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/*
* iemmatrix
*
* objects for manipulating simple matrices
* mostly refering to matlab/octave matrix functions
*
* Copyright (c) IOhannes m zmölnig, forum::für::umläute
* IEM, Graz, Austria
*
* For information on usage and redistribution, and for a DISCLAIMER OF ALL
* WARRANTIES, see the file, "LICENSE.txt," in this distribution.
*
*/
#include "iemmatrix.h"
/* mtx_cholesky */
/*
* calculate the "Cholesky Decomposition" of a "symmetric and positive definite matrix "
* no check is done, whether the input matrix is really symmetric and positive definite.
*/
static t_class *mtx_cholesky_class;
static void mtx_cholesky_matrix(t_matrix *x, t_symbol *s, int argc, t_atom *argv)
{
/* maybe we should do this in double or long double ? */
int row=atom_getfloat(argv);
int col=atom_getfloat(argv+1);
int i, j, k, row2=row*row;
t_matrixfloat *original, *cholesky;
if(row*col+2>argc){
post("mtx_print : sparse matrices not yet supported : use \"mtx_check\"");
return;
}
if (row!=col){
post("mtx_cholesky: only symmetric and positive definite matrices can be cholesky-decomposed");
return;
}
// reserve memory for outputting afterwards
adjustsize(x, row, row);
// 1. get the 2 matrices : orig; invert (create as eye, but will be orig^(-1))
cholesky = (t_matrixfloat *)getbytes(sizeof(t_matrixfloat)*row2);
// 1a extract values of A to float-buf
original=matrix2float(argv);
// 2 set the cholesky matrix to zero
for(i=0; i<row2; i++)cholesky[i]=0.;
// 3 do the cholesky decomposition
for(i=0; i<col; i++){
// 3a get the diagonal element
// l_ii=sqrt(a_ii-sum(k=1..i-1)((l_ik)^2))
t_matrixfloat sum=0.;
t_matrixfloat result=0.f;
for(k=0; k<i; k++){
t_matrixfloat lik=cholesky[k*col+i];
sum+=lik*lik;
}
if((result=original[i*(col+1)]-sum)<0){
post("[mtx_cholesky]: only symmetric and positive definite matrices can be cholesky-decomposed");
return;
}
result=sqrtf(result); // LATER check whether this is real
cholesky[i*(col+1)]=result;
// 3b get the other elements within this row/col
// l_ji=(a_ji-sum(k=1..i-1)(l_jk*l_ik))/l_ii
for(j=i+1; j<row; j++){
sum=0.;
for(k=0; k<i; k++){
t_matrixfloat ljk=cholesky[k*col+j];
t_matrixfloat lik=cholesky[k*col+i];
sum+=ljk*lik;
}
cholesky[i*row+j]=(original[i*col+j]-sum)/result;
}
}
// 4. output the matrix
// 4a convert the floatbuf to an atombuf;
float2matrix(x->atombuffer, cholesky);
// 4b destroy the buffers
freebytes(original, sizeof(t_matrixfloat)*row2);
// 4c output the atombuf;
matrix_bang(x);
}
static void *mtx_cholesky_new(t_symbol *s, int argc, t_atom *argv)
{
t_matrix *x = (t_matrix *)pd_new(mtx_cholesky_class);
outlet_new(&x->x_obj, 0);
x->col=x->row=0;
x->atombuffer=0;
return (x);
}
void mtx_cholesky_setup(void)
{
mtx_cholesky_class = class_new(gensym("mtx_cholesky"), (t_newmethod)mtx_cholesky_new,
(t_method)matrix_free, sizeof(t_matrix), 0, A_GIMME, 0);
class_addbang (mtx_cholesky_class, matrix_bang);
class_addmethod(mtx_cholesky_class, (t_method)mtx_cholesky_matrix, gensym("matrix"), A_GIMME, 0);
class_sethelpsymbol(mtx_cholesky_class, gensym("iemmatrix/mtx_cholesky"));
}
void iemtx_cholesky_setup(void){
mtx_cholesky_setup();
}
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