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
|
# Copyright 2017, 2018 Christoph Groth (CEA).
#
# This file is part of Vquad. It is subject to the license terms in the file
# LICENSE.rst found in the top-level directory of this distribution.
import numpy as np
from numpy.testing import assert_allclose
from pytest import raises
from .. import core
def f0(x):
return x * np.sin(1/x) * np.sqrt(abs(1 - x))
def f7(x):
return x**-0.5
def f24(x):
return np.floor(np.exp(x))
def f21(x):
y = 0
for i in range(1, 4):
y += 1 / np.cosh(20**i * (x - 2 * i / 10))
return y
def f63(x, alpha, beta):
return abs(x - beta) ** alpha
def F63(x, alpha, beta):
return (x - beta) * abs(x - beta) ** alpha / (alpha + 1)
def fdiv(x):
return abs(x - 0.987654321) ** -1.1
def f_one_with_nan(x):
x = np.asarray(x)
result = np.ones(x.shape)
result[x == 0] = np.inf
return result
def test_coeffs(level=3):
vals = np.abs(core.tbls.nodes[level])
vals[1::2] = np.nan
c_downdated = core._calc_coeffs(vals, level)
level -= 1
vals = np.abs(core.tbls.nodes[level])
c = core._calc_coeffs(vals, level)
assert_allclose(c_downdated[:len(c)], c, rtol=0, atol=1e-12)
vals_from_c = core._eval_legendre(c, core.tbls.nodes[level])
assert_allclose(vals_from_c, vals, rtol=0, atol=1e-15)
def test_integration():
old_settings = np.seterr(all='ignore')
igral, err = core.vquad(f0, 0, 3, 1e-5)
assert_allclose(igral, 1.98194117954329, 1e-15)
assert_allclose(err, 1.9563545589988155e-05, 1e-10)
igral, err = core.vquad(f7, 0, 1, 1e-6)
assert_allclose(igral, 1.9999998579359648, 1e-15)
assert_allclose(err, 1.8561437334964041e-06, 1e-10)
igral, err = core.vquad(f24, 0, 3, 1e-3)
assert_allclose(igral, 17.664696186312934, 1e-15)
assert_allclose(err, 0.017602618074957457, 1e-10)
igral, err = core.vquad(f21, 0, 1, 1e-3)
assert_allclose(igral, 0.16310022131213361, 1e-15)
assert_allclose(err, 0.00011848806384952786, 1e-10)
igral, err = core.vquad(f_one_with_nan, -1, 1, 1e-12)
assert_allclose(igral, 2, 1e-15)
assert_allclose(err, 2.4237853822937613e-15, 1e-7)
try:
igral, err = core.vquad(fdiv, 0, 1, 1e-6)
except core.DivergentIntegralError as e:
assert e.igral == np.inf
assert e.err is None
np.seterr(**old_settings)
def test_interpolation():
vquad = core.Vquad(f24, 0, 3)
vquad.improve_until(1e-6)
rng = np.random.RandomState(123)
x = np.linspace(0, 3, 100)
rng.shuffle(x)
for x in [x, 1.23, [[2, 0], [1, 2]], [], [[]]]:
assert_allclose(vquad(x), f24(x))
for x in [-1e-100, 3.0001, 1e100, [1, 2, -1e50]]:
raises(ValueError, vquad, x)
def test_analytic(n=200):
def f(x):
return f63(x, alpha, beta)
def F(x):
return F63(x, alpha, beta)
old_settings = np.seterr(all='ignore')
np.random.seed(123)
params = np.empty((n, 2))
params[:, 0] = np.linspace(-0.5, -1.5, n)
params[:, 1] = np.random.random_sample(n)
false_negatives = 0
false_positives = 0
for alpha, beta in params:
try:
igral, err = core.vquad(f, 0, 1, 1e-3)
except core.DivergentIntegralError:
assert alpha < -0.8
false_negatives += alpha > -1
else:
if alpha <= -1:
false_positives += 1
else:
igral_exact = F(1) - F(0)
assert alpha < -0.7 or abs(igral - igral_exact) < err
assert false_negatives < 0.05 * n
assert false_positives < 0.05 * n
np.seterr(**old_settings)
|
