""" Test functions for linalg module """ import warnings import numpy as np from numpy import linalg, arange, float64, array, dot, transpose from numpy.testing import ( assert_, assert_raises, assert_equal, assert_array_equal, assert_array_almost_equal, assert_array_less ) class TestRegression: def test_eig_build(self): # Ticket #652 rva = array([1.03221168e+02 + 0.j, -1.91843603e+01 + 0.j, -6.04004526e-01 + 15.84422474j, -6.04004526e-01 - 15.84422474j, -1.13692929e+01 + 0.j, -6.57612485e-01 + 10.41755503j, -6.57612485e-01 - 10.41755503j, 1.82126812e+01 + 0.j, 1.06011014e+01 + 0.j, 7.80732773e+00 + 0.j, -7.65390898e-01 + 0.j, 1.51971555e-15 + 0.j, -1.51308713e-15 + 0.j]) a = arange(13 * 13, dtype=float64) a.shape = (13, 13) a = a % 17 va, ve = linalg.eig(a) va.sort() rva.sort() assert_array_almost_equal(va, rva) def test_eigh_build(self): # Ticket 662. rvals = [68.60568999, 89.57756725, 106.67185574] cov = array([[77.70273908, 3.51489954, 15.64602427], [3.51489954, 88.97013878, -1.07431931], [15.64602427, -1.07431931, 98.18223512]]) vals, vecs = linalg.eigh(cov) assert_array_almost_equal(vals, rvals) def test_svd_build(self): # Ticket 627. a = array([[0., 1.], [1., 1.], [2., 1.], [3., 1.]]) m, n = a.shape u, s, vh = linalg.svd(a) b = dot(transpose(u[:, n:]), a) assert_array_almost_equal(b, np.zeros((2, 2))) def test_norm_vector_badarg(self): # Regression for #786: Frobenius norm for vectors raises # ValueError. assert_raises(ValueError, linalg.norm, array([1., 2., 3.]), 'fro') def test_lapack_endian(self): # For bug #1482 a = array([[5.7998084, -2.1825367], [-2.1825367, 9.85910595]], dtype='>f8') b = array(a, dtype=' 0.5) assert_equal(c, 1) assert_equal(np.linalg.matrix_rank(a), 1) assert_array_less(1, np.linalg.norm(a, ord=2)) def test_norm_object_array(self): # gh-7575 testvector = np.array([np.array([0, 1]), 0, 0], dtype=object) norm = linalg.norm(testvector) assert_array_equal(norm, [0, 1]) assert_(norm.dtype == np.dtype('float64')) norm = linalg.norm(testvector, ord=1) assert_array_equal(norm, [0, 1]) assert_(norm.dtype != np.dtype('float64')) norm = linalg.norm(testvector, ord=2) assert_array_equal(norm, [0, 1]) assert_(norm.dtype == np.dtype('float64')) assert_raises(ValueError, linalg.norm, testvector, ord='fro') assert_raises(ValueError, linalg.norm, testvector, ord='nuc') assert_raises(ValueError, linalg.norm, testvector, ord=np.inf) assert_raises(ValueError, linalg.norm, testvector, ord=-np.inf) assert_raises(ValueError, linalg.norm, testvector, ord=0) assert_raises(ValueError, linalg.norm, testvector, ord=-1) assert_raises(ValueError, linalg.norm, testvector, ord=-2) testmatrix = np.array([[np.array([0, 1]), 0, 0], [0, 0, 0]], dtype=object) norm = linalg.norm(testmatrix) assert_array_equal(norm, [0, 1]) assert_(norm.dtype == np.dtype('float64')) norm = linalg.norm(testmatrix, ord='fro') assert_array_equal(norm, [0, 1]) assert_(norm.dtype == np.dtype('float64')) assert_raises(TypeError, linalg.norm, testmatrix, ord='nuc') assert_raises(ValueError, linalg.norm, testmatrix, ord=np.inf) assert_raises(ValueError, linalg.norm, testmatrix, ord=-np.inf) assert_raises(ValueError, linalg.norm, testmatrix, ord=0) assert_raises(ValueError, linalg.norm, testmatrix, ord=1) assert_raises(ValueError, linalg.norm, testmatrix, ord=-1) assert_raises(TypeError, linalg.norm, testmatrix, ord=2) assert_raises(TypeError, linalg.norm, testmatrix, ord=-2) assert_raises(ValueError, linalg.norm, testmatrix, ord=3) def test_lstsq_complex_larger_rhs(self): # gh-9891 size = 20 n_rhs = 70 G = np.random.randn(size, size) + 1j * np.random.randn(size, size) u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs) b = G.dot(u) # This should work without segmentation fault. u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None) # check results just in case assert_array_almost_equal(u_lstsq, u)