/*

  * principal component analysis (PCA)

  * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
  *

  * This file is part of FFmpeg.
  *
  * FFmpeg is free software; you can redistribute it and/or

  * modify it under the terms of the GNU Lesser General Public
  * License as published by the Free Software Foundation; either

  * version 2.1 of the License, or (at your option) any later version.

  *

  * FFmpeg is distributed in the hope that it will be useful,

  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  * Lesser General Public License for more details.
  *
  * You should have received a copy of the GNU Lesser General Public

  * License along with FFmpeg; if not, write to the Free Software
  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

  */
 
 /**

  * @file

  * principal component analysis (PCA)

  */
 

 #include "common.h"

 #include "pca.h"
 

 typedef struct PCA{
     int count;
     int n;
     double *covariance;
     double *mean;

     double *z;

 }PCA;
 

 PCA *ff_pca_init(int n){
     PCA *pca;

     if(n<=0)

         return NULL;

     pca= av_mallocz(sizeof(*pca));

     if (!pca)
         return NULL;
 

     pca->n= n;

     pca->z = av_malloc_array(n, sizeof(*pca->z));

     pca->count=0;

     pca->covariance= av_calloc(n*n, sizeof(double));
     pca->mean= av_calloc(n, sizeof(double));

     if (!pca->z || !pca->covariance || !pca->mean) {
         ff_pca_free(pca);
         return NULL;
     }
 

     return pca;

 }
 
 void ff_pca_free(PCA *pca){
     av_freep(&pca->covariance);
     av_freep(&pca->mean);

     av_freep(&pca->z);

     av_free(pca);

 }
 

 void ff_pca_add(PCA *pca, const double *v){

     int i, j;
     const int n= pca->n;
 
     for(i=0; i<n; i++){
         pca->mean[i] += v[i];
         for(j=i; j<n; j++)
             pca->covariance[j + i*n] += v[i]*v[j];
     }
     pca->count++;
 }
 
 int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){

     int i, j, pass;
     int k=0;

     const int n= pca->n;

     double *z = pca->z;

 
     memset(eigenvector, 0, sizeof(double)*n*n);
 
     for(j=0; j<n; j++){
         pca->mean[j] /= pca->count;
         eigenvector[j + j*n] = 1.0;
         for(i=0; i<=j; i++){
             pca->covariance[j + i*n] /= pca->count;
             pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
             pca->covariance[i + j*n] = pca->covariance[j + i*n];
         }
         eigenvalue[j]= pca->covariance[j + j*n];
         z[j]= 0;
     }
 
     for(pass=0; pass < 50; pass++){
         double sum=0;
 
         for(i=0; i<n; i++)
             for(j=i+1; j<n; j++)
                 sum += fabs(pca->covariance[j + i*n]);
 
         if(sum == 0){
             for(i=0; i<n; i++){
                 double maxvalue= -1;
                 for(j=i; j<n; j++){
                     if(eigenvalue[j] > maxvalue){
                         maxvalue= eigenvalue[j];
                         k= j;
                     }
                 }
                 eigenvalue[k]= eigenvalue[i];
                 eigenvalue[i]= maxvalue;
                 for(j=0; j<n; j++){
                     double tmp= eigenvector[k + j*n];
                     eigenvector[k + j*n]= eigenvector[i + j*n];
                     eigenvector[i + j*n]= tmp;
                 }
             }
             return pass;
         }
 
         for(i=0; i<n; i++){
             for(j=i+1; j<n; j++){
                 double covar= pca->covariance[j + i*n];
                 double t,c,s,tau,theta, h;
 
                 if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
                     continue;

                 if(fabs(covar) == 0.0) //FIXME should not be needed

                     continue;
                 if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
                     pca->covariance[j + i*n]=0.0;
                     continue;
                 }
 
                 h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
                 theta=0.5*h/covar;
                 t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
                 if(theta < 0.0) t = -t;
 
                 c=1.0/sqrt(1+t*t);
                 s=t*c;
                 tau=s/(1.0+c);
                 z[i] -= t*covar;
                 z[j] += t*covar;
 

 #define ROTATE(a,i,j,k,l) {\

     double g=a[j + i*n];\
     double h=a[l + k*n];\
     a[j + i*n]=g-s*(h+g*tau);\

     a[l + k*n]=h+s*(g-h*tau); }

                 for(k=0; k<n; k++) {
                     if(k!=i && k!=j){
                         ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
                     }
                     ROTATE(eigenvector,k,i,k,j)
                 }
                 pca->covariance[j + i*n]=0.0;
             }
         }
         for (i=0; i<n; i++) {
             eigenvalue[i] += z[i];
             z[i]=0.0;
         }
     }
 
     return -1;
 }