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159 lines
4.5 KiB
Python
159 lines
4.5 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 # @UnusedImport
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from numpy import pi, inf # @UnusedImport
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# @UnusedImport
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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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'''
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>>> Et = 0.001946 # # exact prob.
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>>> n = 5
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>>> Blo =-np.inf; Bup=-1.2; indI=[-1, n-1] # Barriers
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>>> m = np.zeros(n); 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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>>> np.abs(E0-Et)< err0+terr0
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array([ True], dtype=bool)
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>>> 'E0 = %2.6f' % E0
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'E0 = 0.001946'
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>>> A = np.repeat(Blo,n); 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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>>> np.abs(E1-Et)< err0+terr0
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array([ True], dtype=bool)
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>>> 'E1 = %2.5f' % E1
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'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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>>> rind(Sc,m,Blo,Bup,indI, xc, nt=0)
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(array([ 0.05494076]), array([ 0.00083066]), array([ 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; Bup2 = np.inf; indI2 = [-1, 1]
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>>> rind2 = Rind(method=1)
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>>> g2 = lambda x : (x*(np.pi/2+np.arcsin(x))+np.sqrt(1-x**2))/(2*np.pi)
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>>> E2 = g2(rho2); E2 # exact value
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0.24137214191774381
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>>> E3, err3, terr3 = rind(Sc2,m2,Blo2,Bup2,indI2,nt=0); E3;err3;terr3
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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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>>> E4, err4, terr4 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0); E4;err4;terr4
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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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>>> E5, err5, terr5 = rind2(Sc2,m2,Blo2,Bup2,indI2,nt=0,abseps=1e-4); E5;err5;terr5
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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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'''
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def test_prbnormtndpc():
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'''
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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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>>> g2 = lambda x : 0.25+np.arcsin(x[0]*x[1])/(2*pi)
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>>> E2 = g2(rho2) #% exact value
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>>> np.abs(E2-val2)<err2
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True
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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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>>> g3 = lambda x : 0.5-sum(np.sort(np.arccos([x[0]*x[1],x[0]*x[2],x[1]*x[2]])))/(4*pi)
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>>> E3 = g3(rho3) # Exact value
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>>> np.abs(E3-val3)<err3
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True
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'''
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def test_prbnormndpc():
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'''
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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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>>> g2 = lambda x : 0.25+np.arcsin(x[0]*x[1])/(2*pi)
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>>> E2 = g2(rho2) #% exact value
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>>> np.abs(E2-val2)<err2
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True
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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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>>> g3 = lambda x : 0.5-sum(np.sort(np.arccos([x[0]*x[1],x[0]*x[2],x[1]*x[2]])))/(4*pi)
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>>> E3 = g3(rho3) # Exact value
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>>> np.abs(E3-val3)<err2
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True
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'''
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def test_prbnormnd():
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'''
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>>> import numpy as np
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>>> Et = 0.001946 # # exact prob.
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>>> n = 5
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>>> Blo =-np.inf; Bup=-1.2
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>>> m = np.zeros(n); 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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>>> np.abs(val-Et)< err
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True
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>>> 'val = %2.5f' % val
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'val = 0.00195'
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'''
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def test_cdfnorm2d():
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'''
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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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>>> cdfnorm2d(b1,b2,r)
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array([[ 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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'''
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def test_prbnorm2d():
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'''
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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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>>> prbnorm2d(a,b,r)
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array([ 0.56659121])
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'''
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if __name__ == '__main__':
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import doctest
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doctest.testmod()
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