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pywafo/wafo/tests/test_gaussian.py

171 lines
4.7 KiB
Python

'''
Created on 17. juli 2010
@author: pab
'''
import unittest
import numpy as np
from numpy import pi, inf
from numpy.testing import assert_array_almost_equal
from wafo.gaussian import (Rind, prbnormtndpc, prbnormndpc, prbnormnd,
cdfnorm2d, prbnorm2d)
def test_rind():
Et = 0.001946 # exact prob.
n = 5
Blo = -np.inf
Bup = -1.2
indI = [-1, n - 1] # Barriers
m = np.zeros(n)
rho = 0.3
Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n)
rind = Rind()
E0, err0, terr0 = rind(Sc, m, Blo, Bup, indI)
assert(np.abs(E0 - Et) < 2*(err0 + terr0))
t = '%2.4f' % E0
t_true = '%2.4f' % Et
assert(t == t_true)
A = np.repeat(Blo, n)
B = np.repeat(Bup, n) # Integration limits
E1, err1, terr1 = rind(np.triu(Sc), m, A, B) # same as E0
assert(np.abs(E1 - Et) < 2*(err1 + terr1))
t = '%2.4f' % E1
assert(t == t_true)
# Compute expectation E( abs(X1*X2*...*X5) )
xc = np.zeros((0, 1))
infinity = 37
dev = np.sqrt(np.diag(Sc)) # std
ind = np.nonzero(indI[1:])[0]
Bup, Blo = np.atleast_2d(Bup, Blo)
Bup[0, ind] = np.minimum(Bup[0, ind], infinity * dev[indI[ind + 1]])
Blo[0, ind] = np.maximum(Blo[0, ind], -infinity * dev[indI[ind + 1]])
val, err, terr = rind(Sc, m, Blo, Bup, indI, xc, nt=0)
assert_array_almost_equal(val, 0.05494076, decimal=3)
assert(err < 0.0013)
assert_array_almost_equal(terr, 1.00000000e-10)
# Compute expectation E( X1^{+}*X2^{+} ) with random
# correlation coefficient,Cov(X1,X2) = rho2.
m2 = [0, 0]
rho2 = 0.3 # np.random.rand(1)
Sc2 = [[1, rho2], [rho2, 1]]
Blo2 = 0
Bup2 = np.inf
indI2 = [-1, 1]
rind2 = Rind(method=1)
def g2(x):
return (x * (np.pi / 2 + np.arcsin(x)) +
np.sqrt(1 - x**2)) / (2 * np.pi)
assert_array_almost_equal(g2(rho2), 0.24137214191774381) # exact value
E3, err3, terr3 = rind(Sc2, m2, Blo2, Bup2, indI2, nt=0)
assert_array_almost_equal(E3, 0.24127499)
assert_array_almost_equal(err3, 0.00013838)
assert_array_almost_equal(terr3, 1.00000000e-10)
E4, err4, terr4 = rind2(Sc2, m2, Blo2, Bup2, indI2, nt=0)
assert_array_almost_equal(E4, 0.24127499)
assert_array_almost_equal(err4, 0.00013838)
assert_array_almost_equal(terr4, 1.00000000e-10)
#
# >>> E5, err5, terr5 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0,abseps=1e-4)
# array([ 0.24127499])
# array([ 0.00013838])
# array([ 1.00000000e-10])
def test_prbnormtndpc():
rho2 = np.random.rand(2)
a2 = np.zeros(2)
b2 = np.repeat(np.inf, 2)
val2, err2, _ift2 = prbnormtndpc(rho2, a2, b2)
def g2(x):
return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi)
E2 = g2(rho2) # exact value
assert(np.abs(E2 - val2) < err2)
rho3 = np.random.rand(3)
a3 = np.zeros(3)
b3 = np.repeat(inf, 3)
val3, err3, _ift3 = prbnormtndpc(rho3, a3, b3)
def g3(x):
return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2],
x[1] * x[2]]))) / (4 * pi)
E3 = g3(rho3) # Exact value
assert(np.abs(E3 - val3) < err3)
def test_prbnormndpc():
rho2 = np.random.rand(2)
a2 = np.zeros(2)
b2 = np.repeat(np.inf, 2)
val2, err2, _ift2 = prbnormndpc(rho2, a2, b2)
def g2(x):
return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi)
E2 = g2(rho2) # exact value
assert(np.abs(E2 - val2) < err2)
rho3 = np.random.rand(3)
a3 = np.zeros(3)
b3 = np.repeat(inf, 3)
val3, err3, _ift3 = prbnormndpc(rho3, a3, b3)
def g3(x):
return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2],
x[1] * x[2]]))) / (4 * pi)
E3 = g3(rho3) # Exact value
assert(np.abs(E3 - val3) < err3)
def test_prbnormnd():
Et = 0.001946 # exact prob.
n = 5
Blo = -np.inf
Bup = -1.2
m = np.zeros(n)
rho = 0.3
Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n)
A = np.repeat(Blo, n)
B = np.repeat(Bup, n) - m
[val, err, _inform] = prbnormnd(Sc, A, B)
assert(np.abs(val - Et) < err)
t = 'val = %2.5f' % val
assert(t == 'val = 0.00195')
def test_cdfnorm2d():
x = np.linspace(-3, 3, 3)
[b1, b2] = np.meshgrid(x, x)
r = 0.3
truth = [[2.38515157e-05, 1.14504149e-03, 1.34987703e-03],
[1.14504149e-03, 2.98493342e-01, 4.99795143e-01],
[1.34987703e-03, 4.99795143e-01, 9.97324055e-01]]
assert_array_almost_equal(cdfnorm2d(b1, b2, r), truth)
def test_prbnorm2d():
a = [-1, -2]
b = [1, 1]
r = 0.3
assert_array_almost_equal(prbnorm2d(a, b, r), 0.56659121)
if __name__ == '__main__':
# import sys;sys.argv = ['', 'Test.testName']
unittest.main()