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"""Test functions for the sparse.linalg.norm module
"""
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.linalg import norm as npnorm
from numpy.testing import (assert_raises, assert_equal, assert_allclose,
TestCase, dec)
from scipy._lib._version import NumpyVersion
import scipy.sparse
from scipy.sparse.linalg import norm as spnorm
class TestNorm(TestCase):
def setUp(self):
a = np.arange(9) - 4
b = a.reshape((3, 3))
self.b = scipy.sparse.csr_matrix(b)
def test_matrix_norm(self):
# Frobenius norm is the default
assert_allclose(spnorm(self.b), 7.745966692414834)
assert_allclose(spnorm(self.b, 'fro'), 7.745966692414834)
assert_allclose(spnorm(self.b, np.inf), 9)
assert_allclose(spnorm(self.b, -np.inf), 2)
assert_allclose(spnorm(self.b, 1), 7)
assert_allclose(spnorm(self.b, -1), 6)
# _multi_svd_norm is not implemented for sparse matrix
assert_raises(NotImplementedError, spnorm, self.b, 2)
assert_raises(NotImplementedError, spnorm, self.b, -2)
def test_matrix_norm_axis(self):
for m, axis in ((self.b, None), (self.b, (0, 1)), (self.b.T, (1, 0))):
assert_allclose(spnorm(m, axis=axis), 7.745966692414834)
assert_allclose(spnorm(m, 'fro', axis=axis), 7.745966692414834)
assert_allclose(spnorm(m, np.inf, axis=axis), 9)
assert_allclose(spnorm(m, -np.inf, axis=axis), 2)
assert_allclose(spnorm(m, 1, axis=axis), 7)
assert_allclose(spnorm(m, -1, axis=axis), 6)
def test_vector_norm(self):
v = [4.5825756949558398, 4.2426406871192848, 4.5825756949558398]
for m, a in (self.b, 0), (self.b.T, 1):
for axis in a, (a, ), a-2, (a-2, ):
assert_allclose(spnorm(m, 1, axis=axis), [7, 6, 7])
assert_allclose(spnorm(m, np.inf, axis=axis), [4, 3, 4])
assert_allclose(spnorm(m, axis=axis), v)
assert_allclose(spnorm(m, ord=2, axis=axis), v)
assert_allclose(spnorm(m, ord=None, axis=axis), v)
def test_norm_exceptions(self):
m = self.b
assert_raises(TypeError, spnorm, m, None, 1.5)
assert_raises(TypeError, spnorm, m, None, [2])
assert_raises(ValueError, spnorm, m, None, ())
assert_raises(ValueError, spnorm, m, None, (0, 1, 2))
assert_raises(ValueError, spnorm, m, None, (0, 0))
assert_raises(ValueError, spnorm, m, None, (0, 2))
assert_raises(ValueError, spnorm, m, None, (-3, 0))
assert_raises(ValueError, spnorm, m, None, 2)
assert_raises(ValueError, spnorm, m, None, -3)
assert_raises(ValueError, spnorm, m, 'plate_of_shrimp', 0)
assert_raises(ValueError, spnorm, m, 'plate_of_shrimp', (0, 1))
class TestVsNumpyNorm(TestCase):
_sparse_types = (
scipy.sparse.bsr_matrix,
scipy.sparse.coo_matrix,
scipy.sparse.csc_matrix,
scipy.sparse.csr_matrix,
scipy.sparse.dia_matrix,
scipy.sparse.dok_matrix,
scipy.sparse.lil_matrix,
)
_test_matrices = (
(np.arange(9) - 4).reshape((3, 3)),
[
[1, 2, 3],
[-1, 1, 4]],
[
[1, 0, 3],
[-1, 1, 4j]],
)
@dec.skipif(NumpyVersion(np.__version__) < '1.8.0')
def test_sparse_matrix_norms(self):
for sparse_type in self._sparse_types:
for M in self._test_matrices:
S = sparse_type(M)
assert_allclose(spnorm(S), npnorm(M))
assert_allclose(spnorm(S, 'fro'), npnorm(M, 'fro'))
assert_allclose(spnorm(S, np.inf), npnorm(M, np.inf))
assert_allclose(spnorm(S, -np.inf), npnorm(M, -np.inf))
assert_allclose(spnorm(S, 1), npnorm(M, 1))
assert_allclose(spnorm(S, -1), npnorm(M, -1))
@dec.skipif(NumpyVersion(np.__version__) < '1.8.0')
def test_sparse_matrix_norms_with_axis(self):
for sparse_type in self._sparse_types:
for M in self._test_matrices:
S = sparse_type(M)
for axis in None, (0, 1), (1, 0):
assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
for ord in 'fro', np.inf, -np.inf, 1, -1:
assert_allclose(spnorm(S, ord, axis=axis),
npnorm(M, ord, axis=axis))
# Some numpy matrix norms are allergic to negative axes.
for axis in (-2, -1), (-1, -2), (1, -2):
assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
assert_allclose(spnorm(S, 'f', axis=axis),
npnorm(M, 'f', axis=axis))
assert_allclose(spnorm(S, 'fro', axis=axis),
npnorm(M, 'fro', axis=axis))
@dec.skipif(NumpyVersion(np.__version__) < '1.8.0')
def test_sparse_vector_norms(self):
for sparse_type in self._sparse_types:
for M in self._test_matrices:
S = sparse_type(M)
for axis in (0, 1, -1, -2, (0, ), (1, ), (-1, ), (-2, )):
assert_allclose(spnorm(S, axis=axis), npnorm(M, axis=axis))
for ord in None, 2, np.inf, -np.inf, 1, 0.5, 0.42:
assert_allclose(spnorm(S, ord, axis=axis),
npnorm(M, ord, axis=axis))
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