+++ /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