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/**
* NMF: Non-Negative Matrix Factorization
*
* Written by Roman Shterenzon
* (Slightly modified by Y.Tsunesada: just added "const" qualifiers etc.)
*/
#include <math.h>
#include <time.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h> /* for multiplication */
#define THRESH 0.000001
#define MAXITER 1000
#undef DEBUG
#define mm(a, b) gsl_matrix_mult(a, b)
//gsl_matrix * gsl_matrix_mult(gsl_matrix *a, gsl_matrix *b)
gsl_matrix * gsl_matrix_mult(const gsl_matrix *a, const gsl_matrix *b)
{
gsl_matrix *c;
c = gsl_matrix_alloc(a->size1, b->size2);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, c);
return c;
}
// pretty print
//void pp(gsl_matrix *m)
void pp(const gsl_matrix *m)
{
int r, c;
for(r = 0; r < (int) m->size1; r++) {
for(c = 0; c < (int) m->size2; c++) {
printf(" %.2f", gsl_matrix_get(m, r, c));
}
printf("\n");
}
}
/* Returns a distance cost */
//double difcost(gsl_matrix *a, gsl_matrix *b)
double difcost(const gsl_matrix *a, const gsl_matrix *b)
{
int i, j;
double dif = 0, d;
for (i = 0; i < (int) a->size1; i++)
{
for (j = 0; j < (int) a->size2; j++)
{
d = gsl_matrix_get(a, i, j) - gsl_matrix_get(b, i, j);
dif += d*d;
// dif += pow(gsl_matrix_get(a, i, j) - gsl_matrix_get(b, i, j), 2);
}
}
return dif;
}
static void initmatrix(gsl_matrix *m, double min, double max)
{
int i,j;
double val;
srand(time(NULL));
for(i = 0; i < (int) m->size1; i++)
{
for(j = 0; j < (int) m->size2; j++)
{
val = min + (int) (max * (rand() / (RAND_MAX + min)));
gsl_matrix_set(m, i, j, val);
}
}
}
static double update(gsl_matrix *v, gsl_matrix *w, gsl_matrix *h)
{
double dist = 0;
gsl_matrix *wt = NULL, *ht = NULL, *wh = NULL;
gsl_matrix *w_h = NULL, *wt_w = NULL;
gsl_matrix *wt_v = NULL;
gsl_matrix *v_ht = NULL, *wt_w_h = NULL, *w_h_ht = NULL;
wt = gsl_matrix_alloc(w->size2, w->size1);
gsl_matrix_transpose_memcpy(wt, w);
ht = gsl_matrix_alloc(h->size2, h->size1);
gsl_matrix_transpose_memcpy(ht, h);
// wt * v
wt_v = mm(wt, v);
// wt * w * h
wt_w = mm(wt, w);
wt_w_h = mm(wt_w, h);
gsl_matrix_free(wt_w);
// h = h.mul_elements(wt * v).div_elements(wt * w * h)
gsl_matrix_mul_elements(h, wt_v);
gsl_matrix_div_elements(h, wt_w_h);
gsl_matrix_free(wt_v);
gsl_matrix_free(wt_w_h);
// v * ht
v_ht = mm(v, ht);
// w * h * ht
w_h = mm(w, h);
w_h_ht = mm(w_h, ht);
gsl_matrix_free(w_h);
// w = w.mul_elements(v * ht).div_elements(w * h * ht)
gsl_matrix_mul_elements(w, v_ht);
gsl_matrix_div_elements(w, w_h_ht);
gsl_matrix_free(v_ht);
gsl_matrix_free(w_h_ht);
gsl_matrix_free(wt);
gsl_matrix_free(ht);
wh = mm(w, h);
dist = difcost(v, wh);
gsl_matrix_free(wh);
// w and h were modified in place
return dist;
}
/* The main thing - compute the nmf */
int gsl_matrix_nmf(gsl_matrix *v, int cols, gsl_matrix **w, gsl_matrix **h)
{
double dist = 1;
int iter = 1;
double min, max;
#ifdef DEBUG
printf("\nCols: %d\nv:\n", cols);
pp(v);
#endif
gsl_matrix_minmax(v, &min, &max);
#ifdef DEBUG
printf("Min: %f, Max: %f\n", min, max);
#endif
*w = gsl_matrix_alloc(v->size1, cols);
initmatrix(*w, min, max/2); // the multiplicative rules tend to increase w
*h = gsl_matrix_alloc(cols, v->size2);
initmatrix(*h, min, max);
while(dist >= THRESH && iter < MAXITER)
{
dist = update(v, *w, *h);
#ifdef DEBUG
printf("Iteration: %d, distance: %f\n", iter, dist);
printf("\nw:\n");
pp(*w);
printf("\nh:\n");
pp(*h);
printf("\n");
#endif
iter++;
}
#ifdef DEBUG
printf("Ended\n");
#endif
return GSL_SUCCESS;
}
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