checks positive definiteness of a matirx (GAMS and R combined solution)

definite.gms

$ontext

"Is there some GAMS template around to determine the definiteness of a given
matrix? (At the moment, I need it for a 5x5 matrix, but the dimension will
eventually be higher.)

Or is it advisable to switch to another math package for solving this?

Stefan"


This version uses the 'corpor' package in R to check definiteness

$offtext


$setlocal R_executable C:\Users\himics\Documents\R\R-3.0.1\bin\x64\R.exe

scalar answer;

set i /i1*i5/;
alias(i,j);

parameter matrix(i,i);

matrix(i,j) = uniform(1,10);

* test: the identity matrix is pos. definite
*matrix(i,j) = 0;
*matrix(i,i) = 1;


execute_unload "is_definite.gdx", matrix;

$onecho > pos_def.r
library(gdxrrw)
igdx("S:/24.1/")
library(corpcor)

mymatrix <- rgdx.param("is_definite.gdx", "matrix")

m <- as.matrix(tapply(mymatrix$value, mymatrix[, c("i","j")], sum))
m[is.na(m)]  <- 0

answer <- is.positive.definite(m)*1
attr(answer, "symName")  <- "answer"
wgdx.scalar("definite.gdx", answer)
$offecho


*
* --- call R terminal
*

execute '%R_executable% CMD BATCH pos_def.r pos_def.log';



execute_load "definite.gdx", answer;

if (answer,
         display "the matrix is positive definite", answer;
else
   display "the matrix is not positive definite", answer;
);