1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
""" Test functions for linalg module
"""
from numpy.testing import *
set_package_path()
from numpy import array, single, double, csingle, cdouble, dot, identity
from numpy import multiply, atleast_2d, inf, asarray, matrix
from numpy import linalg
from linalg import matrix_power
restore_path()
def ifthen(a, b):
return not a or b
old_assert_almost_equal = assert_almost_equal
def imply(a, b):
return not a or b
def assert_almost_equal(a, b, **kw):
if asarray(a).dtype.type in (single, csingle):
decimal = 6
else:
decimal = 12
old_assert_almost_equal(a, b, decimal=decimal, **kw)
class LinalgTestCase(NumpyTestCase):
def check_single(self):
a = array([[1.,2.], [3.,4.]], dtype=single)
b = array([2., 1.], dtype=single)
self.do(a, b)
def check_double(self):
a = array([[1.,2.], [3.,4.]], dtype=double)
b = array([2., 1.], dtype=double)
self.do(a, b)
def check_csingle(self):
a = array([[1.+2j,2+3j], [3+4j,4+5j]], dtype=csingle)
b = array([2.+1j, 1.+2j], dtype=csingle)
self.do(a, b)
def check_cdouble(self):
a = array([[1.+2j,2+3j], [3+4j,4+5j]], dtype=cdouble)
b = array([2.+1j, 1.+2j], dtype=cdouble)
self.do(a, b)
def check_empty(self):
a = atleast_2d(array([], dtype = double))
b = atleast_2d(array([], dtype = double))
try:
self.do(a, b)
raise AssertionError("%s should fail with empty matrices", self.__name__[5:])
except linalg.LinAlgError, e:
pass
def check_nonarray(self):
a = [[1,2], [3,4]]
b = [2, 1]
self.do(a,b)
def check_matrix_b_only(self):
"""Check that matrix type is preserved."""
a = array([[1.,2.], [3.,4.]])
b = matrix([2., 1.]).T
self.do(a, b)
def check_matrix_a_and_b(self):
"""Check that matrix type is preserved."""
a = matrix([[1.,2.], [3.,4.]])
b = matrix([2., 1.]).T
self.do(a, b)
class TestSolve(LinalgTestCase):
def do(self, a, b):
x = linalg.solve(a, b)
assert_almost_equal(b, dot(a, x))
assert imply(isinstance(b, matrix), isinstance(x, matrix))
class TestInv(LinalgTestCase):
def do(self, a, b):
a_inv = linalg.inv(a)
assert_almost_equal(dot(a, a_inv), identity(asarray(a).shape[0]))
assert imply(isinstance(a, matrix), isinstance(a_inv, matrix))
class TestEigvals(LinalgTestCase):
def do(self, a, b):
ev = linalg.eigvals(a)
evalues, evectors = linalg.eig(a)
assert_almost_equal(ev, evalues)
class TestEig(LinalgTestCase):
def do(self, a, b):
evalues, evectors = linalg.eig(a)
assert_almost_equal(dot(a, evectors), multiply(evectors, evalues))
assert imply(isinstance(a, matrix), isinstance(evectors, matrix))
class TestSVD(LinalgTestCase):
def do(self, a, b):
u, s, vt = linalg.svd(a, 0)
assert_almost_equal(a, dot(multiply(u, s), vt))
assert imply(isinstance(a, matrix), isinstance(u, matrix))
assert imply(isinstance(a, matrix), isinstance(vt, matrix))
class TestCondSVD(LinalgTestCase):
def do(self, a, b):
c = asarray(a) # a might be a matrix
s = linalg.svd(c, compute_uv=False)
old_assert_almost_equal(s[0]/s[-1], linalg.cond(a), decimal=5)
class TestCond2(LinalgTestCase):
def do(self, a, b):
c = asarray(a) # a might be a matrix
s = linalg.svd(c, compute_uv=False)
old_assert_almost_equal(s[0]/s[-1], linalg.cond(a,2), decimal=5)
class TestCondInf(NumpyTestCase):
def test(self):
A = array([[1.,0,0],[0,-2.,0],[0,0,3.]])
assert_almost_equal(linalg.cond(A,inf),3.)
class TestPinv(LinalgTestCase):
def do(self, a, b):
a_ginv = linalg.pinv(a)
assert_almost_equal(dot(a, a_ginv), identity(asarray(a).shape[0]))
assert imply(isinstance(a, matrix), isinstance(a_ginv, matrix))
class TestDet(LinalgTestCase):
def do(self, a, b):
d = linalg.det(a)
if asarray(a).dtype.type in (single, double):
ad = asarray(a).astype(double)
else:
ad = asarray(a).astype(cdouble)
ev = linalg.eigvals(ad)
assert_almost_equal(d, multiply.reduce(ev))
class TestLstsq(LinalgTestCase):
def do(self, a, b):
u, s, vt = linalg.svd(a, 0)
x, residuals, rank, sv = linalg.lstsq(a, b)
assert_almost_equal(b, dot(a, x))
assert_equal(rank, asarray(a).shape[0])
assert_almost_equal(sv, sv.__array_wrap__(s))
assert imply(isinstance(b, matrix), isinstance(x, matrix))
assert imply(isinstance(b, matrix), isinstance(residuals, matrix))
class TestMatrixPower(ParametricTestCase):
R90 = array([[0,1],[-1,0]])
Arb22 = array([[4,-7],[-2,10]])
noninv = array([[1,0],[0,0]])
arbfloat = array([[0.1,3.2],[1.2,0.7]])
large = identity(10)
t = large[1,:].copy()
large[1,:] = large[0,:]
large[0,:] = t
def test_large_power(self):
assert_equal(matrix_power(self.R90,2L**100+2**10+2**5+1),self.R90)
def test_large_power_trailing_zero(self):
assert_equal(matrix_power(self.R90,2L**100+2**10+2**5),identity(2))
def testip_zero(self):
def tz(M):
mz = matrix_power(M,0)
assert_equal(mz, identity(M.shape[0]))
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_one(self):
def tz(M):
mz = matrix_power(M,1)
assert_equal(mz, M)
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_two(self):
def tz(M):
mz = matrix_power(M,2)
assert_equal(mz, dot(M,M))
assert_equal(mz.dtype, M.dtype)
for M in [self.Arb22, self.arbfloat, self.large]:
yield tz, M
def testip_invert(self):
def tz(M):
mz = matrix_power(M,-1)
assert_almost_equal(identity(M.shape[0]), dot(mz,M))
for M in [self.R90, self.Arb22, self.arbfloat, self.large]:
yield tz, M
def test_invert_noninvertible(self):
import numpy.linalg
self.assertRaises(numpy.linalg.linalg.LinAlgError,
lambda: matrix_power(self.noninv,-1))
class TestBoolPower(NumpyTestCase):
def check_square(self):
A = array([[True,False],[True,True]])
assert_equal(matrix_power(A,2),A)
if __name__ == '__main__':
NumpyTest().run()
|
