lyap_spec.c

时间序列工具

      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;
}