from scipy.interpolate import interp1d from scipy.weave import inline, converters n_int = 10 # number of discretization points n_k = 2 # number of random variables # set the mean and standard deviation of the two random variables la_mean, la_stdev = 0.0, 0.2 xi_mean, xi_stdev = 0.019027, 0.0022891 # construct the normal distributions and get the methods # for the evaluation of the probability density functions g_la = uniform( loc = la_mean, scale = la_stdev ) g_xi = weibull_min( 10., scale = 0.02 ) # generate the grids for integration covering major part of the random domains Theta_la = linspace( la_mean + 0.5 * la_stdev / n_int, la_mean + la_stdev - 0.5 * la_stdev / n_int, n_int ) delta_xi = ( xi_mean + ( 4 * xi_stdev ) - xi_mean + ( 4 * xi_stdev ) ) / n_int Theta_xi = linspace( xi_mean - ( 4 * xi_stdev ) + 0.5 * delta_xi, xi_mean + ( 4 * xi_stdev ) - 0.5 * delta_xi, n_int ) # LHS generate the grids for integration covering major part of the random domains T_la = g_la.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ) ) T_xi = g_xi.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ) ) # MC generation T_la_MC = g_la.rvs( n_int ** n_k ) T_xi_MC = g_xi.rvs( n_int ** n_k ) #T_la_MC = array( zip( *sorted( zip( random( n_int ** n_k ), g_la.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ** n_k ) ) ) ) )[1] ) #T_xi_MC = array( zip( *sorted( zip( random( n_int ** n_k ), g_xi.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ** n_k ) ) ) ) )[1] ) print diff( sort( g_la.cdf( g_la.rvs( 10 ) ) ) ) print 'MC - correlation between la and xi', corrcoef( T_la_MC, T_xi_MC )
from numpy import vectorize, linspace, zeros_like, sign, sum as nsum, ones, \
corrcoef, sort, diff, array, exp, min, sqrt
from numpy.random import random
from time import clock
n_int = 10 # number of discretization points
n_k = 1 # number of random variables
# set the mean and standard deviation of the two random variables
xi_mean, xi_stdev = 0.019027, 0.0022891
# construct the normal distributions and get the methods
# for the evaluation of the probability density functions
s = 0.02
m = 10.
g_xi = weibull_min( m, scale = s ) #norm( loc = xi_mean, scale = xi_stdev )
# generate the grids for integration covering major part of the random domains
delta_xi = ( xi_mean + ( 4 * xi_stdev ) - xi_mean + ( 4 * xi_stdev ) ) / n_int
Theta_xi = linspace( xi_mean - ( 4 * xi_stdev ) + 0.5 * delta_xi, xi_mean + ( 4 * xi_stdev ) - 0.5 * delta_xi, n_int )
# LHS generate the grids for integration covering major part of the random domains
T_xi = g_xi.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ) ) #g_xi.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ) )
# MC generation
T_xi_MC = g_xi.rvs( n_int ** n_k )
#T_xi_MC = array( zip( *sorted( zip( random( n_int ** n_k ), g_xi.ppf( linspace( 0.5 / n_int, 1. - 0.5 / n_int, n_int ** n_k ) ) ) ) )[1] )
# grid spacing
d_xi = delta_xi#( Theta_xi[-1] - Theta_xi[0] ) / n_int
def Heaviside( x ):
''' Heaviside function '''
