/*

  * 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;
 }PCA;
 

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

     if(n<=0)

         return NULL;

     pca= av_mallocz(sizeof(PCA));

     pca->n= n;
     pca->count=0;
     pca->covariance= av_mallocz(sizeof(double)*n*n);
     pca->mean= av_mallocz(sizeof(double)*n);
 

     return pca;

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

     av_free(pca);

 }
 
 void ff_pca_add(PCA *pca, 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[n];
 
     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;
 }
 

 #ifdef TEST

 
 #undef printf
 #include <stdio.h>
 #include <stdlib.h>

 #include "lfg.h"

 int main(void){

     PCA *pca;

     int i, j, k;
 #define LEN 8
     double eigenvector[LEN*LEN];
     double eigenvalue[LEN];

     AVLFG prng;

     av_lfg_init(&prng, 1);

     pca= ff_pca_init(LEN);

 
     for(i=0; i<9000000; i++){
         double v[2*LEN+100];
         double sum=0;

         int pos = av_lfg_get(&prng) % LEN;
         int v2  = av_lfg_get(&prng) % 101 - 50;
         v[0]    = av_lfg_get(&prng) % 101 - 50;

         for(j=1; j<8; j++){
             if(j<=pos) v[j]= v[0];
             else       v[j]= v2;
             sum += v[j];
         }
 /*        for(j=0; j<LEN; j++){
             v[j] -= v[pos];
         }*/

 //        sum += av_lfg_get(&prng) % 10;

 /*        for(j=0; j<LEN; j++){
             v[j] -= sum/LEN;
         }*/
 //        lbt1(v+100,v+100,LEN);

         ff_pca_add(pca, v);

     }
 
 

     ff_pca(pca, eigenvector, eigenvalue);

     for(i=0; i<LEN; i++){

         pca->count= 1;
         pca->mean[i]= 0;

 
 //        (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
 
 
 //        pca.covariance[i + i*LEN]= pow(0.5, fabs
         for(j=i; j<LEN; j++){

             printf("%f ", pca->covariance[i + j*LEN]);

         }
         printf("\n");
     }
 
     for(i=0; i<LEN; i++){
         double v[LEN];
         double error=0;
         memset(v, 0, sizeof(v));
         for(j=0; j<LEN; j++){
             for(k=0; k<LEN; k++){

                 v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];

             }
             v[j] /= eigenvalue[i];
             error += fabs(v[j] - eigenvector[i + j*LEN]);
         }
         printf("%f ", error);
     }
     printf("\n");

     for(i=0; i<LEN; i++){
         for(j=0; j<LEN; j++){
             printf("%9.6f ", eigenvector[i + j*LEN]);
         }
         printf("  %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
     }
 
     return 0;
 }
 #endif