"""Test functions for matrix module
"""
from __future__ import division, absolute_import, print_function
from numpy.testing import (
TestCase, run_module_suite, assert_equal, assert_array_equal,
assert_array_max_ulp, assert_array_almost_equal, assert_raises,
)
from numpy import (
arange, add, fliplr, flipud, zeros, ones, eye, array, diag,
histogram2d, tri, mask_indices, triu_indices, triu_indices_from,
tril_indices, tril_indices_from, vander,
)
import numpy as np
from numpy.compat import asbytes_nested
def get_mat(n):
data = arange(n)
data = add.outer(data, data)
return data
class TestEye(TestCase):
def test_basic(self):
assert_equal(eye(4),
array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
assert_equal(eye(4, dtype='f'),
array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]], 'f'))
assert_equal(eye(3) == 1,
eye(3, dtype=bool))
def test_diag(self):
assert_equal(eye(4, k=1),
array([[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
[0, 0, 0, 0]]))
assert_equal(eye(4, k=-1),
array([[0, 0, 0, 0],
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0]]))
def test_2d(self):
assert_equal(eye(4, 3),
array([[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[0, 0, 0]]))
assert_equal(eye(3, 4),
array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0]]))
def test_diag2d(self):
assert_equal(eye(3, 4, k=2),
array([[0, 0, 1, 0],
[0, 0, 0, 1],
[0, 0, 0, 0]]))
assert_equal(eye(4, 3, k=-2),
array([[0, 0, 0],
[0, 0, 0],
[1, 0, 0],
[0, 1, 0]]))
def test_eye_bounds(self):
assert_equal(eye(2, 2, 1), [[0, 1], [0, 0]])
assert_equal(eye(2, 2, -1), [[0, 0], [1, 0]])
assert_equal(eye(2, 2, 2), [[0, 0], [0, 0]])
assert_equal(eye(2, 2, -2), [[0, 0], [0, 0]])
assert_equal(eye(3, 2, 2), [[0, 0], [0, 0], [0, 0]])
assert_equal(eye(3, 2, 1), [[0, 1], [0, 0], [0, 0]])
assert_equal(eye(3, 2, -1), [[0, 0], [1, 0], [0, 1]])
assert_equal(eye(3, 2, -2), [[0, 0], [0, 0], [1, 0]])
assert_equal(eye(3, 2, -3), [[0, 0], [0, 0], [0, 0]])
def test_strings(self):
assert_equal(eye(2, 2, dtype='S3'),
asbytes_nested([['1', ''], ['', '1']]))
def test_bool(self):
assert_equal(eye(2, 2, dtype=bool), [[True, False], [False, True]])
class TestDiag(TestCase):
def test_vector(self):
vals = (100 * arange(5)).astype('l')
b = zeros((5, 5))
for k in range(5):
b[k, k] = vals[k]
assert_equal(diag(vals), b)
b = zeros((7, 7))
c = b.copy()
for k in range(5):
b[k, k + 2] = vals[k]
c[k + 2, k] = vals[k]
assert_equal(diag(vals, k=2), b)
assert_equal(diag(vals, k=-2), c)
def test_matrix(self, vals=None):
if vals is None:
vals = (100 * get_mat(5) + 1).astype('l')
b = zeros((5,))
for k in range(5):
b[k] = vals[k, k]
assert_equal(diag(vals), b)
b = b * 0
for k in range(3):
b[k] = vals[k, k + 2]
assert_equal(diag(vals, 2), b[:3])
for k in range(3):
b[k] = vals[k + 2, k]
assert_equal(diag(vals, -2), b[:3])
def test_fortran_order(self):
vals = array((100 * get_mat(5) + 1), order='F', dtype='l')
self.test_matrix(vals)
def test_diag_bounds(self):
A = [[1, 2], [3, 4], [5, 6]]
assert_equal(diag(A, k=2), [])
assert_equal(diag(A, k=1), [2])
assert_equal(diag(A, k=0), [1, 4])
assert_equal(diag(A, k=-1), [3, 6])
assert_equal(diag(A, k=-2), [5])
assert_equal(diag(A, k=-3), [])
def test_failure(self):
self.assertRaises(ValueError, diag, [[[1]]])
class TestFliplr(TestCase):
def test_basic(self):
self.assertRaises(ValueError, fliplr, ones(4))
a = get_mat(4)
b = a[:, ::-1]
assert_equal(fliplr(a), b)
a = [[0, 1, 2],
[3, 4, 5]]
b = [[2, 1, 0],
[5, 4, 3]]
assert_equal(fliplr(a), b)
class TestFlipud(TestCase):
def test_basic(self):
a = get_mat(4)
b = a[::-1, :]
assert_equal(flipud(a), b)
a = [[0, 1, 2],
[3, 4, 5]]
b = [[3, 4, 5],
[0, 1, 2]]
assert_equal(flipud(a), b)
class TestHistogram2d(TestCase):
def test_simple(self):
x = array(
[0.41702200, 0.72032449, 1.1437481e-4, 0.302332573, 0.146755891])
y = array(
[0.09233859, 0.18626021, 0.34556073, 0.39676747, 0.53881673])
xedges = np.linspace(0, 1, 10)
yedges = np.linspace(0, 1, 10)
H = histogram2d(x, y, (xedges, yedges))[0]
answer = array(
[[0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]])
assert_array_equal(H.T, answer)
H = histogram2d(x, y, xedges)[0]
assert_array_equal(H.T, answer)
H, xedges, yedges = histogram2d(list(range(10)), list(range(10)))
assert_array_equal(H, eye(10, 10))
assert_array_equal(xedges, np.linspace(0, 9, 11))
assert_array_equal(yedges, np.linspace(0, 9, 11))
def test_asym(self):
x = array([1, 1, 2, 3, 4, 4, 4, 5])
y = array([1, 3, 2, 0, 1, 2, 3, 4])
H, xed, yed = histogram2d(
x, y, (6, 5), range=[[0, 6], [0, 5]], normed=True)
answer = array(
[[0., 0, 0, 0, 0],
[0, 1, 0, 1, 0],
[0, 0, 1, 0, 0],
[1, 0, 0, 0, 0],
[0, 1, 1, 1, 0],
[0, 0, 0, 0, 1]])
assert_array_almost_equal(H, answer/8., 3)
assert_array_equal(xed, np.linspace(0, 6, 7))
assert_array_equal(yed, np.linspace(0, 5, 6))
def test_norm(self):
x = array([1, 2, 3, 1, 2, 3, 1, 2, 3])
y = array([1, 1, 1, 2, 2, 2, 3, 3, 3])
H, xed, yed = histogram2d(
x, y, [[1, 2, 3, 5], [1, 2, 3, 5]], normed=True)
answer = array([[1, 1, .5],
[1, 1, .5],
[.5, .5, .25]])/9.
assert_array_almost_equal(H, answer, 3)
def test_all_outliers(self):
r = np.random.rand(100) + 1. + 1e6 # histogramdd rounds by decimal=6
H, xed, yed = histogram2d(r, r, (4, 5), range=([0, 1], [0, 1]))
assert_array_equal(H, 0)
def test_empty(self):
a, edge1, edge2 = histogram2d([], [], bins=([0, 1], [0, 1]))
assert_array_max_ulp(a, array([[0.]]))
a, edge1, edge2 = histogram2d([], [], bins=4)
assert_array_max_ulp(a, np.zeros((4, 4)))
def test_binparameter_combination(self):
x = array(
[0, 0.09207008, 0.64575234, 0.12875982, 0.47390599,
0.59944483, 1])
y = array(
[0, 0.14344267, 0.48988575, 0.30558665, 0.44700682,
0.15886423, 1])
edges = (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1)
H, xe, ye = histogram2d(x, y, (edges, 4))
answer = array(
[[ 2., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 1., 0., 0., 0.],
[ 0., 1., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 1.]])
assert_array_equal(H, answer)
assert_array_equal(ye, array([0., 0.25, 0.5, 0.75, 1]))
H, xe, ye = histogram2d(x, y, (4, edges))
answer = array(
[[ 1., 1., 0., 1., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[ 0., 1., 0., 0., 1., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]])
assert_array_equal(H, answer)
assert_array_equal(xe, array([0., 0.25, 0.5, 0.75, 1]))
class TestTri(TestCase):
def test_dtype(self):
out = array([[1, 0, 0],
[1, 1, 0],
[1, 1, 1]])
assert_array_equal(tri(3), out)
assert_array_equal(tri(3, dtype=bool), out.astype(bool))
def test_tril_triu_ndim2():
for dtype in np.typecodes['AllFloat'] + np.typecodes['AllInteger']:
a = np.ones((2, 2), dtype=dtype)
b = np.tril(a)
c = np.triu(a)
yield assert_array_equal, b, [[1, 0], [1, 1]]
yield assert_array_equal, c, b.T
# should return the same dtype as the original array
yield assert_equal, b.dtype, a.dtype
yield assert_equal, c.dtype, a.dtype
def test_tril_triu_ndim3():
for dtype in np.typecodes['AllFloat'] + np.typecodes['AllInteger']:
a = np.array([
[[1, 1], [1, 1]],
[[1, 1], [1, 0]],
[[1, 1], [0, 0]],
], dtype=dtype)
a_tril_desired = np.array([
[[1, 0], [1, 1]],
[[1, 0], [1, 0]],
[[1, 0], [0, 0]],
], dtype=dtype)
a_triu_desired = np.array([
[[1, 1], [0, 1]],
[[1, 1], [0, 0]],
[[1, 1], [0, 0]],
], dtype=dtype)
a_triu_observed = np.triu(a)
a_tril_observed = np.tril(a)
yield assert_array_equal, a_triu_observed, a_triu_desired
yield assert_array_equal, a_tril_observed, a_tril_desired
yield assert_equal, a_triu_observed.dtype, a.dtype
yield assert_equal, a_tril_observed.dtype, a.dtype
def test_tril_triu_with_inf():
# Issue 4859
arr = np.array([[1, 1, np.inf],
[1, 1, 1],
[np.inf, 1, 1]])
out_tril = np.array([[1, 0, 0],
[1, 1, 0],
[np.inf, 1, 1]])
out_triu = out_tril.T
assert_array_equal(np.triu(arr), out_triu)
assert_array_equal(np.tril(arr), out_tril)
def test_tril_triu_dtype():
# Issue 4916
# tril and triu should return the same dtype as input
for c in np.typecodes['All']:
if c == 'V':
continue
arr = np.zeros((3, 3), dtype=c)
assert_equal(np.triu(arr).dtype, arr.dtype)
assert_equal(np.tril(arr).dtype, arr.dtype)
# check special cases
arr = np.array([['2001-01-01T12:00', '2002-02-03T13:56'],
['2004-01-01T12:00', '2003-01-03T13:45']],
dtype='datetime64')
assert_equal(np.triu(arr).dtype, arr.dtype)
assert_equal(np.tril(arr).dtype, arr.dtype)
arr = np.zeros((3,3), dtype='f4,f4')
assert_equal(np.triu(arr).dtype, arr.dtype)
assert_equal(np.tril(arr).dtype, arr.dtype)
def test_mask_indices():
# simple test without offset
iu = mask_indices(3, np.triu)
a = np.arange(9).reshape(3, 3)
yield (assert_array_equal, a[iu], array([0, 1, 2, 4, 5, 8]))
# Now with an offset
iu1 = mask_indices(3, np.triu, 1)
yield (assert_array_equal, a[iu1], array([1, 2, 5]))
def test_tril_indices():
# indices without and with offset
il1 = tril_indices(4)
il2 = tril_indices(4, k=2)
il3 = tril_indices(4, m=5)
il4 = tril_indices(4, k=2, m=5)
a = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
b = np.arange(1, 21).reshape(4, 5)
# indexing:
yield (assert_array_equal, a[il1],
array([1, 5, 6, 9, 10, 11, 13, 14, 15, 16]))
yield (assert_array_equal, b[il3],
array([1, 6, 7, 11, 12, 13, 16, 17, 18, 19]))
# And for assigning values:
a[il1] = -1
yield (assert_array_equal, a,
array([[-1, 2, 3, 4],
[-1, -1, 7, 8],
[-1, -1, -1, 12],
[-1, -1, -1, -1]]))
b[il3] = -1
yield (assert_array_equal, b,
array([[-1, 2, 3, 4, 5],
[-1, -1, 8, 9, 10],
[-1, -1, -1, 14, 15],
[-1, -1, -1, -1, 20]]))
# These cover almost the whole array (two diagonals right of the main one):
a[il2] = -10
yield (assert_array_equal, a,
array([[-10, -10, -10, 4],
[-10, -10, -10, -10],
[-10, -10, -10, -10],
[-10, -10, -10, -10]]))
b[il4] = -10
yield (assert_array_equal, b,
array([[-10, -10, -10, 4, 5],
[-10, -10, -10, -10, 10],
[-10, -10, -10, -10, -10],
[-10, -10, -10, -10, -10]]))
class TestTriuIndices(object):
def test_triu_indices(self):
iu1 = triu_indices(4)
iu2 = triu_indices(4, k=2)
iu3 = triu_indices(4, m=5)
iu4 = triu_indices(4, k=2, m=5)
a = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
b = np.arange(1, 21).reshape(4, 5)
# Both for indexing:
yield (assert_array_equal, a[iu1],
array([1, 2, 3, 4, 6, 7, 8, 11, 12, 16]))
yield (assert_array_equal, b[iu3],
array([1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 19, 20]))
# And for assigning values:
a[iu1] = -1
yield (assert_array_equal, a,
array([[-1, -1, -1, -1],
[5, -1, -1, -1],
[9, 10, -1, -1],
[13, 14, 15, -1]]))
b[iu3] = -1
yield (assert_array_equal, b,
array([[-1, -1, -1, -1, -1],
[6, -1, -1, -1, -1],
[11, 12, -1, -1, -1],
[16, 17, 18, -1, -1]]))
# These cover almost the whole array (two diagonals right of the
# main one):
a[iu2] = -10
yield (assert_array_equal, a,
array([[-1, -1, -10, -10],
[5, -1, -1, -10],
[9, 10, -1, -1],
[13, 14, 15, -1]]))
b[iu4] = -10
yield (assert_array_equal, b,
array([[-1, -1, -10, -10, -10],
[6, -1, -1, -10, -10],
[11, 12, -1, -1, -10],
[16, 17, 18, -1, -1]]))
class TestTrilIndicesFrom(object):
def test_exceptions(self):
assert_raises(ValueError, tril_indices_from, np.ones((2,)))
assert_raises(ValueError, tril_indices_from, np.ones((2, 2, 2)))
# assert_raises(ValueError, tril_indices_from, np.ones((2, 3)))
class TestTriuIndicesFrom(object):
def test_exceptions(self):
assert_raises(ValueError, triu_indices_from, np.ones((2,)))
assert_raises(ValueError, triu_indices_from, np.ones((2, 2, 2)))
# assert_raises(ValueError, triu_indices_from, np.ones((2, 3)))
class TestVander(object):
def test_basic(self):
c = np.array([0, 1, -2, 3])
v = vander(c)
powers = np.array([[0, 0, 0, 0, 1],
[1, 1, 1, 1, 1],
[16, -8, 4, -2, 1],
[81, 27, 9, 3, 1]])
# Check default value of N:
yield (assert_array_equal, v, powers[:, 1:])
# Check a range of N values, including 0 and 5 (greater than default)
m = powers.shape[1]
for n in range(6):
v = vander(c, N=n)
yield (assert_array_equal, v, powers[:, m-n:m])
def test_dtypes(self):
c = array([11, -12, 13], dtype=np.int8)
v = vander(c)
expected = np.array([[121, 11, 1],
[144, -12, 1],
[169, 13, 1]])
yield (assert_array_equal, v, expected)
c = array([1.0+1j, 1.0-1j])
v = vander(c, N=3)
expected = np.array([[2j, 1+1j, 1],
[-2j, 1-1j, 1]])
# The data is floating point, but the values are small integers,
# so assert_array_equal *should* be safe here (rather than, say,
# assert_array_almost_equal).
yield (assert_array_equal, v, expected)
if __name__ == "__main__":
run_module_suite()
