pywafo/wafo/tests/test_gaussian.py

'''
Created on 17. juli 2010

@author: pab
'''
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) < err0 + terr0)

    t = 'E0 = %2.5f' % E0
    t_true = 'E0 = %2.5f' % 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) < err0 + terr0)

    t = 'E1 = %2.5f' % E1
    assert(t == 'E1 = 0.00195')

    # 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)
    assert(err < 0.001)
    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 doctest
    doctest.testmod()