CHOLESKY calculates the Cholesky decomposition of a symmetric positive definite matrix. Matrix decomposition A=LL^T.

Attention

CHOLESKY is deprecated (see GAMS 36 Cholesky, Eigenvalue, Eigenvector, Invert release notes). Please use $libInclude linalg Cholesky instead.

Usage

cholesky gdxin i a gdxout L

where

gdxin

name of gdxfile with matrix

i

name of set used in matrix

a

name of 2 dimensional parameter inside gdxin

gdxout

name of gdxfile for results (factor L)

L

name of 2 dimensional parameter inside gdxout

Calculates the Cholesky decomposition A=LL^t of a symmetric positive definite matrix A=a(i,j) where i and j are aliased sets. L will contain the Cholesky factor L(i,j).

Example

$onText
Finds the Cholesky decomposition A=LL' of a positive definite symmetric matrix
A through an external program.

Erwin Kalvelagen, may 2008
$offText

Set i / i1*i5 /;

Alias (i,j);

Table a(i,j) 'original matrix'
        i1   i2   i3   i4   i5
   i1   64   48   24    8    8
   i2   48   72   42   54   36
   i3   24   42   89  107   95
   i4    8   54  107  210  186
   i5    8   36   95  186  187;

Parameter L(i,j) 'cholesky factor';

execute_unload 'a.gdx', i, a;
execute '=cholesky.exe a.gdx i a b.gdx L';
execute_load 'b.gdx', L;

display a, L;

*
* only lower triangular part of A is used
*
Table a2(i,j) 'original matrix'
        i1   i2   i3   i4   i5
   i1   64
   i2   48   72
   i3   24   42   89
   i4    8   54  107  210
   i5    8   36   95  186  187;

Parameter L2(i,j) 'cholesky factor';

execute_unload 'a.gdx', i, a2;
execute '=cholesky.exe a.gdx i a2 b.gdx L2';
execute_load 'b.gdx', L2;

display a2, L2;