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

import pytest

import numpy as np
import scipy.sparse as sp
import scipy.sparse.linalg as splin

from numpy.testing import assert_allclose, assert_equal

try:
    import sparse
except Exception:
    sparse = None

pytestmark = pytest.mark.skipif(sparse is None,
                                reason="pydata/sparse not installed")


msg = "pydata/sparse (0.8) does not implement necessary operations"


sparse_params = (pytest.param("COO"),
                 pytest.param("DOK", marks=[pytest.mark.xfail(reason=msg)]))

scipy_sparse_classes = [
    sp.bsr_matrix,
    sp.csr_matrix,
    sp.coo_matrix,
    sp.csc_matrix,
    sp.dia_matrix,
    sp.dok_matrix
]


@pytest.fixture(params=sparse_params)
def sparse_cls(request):
    return getattr(sparse, request.param)


@pytest.fixture(params=scipy_sparse_classes)
def sp_sparse_cls(request):
    return request.param


@pytest.fixture
def same_matrix(sparse_cls, sp_sparse_cls):
    np.random.seed(1234)
    A_dense = np.random.rand(9, 9)
    return sp_sparse_cls(A_dense), sparse_cls(A_dense)


@pytest.fixture
def matrices(sparse_cls):
    np.random.seed(1234)
    A_dense = np.random.rand(9, 9)
    A_dense = A_dense @ A_dense.T
    A_sparse = sparse_cls(A_dense)
    b = np.random.rand(9)
    return A_dense, A_sparse, b


def test_isolve_gmres(matrices):
    # Several of the iterative solvers use the same
    # isolve.utils.make_system wrapper code, so test just one of them.
    A_dense, A_sparse, b = matrices
    x, info = splin.gmres(A_sparse, b, atol=1e-15)
    assert info == 0
    assert isinstance(x, np.ndarray)
    assert_allclose(A_sparse @ x, b)


def test_lsmr(matrices):
    A_dense, A_sparse, b = matrices
    res0 = splin.lsmr(A_dense, b)
    res = splin.lsmr(A_sparse, b)
    assert_allclose(res[0], res0[0], atol=1.8e-5)


# test issue 17012
def test_lsmr_output_shape():
    x = splin.lsmr(A=np.ones((10, 1)), b=np.zeros(10), x0=np.ones(1))[0]
    assert_equal(x.shape, (1,))


def test_lsqr(matrices):
    A_dense, A_sparse, b = matrices
    res0 = splin.lsqr(A_dense, b)
    res = splin.lsqr(A_sparse, b)
    assert_allclose(res[0], res0[0], atol=1e-5)


def test_eigs(matrices):
    A_dense, A_sparse, v0 = matrices

    M_dense = np.diag(v0**2)
    M_sparse = A_sparse.__class__(M_dense)

    w_dense, v_dense = splin.eigs(A_dense, k=3, v0=v0)
    w, v = splin.eigs(A_sparse, k=3, v0=v0)

    assert_allclose(w, w_dense)
    assert_allclose(v, v_dense)

    for M in [M_sparse, M_dense]:
        w_dense, v_dense = splin.eigs(A_dense, M=M_dense, k=3, v0=v0)
        w, v = splin.eigs(A_sparse, M=M, k=3, v0=v0)

        assert_allclose(w, w_dense)
        assert_allclose(v, v_dense)

        w_dense, v_dense = splin.eigsh(A_dense, M=M_dense, k=3, v0=v0)
        w, v = splin.eigsh(A_sparse, M=M, k=3, v0=v0)

        assert_allclose(w, w_dense)
        assert_allclose(v, v_dense)


def test_svds(matrices):
    A_dense, A_sparse, v0 = matrices

    u0, s0, vt0 = splin.svds(A_dense, k=2, v0=v0)
    u, s, vt = splin.svds(A_sparse, k=2, v0=v0)

    assert_allclose(s, s0)
    assert_allclose(u, u0)
    assert_allclose(vt, vt0)


def test_lobpcg(matrices):
    A_dense, A_sparse, x = matrices
    X = x[:,None]

    w_dense, v_dense = splin.lobpcg(A_dense, X)
    w, v = splin.lobpcg(A_sparse, X)

    assert_allclose(w, w_dense)
    assert_allclose(v, v_dense)


def test_spsolve(matrices):
    A_dense, A_sparse, b = matrices
    b2 = np.random.rand(len(b), 3)

    x0 = splin.spsolve(sp.csc_matrix(A_dense), b)
    x = splin.spsolve(A_sparse, b)
    assert isinstance(x, np.ndarray)
    assert_allclose(x, x0)

    x0 = splin.spsolve(sp.csc_matrix(A_dense), b)
    x = splin.spsolve(A_sparse, b, use_umfpack=True)
    assert isinstance(x, np.ndarray)
    assert_allclose(x, x0)

    x0 = splin.spsolve(sp.csc_matrix(A_dense), b2)
    x = splin.spsolve(A_sparse, b2)
    assert isinstance(x, np.ndarray)
    assert_allclose(x, x0)

    x0 = splin.spsolve(sp.csc_matrix(A_dense),
                       sp.csc_matrix(A_dense))
    x = splin.spsolve(A_sparse, A_sparse)
    assert isinstance(x, type(A_sparse))
    assert_allclose(x.toarray(), x0.toarray())


def test_splu(matrices):
    A_dense, A_sparse, b = matrices
    n = len(b)
    sparse_cls = type(A_sparse)

    lu = splin.splu(A_sparse)

    assert isinstance(lu.L, sparse_cls)
    assert isinstance(lu.U, sparse_cls)

    Pr = sparse_cls(sp.csc_matrix((np.ones(n), (lu.perm_r, np.arange(n)))))
    Pc = sparse_cls(sp.csc_matrix((np.ones(n), (np.arange(n), lu.perm_c))))
    A2 = Pr.T @ lu.L @ lu.U @ Pc.T

    assert_allclose(A2.toarray(), A_sparse.toarray())

    z = lu.solve(A_sparse.toarray())
    assert_allclose(z, np.eye(n), atol=1e-10)


def test_spilu(matrices):
    A_dense, A_sparse, b = matrices
    sparse_cls = type(A_sparse)

    lu = splin.spilu(A_sparse)

    assert isinstance(lu.L, sparse_cls)
    assert isinstance(lu.U, sparse_cls)

    z = lu.solve(A_sparse.toarray())
    assert_allclose(z, np.eye(len(b)), atol=1e-3)


def test_spsolve_triangular(matrices):
    A_dense, A_sparse, b = matrices
    A_sparse = sparse.tril(A_sparse)

    x = splin.spsolve_triangular(A_sparse, b)
    assert_allclose(A_sparse @ x, b)


def test_onenormest(matrices):
    A_dense, A_sparse, b = matrices
    est0 = splin.onenormest(A_dense)
    est = splin.onenormest(A_sparse)
    assert_allclose(est, est0)


def test_inv(matrices):
    A_dense, A_sparse, b = matrices
    x0 = splin.inv(sp.csc_matrix(A_dense))
    x = splin.inv(A_sparse)
    assert_allclose(x.toarray(), x0.toarray())


def test_expm(matrices):
    A_dense, A_sparse, b = matrices
    x0 = splin.expm(sp.csc_matrix(A_dense))
    x = splin.expm(A_sparse)
    assert_allclose(x.toarray(), x0.toarray())


def test_expm_multiply(matrices):
    A_dense, A_sparse, b = matrices
    x0 = splin.expm_multiply(A_dense, b)
    x = splin.expm_multiply(A_sparse, b)
    assert_allclose(x, x0)


def test_eq(same_matrix):
    sp_sparse, pd_sparse = same_matrix
    assert (sp_sparse == pd_sparse).all()


def test_ne(same_matrix):
    sp_sparse, pd_sparse = same_matrix
    assert not (sp_sparse != pd_sparse).any()