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# Copyright 2017 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 .. 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_downdate(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-9)
def test_integration():
old_settings = np.seterr(all='ignore')
igral, err, nr_points = core.vquad(f0, 0, 3, 1e-5)
assert_allclose(igral, 1.98194117954329, 1e-15)
assert_allclose(err, 1.9563545589988155e-05, 1e-10)
assert nr_points == 1129
igral, err, nr_points = core.vquad(f7, 0, 1, 1e-6)
assert_allclose(igral, 1.9999998579359648, 1e-15)
assert_allclose(err, 1.8561437334964041e-06, 1e-10)
assert nr_points == 693
igral, err, nr_points = core.vquad(f24, 0, 3, 1e-3)
assert_allclose(igral, 17.664696186312934, 1e-15)
assert_allclose(err, 0.017602618074957457, 1e-10)
assert nr_points == 4519
igral, err, nr_points = core.vquad(f21, 0, 1, 1e-3)
assert_allclose(igral, 0.16310022131213361, 1e-15)
assert_allclose(err, 0.00011848806384952786, 1e-10)
assert nr_points == 191
igral, err, nr_points = core.vquad(f_one_with_nan, -1, 1, 1e-12)
assert_allclose(igral, 2, 1e-15)
assert_allclose(err, 2.4237853822937613e-15, 1e-7)
assert nr_points == 33
try:
igral, err, nr_points = core.vquad(fdiv, 0, 1, 1e-6)
except core.DivergentIntegralError as e:
assert e.igral == np.inf
assert e.err is None
assert e.nr_points == 431
np.seterr(**old_settings)
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, nr_points = 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)
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