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182 lines
6.5 KiB
Python
182 lines
6.5 KiB
Python
""" Test functions for linalg module
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"""
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import pytest
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import numpy as np
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from numpy import arange, array, dot, float64, linalg, transpose
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from numpy.testing import (
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assert_,
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assert_array_almost_equal,
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assert_array_equal,
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assert_array_less,
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assert_equal,
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assert_raises,
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)
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class TestRegression:
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def test_eig_build(self):
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# Ticket #652
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rva = array([1.03221168e+02 + 0.j,
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-1.91843603e+01 + 0.j,
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-6.04004526e-01 + 15.84422474j,
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-6.04004526e-01 - 15.84422474j,
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-1.13692929e+01 + 0.j,
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-6.57612485e-01 + 10.41755503j,
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-6.57612485e-01 - 10.41755503j,
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1.82126812e+01 + 0.j,
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1.06011014e+01 + 0.j,
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7.80732773e+00 + 0.j,
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-7.65390898e-01 + 0.j,
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1.51971555e-15 + 0.j,
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-1.51308713e-15 + 0.j])
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a = arange(13 * 13, dtype=float64)
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a.shape = (13, 13)
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a = a % 17
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va, ve = linalg.eig(a)
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va.sort()
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rva.sort()
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assert_array_almost_equal(va, rva)
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def test_eigh_build(self):
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# Ticket 662.
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rvals = [68.60568999, 89.57756725, 106.67185574]
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cov = array([[77.70273908, 3.51489954, 15.64602427],
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[ 3.51489954, 88.97013878, -1.07431931],
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[15.64602427, -1.07431931, 98.18223512]])
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vals, vecs = linalg.eigh(cov)
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assert_array_almost_equal(vals, rvals)
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def test_svd_build(self):
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# Ticket 627.
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a = array([[0., 1.], [1., 1.], [2., 1.], [3., 1.]])
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m, n = a.shape
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u, s, vh = linalg.svd(a)
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b = dot(transpose(u[:, n:]), a)
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assert_array_almost_equal(b, np.zeros((2, 2)))
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def test_norm_vector_badarg(self):
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# Regression for #786: Frobenius norm for vectors raises
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# ValueError.
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assert_raises(ValueError, linalg.norm, array([1., 2., 3.]), 'fro')
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def test_lapack_endian(self):
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# For bug #1482
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a = array([[ 5.7998084, -2.1825367],
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[-2.1825367, 9.85910595]], dtype='>f8')
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b = array(a, dtype='<f8')
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ap = linalg.cholesky(a)
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bp = linalg.cholesky(b)
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assert_array_equal(ap, bp)
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def test_large_svd_32bit(self):
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# See gh-4442, 64bit would require very large/slow matrices.
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x = np.eye(1000, 66)
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np.linalg.svd(x)
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def test_svd_no_uv(self):
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# gh-4733
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for shape in (3, 4), (4, 4), (4, 3):
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for t in float, complex:
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a = np.ones(shape, dtype=t)
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w = linalg.svd(a, compute_uv=False)
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c = np.count_nonzero(np.absolute(w) > 0.5)
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assert_equal(c, 1)
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assert_equal(np.linalg.matrix_rank(a), 1)
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assert_array_less(1, np.linalg.norm(a, ord=2))
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w_svdvals = linalg.svdvals(a)
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assert_array_almost_equal(w, w_svdvals)
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def test_norm_object_array(self):
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# gh-7575
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testvector = np.array([np.array([0, 1]), 0, 0], dtype=object)
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norm = linalg.norm(testvector)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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norm = linalg.norm(testvector, ord=1)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype != np.dtype('float64'))
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norm = linalg.norm(testvector, ord=2)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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assert_raises(ValueError, linalg.norm, testvector, ord='fro')
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assert_raises(ValueError, linalg.norm, testvector, ord='nuc')
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assert_raises(ValueError, linalg.norm, testvector, ord=np.inf)
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assert_raises(ValueError, linalg.norm, testvector, ord=-np.inf)
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assert_raises(ValueError, linalg.norm, testvector, ord=0)
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assert_raises(ValueError, linalg.norm, testvector, ord=-1)
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assert_raises(ValueError, linalg.norm, testvector, ord=-2)
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testmatrix = np.array([[np.array([0, 1]), 0, 0],
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[0, 0, 0]], dtype=object)
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norm = linalg.norm(testmatrix)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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norm = linalg.norm(testmatrix, ord='fro')
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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assert_raises(TypeError, linalg.norm, testmatrix, ord='nuc')
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assert_raises(ValueError, linalg.norm, testmatrix, ord=np.inf)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=-np.inf)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=0)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=1)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=-1)
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assert_raises(TypeError, linalg.norm, testmatrix, ord=2)
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assert_raises(TypeError, linalg.norm, testmatrix, ord=-2)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=3)
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def test_lstsq_complex_larger_rhs(self):
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# gh-9891
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size = 20
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n_rhs = 70
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G = np.random.randn(size, size) + 1j * np.random.randn(size, size)
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u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs)
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b = G.dot(u)
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# This should work without segmentation fault.
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u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None)
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# check results just in case
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assert_array_almost_equal(u_lstsq, u)
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@pytest.mark.parametrize("upper", [True, False])
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def test_cholesky_empty_array(self, upper):
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# gh-25840 - upper=True hung before.
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res = np.linalg.cholesky(np.zeros((0, 0)), upper=upper)
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assert res.size == 0
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@pytest.mark.parametrize("rtol", [0.0, [0.0] * 4, np.zeros((4,))])
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def test_matrix_rank_rtol_argument(self, rtol):
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# gh-25877
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x = np.zeros((4, 3, 2))
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res = np.linalg.matrix_rank(x, rtol=rtol)
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assert res.shape == (4,)
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def test_openblas_threading(self):
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# gh-27036
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# Test whether matrix multiplication involving a large matrix always
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# gives the same (correct) answer
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x = np.arange(500000, dtype=np.float64)
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src = np.vstack((x, -10 * x)).T
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matrix = np.array([[0, 1], [1, 0]])
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expected = np.vstack((-10 * x, x)).T # src @ matrix
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for i in range(200):
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result = src @ matrix
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mismatches = (~np.isclose(result, expected)).sum()
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if mismatches != 0:
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assert False, ("unexpected result from matmul, "
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"probably due to OpenBLAS threading issues")
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