--- /dev/null
+/*
+ * This file is part of TISEAN
+ *
+ * Copyright (c) 1998-2007 Rainer Hegger, Holger Kantz, Thomas Schreiber
+ *
+ * TISEAN is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * TISEAN 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 General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with TISEAN; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+/*Author: Rainer Hegger, last modified Dec 4, 2005 */
+/*Changes:
+ 7/14/05: Changed borders of the sort routine to speed things up
+ 11/25/05: Show also absolute forecast errors
+ 12/04/05: Some more changes in sort
+ 12/20/05: Change in increase neighborhood size loop
+ 12/28/05: Found bug in memory allocation (index)
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <limits.h>
+#include <time.h>
+#include <string.h>
+#include "routines/tsa.h"
+
+#define WID_STR "Estimates the spectrum of Lyapunov exponents using the\n\t\
+method of Sano and Sawada."
+
+#define OUT 10
+
+#define BOX 512
+#define EPSMAX 1.0
+#define DELAY 1
+
+char epsset=0,stdo=1;
+char INVERSE,*outfile=NULL;
+char *infile=NULL;
+char dimset=0;
+char *COLUMNS=NULL;
+unsigned long LENGTH=ULONG_MAX,ITERATIONS,exclude=0;
+unsigned int EMBED=2,DIMENSION=1/*,DELAY=1*/,MINNEIGHBORS=30;
+unsigned int verbosity=0xff;
+double EPSSTEP=1.2;
+
+double **series,*averr,avneig=0.0,aveps=0.0;
+double **mat,*vec,*abstand;
+double epsmin;
+long imax=BOX-1,count=0;
+long **box,*list;
+unsigned long *found;
+unsigned int alldim,**indexes;
+
+void show_options(char *progname)
+{
+ what_i_do(progname,WID_STR);
+ fprintf(stderr," Usage: %s [options]\n",progname);
+ fprintf(stderr," Options:\n");
+ fprintf(stderr,"Everything not being a valid option will be interpreted"
+ " as a possible"
+ " datafile.\nIf no datafile is given stdin is read. Just - also"
+ " means stdin\n");
+ fprintf(stderr,"\t-l # of datapoints [default is whole file]\n");
+ fprintf(stderr,"\t-x # of lines to be ignored [default is 0]\n");
+ fprintf(stderr,"\t-c column to read[default 1]\n");
+ fprintf(stderr,"\t-m # of components,embedding dimension [default %d,%d]\n",
+ DIMENSION,EMBED);
+ // fprintf(stderr,"\t-d delay [default %d]\n",DELAY);
+ fprintf(stderr,"\t-r epsilon size to start with [default "
+ "(data interval)/1000]\n");
+ fprintf(stderr,"\t-f factor to increase epsilon [default: 1.2]\n");
+ fprintf(stderr,"\t-k # of neighbors to use [default: 30]\n");
+ fprintf(stderr,"\t-n # of iterations [default: length]\n");
+ fprintf(stderr,"\t-I invert the time series [default: no]\n");
+ fprintf(stderr,"\t-o name of output file [default 'datafile'.lyaps]\n");
+ fprintf(stderr,"\t-V verbosity level [default: 1]\n\t\t"
+ "0='only panic messages'\n\t\t"
+ "1='+ input/output messages'\n");
+ fprintf(stderr,"\t-h show these options\n");
+ fprintf(stderr,"\n");
+ exit(0);
+}
+
+void scan_options(int n,char **argv)
+{
+ char *out;
+
+ if ((out=check_option(argv,n,'l','u')) != NULL)
+ sscanf(out,"%lu",&LENGTH);
+ if ((out=check_option(argv,n,'x','u')) != NULL)
+ sscanf(out,"%lu",&exclude);
+ if ((out=check_option(argv,n,'c','s')) != NULL)
+ COLUMNS=out;
+ /* if ((out=check_option(argv,n,'d','u')) != NULL)
+ sscanf(out,"%u",&DELAY);*/
+ if ((out=check_option(argv,n,'m','2')) != NULL) {
+ sscanf(out,"%u,%u",&DIMENSION,&EMBED);
+ dimset=1;
+ }
+ if ((out=check_option(argv,n,'n','u')) != NULL)
+ sscanf(out,"%lu",&ITERATIONS);
+ if ((out=check_option(argv,n,'r','f')) != NULL) {
+ epsset=1;
+ sscanf(out,"%lf",&epsmin);
+ }
+ if ((out=check_option(argv,n,'f','f')) != NULL)
+ sscanf(out,"%lf",&EPSSTEP);
+ if ((out=check_option(argv,n,'k','u')) != NULL)
+ sscanf(out,"%u",&MINNEIGHBORS);
+ if ((out=check_option(argv,n,'V','u')) != NULL)
+ sscanf(out,"%u",&verbosity);
+ if ((out=check_option(argv,n,'I','n')) != NULL)
+ INVERSE=1;
+ if ((out=check_option(argv,n,'o','o')) != NULL) {
+ stdo=0;
+ if (strlen(out) > 0)
+ outfile=out;
+ }
+}
+
+double sort(long act,unsigned long* nfound,char *enough)
+{
+ double maxeps=0.0,dx,dswap,maxdx;
+ long self=0,i,j,del,hf,iswap,n1;
+ unsigned long imax=*nfound;
+
+ *enough=0;
+
+ for (i=0;i<imax;i++) {
+ hf=found[i];
+ if (hf != act) {
+ maxdx=fabs(series[0][act]-series[0][hf]);
+ for (j=1;j<alldim;j++) {
+ n1=indexes[0][j];
+ del=indexes[1][j];
+ dx=fabs(series[n1][act-del]-series[n1][hf-del]);
+ if (dx > maxdx) maxdx=dx;
+ }
+ abstand[i]=maxdx;
+ }
+ else {
+ self=i;
+ }
+ }
+
+ if (self != (imax-1)) {
+ abstand[self]=abstand[imax-1];
+ found[self]=found[imax-1];
+ }
+
+ for (i=0;i<MINNEIGHBORS;i++) {
+ for (j=i+1;j<imax-1;j++) {
+ if (abstand[j]<abstand[i]) {
+ dswap=abstand[i];
+ abstand[i]=abstand[j];
+ abstand[j]=dswap;
+ iswap=found[i];
+ found[i]=found[j];
+ found[j]=iswap;
+ }
+ }
+ }
+
+ if (!epsset || (abstand[MINNEIGHBORS-1] >= epsmin)) {
+ *nfound=MINNEIGHBORS;
+ *enough=1;
+ maxeps=abstand[MINNEIGHBORS-1];
+
+ return maxeps;
+ }
+
+ for (i=MINNEIGHBORS;i<imax-2;i++) {
+ for (j=i+1;j<imax-1;j++) {
+ if (abstand[j]<abstand[i]) {
+ dswap=abstand[i];
+ abstand[i]=abstand[j];
+ abstand[j]=dswap;
+ iswap=found[i];
+ found[i]=found[j];
+ found[j]=iswap;
+ }
+ }
+ if (abstand[i] > epsmin) {
+ (*nfound)=i+1;
+ *enough=1;
+ maxeps=abstand[i];
+
+ return maxeps;
+ }
+ }
+
+ maxeps=abstand[imax-2];
+
+ return maxeps;
+}
+
+void make_dynamics(double **dynamics,long act)
+{
+ long i,hi,j,hj,k,t=act,d;
+ unsigned long nfound=0;
+ double **hser,**imat;
+ double foundeps=0.0,epsilon,hv,hv1;
+ double new_vec;
+ char got_enough;
+
+ check_alloc(hser=(double**)malloc(sizeof(double*)*DIMENSION));
+ for (i=0;i<DIMENSION;i++)
+ hser[i]=series[i]+act;
+
+ epsilon=epsmin/EPSSTEP;
+ do {
+ epsilon *= EPSSTEP;
+ if (epsilon > EPSMAX)
+ epsilon=EPSMAX;
+ make_multi_box(series,box,list,LENGTH-DELAY,BOX,DIMENSION,EMBED,
+ DELAY,epsilon);
+ nfound=find_multi_neighbors(series,box,list,hser,LENGTH-DELAY,BOX,
+ DIMENSION,EMBED,DELAY,epsilon,found);
+ if (nfound > MINNEIGHBORS) {
+ foundeps=sort(act,&nfound,&got_enough);
+ if (got_enough)
+ break;
+ }
+ } while (epsilon < EPSMAX);
+
+ free(hser);
+
+ avneig += nfound;
+ aveps += foundeps;
+ if (!epsset)
+ epsmin=aveps/count;
+ if (nfound < MINNEIGHBORS) {
+ fprintf(stderr,"#Not enough neighbors found. Exiting\n");
+ exit(LYAP_SPEC_NOT_ENOUGH_NEIGHBORS);
+ }
+
+ for (i=0;i<=alldim;i++) {
+ vec[i]=0.0;
+ for (j=0;j<=alldim;j++)
+ mat[i][j]=0.0;
+ }
+
+ for (i=0;i<nfound;i++) {
+ act=found[i];
+ mat[0][0] += 1.0;
+ for (j=0;j<alldim;j++)
+ mat[0][j+1] += series[indexes[0][j]][act-indexes[1][j]];
+ for (j=0;j<alldim;j++) {
+ hv1=series[indexes[0][j]][act-indexes[1][j]];
+ hj=j+1;
+ for (k=j;k<alldim;k++)
+ mat[hj][k+1] += series[indexes[0][k]][act-indexes[1][k]]*hv1;
+ }
+ }
+
+ for (i=0;i<=alldim;i++)
+ for (j=i;j<=alldim;j++)
+ mat[j][i]=(mat[i][j]/=(double)nfound);
+
+ imat=invert_matrix(mat,alldim+1);
+
+ for (d=0;d<DIMENSION;d++) {
+ for (i=0;i<=alldim;i++)
+ vec[i]=0.0;
+ for (i=0;i<nfound;i++) {
+ act=found[i];
+ hv=series[d][act+DELAY];
+ vec[0] += hv;
+ for (j=0;j<alldim;j++)
+ vec[j+1] += hv*series[indexes[0][j]][act-indexes[1][j]];
+ }
+ for (i=0;i<=alldim;i++)
+ vec[i] /= (double)nfound;
+
+ new_vec=0.0;
+ for (i=0;i<=alldim;i++)
+ new_vec += imat[0][i]*vec[i];
+ for (i=1;i<=alldim;i++) {
+ hi=i-1;
+ dynamics[d][hi]=0.0;
+ for (j=0;j<=alldim;j++)
+ dynamics[d][hi] += imat[i][j]*vec[j];
+ }
+ for (i=0;i<alldim;i++)
+ new_vec += dynamics[d][i]*series[indexes[0][i]][t-indexes[1][i]];
+ averr[d] += (new_vec-series[d][t+DELAY])*(new_vec-series[d][t+DELAY]);
+ }
+
+ for (i=0;i<=alldim;i++)
+ free(imat[i]);
+ free(imat);
+}
+
+void gram_schmidt(double **delta,
+ double *stretch)
+{
+ double **dnew,norm,*diff;
+ long i,j,k;
+
+ check_alloc(diff=(double*)malloc(sizeof(double)*alldim));
+ check_alloc(dnew=(double**)malloc(sizeof(double*)*alldim));
+ for (i=0;i<alldim;i++)
+ check_alloc(dnew[i]=(double*)malloc(sizeof(double)*alldim));
+
+ for (i=0;i<alldim;i++) {
+ for (j=0;j<alldim;j++)
+ diff[j]=0.0;
+ for (j=0;j<i;j++) {
+ norm=0.0;
+ for (k=0;k<alldim;k++)
+ norm += delta[i][k]*dnew[j][k];
+ for (k=0;k<alldim;k++)
+ diff[k] -= norm*dnew[j][k];
+ }
+ norm=0.0;
+ for (j=0;j<alldim;j++)
+ norm += sqr(delta[i][j]+diff[j]);
+ stretch[i]=(norm=sqrt(norm));
+ for (j=0;j<alldim;j++)
+ dnew[i][j]=(delta[i][j]+diff[j])/norm;
+ }
+ for (i=0;i<alldim;i++)
+ for (j=0;j<alldim;j++)
+ delta[i][j]=dnew[i][j];
+
+ free(diff);
+ for (i=0;i<alldim;i++)
+ free(dnew[i]);
+ free(dnew);
+}
+
+void make_iteration(double **dynamics,
+ double **delta)
+{
+ double **dnew;
+ long i,j,k;
+
+ check_alloc(dnew=(double**)malloc(sizeof(double*)*alldim));
+ for (i=0;i<alldim;i++)
+ check_alloc(dnew[i]=(double*)malloc(sizeof(double)*alldim));
+
+ for (i=0;i<alldim;i++) {
+ for (j=0;j<DIMENSION;j++) {
+ dnew[i][j]=dynamics[j][0]*delta[i][0];
+ for (k=1;k<alldim;k++)
+ dnew[i][j] += dynamics[j][k]*delta[i][k];
+ }
+ for (j=DIMENSION;j<alldim;j++)
+ dnew[i][j]=delta[i][j-1];
+ }
+
+ for (i=0;i<alldim;i++)
+ for (j=0;j<alldim;j++)
+ delta[i][j]=dnew[i][j];
+
+ for (i=0;i<alldim;i++)
+ free(dnew[i]);
+ free(dnew);
+}
+
+int main(int argc,char **argv)
+{
+ char stdi=0;
+ double **delta,**dynamics,*lfactor;
+ double *factor,dim;
+ double *hseries;
+ double *interval,*min,*av,*var,maxinterval;
+ long start,i,j;
+ time_t lasttime,newtime;
+ FILE *file=NULL;
+
+ if (scan_help(argc,argv))
+ show_options(argv[0]);
+
+ ITERATIONS=ULONG_MAX;
+
+ scan_options(argc,argv);
+#ifndef OMIT_WHAT_I_DO
+ if (verbosity&VER_INPUT)
+ what_i_do(argv[0],WID_STR);
+#endif
+
+ infile=search_datafile(argc,argv,NULL,verbosity);
+ if (infile == NULL)
+ stdi=1;
+
+ if (outfile == NULL) {
+ if (!stdi) {
+ check_alloc(outfile=(char*)calloc(strlen(infile)+7,(size_t)1));
+ strcpy(outfile,infile);
+ strcat(outfile,".lyaps");
+ }
+ else {
+ check_alloc(outfile=(char*)calloc((size_t)12,(size_t)1));
+ strcpy(outfile,"stdin.lyaps");
+ }
+ }
+ if (!stdo)
+ test_outfile(outfile);
+
+ alldim=DIMENSION*EMBED;
+
+ if (COLUMNS == NULL)
+ series=(double**)get_multi_series(infile,&LENGTH,exclude,&DIMENSION,"",
+ dimset,verbosity);
+ else
+ series=(double**)get_multi_series(infile,&LENGTH,exclude,&DIMENSION,
+ COLUMNS,dimset,verbosity);
+
+ if (MINNEIGHBORS > (LENGTH-DELAY*(EMBED-1)-1)) {
+ fprintf(stderr,"Your time series is not long enough to find %d neighbors!"
+ " Exiting.\n",MINNEIGHBORS);
+ exit(LYAP_SPEC_DATA_TOO_SHORT);
+ }
+
+ check_alloc(min=(double*)malloc(sizeof(double)*DIMENSION));
+ check_alloc(interval=(double*)malloc(sizeof(double)*DIMENSION));
+ check_alloc(av=(double*)malloc(sizeof(double)*DIMENSION));
+ check_alloc(var=(double*)malloc(sizeof(double)*DIMENSION));
+ check_alloc(averr=(double*)malloc(sizeof(double)*DIMENSION));
+ maxinterval=0.0;
+ for (i=0;i<DIMENSION;i++) {
+ averr[i]=0.0;
+ rescale_data(series[i],LENGTH,&min[i],&interval[i]);
+ if (interval[i] > maxinterval)
+ maxinterval=interval[i];
+ variance(series[i],LENGTH,&av[i],&var[i]);
+ }
+
+ if (INVERSE) {
+ check_alloc(hseries=(double*)malloc(sizeof(double)*LENGTH));
+ for (j=0;j<DIMENSION;j++) {
+ for (i=0;i<LENGTH;i++)
+ hseries[LENGTH-1-i]=series[j][i];
+ for (i=0;i<LENGTH;i++)
+ series[j][i]=hseries[i];
+ }
+ free(hseries);
+ }
+
+ if (!epsset)
+ epsmin=1./1000.;
+ else
+ epsmin /= maxinterval;
+
+ check_alloc(box=(long**)malloc(sizeof(long*)*BOX));
+ for (i=0;i<BOX;i++)
+ check_alloc(box[i]=(long*)malloc(sizeof(long)*BOX));
+
+ check_alloc(list=(long*)malloc(sizeof(long)*LENGTH));
+ check_alloc(found=(unsigned long*)malloc(sizeof(long)*LENGTH));
+
+ check_alloc(dynamics=(double**)malloc(sizeof(double*)*DIMENSION));
+ for (i=0;i<DIMENSION;i++)
+ check_alloc(dynamics[i]=(double*)malloc(sizeof(double)*alldim));
+ check_alloc(factor=(double*)malloc(sizeof(double)*alldim));
+ check_alloc(lfactor=(double*)malloc(sizeof(double)*alldim));
+ check_alloc(delta=(double**)malloc(sizeof(double*)*alldim));
+ for (i=0;i<alldim;i++)
+ check_alloc(delta[i]=(double*)malloc(sizeof(double)*alldim));
+
+ check_alloc(vec=(double*)malloc(sizeof(double)*(alldim+1)));
+ check_alloc(mat=(double**)malloc(sizeof(double*)*(alldim+1)));
+ for (i=0;i<=alldim;i++)
+ check_alloc(mat[i]=(double*)malloc(sizeof(double)*(alldim+1)));
+
+ indexes=(unsigned int**)make_multi_index(DIMENSION,EMBED,DELAY);
+
+ rnd_init(0x098342L);
+ for (i=0;i<10000;i++)
+ rnd_long();
+ for (i=0;i<alldim;i++) {
+ factor[i]=0.0;
+ for (j=0;j<alldim;j++)
+ delta[i][j]=(double)rnd_long()/(double)ULONG_MAX;
+ }
+ gram_schmidt(delta,lfactor);
+
+ start=ITERATIONS;
+ if (start>(LENGTH-DELAY))
+ start=LENGTH-DELAY;
+
+ if (!stdo) {
+ file=fopen(outfile,"w");
+ if (verbosity&VER_INPUT)
+ fprintf(stderr,"Opened %s for writing\n",outfile);
+ }
+ else {
+ if (verbosity&VER_INPUT)
+ fprintf(stderr,"Writing to stdout\n");
+ }
+
+ check_alloc(abstand=(double*)malloc(sizeof(double)*LENGTH));
+
+ time(&lasttime);
+ for (i=(EMBED-1)*DELAY;i<start;i++) {
+ count++;
+ make_dynamics(dynamics,i);
+ make_iteration(dynamics,delta);
+ gram_schmidt(delta,lfactor);
+ for (j=0;j<alldim;j++) {
+ factor[j] += log(lfactor[j])/(double)DELAY;
+ }
+ if (((time(&newtime)-lasttime) > OUT) || (i == (start-1))) {
+ time(&lasttime);
+ if (!stdo) {
+ fprintf(file,"%ld ",count);
+ for (j=0;j<alldim;j++)
+ fprintf(file,"%e ",factor[j]/count);
+ fprintf(file,"\n");
+ fflush(file);
+ }
+ else {
+ fprintf(stdout,"%ld ",count);
+ for (j=0;j<alldim;j++)
+ fprintf(stdout,"%e ",factor[j]/count);
+ fprintf(stdout,"\n");
+ }
+ }
+ }
+
+ dim=0.0;
+ for (i=0;i<alldim;i++) {
+ dim += factor[i];
+ if (dim < 0.0)
+ break;
+ }
+ if (i < alldim)
+ dim=i+(dim-factor[i])/fabs(factor[i]);
+ else
+ dim=alldim;
+ if (!stdo) {
+ fprintf(file,"#Average relative forecast errors:= ");
+ for (i=0;i<DIMENSION;i++)
+ fprintf(file,"%e ",sqrt(averr[i]/count)/var[i]);
+ fprintf(file,"\n");
+ fprintf(file,"#Average absolute forecast errors:= ");
+ for (i=0;i<DIMENSION;i++)
+ fprintf(file,"%e ",sqrt(averr[i]/count)*interval[i]);
+ fprintf(file,"\n");
+ fprintf(file,"#Average Neighborhood Size= %e\n",aveps*maxinterval/count);
+ fprintf(file,"#Average num. of neighbors= %e\n",avneig/count);
+ fprintf(file,"#estimated KY-Dimension= %f\n",dim);
+ }
+ else {
+ fprintf(stdout,"#Average relative forecast errors:= ");
+ for (i=0;i<DIMENSION;i++)
+ fprintf(stdout,"%e ",sqrt(averr[i]/count)/var[i]);
+ fprintf(stdout,"\n");
+ fprintf(stdout,"#Average absolute forecast errors:= ");
+ for (i=0;i<DIMENSION;i++)
+ fprintf(stdout,"%e ",sqrt(averr[i]/count)*interval[i]);
+ fprintf(stdout,"\n");
+ fprintf(stdout,"#Average Neighborhood Size= %e\n",aveps*maxinterval/count);
+ fprintf(stdout,"#Average num. of neighbors= %e\n",avneig/count);
+ fprintf(stdout,"#estimated KY-Dimension= %f\n",dim);
+ }
+ if (!stdo)
+ fclose(file);
+
+ free(abstand);
+
+ return 0;
+}
git://source.jalview.org / jabaws.git / blobdiff