#****************************************************************************** # Copyright (C) 2013 Kenneth L. Ho # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are met: # # Redistributions of source code must retain the above copyright notice, this # list of conditions and the following disclaimer. Redistributions in binary # form must reproduce the above copyright notice, this list of conditions and # the following disclaimer in the documentation and/or other materials # provided with the distribution. # # None of the names of the copyright holders may be used to endorse or # promote products derived from this software without specific prior written # permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" # AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE # LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR # CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF # SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS # INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN # CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. #****************************************************************************** import scipy.linalg.interpolative as pymatrixid import numpy as np from scipy.linalg import hilbert, svdvals, norm from scipy.sparse.linalg import aslinearoperator from scipy.linalg.interpolative import interp_decomp from numpy.testing import (assert_, assert_allclose, assert_equal, assert_array_equal) import pytest from pytest import raises as assert_raises import sys _IS_32BIT = (sys.maxsize < 2**32) @pytest.fixture() def eps(): yield 1e-12 @pytest.fixture(params=[np.float64, np.complex128]) def A(request): # construct Hilbert matrix # set parameters n = 300 yield hilbert(n).astype(request.param) @pytest.fixture() def L(A): yield aslinearoperator(A) @pytest.fixture() def rank(A, eps): S = np.linalg.svd(A, compute_uv=False) try: rank = np.nonzero(S < eps)[0][0] except IndexError: rank = A.shape[0] return rank class TestInterpolativeDecomposition: @pytest.mark.parametrize( "rand,lin_op", [(False, False), (True, False), (True, True)]) def test_real_id_fixed_precision(self, A, L, eps, rand, lin_op): if _IS_32BIT and A.dtype == np.complex_ and rand: pytest.xfail("bug in external fortran code") # Test ID routines on a Hilbert matrix. A_or_L = A if not lin_op else L k, idx, proj = pymatrixid.interp_decomp(A_or_L, eps, rand=rand) B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj) assert_allclose(A, B, rtol=eps, atol=1e-08) @pytest.mark.parametrize( "rand,lin_op", [(False, False), (True, False), (True, True)]) def test_real_id_fixed_rank(self, A, L, eps, rank, rand, lin_op): if _IS_32BIT and A.dtype == np.complex_ and rand: pytest.xfail("bug in external fortran code") k = rank A_or_L = A if not lin_op else L idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand) B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj) assert_allclose(A, B, rtol=eps, atol=1e-08) @pytest.mark.parametrize("rand,lin_op", [(False, False)]) def test_real_id_skel_and_interp_matrices( self, A, L, eps, rank, rand, lin_op): k = rank A_or_L = A if not lin_op else L idx, proj = pymatrixid.interp_decomp(A_or_L, k, rand=rand) P = pymatrixid.reconstruct_interp_matrix(idx, proj) B = pymatrixid.reconstruct_skel_matrix(A, k, idx) assert_allclose(B, A[:, idx[:k]], rtol=eps, atol=1e-08) assert_allclose(B @ P, A, rtol=eps, atol=1e-08) @pytest.mark.parametrize( "rand,lin_op", [(False, False), (True, False), (True, True)]) def test_svd_fixed_precison(self, A, L, eps, rand, lin_op): if _IS_32BIT and A.dtype == np.complex_ and rand: pytest.xfail("bug in external fortran code") A_or_L = A if not lin_op else L U, S, V = pymatrixid.svd(A_or_L, eps, rand=rand) B = U * S @ V.T.conj() assert_allclose(A, B, rtol=eps, atol=1e-08) @pytest.mark.parametrize( "rand,lin_op", [(False, False), (True, False), (True, True)]) def test_svd_fixed_rank(self, A, L, eps, rank, rand, lin_op): if _IS_32BIT and A.dtype == np.complex_ and rand: pytest.xfail("bug in external fortran code") k = rank A_or_L = A if not lin_op else L U, S, V = pymatrixid.svd(A_or_L, k, rand=rand) B = U * S @ V.T.conj() assert_allclose(A, B, rtol=eps, atol=1e-08) def test_id_to_svd(self, A, eps, rank): k = rank idx, proj = pymatrixid.interp_decomp(A, k, rand=False) U, S, V = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj) B = U * S @ V.T.conj() assert_allclose(A, B, rtol=eps, atol=1e-08) def test_estimate_spectral_norm(self, A): s = svdvals(A) norm_2_est = pymatrixid.estimate_spectral_norm(A) assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8) def test_estimate_spectral_norm_diff(self, A): B = A.copy() B[:, 0] *= 1.2 s = svdvals(A - B) norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B) assert_allclose(norm_2_est, s[0], rtol=1e-6, atol=1e-8) def test_rank_estimates_array(self, A): B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype) for M in [A, B]: rank_tol = 1e-9 rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol) rank_est = pymatrixid.estimate_rank(M, rank_tol) assert_(rank_est >= rank_np) assert_(rank_est <= rank_np + 10) def test_rank_estimates_lin_op(self, A): B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=A.dtype) for M in [A, B]: ML = aslinearoperator(M) rank_tol = 1e-9 rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol) rank_est = pymatrixid.estimate_rank(ML, rank_tol) assert_(rank_est >= rank_np - 4) assert_(rank_est <= rank_np + 4) def test_rand(self): pymatrixid.seed('default') assert_allclose(pymatrixid.rand(2), [0.8932059, 0.64500803], rtol=1e-4, atol=1e-8) pymatrixid.seed(1234) x1 = pymatrixid.rand(2) assert_allclose(x1, [0.7513823, 0.06861718], rtol=1e-4, atol=1e-8) np.random.seed(1234) pymatrixid.seed() x2 = pymatrixid.rand(2) np.random.seed(1234) pymatrixid.seed(np.random.rand(55)) x3 = pymatrixid.rand(2) assert_allclose(x1, x2) assert_allclose(x1, x3) def test_badcall(self): A = hilbert(5).astype(np.float32) with assert_raises(ValueError): pymatrixid.interp_decomp(A, 1e-6, rand=False) def test_rank_too_large(self): # svd(array, k) should not segfault a = np.ones((4, 3)) with assert_raises(ValueError): pymatrixid.svd(a, 4) def test_full_rank(self): eps = 1.0e-12 # fixed precision A = np.random.rand(16, 8) k, idx, proj = pymatrixid.interp_decomp(A, eps) assert_equal(k, A.shape[1]) P = pymatrixid.reconstruct_interp_matrix(idx, proj) B = pymatrixid.reconstruct_skel_matrix(A, k, idx) assert_allclose(A, B @ P) # fixed rank idx, proj = pymatrixid.interp_decomp(A, k) P = pymatrixid.reconstruct_interp_matrix(idx, proj) B = pymatrixid.reconstruct_skel_matrix(A, k, idx) assert_allclose(A, B @ P) @pytest.mark.parametrize("dtype", [np.float_, np.complex_]) @pytest.mark.parametrize("rand", [True, False]) @pytest.mark.parametrize("eps", [1, 0.1]) def test_bug_9793(self, dtype, rand, eps): if _IS_32BIT and dtype == np.complex_ and rand: pytest.xfail("bug in external fortran code") A = np.array([[-1, -1, -1, 0, 0, 0], [0, 0, 0, 1, 1, 1], [1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1]], dtype=dtype, order="C") B = A.copy() interp_decomp(A.T, eps, rand=rand) assert_array_equal(A, B)