function: build a VQ codebook
author: Monty <xiphmont@mit.edu>
modifications by: Monty
- last modification date: Nov 18 1999
+ last modification date: Oct 04 1999
********************************************************************/
#include <stdio.h>
#include <math.h>
#include <string.h>
+#include "minit.h"
/************************************************************************
* The basic idea here is that a VQ codebook is like an m-dimensional
* 'pressurized' [biased] according to some metric. The basic alg
* iterates through allowing the bubbles to compete for space until
* they converge (if the damping is dome properly) on a steady-state
- * solution.
- *
- * We use the ratio of local to average 'error' as the metric to bias a
- * variable-length word codebook, and probability of occurrence within
- * that bubble as the metric to bias fixed length word
- * codebooks. Individual input points, collected from libvorbis, are
+ * solution. Individual input points, collected from libvorbis, are
* used to train the algorithm monte-carlo style. */
typedef struct vqgen{
long allocated;
/* entries */
- double *entry_now;
- double *entry_next;
+ double *entrylist;
long *assigned;
- double *metric;
double *bias;
long entries;
double (*metric_func) (struct vqgen *v,double *a,double *b);
} vqgen;
+typedef struct vqbook{
+
+
+
+} vqbook;
+
/* internal helpers *****************************************************/
+#define vN(data,i) (data+v->elements*i)
+
double *_point(vqgen *v,long ptr){
return v->pointlist+(v->elements*ptr);
}
double *_now(vqgen *v,long ptr){
- return v->entry_now+(v->elements*ptr);
-}
-
-double *_next(vqgen *v,long ptr){
- return v->entry_next+(v->elements*ptr);
+ return v->entrylist+(v->elements*ptr);
}
+/* default metric; squared 'distance' from desired value. */
double _dist_sq(vqgen *v,double *a, double *b){
int i;
int el=v->elements;
return acc;
}
+/* *must* be beefed up. Perhaps a Floyd-Steinberg like scattering? */
+void _vqgen_seed(vqgen *v){
+ memcpy(v->entrylist,v->pointlist,sizeof(double)*v->entries*v->elements);
+}
+
+void _limited_sort(double *vals,long *index,long total,int desired){
+ if(total>1){
+ long bisect=total>>1;
+ if(bisect>1)_limited_sort(vals,index,bisect,desired);
+ if(total-bisect>1)_limited_sort(vals,index+bisect,total-bisect,
+ desired);
+ if(desired>total)desired=total;
+
+ {
+ int i;
+ long ptra=0;
+ long ptrb=bisect;
+ long *temp=alloca(desired*sizeof(long));
+
+ for(i=0;i<desired;i++){
+ if(vals[index[ptra]]>vals[index[ptrb]]){
+ temp[i]=index[ptra++];
+ }else{
+ temp[i]=index[ptrb++];
+ }
+ if(ptra==bisect)
+ for(i++;i<desired;i++)temp[i]=index[ptrb++];
+ else
+ if(ptrb==total)
+ for(i++;i<desired;i++)temp[i]=index[ptra++];
+
+ }
+
+ memcpy(index,temp,desired*sizeof(long));
+ }
+ }
+}
+
+/* External calls *******************************************************/
+
void vqgen_init(vqgen *v,int elements,int entries,
double (*metric)(vqgen *,double *, double *),
double spread){
v->second=malloc(v->allocated*sizeof(long));
v->entries=entries;
- v->entry_now=malloc(v->entries*v->elements*sizeof(double));
- v->entry_next=malloc(v->entries*v->elements*sizeof(double));
+ v->entrylist=malloc(v->entries*v->elements*sizeof(double));
v->assigned=malloc(v->entries*sizeof(long));
- v->metric=malloc(v->entries*sizeof(double));
v->bias=calloc(v->entries,sizeof(double));
if(metric)
v->metric_func=metric;
v->metric_func=_dist_sq;
}
-/* *must* be beefed up. Perhaps a Floyd-Steinberg like scattering? */
-void _vqgen_seed(vqgen *v){
- memcpy(v->entry_now,v->pointlist,sizeof(double)*v->entries*v->elements);
-}
-
void vqgen_addpoint(vqgen *v, double *p){
if(v->points>=v->allocated){
v->allocated*=2;
if(v->points==v->entries)_vqgen_seed(v);
}
-double *sort_t_vals;
-int sort_t_compare(const void *ap,const void *bp){
- long a=*(long *)ap;
- long b=*(long *)bp;
- double val=sort_t_vals[a]-sort_t_vals[b];
- if(val<0)return(1);
- if(val>0)return(-1);
- return(0);
-}
+void vqgen_recenter(vqgen *v){
+ long i,j,k;
+ double fdesired=(double)v->points/v->entries;
+ double asserror=0.;
+ double meterror=0.;
+
+ if(v->entries<2)exit(1);
-void vqgen_iterate(vqgen *v,int biasp){
- static int iteration=0;
- long i,j;
- double avmetric=0.;
+ /* first round: new midpoints */
+ {
+ double *newlo=malloc(sizeof(double)*v->entries*v->elements);
+ double *newhi=malloc(sizeof(double)*v->entries*v->elements);
- FILE *as;
- FILE *graph;
- FILE *err;
- FILE *bias;
- char name[80];
-
+ memset(v->assigned,0,sizeof(long)*v->entries);
+
+ for(i=0;i<v->points;i++){
+ double firstmetric=v->metric_func(v,_now(v,0),_point(v,i))+v->bias[0];
+ long firstentry=0;
+
+ for(j=1;j<v->entries;j++){
+ double thismetric=v->metric_func(v,_now(v,j),_point(v,i))+v->bias[j];
+ if(thismetric<firstmetric){
+ firstmetric=thismetric;
+ firstentry=j;
+ }
+ }
- sprintf(name,"space%d.m",iteration);
- graph=fopen(name,"w");
+ j=firstentry;
+ meterror+=firstmetric-v->bias[firstentry];
+ if(v->assigned[j]++){
+ for(k=0;k<v->elements;k++){
+ if(_point(v,i)[k]<vN(newlo,j)[k])vN(newlo,j)[k]=_point(v,i)[k];
+ if(_point(v,i)[k]>vN(newhi,j)[k])vN(newhi,j)[k]=_point(v,i)[k];
+ }
+ }else{
+ for(k=0;k<v->elements;k++){
+ vN(newlo,j)[k]=_point(v,i)[k];
+ vN(newhi,j)[k]=_point(v,i)[k];
+ }
+ }
+ }
- sprintf(name,"err%d.m",iteration);
- err=fopen(name,"w");
+ for(j=0;j<v->entries;j++){
+ if(v->assigned[j]){
+ for(k=0;k<v->elements;k++)
+ _now(v,j)[k]=(vN(newlo,j)[k]+vN(newhi,j)[k])/2.;
+ }
+ }
+ free(newlo);
+ free(newhi);
+ }
- sprintf(name,"bias%d.m",iteration);
- bias=fopen(name,"w");
+ for(i=0;i<v->entries;i++){
+ asserror+=fabs(fdesired-v->assigned[i]);
+ }
- sprintf(name,"as%d.m",iteration);
- as=fopen(name,"w");
+ fprintf(stderr,"recenter: dist error=%g(%g) metric error=%g\n",
+ asserror/v->entries,fdesired,meterror/v->points);
+
+ memset(v->bias,0,sizeof(double)*v->entries);
+}
+void vqgen_rebias(vqgen *v){
+ long i,j,k;
+ double fdesired=(float)v->points/v->entries;
+ long desired=(v->points+v->entries-1)/v->entries;
- /* init */
- memset(v->entry_next,0,sizeof(double)*v->elements*v->entries);
- memset(v->assigned,0,sizeof(long)*v->entries);
- memset(v->metric,0,sizeof(double)*v->entries);
+ double asserror=0.;
+ double meterror=0.;
+ long *nearcount=calloc(v->entries,sizeof(long));
+ double *nearbias=malloc(v->entries*desired*sizeof(double));
if(v->entries<2)exit(1);
- /* assign all the points, accumulate metric */
+ /* second round: fill in nearest points for entries */
+
+ memset(v->assigned,0,sizeof(long)*v->entries);
for(i=0;i<v->points;i++){
- double firstmetric=v->metric_func(v,_now(v,0),_point(v,i))+v->bias[0];
- double secondmetric=v->metric_func(v,_now(v,1),_point(v,i))+v->bias[1];
+ /* not clear this should be biased */
+ double firstmetric=v->metric_func(v,_now(v,0),_point(v,i));
+ double secondmetric=v->metric_func(v,_now(v,1),_point(v,i));
long firstentry=0;
- long secondentry=0;
-
+ long secondentry=1;
if(firstmetric>secondmetric){
- double tempmetric=firstmetric;
+ double temp=firstmetric;
firstmetric=secondmetric;
- secondmetric=tempmetric;
+ secondmetric=temp;
firstentry=1;
- secondentry=1;
+ secondentry=0;
}
-
+
for(j=2;j<v->entries;j++){
- double thismetric=v->metric_func(v,_now(v,j),_point(v,i))+v->bias[j];
+ double thismetric=v->metric_func(v,_now(v,j),_point(v,i));
if(thismetric<secondmetric){
if(thismetric<firstmetric){
secondmetric=firstmetric;
}
}
}
-
- v->first[i]=firstentry;
- v->second[i]=secondentry;
- v->metric[firstentry]+=firstmetric-v->bias[firstentry];
v->assigned[firstentry]++;
+ meterror+=firstmetric;
+
+ for(j=0;j<v->entries;j++){
+
+ double thismetric;
+ double *nearbiasptr=nearbias+desired*j;
+ long k=nearcount[j]-1;
+
+ /* 'thismetric' is to be the bias value necessary in the current
+ arrangement for entry j to capture point i */
+ if(firstentry==j){
+ /* use the secondary entry as the threshhold */
+ thismetric=secondmetric-v->metric_func(v,_now(v,j),_point(v,i));
+ }else{
+ /* use the primary entry as the threshhold */
+ thismetric=firstmetric-v->metric_func(v,_now(v,j),_point(v,i));
+ }
- {
- double *no=_now(v,firstentry);
- double *ne=_next(v,firstentry);
- double *p=_point(v,i);
- for(j=0;j<v->elements;j++)
- ne[j]+=p[j];
- fprintf(graph,"%g %g\n%g %g\n\n",p[0],p[1],no[0],no[1]);
+ if(k>=0 && thismetric>nearbiasptr[k]){
+
+ /* start at the end and search backward for where this entry
+ belongs */
+
+ for(;k>0;k--) if(nearbiasptr[k-1]>=thismetric)break;
+
+ /* insert at k. Shift and inject. */
+ memmove(nearbiasptr+k+1,nearbiasptr+k,(desired-k-1)*sizeof(double));
+ nearbiasptr[k]=thismetric;
+
+ if(nearcount[j]<desired)nearcount[j]++;
+
+ }else{
+ if(nearcount[j]<desired){
+ /* we checked the thresh earlier. We know this is the
+ last entry */
+ nearbiasptr[nearcount[j]++]=thismetric;
+ }
+ }
+ }
+ }
+
+ /* third round: inflate/deflate */
+ {
+ for(i=0;i<v->entries;i++){
+ v->bias[i]=nearbias[(i+1)*desired-1];
}
}
- /* new midpoints */
for(i=0;i<v->entries;i++){
- double *next=_next(v,i);
- double *now=_now(v,i);
- if(v->assigned[i]){
- for(j=0;j<v->elements;j++)
- next[j]/=v->assigned[i];
- }else{
- for(j=0;j<v->elements;j++)
- next[j]=now[j];
- }
+ asserror+=fabs(fdesired-v->assigned[i]);
}
+
+ fprintf(stderr,"rebias: dist error=%g(%g) metric error=%g\n",
+ asserror/v->entries,fdesired,meterror/v->points);
- /* average global metric */
- for(i=0;i<v->entries;i++){
- avmetric+=v->metric[i];
+ free(nearcount);
+ free(nearbias);
+}
+
+/* the additional fields are the hyperplanes we've already used to
+ split the set. The additional hyperplanes are necessary to bound
+ later splits. One per depth */
+
+int lp_split(vqgen *v,long *index,long points,
+ double *additional_a, double *additional_b, long depth){
+ static int frameno=0;
+ long A[points];
+ long B[points];
+ long ap=0;
+ long bp=0;
+ long cp=0;
+ long i,j,k;
+ long leaves=0;
+
+ double best=0.;
+ long besti=-1;
+ long bestj=-1;
+
+ if(depth>7){
+ printf("leaf: points %ld, depth %ld\n",points,depth);
+ return(1);
}
- avmetric/=v->entries;
- fprintf(stderr,"%ld... ",iteration);
-
- /* positive/negative 'pressure' */
- if(biasp){
- /* Another round of n*m. Above we had to index by point. Now, we
- have to index by entry */
- long *index=alloca(v->points*sizeof(long));
- double *vals =alloca(v->points*sizeof(double));
- double *met =alloca(v->points*sizeof(double));
- for(i=0;i<v->entries;i++){
- /* sort all n-thousand points by effective metric */
+ if(points==1){
+ printf("leaf: point %ld, depth %ld\n",index[0],depth);
+ return(1);
+ }
- for(j=0;j<v->points;j++){
- int threshentry;
- index[j]=j;
- if(v->first[j]==i){
- /* use the secondary entry as the threshhold */
- threshentry=v->second[j];
- }else{
- /* use the primary entry as the threshhold */
- threshentry=v->first[j];
+ if(points==2){
+ /* The result must be an even split */
+ B[bp++]=index[0];
+ A[ap++]=index[1];
+ printf("even split: depth %ld\n",depth);
+ return(2);
+ }else{
+ /* We need to find the best split */
+ for(i=0;i<points-1;i++){
+ for(j=i+1;j<points;j++){
+ if(_dist_sq(v,_now(v,index[i]),_now(v,index[j]))>best){
+ besti=i;
+ bestj=j;
+ best=_dist_sq(v,_now(v,index[i]),_now(v,index[j]));
}
-
- /* bias value right at the threshhold to grab this point */
- met[j]=v->metric_func(v,_now(v,i),_point(v,j));
- vals[j]=
- v->metric_func(v,_now(v,threshentry),_point(v,j))+
- v->bias[threshentry]-
- v->metric_func(v,_now(v,i),_point(v,j));
}
-
- sort_t_vals=vals;
- qsort(index,v->points,sizeof(long),sort_t_compare);
+ }
- {
- /* find the desired number of points and level of bias. We
- nominally want all entries to represent the same number of
- points, but we may also have a metric range restriction */
- int desired=(v->points+v->entries-1)/v->entries;
+ /* We have our endpoints. initial divvy */
+ {
+ double *cA=malloc(v->elements*sizeof(double));
+ double *cB=malloc(v->elements*sizeof(double));
+ double **a=malloc((points+depth)*sizeof(double *));
+ double *b=malloc((points+depth)*sizeof(double));
+ double *aa=malloc((points+depth)*v->elements*sizeof(double));
+ double dA=0.,dB=0.;
+ minit l;
+
+ minit_init(&l,v->elements,points+depth-1,0);
+
+ /* divisor hyperplane */
+ for(i=0;i<v->elements;i++){
+ double m=(_now(v,index[besti])[i]+_now(v,index[bestj])[i])/2;
+ cA[i]=_now(v,index[besti])[i]-_now(v,index[bestj])[i];
+ cB[i]=-cA[i];
+ dA+=cA[i]*m;
+ dB-=cA[i]*m;
+ }
+
+ for(i=0;i<points+depth;i++)
+ a[i]=aa+i*v->elements;
+
+ /* check each bubble to see if it intersects the divisor hyperplane */
+ for(j=0;j<points;j++){
+ long count=0,m=0;
+ double d1=0.,d2=0.;
+ int ret;
- if(v->errspread>=1.){
- double acc=0.;
- for(j=0;j<desired;j++){
- acc+=met[index[j]];
- if(acc*v->errspread>avmetric)break;
+ if(j==besti){
+ B[bp++]=index[j];
+ }else if (j==bestj){
+ A[ap++]=index[j];
+ }else{
+
+ for(i=0;i<points;i++){
+ if(i!=j){
+ b[count]=0.;
+ for(k=0;k<v->elements;k++){
+ double m=(_now(v,index[i])[k]+_now(v,index[j])[k])/2;
+ a[count][k]=_now(v,index[i])[k]-_now(v,index[j])[k];
+ b[count]+=a[count][k]*m;
+ }
+ count++;
+ }
}
- }else
- j=desired;
- v->bias[i]=vals[index[j-1]];
+
+ /* additional bounding hyperplanes from previous splits */
+ for(i=0;i<depth;i++){
+ b[count]=0.;
+ for(k=0;k<v->elements;k++)
+ a[count][k]=additional_a[m++];
+ b[count++]=additional_b[i];
+ }
+
+ /* on what side of the dividing hyperplane is the current test
+ point? */
+ for(i=0;i<v->elements;i++)
+ d1+=_now(v,index[j])[i]*cA[i];
+
+
+ if(d1<dA){
+ fprintf(stderr,"+");
+ ret=minit_solve(&l,a,b,cA,1e-6,NULL,NULL,&d2);
+ }else{
+ fprintf(stderr,"-");
+ ret=minit_solve(&l,a,b,cB,1e-6,NULL,NULL,&d2);
+ d2= -d2;
+ }
+
+ switch(ret){
+ case 0:
+ /* bounded solution */
+ if(d1<dA){
+ A[ap++]=index[j];
+ if(d2>dA){cp++;B[bp++]=index[j];}
+ }else{
+ B[bp++]=index[j];
+ if(d2<dA){cp++;A[ap++]=index[j];}
+ }
+ break;
+ default:
+ /* unbounded solution or no solution; we're in both sets */
+ B[bp++]=index[j];
+ A[ap++]=index[j];
+ cp++;
+ break;
+ }
+ }
+ }
+
+ /*{
+ char buffer[80];
+ FILE *o;
+ int i;
+
+ sprintf(buffer,"set%d.m",frameno);
+ o=fopen(buffer,"w");
+ for(i=0;i<points;i++)
+ fprintf(o,"%g %g\n\n",_now(v,index[i])[0],_now(v,index[i])[1]);
+ fclose(o);
+
+ sprintf(buffer,"setA%d.m",frameno);
+ o=fopen(buffer,"w");
+ for(i=0;i<ap;i++)
+ fprintf(o,"%g %g\n\n",_now(v,A[i])[0],_now(v,A[i])[1]);
+ fclose(o);
+
+ sprintf(buffer,"setB%d.m",frameno);
+ o=fopen(buffer,"w");
+ for(i=0;i<bp;i++)
+ fprintf(o,"%g %g\n\n",_now(v,B[i])[0],_now(v,B[i])[1]);
+ fclose(o);
+
+ sprintf(buffer,"div%d.m",frameno);
+ o=fopen(buffer,"w");
+ fprintf(o,"%g %g\n%g %g\n\n",
+ _now(v,index[besti])[0],
+ (dA-cA[0]*_now(v,index[besti])[0])/cA[1],
+ _now(v,index[bestj])[0],
+ (dA-cA[0]*_now(v,index[bestj])[0])/cA[1]);
+ fclose(o);
+
+ sprintf(buffer,"bound%d.m",frameno);
+ o=fopen(buffer,"w");
+ for(i=0;i<depth;i++)
+ fprintf(o,"%g %g\n%g %g\n\n",
+ _now(v,index[besti])[0],
+ (additional_b[i]-
+ additional_a[i*2]*_now(v,index[besti])[0])/
+ additional_a[i*2+1],
+ _now(v,index[bestj])[0],
+ (additional_b[i]-
+ additional_a[i*2]*_now(v,index[bestj])[0])/
+ additional_a[i*2+1]);
+ fclose(o);
+ frameno++;
+ }*/
+
+
+ minit_clear(&l);
+ free(a);
+ free(b);
+ free(aa);
+
+ fprintf(stderr,"split: total=%ld depth=%ld set A=%ld:%ld:%ld=B\n",
+ points,depth,ap-cp,cp,bp-cp);
+
+ /* handle adding this divisor hyperplane to the additional
+ constraints. The 'inside' side is different for A and B */
+
+ {
+ /* marginally wasteful */
+ double *newadd_a=alloca(sizeof(double)*v->elements*(depth+1));
+ double *newadd_b=alloca(sizeof(double)*(depth+1));
+ if(additional_a){
+ memcpy(newadd_a,additional_a,sizeof(double)*v->elements*depth);
+ memcpy(newadd_b,additional_b,sizeof(double)*depth);
+ }
+
+ memcpy(newadd_a+v->elements*depth,cA,sizeof(double)*v->elements);
+ newadd_b[depth]=dA;
+ leaves=lp_split(v,A,ap,newadd_a,newadd_b,depth+1);
+
+ memcpy(newadd_a+v->elements*depth,cB,sizeof(double)*v->elements);
+ newadd_b[depth]=dB;
+ leaves+=lp_split(v,B,bp,newadd_a,newadd_b,depth+1);
+
}
+ free(cA);
+ free(cB);
+ return(leaves);
}
- }else{
- memset(v->bias,0,sizeof(double)*v->entries);
}
+}
+
+void vqgen_book(vqgen *v){
+
- /* dump state, report metric */
- for(i=0;i<v->entries;i++){
- for(j=0;j<v->assigned[i];j++)
- fprintf(err,"%g\n",v->metric[i]/v->assigned[i]);
- fprintf(bias,"%g\n",v->bias[i]);
- fprintf(as,"%ld\n",v->assigned[i]);
- }
- fprintf(stderr,"average metric: %g\n",avmetric/v->elements/v->points*v->entries);
- fclose(as);
- fclose(err);
- fclose(bias);
- fclose(graph);
- memcpy(v->entry_now,v->entry_next,sizeof(double)*v->entries*v->elements);
- iteration++;
}
+static double testset24[48]={
+1.047758,1.245406,
+1.007972,1.150078,
+1.064390,1.146266,
+0.761842,0.826055,
+0.862073,1.243707,
+0.746351,1.055368,
+0.956844,1.048223,
+0.877782,1.111871,
+0.964564,1.309219,
+0.920062,1.168658,
+0.787654,0.895163,
+0.974003,1.200115,
+0.788360,1.142671,
+0.978414,1.122249,
+0.869938,0.954436,
+1.131220,1.348747,
+0.934630,1.108564,
+0.896666,1.045772,
+0.707360,0.920954,
+0.788914,0.970626,
+0.828682,1.043673,
+1.042016,1.190406,
+1.031643,1.068194,
+1.120824,1.220326,
+};
+
+static double testset256[1024]={
+1.047758,1.245406,1.007972,1.150078,
+1.064390,1.146266,0.761842,0.826055,
+0.862073,1.243707,0.746351,1.055368,
+0.956844,1.048223,0.877782,1.111871,
+0.964564,1.309219,0.920062,1.168658,
+0.787654,0.895163,0.974003,1.200115,
+0.788360,1.142671,0.978414,1.122249,
+0.869938,0.954436,1.131220,1.348747,
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+
+};
+
int main(int argc,char *argv[]){
FILE *in=fopen(argv[1],"r");
vqgen v;
char buffer[160];
- int i;
-
- vqgen_init(&v,4,24,_dist_sq,1.);
+ int i,j;
+ vqgen_init(&v,4,256,_dist_sq,0.);
+
while(fgets(buffer,160,in)){
double a[8];
if(sscanf(buffer,"%lf %lf %lf %lf",
vqgen_addpoint(&v,a);
}
fclose(in);
+
+ for(i=0;i<10;i++)
+ vqgen_recenter(&v);
+
+ for(i=0;i<100;i++){
+ vqgen_rebias(&v);
+ vqgen_recenter(&v);
+ fprintf(stderr,"%d ",i);
+ }
- for(i=0;i<20;i++)
- vqgen_iterate(&v,0);
+ vqgen_recenter(&v);
- for(i=0;i<100;i++)
- vqgen_iterate(&v,1);
+ exit(0);
- for(i=0;i<5;i++)
- vqgen_iterate(&v,0);
+ memcpy(v.entrylist,testset256,sizeof(testset256));
+ for(i=0;i<v.entries;i++){
+ printf("\n");
+ for(j=0;j<v.elements;j++)
+ printf("%f,",_now(&v,i)[j]);
+ }
+ printf("\n");
+
+
+ /* try recursively splitting the space using LP
+ {
+ long index[v.entries];
+ for(i=0;i<v.entries;i++)index[i]=i;
+ fprintf(stderr,"\n\nleaves=%d\n",
+ lp_split(&v,index,v.entries,NULL,NULL,0));
+ }*/
+
return(0);
}
+
+
+
+
+
+
+
+
+
+
+
+
projects / platform / upstream / libvorbis.git / commitdiff