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236 lines
5.8 KiB
Python
236 lines
5.8 KiB
Python
import pytest
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import numpy as np
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import scipy.sparse as sp
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import scipy.sparse.linalg as splin
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from numpy.testing import assert_allclose
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try:
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import sparse
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except Exception:
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sparse = None
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pytestmark = pytest.mark.skipif(sparse is None,
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reason="pydata/sparse not installed")
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msg = "pydata/sparse (0.8) does not implement necessary operations"
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sparse_params = [pytest.param("COO"),
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pytest.param("DOK", marks=[pytest.mark.xfail(reason=msg)])]
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scipy_sparse_classes = [
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sp.bsr_matrix,
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sp.csr_matrix,
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sp.coo_matrix,
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sp.csc_matrix,
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sp.dia_matrix,
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sp.dok_matrix
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]
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@pytest.fixture(params=sparse_params)
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def sparse_cls(request):
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return getattr(sparse, request.param)
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@pytest.fixture(params=scipy_sparse_classes)
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def sp_sparse_cls(request):
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return request.param
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@pytest.fixture
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def same_matrix(sparse_cls, sp_sparse_cls):
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np.random.seed(1234)
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A_dense = np.random.rand(9, 9)
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return sp_sparse_cls(A_dense), sparse_cls(A_dense)
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@pytest.fixture
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def matrices(sparse_cls):
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np.random.seed(1234)
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A_dense = np.random.rand(9, 9)
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A_dense = A_dense @ A_dense.T
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A_sparse = sparse_cls(A_dense)
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b = np.random.rand(9)
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return A_dense, A_sparse, b
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def test_isolve_gmres(matrices):
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# Several of the iterative solvers use the same
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# isolve.utils.make_system wrapper code, so test just one of them.
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A_dense, A_sparse, b = matrices
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x, info = splin.gmres(A_sparse, b, atol=1e-15)
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assert info == 0
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assert isinstance(x, np.ndarray)
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assert_allclose(A_sparse @ x, b)
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def test_lsmr(matrices):
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A_dense, A_sparse, b = matrices
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res0 = splin.lsmr(A_dense, b)
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res = splin.lsmr(A_sparse, b)
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assert_allclose(res[0], res0[0], atol=1.8e-5)
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def test_lsqr(matrices):
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A_dense, A_sparse, b = matrices
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res0 = splin.lsqr(A_dense, b)
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res = splin.lsqr(A_sparse, b)
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assert_allclose(res[0], res0[0], atol=1e-5)
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def test_eigs(matrices):
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A_dense, A_sparse, v0 = matrices
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M_dense = np.diag(v0**2)
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M_sparse = A_sparse.__class__(M_dense)
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w_dense, v_dense = splin.eigs(A_dense, k=3, v0=v0)
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w, v = splin.eigs(A_sparse, k=3, v0=v0)
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assert_allclose(w, w_dense)
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assert_allclose(v, v_dense)
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for M in [M_sparse, M_dense]:
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w_dense, v_dense = splin.eigs(A_dense, M=M_dense, k=3, v0=v0)
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w, v = splin.eigs(A_sparse, M=M, k=3, v0=v0)
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assert_allclose(w, w_dense)
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assert_allclose(v, v_dense)
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w_dense, v_dense = splin.eigsh(A_dense, M=M_dense, k=3, v0=v0)
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w, v = splin.eigsh(A_sparse, M=M, k=3, v0=v0)
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assert_allclose(w, w_dense)
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assert_allclose(v, v_dense)
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def test_svds(matrices):
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A_dense, A_sparse, v0 = matrices
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u0, s0, vt0 = splin.svds(A_dense, k=2, v0=v0)
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u, s, vt = splin.svds(A_sparse, k=2, v0=v0)
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assert_allclose(s, s0)
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assert_allclose(u, u0)
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assert_allclose(vt, vt0)
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def test_lobpcg(matrices):
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A_dense, A_sparse, x = matrices
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X = x[:,None]
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w_dense, v_dense = splin.lobpcg(A_dense, X)
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w, v = splin.lobpcg(A_sparse, X)
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assert_allclose(w, w_dense)
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assert_allclose(v, v_dense)
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def test_spsolve(matrices):
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A_dense, A_sparse, b = matrices
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b2 = np.random.rand(len(b), 3)
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x0 = splin.spsolve(sp.csc_matrix(A_dense), b)
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x = splin.spsolve(A_sparse, b)
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assert isinstance(x, np.ndarray)
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assert_allclose(x, x0)
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x0 = splin.spsolve(sp.csc_matrix(A_dense), b)
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x = splin.spsolve(A_sparse, b, use_umfpack=True)
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assert isinstance(x, np.ndarray)
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assert_allclose(x, x0)
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x0 = splin.spsolve(sp.csc_matrix(A_dense), b2)
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x = splin.spsolve(A_sparse, b2)
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assert isinstance(x, np.ndarray)
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assert_allclose(x, x0)
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x0 = splin.spsolve(sp.csc_matrix(A_dense),
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sp.csc_matrix(A_dense))
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x = splin.spsolve(A_sparse, A_sparse)
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assert isinstance(x, type(A_sparse))
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assert_allclose(x.todense(), x0.todense())
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def test_splu(matrices):
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A_dense, A_sparse, b = matrices
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n = len(b)
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sparse_cls = type(A_sparse)
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lu = splin.splu(A_sparse)
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assert isinstance(lu.L, sparse_cls)
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assert isinstance(lu.U, sparse_cls)
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Pr = sparse_cls(sp.csc_matrix((np.ones(n), (lu.perm_r, np.arange(n)))))
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Pc = sparse_cls(sp.csc_matrix((np.ones(n), (np.arange(n), lu.perm_c))))
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A2 = Pr.T @ lu.L @ lu.U @ Pc.T
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assert_allclose(A2.todense(), A_sparse.todense())
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z = lu.solve(A_sparse.todense())
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assert_allclose(z, np.eye(n), atol=1e-10)
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def test_spilu(matrices):
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A_dense, A_sparse, b = matrices
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sparse_cls = type(A_sparse)
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lu = splin.spilu(A_sparse)
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assert isinstance(lu.L, sparse_cls)
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assert isinstance(lu.U, sparse_cls)
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z = lu.solve(A_sparse.todense())
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assert_allclose(z, np.eye(len(b)), atol=1e-3)
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def test_spsolve_triangular(matrices):
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A_dense, A_sparse, b = matrices
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A_sparse = sparse.tril(A_sparse)
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x = splin.spsolve_triangular(A_sparse, b)
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assert_allclose(A_sparse @ x, b)
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def test_onenormest(matrices):
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A_dense, A_sparse, b = matrices
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est0 = splin.onenormest(A_dense)
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est = splin.onenormest(A_sparse)
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assert_allclose(est, est0)
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def test_inv(matrices):
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A_dense, A_sparse, b = matrices
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x0 = splin.inv(sp.csc_matrix(A_dense))
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x = splin.inv(A_sparse)
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assert_allclose(x.todense(), x0.todense())
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def test_expm(matrices):
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A_dense, A_sparse, b = matrices
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x0 = splin.expm(sp.csc_matrix(A_dense))
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x = splin.expm(A_sparse)
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assert_allclose(x.todense(), x0.todense())
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def test_expm_multiply(matrices):
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A_dense, A_sparse, b = matrices
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x0 = splin.expm_multiply(A_dense, b)
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x = splin.expm_multiply(A_sparse, b)
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assert_allclose(x, x0)
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def test_eq(same_matrix):
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sp_sparse, pd_sparse = same_matrix
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assert (sp_sparse == pd_sparse).all()
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def test_ne(same_matrix):
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sp_sparse, pd_sparse = same_matrix
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assert not (sp_sparse != pd_sparse).any()
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