1/*
2 * principal component analysis (PCA)
3 * Copyright (c) 2004 Michael Niedermayer <michaelni@gmx.at>
4 *
5 * This file is part of FFmpeg.
6 *
7 * FFmpeg is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Lesser General Public
9 * License as published by the Free Software Foundation; either
10 * version 2.1 of the License, or (at your option) any later version.
11 *
12 * FFmpeg is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
15 * Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with FFmpeg; if not, write to the Free Software
19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20 */
21
22/**
23 * @file
24 * principal component analysis (PCA)
25 */
26
27#include "common.h"
28#include "pca.h"
29
30typedef struct PCA{
31    int count;
32    int n;
33    double *covariance;
34    double *mean;
35    double *z;
36}PCA;
37
38PCA *ff_pca_init(int n){
39    PCA *pca;
40    if(n<=0)
41        return NULL;
42
43    pca= av_mallocz(sizeof(*pca));
44    pca->n= n;
45    pca->z = av_malloc_array(n, sizeof(*pca->z));
46    pca->count=0;
47    pca->covariance= av_calloc(n*n, sizeof(double));
48    pca->mean= av_calloc(n, sizeof(double));
49
50    return pca;
51}
52
53void ff_pca_free(PCA *pca){
54    av_freep(&pca->covariance);
55    av_freep(&pca->mean);
56    av_freep(&pca->z);
57    av_free(pca);
58}
59
60void ff_pca_add(PCA *pca, double *v){
61    int i, j;
62    const int n= pca->n;
63
64    for(i=0; i<n; i++){
65        pca->mean[i] += v[i];
66        for(j=i; j<n; j++)
67            pca->covariance[j + i*n] += v[i]*v[j];
68    }
69    pca->count++;
70}
71
72int ff_pca(PCA *pca, double *eigenvector, double *eigenvalue){
73    int i, j, pass;
74    int k=0;
75    const int n= pca->n;
76    double *z = pca->z;
77
78    memset(eigenvector, 0, sizeof(double)*n*n);
79
80    for(j=0; j<n; j++){
81        pca->mean[j] /= pca->count;
82        eigenvector[j + j*n] = 1.0;
83        for(i=0; i<=j; i++){
84            pca->covariance[j + i*n] /= pca->count;
85            pca->covariance[j + i*n] -= pca->mean[i] * pca->mean[j];
86            pca->covariance[i + j*n] = pca->covariance[j + i*n];
87        }
88        eigenvalue[j]= pca->covariance[j + j*n];
89        z[j]= 0;
90    }
91
92    for(pass=0; pass < 50; pass++){
93        double sum=0;
94
95        for(i=0; i<n; i++)
96            for(j=i+1; j<n; j++)
97                sum += fabs(pca->covariance[j + i*n]);
98
99        if(sum == 0){
100            for(i=0; i<n; i++){
101                double maxvalue= -1;
102                for(j=i; j<n; j++){
103                    if(eigenvalue[j] > maxvalue){
104                        maxvalue= eigenvalue[j];
105                        k= j;
106                    }
107                }
108                eigenvalue[k]= eigenvalue[i];
109                eigenvalue[i]= maxvalue;
110                for(j=0; j<n; j++){
111                    double tmp= eigenvector[k + j*n];
112                    eigenvector[k + j*n]= eigenvector[i + j*n];
113                    eigenvector[i + j*n]= tmp;
114                }
115            }
116            return pass;
117        }
118
119        for(i=0; i<n; i++){
120            for(j=i+1; j<n; j++){
121                double covar= pca->covariance[j + i*n];
122                double t,c,s,tau,theta, h;
123
124                if(pass < 3 && fabs(covar) < sum / (5*n*n)) //FIXME why pass < 3
125                    continue;
126                if(fabs(covar) == 0.0) //FIXME should not be needed
127                    continue;
128                if(pass >=3 && fabs((eigenvalue[j]+z[j])/covar) > (1LL<<32) && fabs((eigenvalue[i]+z[i])/covar) > (1LL<<32)){
129                    pca->covariance[j + i*n]=0.0;
130                    continue;
131                }
132
133                h= (eigenvalue[j]+z[j]) - (eigenvalue[i]+z[i]);
134                theta=0.5*h/covar;
135                t=1.0/(fabs(theta)+sqrt(1.0+theta*theta));
136                if(theta < 0.0) t = -t;
137
138                c=1.0/sqrt(1+t*t);
139                s=t*c;
140                tau=s/(1.0+c);
141                z[i] -= t*covar;
142                z[j] += t*covar;
143
144#define ROTATE(a,i,j,k,l) {\
145    double g=a[j + i*n];\
146    double h=a[l + k*n];\
147    a[j + i*n]=g-s*(h+g*tau);\
148    a[l + k*n]=h+s*(g-h*tau); }
149                for(k=0; k<n; k++) {
150                    if(k!=i && k!=j){
151                        ROTATE(pca->covariance,FFMIN(k,i),FFMAX(k,i),FFMIN(k,j),FFMAX(k,j))
152                    }
153                    ROTATE(eigenvector,k,i,k,j)
154                }
155                pca->covariance[j + i*n]=0.0;
156            }
157        }
158        for (i=0; i<n; i++) {
159            eigenvalue[i] += z[i];
160            z[i]=0.0;
161        }
162    }
163
164    return -1;
165}
166
167#ifdef TEST
168
169#undef printf
170#include <stdio.h>
171#include <stdlib.h>
172#include "lfg.h"
173
174int main(void){
175    PCA *pca;
176    int i, j, k;
177#define LEN 8
178    double eigenvector[LEN*LEN];
179    double eigenvalue[LEN];
180    AVLFG prng;
181
182    av_lfg_init(&prng, 1);
183
184    pca= ff_pca_init(LEN);
185
186    for(i=0; i<9000000; i++){
187        double v[2*LEN+100];
188        double sum=0;
189        int pos = av_lfg_get(&prng) % LEN;
190        int v2  = av_lfg_get(&prng) % 101 - 50;
191        v[0]    = av_lfg_get(&prng) % 101 - 50;
192        for(j=1; j<8; j++){
193            if(j<=pos) v[j]= v[0];
194            else       v[j]= v2;
195            sum += v[j];
196        }
197/*        for(j=0; j<LEN; j++){
198            v[j] -= v[pos];
199        }*/
200//        sum += av_lfg_get(&prng) % 10;
201/*        for(j=0; j<LEN; j++){
202            v[j] -= sum/LEN;
203        }*/
204//        lbt1(v+100,v+100,LEN);
205        ff_pca_add(pca, v);
206    }
207
208
209    ff_pca(pca, eigenvector, eigenvalue);
210    for(i=0; i<LEN; i++){
211        pca->count= 1;
212        pca->mean[i]= 0;
213
214//        (0.5^|x|)^2 = 0.5^2|x| = 0.25^|x|
215
216
217//        pca.covariance[i + i*LEN]= pow(0.5, fabs
218        for(j=i; j<LEN; j++){
219            printf("%f ", pca->covariance[i + j*LEN]);
220        }
221        printf("\n");
222    }
223
224    for(i=0; i<LEN; i++){
225        double v[LEN];
226        double error=0;
227        memset(v, 0, sizeof(v));
228        for(j=0; j<LEN; j++){
229            for(k=0; k<LEN; k++){
230                v[j] += pca->covariance[FFMIN(k,j) + FFMAX(k,j)*LEN] * eigenvector[i + k*LEN];
231            }
232            v[j] /= eigenvalue[i];
233            error += fabs(v[j] - eigenvector[i + j*LEN]);
234        }
235        printf("%f ", error);
236    }
237    printf("\n");
238
239    for(i=0; i<LEN; i++){
240        for(j=0; j<LEN; j++){
241            printf("%9.6f ", eigenvector[i + j*LEN]);
242        }
243        printf("  %9.1f %f\n", eigenvalue[i], eigenvalue[i]/eigenvalue[0]);
244    }
245
246    return 0;
247}
248#endif
249