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170 lines
4.6 KiB
Python
170 lines
4.6 KiB
Python
'''
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Created on 17. juli 2010
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@author: pab
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'''
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import numpy as np
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from numpy import pi, inf
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from numpy.testing import assert_array_almost_equal
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from wafo.gaussian import (Rind, prbnormtndpc, prbnormndpc, prbnormnd,
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cdfnorm2d, prbnorm2d)
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def test_rind():
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Et = 0.001946 # exact prob.
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n = 5
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Blo = -np.inf
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Bup = -1.2
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indI = [-1, n - 1] # Barriers
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m = np.zeros(n)
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rho = 0.3
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Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n)
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rind = Rind()
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E0, err0, terr0 = rind(Sc, m, Blo, Bup, indI)
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assert(np.abs(E0 - Et) < err0 + terr0)
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t = 'E0 = %2.5f' % E0
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t_true = 'E0 = %2.5f' % Et
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assert(t == t_true)
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A = np.repeat(Blo, n)
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B = np.repeat(Bup, n) # Integration limits
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E1, _err1, _terr1 = rind(np.triu(Sc), m, A, B) # same as E0
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assert(np.abs(E1 - Et) < err0 + terr0)
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t = 'E1 = %2.5f' % E1
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assert(t == 'E1 = 0.00195')
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# Compute expectation E( abs(X1*X2*...*X5) )
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xc = np.zeros((0, 1))
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infinity = 37
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dev = np.sqrt(np.diag(Sc)) # std
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ind = np.nonzero(indI[1:])[0]
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Bup, Blo = np.atleast_2d(Bup, Blo)
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Bup[0, ind] = np.minimum(Bup[0, ind], infinity * dev[indI[ind + 1]])
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Blo[0, ind] = np.maximum(Blo[0, ind], -infinity * dev[indI[ind + 1]])
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val, err, terr = rind(Sc, m, Blo, Bup, indI, xc, nt=0)
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assert_array_almost_equal(val, 0.05494076)
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assert(err < 0.001)
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assert_array_almost_equal(terr, 1.00000000e-10)
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# Compute expectation E( X1^{+}*X2^{+} ) with random
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# correlation coefficient,Cov(X1,X2) = rho2.
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m2 = [0, 0]
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rho2 = 0.3 # np.random.rand(1)
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Sc2 = [[1, rho2], [rho2, 1]]
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Blo2 = 0
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Bup2 = np.inf
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indI2 = [-1, 1]
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rind2 = Rind(method=1)
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def g2(x):
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return (x * (np.pi / 2 + np.arcsin(x)) +
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np.sqrt(1 - x**2)) / (2 * np.pi)
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assert_array_almost_equal(g2(rho2), 0.24137214191774381) # exact value
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E3, err3, terr3 = rind(Sc2, m2, Blo2, Bup2, indI2, nt=0)
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assert_array_almost_equal(E3, 0.24127499)
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assert_array_almost_equal(err3, 0.00013838)
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assert_array_almost_equal(terr3, 1.00000000e-10)
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E4, err4, terr4 = rind2(Sc2, m2, Blo2, Bup2, indI2, nt=0)
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assert_array_almost_equal(E4, 0.24127499)
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assert_array_almost_equal(err4, 0.00013838)
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assert_array_almost_equal(terr4, 1.00000000e-10)
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#
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# >>> E5, err5, terr5 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0,abseps=1e-4)
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# array([ 0.24127499])
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# array([ 0.00013838])
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# array([ 1.00000000e-10])
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def test_prbnormtndpc():
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rho2 = np.random.rand(2)
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a2 = np.zeros(2)
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b2 = np.repeat(np.inf, 2)
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val2, err2, _ift2 = prbnormtndpc(rho2, a2, b2)
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def g2(x):
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return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi)
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E2 = g2(rho2) # exact value
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assert(np.abs(E2 - val2) < err2)
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rho3 = np.random.rand(3)
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a3 = np.zeros(3)
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b3 = np.repeat(inf, 3)
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val3, err3, _ift3 = prbnormtndpc(rho3, a3, b3)
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def g3(x):
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return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2],
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x[1] * x[2]]))) / (4 * pi)
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E3 = g3(rho3) # Exact value
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assert(np.abs(E3 - val3) < err3)
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def test_prbnormndpc():
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rho2 = np.random.rand(2)
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a2 = np.zeros(2)
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b2 = np.repeat(np.inf, 2)
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val2, err2, _ift2 = prbnormndpc(rho2, a2, b2)
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def g2(x):
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return 0.25 + np.arcsin(x[0] * x[1]) / (2 * pi)
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E2 = g2(rho2) # exact value
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assert(np.abs(E2 - val2) < err2)
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rho3 = np.random.rand(3)
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a3 = np.zeros(3)
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b3 = np.repeat(inf, 3)
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val3, err3, _ift3 = prbnormndpc(rho3, a3, b3)
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def g3(x):
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return 0.5 - sum(np.sort(np.arccos([x[0] * x[1], x[0] * x[2],
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x[1] * x[2]]))) / (4 * pi)
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E3 = g3(rho3) # Exact value
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assert(np.abs(E3 - val3) < err3)
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def test_prbnormnd():
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Et = 0.001946 # exact prob.
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n = 5
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Blo = -np.inf
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Bup = -1.2
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m = np.zeros(n)
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rho = 0.3
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Sc = (np.ones((n, n)) - np.eye(n)) * rho + np.eye(n)
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A = np.repeat(Blo, n)
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B = np.repeat(Bup, n) - m
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[val, err, _inform] = prbnormnd(Sc, A, B)
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assert(np.abs(val - Et) < err)
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t = 'val = %2.5f' % val
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assert(t == 'val = 0.00195')
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def test_cdfnorm2d():
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x = np.linspace(-3, 3, 3)
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[b1, b2] = np.meshgrid(x, x)
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r = 0.3
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truth = [[2.38515157e-05, 1.14504149e-03, 1.34987703e-03],
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[1.14504149e-03, 2.98493342e-01, 4.99795143e-01],
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[1.34987703e-03, 4.99795143e-01, 9.97324055e-01]]
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assert_array_almost_equal(cdfnorm2d(b1, b2, r), truth)
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def test_prbnorm2d():
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a = [-1, -2]
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b = [1, 1]
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r = 0.3
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assert_array_almost_equal(prbnorm2d(a, b, r), 0.56659121)
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if __name__ == '__main__':
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import doctest
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doctest.testmod()
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