrix([[1], [6]]),
            array([[1., 2., 3.], [6., 8., 10.]]),
            csc_matrix([[1., 2., 3.], [6., 8., 10.]]),
            csr_matrix([[1., 2., 3.], [6., 8., 10.]]),
            dok_matrix([[1., 2., 3.], [6., 8., 10.]]),
            bsr_matrix([[1., 2., 3.], [6., 8., 10.]]),
            ]

        for b in bs:
            x = np.linalg.solve(A.toarray(), toarray(b))
            for spmattype in [csc_matrix, csr_matrix, dok_matrix, lil_matrix]:
                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 isspmatrix(b) and x.ndim > 1:
                    assert_(isspmatrix(x1), repr((b, spmattype, 1)))
                    assert_(isspmatrix(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_matrix((3, 3))
        b = csc_matrix((1, 3))
        assert_raises(ValueError, spsolve, A, b)

    @sup_sparse_efficiency
    def test_ndarray_support(self):
        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 = spdiags((d, 2*d, d[::-1]), (-3, 0, 5), N, N)

        for spmatrix in (csc_matrix, csr_matrix):
            A = spmatrix(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 = "%r %r" % (spmatrix, badop)
                # Not C-contiguous
                assert_raises((ValueError, TypeError), _superlu.gssv,
                              N, A.nnz, badop(A.data), A.indices, A.indptr,
                              b, int(spmatrix == csc_matrix), err_msg=msg)
                assert_raises((ValueError, TypeError), _superlu.gssv,
                              N, A.nnz, A.data, badop(A.indices), A.indptr,
                              b, int(spmatrix == csc_matrix), err_msg=msg)
                assert_raises((ValueError, TypeError), _superlu.gssv,
                              N, A.nnz, A.data, A.indices, badop(A.indptr),
                              b, int(spmatrix == csc_matrix), err_msg=msg)

    def test_sparsity_preservation(self):
        ident = csc_matrix([
            [1, 0, 0],
            [0, 1, 0],
            [0, 0, 1]])
        b = csc_matrix([
            [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.A, b.A, atol=1e-12, rtol=1e-12)

    def test_dtype_cast(self):
        A_real = scipy.sparse.csr_matrix([[1, 2, 0],
                                          [0, 0, 3],
                                          [4, 0, 5]])
        A_complex = scipy.sparse.csr_matrix([[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 = 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)