pywafo/wafo/tests/test_gaussian.py

'''
Created on 17. juli 2010

@author: pab
'''
import numpy as np  # @UnusedImport
from numpy import pi, inf  # @UnusedImport
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 = %2.6f' % E0
    assert(t == 'E0 = 0.001946')

    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)
    g2 = lambda x: (
        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)
    >>> g2 = lambda x : 0.25+np.arcsin(x[0]*x[1])/(2*pi)
    >>> E2 = g2(rho2)  #% exact value
    >>> np.abs(E2-val2)<err2
    True

    >>> rho3 = np.random.rand(3)
    >>> a3   = np.zeros(3)
    >>> b3   = np.repeat(inf,3)
    >>> [val3,err3, ift3] = prbnormtndpc(rho3,a3,b3)
    >>> g3 = lambda x : 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
    >>> np.abs(E3-val3)<err3
    True
    '''


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)
    >>> g2 = lambda x : 0.25+np.arcsin(x[0]*x[1])/(2*pi)
    >>> E2 = g2(rho2)  #% exact value
    >>> np.abs(E2-val2)<err2
    True

    >>> rho3 = np.random.rand(3)
    >>> a3   = np.zeros(3)
    >>> b3   = np.repeat(inf,3)
    >>> [val3,err3, ift3] = prbnormndpc(rho3,a3,b3)
    >>> g3 = lambda x : 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
    >>> np.abs(E3-val3)<err2
    True
    '''


def test_prbnormnd():
    '''
    >>> import numpy as np
    >>> 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)
    >>> np.abs(val-Et)< err
    True
    >>> 'val = %2.5f' % val
    'val = 0.00195'
    '''


def test_cdfnorm2d():
    '''
    >>> x = np.linspace(-3,3,3)
    >>> [b1,b2] = np.meshgrid(x,x)
    >>> r  = 0.3
    >>> cdfnorm2d(b1,b2,r)
    array([[  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]])
    '''


def test_prbnorm2d():
    '''
    >>> a = [-1, -2]
    >>> b = [1, 1]
    >>> r = 0.3
    >>> prbnorm2d(a,b,r)
    array([ 0.56659121])
    '''
if __name__ == '__main__':
    import doctest
    doctest.testmod()