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*! version 1 03 January 2012
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************************************************************************************************************
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* gausshermite2 : Estimate an integral of the form : f(x,y)g(x,y/mu,Sigma)dxdy where g(x,y/mu,Sigma) is the distribution function
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* of the bivariate normal distribution of mean mu and covariance matrix Sigma by Gauss Hermite quadratures
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*
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* Version 1: 03 January 2012
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*
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*
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* Mohand Feddag, University of Nantes - France
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* Mohand-Larbi.Feddag@univ-nantes.fr *
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* News about this program : http://anaqol.free.fr
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* FreeIRT Project : http://freeirt.free.fr
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*
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* Copyright 2012 Mohand Feddag
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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************************************************************************************************************
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program define gausshermite2,rclass
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version 11
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syntax anything [, Mu(string) Sigma(string) Nodes(integer 12) Display]
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tempfile gauss2
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qui capture save `gauss2',replace
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local save=0
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if _rc==0 {
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qui save `gauss2',replace
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local save=1
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}
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if "`mu'"=="" {
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tempname mu
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matrix `mu'=[0,0]
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}
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if "`sigma'"=="" {
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tempname sigma
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matrix `sigma'=[1,0\0,1]
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}
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tokenize `anything'
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drop _all
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qui set obs `=`nodes'*`nodes''
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tempname noeuds poids
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qui ghquadm `nodes' `noeuds' `poids'
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* Cholesky transformation for the covariance matrix sigma
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matrix C=cholesky(`sigma')
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*matrix list C
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local line=1
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qui gen x1=.
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qui gen x2=.
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qui gen poids1=.
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qui gen poids2=.
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forvalues i=1/`nodes' {
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forvalues j=1/`nodes' {
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qui replace x1=`noeuds'[1,`i'] *(sqrt(2)*C[1,1])+`mu'[1,1] in `line'
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qui replace x2=`noeuds'[1,`i'] *(sqrt(2)*C[2,1])+`noeuds'[1,`j'] *(sqrt(2)*C[2,2])+`mu'[1,2] in `line'
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qui replace poids1=`poids'[1,`i'] in `line'
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qui replace poids2=`poids'[1,`j'] in `line'
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local ++line
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}
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}
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* Double somme du produit poids[i]*poids[j]*f(x1,x2) qui est affect<63> a la variable sum
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qui gen f=poids1*poids2*(`1')/(_pi)
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*list x1 x2 poids1 f (sqrt(2)*_pi)
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qui su f
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local sum=r(sum)
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return scalar int=`sum'
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if "`display'"!="" {
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di in green "int_R^2 (`1')g(x1,x2/mu=`mu',Sigma=`Sigma')dx1dx2=" in yellow %12.8f `sum'
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}
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drop _all
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if `save'==1 {
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qui use `gauss2',clear
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}
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end
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