linear least squares solver using cholesky factorization

Originally committed as revision 5740 to svn://svn.ffmpeg.org/ffmpeg/trunk

libavutil/Makefile

@@ -12,6 +12,7 @@ OBJS= mathematics.o \
       intfloat_readwrite.o \
       crc.o \
       md5.o \
+      lls.o \
       adler32.o
 
 HEADERS = avutil.h common.h mathematics.h integer.h rational.h \

libavutil/lls.c

+/*
+ * linear least squares model
+ *
+ * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
+ *
+ * This library 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 of the License, or (at your option) any later version.
+ *
+ * This library 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 this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ */
+
+/**
+ * @file lls.c
+ * linear least squares model
+ */
+
+#include <math.h>
+#include <string.h>
+
+#include "lls.h"
+
+#undef NDEBUG // allways check asserts, the speed effect is far too small to disable them
+#include <assert.h>
+
+#ifdef TEST
+#define av_log(a,b,...) printf(__VA_ARGS__)
+#endif
+
+void av_init_lls(LLSModel *m, int indep_count){
+    memset(m, 0, sizeof(LLSModel));
+
+    m->indep_count= indep_count;
+}
+
+void av_update_lls(LLSModel *m, double *var, double decay){
+    int i,j;
+
+    for(i=0; i<=m->indep_count; i++){
+        for(j=i; j<=m->indep_count; j++){
+            m->covariance[i][j] *= decay;
+            m->covariance[i][j] += var[i]*var[j];
+        }
+    }
+}
+
+double av_solve_lls(LLSModel *m, double threshold){
+    int i,j,k;
+    double (*factor)[MAX_VARS+1]= &m->covariance[1][0];
+    double (*covar )[MAX_VARS+1]= &m->covariance[1][1];
+    double  *covar_y            =  m->covariance[0];
+    double variance;
+    int count= m->indep_count;
+
+    for(i=0; i<count; i++){
+        for(j=i; j<count; j++){
+            double sum= covar[i][j];
+
+            for(k=i-1; k>=0; k--)
+                sum -= factor[i][k]*factor[j][k];
+
+            if(i==j){
+                if(sum < threshold)
+                    sum= 1.0;
+                factor[i][i]= sqrt(sum);
+            }else
+                factor[j][i]= sum / factor[i][i];
+        }
+    }
+    for(i=0; i<count; i++){
+        double sum= covar_y[i+1];
+        for(k=i-1; k>=0; k--)
+            sum -= factor[i][k]*m->coeff[k];
+        m->coeff[i]= sum / factor[i][i];
+    }
+
+    for(i=count-1; i>=0; i--){
+        double sum= m->coeff[i];
+        for(k=i+1; k<count; k++)
+            sum -= factor[k][i]*m->coeff[k];
+        m->coeff[i]= sum / factor[i][i];
+    }
+
+    variance= covar_y[0];
+    for(i=0; i<count; i++){
+        double sum= m->coeff[i]*covar[i][i] - 2*covar_y[i+1];
+        for(j=0; j<i; j++)
+            sum += 2*m->coeff[j]*covar[j][i];
+        variance += m->coeff[i]*sum;
+    }
+    return variance;
+}
+
+double av_evaluate_lls(LLSModel *m, double *param){
+    int i;
+    double out= 0;
+
+    for(i=0; i<m->indep_count; i++)
+        out+= param[i]*m->coeff[i];
+
+    return out;
+}
+
+#ifdef TEST
+
+#include <stdlib.h>
+#include <stdio.h>
+
+int main(){
+    LLSModel m;
+    int i;
+
+    av_init_lls(&m, 3);
+
+    for(i=0; i<100; i++){
+        double var[4];
+        double eval, variance;
+        var[1] = rand() / (double)RAND_MAX;
+        var[2] = rand() / (double)RAND_MAX;
+        var[3] = rand() / (double)RAND_MAX;
+
+        var[2]= var[1] + var[3];
+
+        var[0] = var[1] + var[2] + var[3] +  var[1]*var[2]/100;
+
+        eval= av_evaluate_lls(&m, var+1);
+        av_update_lls(&m, var, 0.99);
+        variance= av_solve_lls(&m, 0.001);
+        av_log(NULL, AV_LOG_DEBUG, "real:%f pred:%f var:%f coeffs:%f %f %f\n",
+            var[0], eval, sqrt(variance / (i+1)),
+            m.coeff[0], m.coeff[1], m.coeff[2]);
+    }
+    return 0;
+}
+
+#endif

libavutil/lls.h

+/*
+ * linear least squares model
+ *
+ * Copyright (c) 2006 Michael Niedermayer <michaelni@gmx.at>
+ *
+ * This library 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 of the License, or (at your option) any later version.
+ *
+ * This library 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 this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ */
+
+#ifndef LLS_H
+#define LLS_H
+
+#define MAX_VARS 32
+
+//FIXME avoid direct access to LLSModel from outside
+
+/**
+ * Linear least squares model.
+ */
+typedef struct LLSModel{
+    double covariance[MAX_VARS+1][MAX_VARS+1];
+    double coeff[MAX_VARS];
+    int indep_count;
+}LLSModel;
+
+void av_init_lls(LLSModel *m, int indep_count);
+void av_update_lls(LLSModel *m, double *param, double decay);
+double av_solve_lls(LLSModel *m, double threshold);
+double av_evaluate_lls(LLSModel *m, double *param);
+
+#endif