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
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
|
"""
Test Scipy functions versus mpmath, if available.
"""
import re
import numpy as np
from numpy.testing import dec
import scipy.special as sc
from scipy.special._testutils import FuncData, assert_func_equal
try:
import mpmath
except ImportError:
try:
import sympy.mpmath as mpmath
except ImportError:
mpmath = None
def mpmath_check(min_ver):
if mpmath is None:
return dec.skipif(True, "mpmath library is not present")
def try_int(v):
try: return int(v)
except ValueError: return v
def get_version(v):
return map(try_int, re.split('[^0-9]', v))
return dec.skipif(get_version(min_ver) > get_version(mpmath.__version__),
"mpmath %s required" % min_ver)
#------------------------------------------------------------------------------
# expi
#------------------------------------------------------------------------------
@mpmath_check('0.10')
def test_expi_complex():
dataset = []
for r in np.logspace(-99, 2, 10):
for p in np.linspace(0, 2*np.pi, 30):
z = r*np.exp(1j*p)
dataset.append((z, complex(mpmath.ei(z))))
dataset = np.array(dataset, dtype=np.complex_)
FuncData(sc.expi, dataset, 0, 1).check()
#------------------------------------------------------------------------------
# hyp2f1
#------------------------------------------------------------------------------
@mpmath_check('0.14')
def test_hyp2f1_strange_points():
pts = [
(2,-1,-1,0.7),
(2,-2,-2,0.7),
]
kw = dict(eliminate=True)
dataset = [p + (float(mpmath.hyp2f1(*p, **kw)),) for p in pts]
dataset = np.array(dataset, dtype=np.float_)
FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
@mpmath_check('0.13')
def test_hyp2f1_real_some_points():
pts = [
(1,2,3,0),
(1./3, 2./3, 5./6, 27./32),
(1./4, 1./2, 3./4, 80./81),
(2,-2,-3,3),
(2,-3,-2,3),
(2,-1.5,-1.5,3),
(1,2,3,0),
(0.7235, -1, -5, 0.3),
(0.25, 1./3, 2, 0.999),
(0.25, 1./3, 2, -1),
(2,3,5,0.99),
(3./2,-0.5,3,0.99),
(2,2.5,-3.25,0.999),
(-8, 18.016500331508873, 10.805295997850628, 0.90875647507000001),
(-10,900,-10.5,0.99),
(-10,900,10.5,0.99),
(-1,2,1,1.0),
(-1,2,1,-1.0),
(-3,13,5,1.0),
(-3,13,5,-1.0),
]
dataset = [p + (float(mpmath.hyp2f1(*p)),) for p in pts]
dataset = np.array(dataset, dtype=np.float_)
olderr = np.seterr(invalid='ignore')
try:
FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
finally:
np.seterr(**olderr)
@mpmath_check('0.14')
def test_hyp2f1_some_points_2():
# Taken from mpmath unit tests -- this point failed for mpmath 0.13 but
# was fixed in their SVN since then
pts = [
(112, (51,10), (-9,10), -0.99999),
(10,-900,10.5,0.99),
(10,-900,-10.5,0.99),
]
def fev(x):
if isinstance(x, tuple):
return float(x[0]) / x[1]
else:
return x
dataset = [tuple(map(fev, p)) + (float(mpmath.hyp2f1(*p)),) for p in pts]
dataset = np.array(dataset, dtype=np.float_)
FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-10).check()
@mpmath_check('0.13')
def test_hyp2f1_real_some():
dataset = []
for a in [-10, -5, -1.8, 1.8, 5, 10]:
for b in [-2.5, -1, 1, 7.4]:
for c in [-9, -1.8, 5, 20.4]:
for z in [-10, -1.01, -0.99, 0, 0.6, 0.95, 1.5, 10]:
try:
v = float(mpmath.hyp2f1(a, b, c, z))
except:
continue
dataset.append((a, b, c, z, v))
dataset = np.array(dataset, dtype=np.float_)
olderr = np.seterr(invalid='ignore')
try:
FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-9).check()
finally:
np.seterr(**olderr)
@mpmath_check('0.12')
@dec.slow
def test_hyp2f1_real_random():
dataset = []
npoints = 500
dataset = np.zeros((npoints, 5), np.float_)
np.random.seed(1234)
dataset[:,0] = np.random.pareto(1.5, npoints)
dataset[:,1] = np.random.pareto(1.5, npoints)
dataset[:,2] = np.random.pareto(1.5, npoints)
dataset[:,3] = 2*np.random.rand(npoints) - 1
dataset[:,0] *= (-1)**np.random.randint(2, npoints)
dataset[:,1] *= (-1)**np.random.randint(2, npoints)
dataset[:,2] *= (-1)**np.random.randint(2, npoints)
for ds in dataset:
if mpmath.__version__ < '0.14':
# mpmath < 0.14 fails for c too much smaller than a, b
if abs(ds[:2]).max() > abs(ds[2]):
ds[2] = abs(ds[:2]).max()
ds[4] = float(mpmath.hyp2f1(*tuple(ds[:4])))
FuncData(sc.hyp2f1, dataset, (0,1,2,3), 4, rtol=1e-9).check()
#------------------------------------------------------------------------------
# erf (complex)
#------------------------------------------------------------------------------
@mpmath_check('0.14')
def test_erf_complex():
# need to increase mpmath precision for this test
old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
try:
mpmath.mp.dps = 70
x1, y1 = np.meshgrid(np.linspace(-10, 1, 11), np.linspace(-10, 1, 11))
x2, y2 = np.meshgrid(np.logspace(-10, .8, 11), np.logspace(-10, .8, 11))
points = np.r_[x1.ravel(),x2.ravel()] + 1j*np.r_[y1.ravel(),y2.ravel()]
# note that the global accuracy of our complex erf algorithm is limited
# roughly to 2e-8
assert_func_equal(sc.erf, lambda x: complex(mpmath.erf(x)), points,
vectorized=False, rtol=2e-8)
finally:
mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
#------------------------------------------------------------------------------
# lpmv
#------------------------------------------------------------------------------
@mpmath_check('0.15')
def test_lpmv():
pts = []
for x in [-0.99, -0.557, 1e-6, 0.132, 1]:
pts.extend([
(1, 1, x),
(1, -1, x),
(-1, 1, x),
(-1, -2, x),
(1, 1.7, x),
(1, -1.7, x),
(-1, 1.7, x),
(-1, -2.7, x),
(1, 10, x),
(1, 11, x),
(3, 8, x),
(5, 11, x),
(-3, 8, x),
(-5, 11, x),
(3, -8, x),
(5, -11, x),
(-3, -8, x),
(-5, -11, x),
(3, 8.3, x),
(5, 11.3, x),
(-3, 8.3, x),
(-5, 11.3, x),
(3, -8.3, x),
(5, -11.3, x),
(-3, -8.3, x),
(-5, -11.3, x),
])
dataset = [p + (mpmath.legenp(p[1], p[0], p[2]),) for p in pts]
dataset = np.array(dataset, dtype=np.float_)
evf = lambda mu,nu,x: sc.lpmv(mu.astype(int), nu, x)
olderr = np.seterr(invalid='ignore')
try:
FuncData(evf, dataset, (0,1,2), 3, rtol=1e-10, atol=1e-14).check()
finally:
np.seterr(**olderr)
|
