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							149 lines
						
					
					
						
							5.5 KiB
						
					
					
				
			
		
		
	
	
							149 lines
						
					
					
						
							5.5 KiB
						
					
					
				""" Test functions for linalg module
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"""
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import warnings
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import numpy as np
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from numpy import linalg, arange, float64, array, dot, transpose
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from numpy.testing import (
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    assert_, assert_raises, assert_equal, assert_array_equal,
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    assert_array_almost_equal, assert_array_less
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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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    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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        with warnings.catch_warnings():
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            warnings.simplefilter("error", DeprecationWarning)
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            assert_raises((AttributeError, DeprecationWarning),
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                              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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