You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
135 lines
3.7 KiB
Plaintext
135 lines
3.7 KiB
Plaintext
*! version 2 11dec2012
|
|
************************************************************************************************************
|
|
* gausshermite : Estimate an integral of the form |f(x)g(x/mu,sigma)dx or f(x,y)g(x,y/mu,Sigma)dxdy where g(x/mu,sigma) is the distribution function
|
|
* of the gaussian distribution of mean mu and variance sigma^2 and g(x,y/mu,Sigma) is the distribution function
|
|
* of the bivariate normal distribution of mean mu and covariance matrix Sigma by Gauss Hermite quadratures
|
|
*
|
|
* Version 1: May 5, 2005
|
|
* Version 1.1: June 14, 2012 /*name option*/
|
|
* Version 2: December 11, 2012 /*bivariate normal distribution*/
|
|
*
|
|
* Jean-benoit Hardouin, Regional Health Observatory of Orléans - France
|
|
* jean-benoit.hardouin@orscentre.org
|
|
*
|
|
* News about this program : http://anaqol.free.fr
|
|
* FreeIRT Project : http://freeirt.free.fr
|
|
*
|
|
* Copyright 2005, 2012 Jean-Benoit Hardouin
|
|
*
|
|
* This program is free software; you can redistribute it and/or modify
|
|
* it under the terms of the GNU General Public License as published by
|
|
* the Free Software Foundation; either version 2 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* This program is distributed in the hope that it will be useful,
|
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
* GNU General Public License for more details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License
|
|
* along with this program; if not, write to the Free Software
|
|
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
|
|
*
|
|
************************************************************************************************************
|
|
|
|
|
|
program define gausshermite3,rclass
|
|
version 7
|
|
syntax anything [, Sigma(string) MU(string) Nodes(integer 12) Display Name(string)]
|
|
tempfile gauss
|
|
qui capture save `gauss',replace
|
|
local save=0
|
|
if _rc==0 {
|
|
qui save `gauss',replace
|
|
local save=1
|
|
}
|
|
|
|
tokenize `anything'
|
|
|
|
drop _all
|
|
qui set obs `=`nodes'*`nodes''
|
|
if "`name'"=="" {
|
|
local name x
|
|
local nb=1
|
|
}
|
|
else {
|
|
local nb=wordcount("`name'")
|
|
if `nb'==2{
|
|
di word("`name'",1)
|
|
local name1=word("`name'",1)
|
|
local name2=word("`name'",2)
|
|
}
|
|
}
|
|
|
|
capture confirm matrix `sigma'
|
|
if !_rc{
|
|
if colsof(`sigma')==1 & rowsof(`sigma')==1{
|
|
local sig=`sigma'[1,1]
|
|
}
|
|
else{
|
|
matrix C=cholesky(`sigma')
|
|
}
|
|
}
|
|
else{
|
|
local sig=`sigma'
|
|
}
|
|
|
|
capture confirm matrix `mu'
|
|
if !_rc{
|
|
if colsof(`mu')==1 & rowsof(`mu')==1{
|
|
local mean=`mu'[1,1]
|
|
}
|
|
else{
|
|
matrix mean=`mu'
|
|
}
|
|
}
|
|
else{
|
|
local mean=`mu'
|
|
}
|
|
|
|
tempname noeuds poids
|
|
qui ghquadm `nodes' `noeuds' `poids'
|
|
|
|
if `nb'==1{
|
|
qui gen `name'=.
|
|
qui gen poids=.
|
|
forvalues i=1/`nodes' {
|
|
qui replace `name'=`noeuds'[1,`i'] in `i'
|
|
qui replace poids=`poids'[1,`i'] in `i'
|
|
}
|
|
qui replace `name'=`name'*(sqrt(2)*`sig')+`mean'
|
|
qui gen f=poids/sqrt(_pi)*(`1')
|
|
*list `name' poids f in 1/5
|
|
}
|
|
else{
|
|
forvalues i=1/`nb'{
|
|
qui gen `name`i''=.
|
|
qui gen poids`i'=.
|
|
}
|
|
local line=1
|
|
forvalues i=1/`nodes' {
|
|
forvalues j=1/`nodes' {
|
|
qui replace `name1'=`noeuds'[1,`i'] *(sqrt(2)*C[1,1])+mean[1,1] in `line'
|
|
qui replace `name2'=`noeuds'[1,`i'] *(sqrt(2)*C[2,1])+`noeuds'[1,`j'] *(sqrt(2)*C[2,2])+mean[1,2] in `line'
|
|
qui replace poids1=`poids'[1,`i'] in `line'
|
|
qui replace poids2=`poids'[1,`j'] in `line'
|
|
local ++line
|
|
}
|
|
}
|
|
qui gen f=poids1*poids2*(`1')/(_pi)
|
|
*list `name1' `name2' poids1 poids2 f in 10/20
|
|
}
|
|
|
|
qui su f
|
|
return scalar int=r(sum)
|
|
if "`display'"!="" {
|
|
di in green "int_R (`1')g(`name'/sigma=`sigma')d`name'=" in yellow %12.8f `r(sum)'
|
|
}
|
|
drop _all
|
|
if `save'==1 {
|
|
qui use `gauss',clear
|
|
}
|
|
end
|
|
|
|
|