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""" 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='<f8')
ap = linalg.cholesky(a)
bp = linalg.cholesky(b)
assert_array_equal(ap, bp)
def test_large_svd_32bit(self):
# See gh-4442, 64bit would require very large/slow matrices.
x = np.eye(1000, 66)
np.linalg.svd(x)
def test_svd_no_uv(self):
# gh-4733
for shape in (3, 4), (4, 4), (4, 3):
for t in float, complex:
a = np.ones(shape, dtype=t)
w = linalg.svd(a, compute_uv=False)
c = np.count_nonzero(np.absolute(w) > 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)
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