checks if a symmetric matrix is pos. definite (GAMS code using the default cholesky decomposition utility)

definite_cholesky.gms

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 Test the positive definiteness of a symmetric matrix

 Extension of the 'choleskyexample.gms' example from the McCarl User Guide


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Set index /i1*i2/;

Table a(index,index) matrix to decompose

             i1   i2

    i1       2     1

    i2       1     3;

parameter LforA(index,index) L matrix that is a decomposition of A;

execute_unload 'gdxforutility.gdx' index,A;

execute 'cholesky gdxforutility.gdx index A gdxfromutility.gdx LforA';

execute_load 'gdxfromutility.gdx' , LforA;

display a, LforA;


* check if all diagonal elements are positive <=> pos. definite (if the matrix is symmetric)

loop(index,
         if (LforA(index,index) < 0,
                 abort "the matrix is not pos.definite";

         );
);

display "the matrix is pos. definite";