+++ /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: Feb 6, 2006 */
-/*Changes:
- Feb 4, 2006: First version
- Feb 6, 2006: Find and remove bugs (1)
- Feb 11, 2006: Add rand_arb_dist to iterate_***_model
- */
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <limits.h>
-#include <math.h>
-#include "routines/tsa.h"
-
-#define WID_STR "Fits an multivariate ARIMA model to the data and gives\
- the coefficients\n\tand the residues (or an iterated model)"
-
-unsigned long length=ULONG_MAX,exclude=0;
-unsigned int dim=1,poles=10,ilength,ITER=50;
-unsigned int arpoles=0,ipoles=0,mapoles=0,offset;
-unsigned int verbosity=1;
-char *outfile=NULL,*column=NULL,stdo=1,dimset=0,run_model=0,arimaset=0;
-char *infile=NULL;
-double **series,convergence=1.0e-3;
-
-double *my_average;
-unsigned long ardim,armadim;
-unsigned int **aindex;
-
-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 length of file [default is whole file]\n");
- fprintf(stderr,"\t-x # of lines to be ignored [default is 0]\n");
- fprintf(stderr,"\t-m dimension [default is 1]\n");
- fprintf(stderr,"\t-c columns to read [default is 1,...,dimension]\n");
- fprintf(stderr,"\t-p order of initial AR-Fit [default is %u]\n",poles);
- fprintf(stderr,"\t-P order of AR,I,MA-Fit [default is %u,%u,%u]\n",
- arpoles,ipoles,mapoles);
- fprintf(stderr,"\t-I # of arima iterations [default is %u]\n",ITER);
- fprintf(stderr,"\t-e accuracy of convergence [default is %lf]\n",convergence);
- fprintf(stderr,"\t-s length of iterated model [default no iteration]\n");
- fprintf(stderr,"\t-o output file name [default is 'datafile'.ari]\n");
- fprintf(stderr,"\t-V verbosity level [default is 1]\n\t\t"
- "0='only panic messages'\n\t\t"
- "1='+ input/output messages'\n\t\t"
- "2='+ print residuals though iterating a model'\n\t\t"
- "4='+ print original data plus residuals'\n");
- fprintf(stderr,"\t-h show these options\n\n");
- exit(0);
-}
-
-void scan_options(int argc,char **argv)
-{
- char *out;
-
- if ((out=check_option(argv,argc,'p','u')) != NULL) {
- sscanf(out,"%u",&poles);
- if (poles < 1) {
- fprintf(stderr,"The order should at least be one!\n");
- exit(127);
- }
- }
- if ((out=check_option(argv,argc,'l','u')) != NULL)
- sscanf(out,"%lu",&length);
- if ((out=check_option(argv,argc,'x','u')) != NULL)
- sscanf(out,"%lu",&exclude);
- if ((out=check_option(argv,argc,'m','u')) != NULL) {
- sscanf(out,"%u",&dim);
- dimset=1;
- }
- if ((out=check_option(argv,argc,'P','3')) != NULL) {
- sscanf(out,"%u,%u,%u",&arpoles,&ipoles,&mapoles);
- if ((arpoles+ipoles+mapoles)>0)
- arimaset=1;
- }
- if ((out=check_option(argv,argc,'I','u')) != NULL)
- sscanf(out,"%u",&ITER);
- if ((out=check_option(argv,argc,'e','f')) != NULL)
- sscanf(out,"%lf",&convergence);
- if ((out=check_option(argv,argc,'c','u')) != NULL)
- column=out;
- if ((out=check_option(argv,argc,'V','u')) != NULL)
- sscanf(out,"%u",&verbosity);
- if ((out=check_option(argv,argc,'s','u')) != NULL) {
- sscanf(out,"%u",&ilength);
- run_model=1;
- }
- if ((out=check_option(argv,argc,'o','o')) != NULL) {
- stdo=0;
- if (strlen(out) > 0)
- outfile=out;
- }
-}
-
-void make_difference(void)
-{
- unsigned long i,d;
-
- for (i=length-1;i>0;i--)
- for (d=0;d<dim;d++)
- series[d][i]=series[d][i]-series[d][i-1];
-}
-
-unsigned int** make_ar_index(void)
-{
- unsigned int** ar_index;
- unsigned long i;
-
- check_alloc(ar_index=(unsigned int**)malloc(sizeof(unsigned int*)*2));
- for (i=0;i<2;i++)
- check_alloc(ar_index[i]=(unsigned int*)
- malloc(sizeof(unsigned int)*ardim));
- for (i=0;i<ardim;i++) {
- ar_index[0][i]=i/poles;
- ar_index[1][i]=i%poles;
- }
- return ar_index;
-}
-
-unsigned int** make_arima_index(unsigned int ars,unsigned int mas)
-{
- unsigned int** arima_index;
- unsigned int armad;
- unsigned long i,i0;
-
- armad=(ars+mas)*dim;
- check_alloc(arima_index=(unsigned int**)malloc(sizeof(unsigned int*)*2));
- for (i=0;i<2;i++)
- check_alloc(arima_index[i]=(unsigned int*)
- malloc(sizeof(unsigned int)*armad));
- for (i=0;i<ars*dim;i++) {
- arima_index[0][i]=i/ars;
- arima_index[1][i]=i%ars;
- }
- i0=ars*dim;
- for (i=0;i<mas*dim;i++) {
- arima_index[0][i+i0]=dim+i/mas;
- arima_index[1][i+i0]=i%mas;
- }
-
- return arima_index;
-}
-
-void set_averages_to_zero(void)
-{
- double var;
- long i,j;
-
- for (i=0;i<dim;i++) {
- variance(series[i],length,&my_average[i],&var);
- for (j=0;j<length;j++)
- series[i][j] -= my_average[i];
- }
-}
-
-double** build_matrix(double **mat,unsigned int size)
-{
- long n,i,j,is,id,js,jd;
- double norm;
-
- norm=1./((double)length-1.0-(double)poles-(double)offset);
-
- for (i=0;i<size;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- for (j=i;j<size;j++) {
- jd=aindex[0][j];
- js=aindex[1][j];
- mat[i][j]=0.0;
- for (n=offset+poles-1;n<length-1;n++)
- mat[i][j] += series[id][n-is]*series[jd][n-js];
- mat[i][j] *= norm;
- mat[j][i]=mat[i][j];
- }
- }
-
- return invert_matrix(mat,size);
-}
-
-void build_vector(double *vec,unsigned int size,long comp)
-{
- long i,is,id,n;
- double norm;
-
- norm=1./((double)length-1.0-(double)poles-(double)offset);
-
- for (i=0;i<size;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- vec[i]=0.0;
- for (n=offset+poles-1;n<length-1;n++)
- vec[i] += series[comp][n+1]*series[id][n-is];
- vec[i] *= norm;
- }
-}
-
-double* multiply_matrix_vector(double **mat,double *vec,unsigned int size)
-{
- long i,j;
- double *new_vec;
-
- check_alloc(new_vec=(double*)malloc(sizeof(double)*size));
-
- for (i=0;i<size;i++) {
- new_vec[i]=0.0;
- for (j=0;j<size;j++)
- new_vec[i] += mat[i][j]*vec[j];
- }
-
- return new_vec;
-}
-
-double* make_residuals(double **diff,double **coeff,unsigned int size)
-{
- long n,n1,d,i,is,id;
- double *resi;
-
- check_alloc(resi=(double*)malloc(sizeof(double)*dim));
- for (i=0;i<dim;i++)
- resi[i]=0.0;
-
- for (n=poles-1;n<length-1;n++) {
- n1=n+1;
- for (d=0;d<dim;d++) {
- diff[d][n1]=series[d][n1];
- for (i=0;i<size;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- diff[d][n1] -= coeff[d][i]*series[id][n-is];
- }
- resi[d] += sqr(diff[d][n1]);
- }
- }
-
- for (i=0;i<dim;i++)
- resi[i]=sqrt(resi[i]/((double)length-(double)poles));
-
- return resi;
-}
-
-void iterate_model(double **coeff,double *sigma,double **diff,FILE *file)
-{
- long i,j,i1,i2,n,d;
- double **iterate,*swap,**myrand;
-
- check_alloc(iterate=(double**)malloc(sizeof(double*)*(poles+1)));
- for (i=0;i<=poles;i++)
- check_alloc(iterate[i]=(double*)malloc(sizeof(double)*dim));
-
- check_alloc(myrand=(double**)malloc(sizeof(double*)*dim));
- for (i=0;i<dim;i++)
- myrand[i]=rand_arb_dist(diff[i],length,ilength+poles,100,0x44325);
-
- rnd_init(0x44325);
- for (i=0;i<1000;i++)
- rnd_long();
- for (i=0;i<dim;i++)
- for (j=0;j<poles;j++)
- iterate[j][i]=myrand[i][j];
-
- for (n=0;n<ilength;n++) {
- for (d=0;d<dim;d++) {
- iterate[poles][d]=myrand[d][n+poles];
- for (i1=0;i1<dim;i1++)
- for (i2=0;i2<poles;i2++)
- iterate[poles][d] += coeff[d][i1*poles+i2]*iterate[poles-1-i2][i1];
- }
- if (file != NULL) {
- for (d=0;d<dim;d++)
- fprintf(file,"%e ",iterate[poles][d]);
- fprintf(file,"\n");
- }
- else {
- for (d=0;d<dim;d++)
- printf("%e ",iterate[poles][d]);
- printf("\n");
- }
-
- swap=iterate[0];
- for (i=0;i<poles;i++)
- iterate[i]=iterate[i+1];
- iterate[poles]=swap;
- }
-
- for (i=0;i<=poles;i++)
- free(iterate[i]);
- free(iterate);
-
- for (i=0;i<dim;i++)
- free(myrand[i]);
- free(myrand);
-}
-
-void iterate_arima_model(double **coeff,double *sigma,double **diff,FILE *file)
-{
- double **iterate,*swap,**myrand;
- unsigned long i,j,n,is,id;
-
- check_alloc(iterate=(double**)malloc(sizeof(double*)*(poles+1)));
- for (i=0;i<=poles;i++)
- check_alloc(iterate[i]=(double*)malloc(sizeof(double)*2*dim));
-
- check_alloc(myrand=(double**)malloc(sizeof(double*)*dim));
- for (i=0;i<dim;i++)
- myrand[i]=rand_arb_dist(diff[i],length,ilength+poles,100,0x44325);
-
- rnd_init(0x44325);
- for (i=0;i<1000;i++)
- rnd_long();
- for (i=0;i<dim;i++)
- for (j=0;j<poles;j++)
- iterate[j][i]=iterate[j][dim+i]=myrand[i][j];
-
- for (n=0;n<ilength;n++) {
- for (i=0;i<dim;i++)
- iterate[poles][i]=iterate[poles][i+dim]=myrand[i][n+poles];
-
- for (j=0;j<dim;j++) {
- for (i=0;i<armadim;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- iterate[poles][j] += coeff[j][i]*iterate[poles-1-is][id];
- }
- }
-
- if (file != NULL) {
- for (i=0;i<dim;i++)
- fprintf(file,"%e ",iterate[poles][i]);
- fprintf(file,"\n");
- }
- else {
- for (i=0;i<dim;i++)
- printf("%e ",iterate[poles][i]);
- printf("\n");
- }
-
- swap=iterate[0];
- for (i=0;i<poles;i++)
- iterate[i]=iterate[i+1];
- iterate[poles]=swap;
- }
-
- for (i=0;i<=poles;i++)
- free(iterate[i]);
- free(iterate);
- for (i=0;i<dim;i++)
- free(myrand[i]);
- free(myrand);
-}
-
-int main(int argc,char **argv)
-{
- char stdi=0;
- double *pm;
- long i,j,iter,hj,realiter=0;
- unsigned int size,is,id;
- FILE *file;
- double **mat,**inverse,*vec,**coeff,**diff,**hseries;
- double **oldcoeff,*diffcoeff=NULL;
- double hdiff,**xdiff=NULL,avpm;
- double loglikelihood,aic,alldiff;
-
- if (scan_help(argc,argv))
- show_options(argv[0]);
-
- 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)+5,(size_t)1));
- strcpy(outfile,infile);
- strcat(outfile,".ari");
- }
- else {
- check_alloc(outfile=(char*)calloc((size_t)10,(size_t)1));
- strcpy(outfile,"stdin.ari");
- }
- }
- if (!stdo)
- test_outfile(outfile);
-
- if (column == NULL)
- series=(double**)get_multi_series(infile,&length,exclude,&dim,"",dimset,
- verbosity);
- else
- series=(double**)get_multi_series(infile,&length,exclude,&dim,column,
- dimset,verbosity);
-
- check_alloc(my_average=(double*)malloc(sizeof(double)*dim));
-
- for (i=0;i<ipoles;i++)
- make_difference();
-
- for (i=0;i<dim;i++)
- series[i] += ipoles;
- length -= ipoles;
-
- set_averages_to_zero();
-
- if (poles >= length) {
- fprintf(stderr,"It makes no sense to have more poles than data! Exiting\n");
- exit(AR_MODEL_TOO_MANY_POLES);
- }
- if (arimaset) {
- if ((arpoles >= length) || (mapoles >= length)) {
- fprintf(stderr,"It makes no sense to have more poles than data! Exiting\n");
- exit(AR_MODEL_TOO_MANY_POLES);
- }
- }
-
- ardim=poles*dim;
- aindex=make_ar_index();
-
- check_alloc(vec=(double*)malloc(sizeof(double)*ardim));
- check_alloc(mat=(double**)malloc(sizeof(double*)*ardim));
- for (i=0;i<ardim;i++)
- check_alloc(mat[i]=(double*)malloc(sizeof(double)*ardim));
-
- check_alloc(coeff=(double**)malloc(sizeof(double*)*dim));
- inverse=build_matrix(mat,ardim);
- for (i=0;i<dim;i++) {
- build_vector(vec,ardim,i);
- coeff[i]=multiply_matrix_vector(inverse,vec,ardim);
- }
-
- check_alloc(diff=(double**)malloc(sizeof(double*)*dim));
- for (i=0;i<dim;i++)
- check_alloc(diff[i]=(double*)malloc(sizeof(double)*length));
-
- pm=make_residuals(diff,coeff,ardim);
-
- free(vec);
- for (i=0;i<ardim;i++) {
- free(mat[i]);
- free(inverse[i]);
- }
- free(mat);
- free(inverse);
- size=ardim;
-
- if (arimaset) {
- offset=poles;
- for (i=0;i<2;i++)
- free(aindex[i]);
- free(aindex);
-
- for (i=0;i<dim;i++)
- free(coeff[i]);
- free(coeff);
- check_alloc(xdiff=(double**)malloc(sizeof(double*)*ITER));
- for (i=0;i<ITER;i++)
- check_alloc(xdiff[i]=(double*)malloc(sizeof(double)*dim));
-
- armadim=(arpoles+mapoles)*dim;
- aindex=make_arima_index(arpoles,mapoles);
- size=armadim;
-
- check_alloc(hseries=(double**)malloc(sizeof(double*)*2*dim));
- for (i=0;i<dim;i++) {
- check_alloc(hseries[i]=(double*)malloc(sizeof(double)*length));
- check_alloc(hseries[i+dim]=(double*)malloc(sizeof(double)*length));
- for (j=0;j<length;j++) {
- hseries[i][j]=series[i][j];
- hseries[i+dim][j]=diff[i][j];
- }
- }
-
- for (i=0;i<dim;i++)
- free(series[i]-ipoles);
- free(series);
-
- series=hseries;
-
- check_alloc(oldcoeff=(double**)malloc(sizeof(double*)*dim));
- for (i=0;i<dim;i++) {
- check_alloc(oldcoeff[i]=(double*)malloc(sizeof(double)*armadim));
- for (j=0;j<armadim;j++)
- oldcoeff[i][j]=0.0;
- }
- check_alloc(diffcoeff=(double*)malloc(sizeof(double)*ITER));
-
- for (iter=1;iter<=ITER;iter++) {
- check_alloc(vec=(double*)malloc(sizeof(double)*armadim));
- check_alloc(mat=(double**)malloc(sizeof(double*)*armadim));
- for (i=0;i<armadim;i++)
- check_alloc(mat[i]=(double*)malloc(sizeof(double)*armadim));
-
- check_alloc(coeff=(double**)malloc(sizeof(double*)*dim));
-
- poles=(arpoles > mapoles)? arpoles:mapoles;
-
- offset += poles;
- inverse=build_matrix(mat,armadim);
-
- for (i=0;i<dim;i++) {
- build_vector(vec,armadim,i);
- coeff[i]=multiply_matrix_vector(inverse,vec,armadim);
- }
-
- pm=make_residuals(diff,coeff,armadim);
-
- for (j=0;j<dim;j++) {
- hdiff=0.0;
- hj=j+dim;
- for (i=offset;i<length;i++)
- hdiff += sqr(series[hj][i]-diff[j][i]);
- for (i=0;i<length;i++) {
- series[hj][i]=diff[j][i];
- }
- xdiff[iter-1][j]=sqrt(hdiff/(double)(length-offset));
- }
-
- free(vec);
- for (i=0;i<armadim;i++) {
- free(mat[i]);
- free(inverse[i]);
- }
- free(mat);
- free(inverse);
-
- diffcoeff[iter-1]=0.0;
- for (i=0;i<dim;i++)
- for (j=0;j<dim;j++) {
- diffcoeff[iter-1] += sqr(coeff[i][j]-oldcoeff[i][j]);
- oldcoeff[i][j]=coeff[i][j];
- }
- diffcoeff[iter-1]=sqrt(diffcoeff[iter-1]/(double)armadim);
- alldiff=xdiff[iter-1][0];
- for (i=1;i<dim;i++)
- if (xdiff[iter-1][i] > alldiff)
- alldiff=xdiff[iter-1][i];
- realiter=iter;
- if (alldiff < convergence)
- iter=ITER;
-
- if (iter < ITER) {
- for (i=0;i<dim;i++)
- free(coeff[i]);
- free(coeff);
- }
- }
- }
-
- if (stdo) {
- if (arimaset) {
- printf("#convergence of residuals in arima fit\n");
- for (i=0;i<realiter;i++) {
- printf("#iteration %ld ",i+1);
- for (j=0;j<dim;j++)
- printf("%e ",xdiff[i][j]);
- printf("%e",diffcoeff[i]);
- printf("\n");
- }
- }
- avpm=pm[0]*pm[0];
- loglikelihood= -log(pm[0]);
- for (i=1;i<dim;i++) {
- avpm += pm[i]*pm[i];
- loglikelihood -= log(pm[i]);
- }
- loglikelihood *= ((double)length);
- loglikelihood += -((double)length)*
- ((1.0+log(2.*M_PI))*dim)/2.0;
- avpm=sqrt(avpm/dim);
- printf("#average forcast error= %e\n",avpm);
- printf("#individual forecast errors: ");
- for (i=0;i<dim;i++)
- printf("%e ",pm[i]);
- printf("\n");
- if (arimaset)
- aic=2.0*(arpoles+mapoles)-2.0*loglikelihood;
- else
- aic=2.0*poles-2.0*loglikelihood;
- printf("#Log-Likelihood= %e\t AIC= %e\n",loglikelihood,aic);
- for (i=0;i<size;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- if (id < dim)
- printf("#x_%u(n-%u) ",id+1,is);
- else
- printf("#e_%u(n-%u) ",id+1-dim,is);
- for (j=0;j<dim;j++)
- printf("%e ",coeff[j][i]);
- printf("\n");
- }
- if (!run_model || (verbosity&VER_USR1)) {
- for (i=poles;i<length;i++) {
- if (run_model)
- printf("#");
- for (j=0;j<dim;j++)
- if (verbosity&VER_USR2)
- printf("%e %e ",series[j][i]+my_average[j],diff[j][i]);
- else
- printf("%e ",diff[j][i]);
- printf("\n");
- }
- }
- if (run_model && (ilength > 0)) {
- if (!arimaset)
- iterate_model(coeff,pm,diff,NULL);
- else
- iterate_arima_model(coeff,pm,diff,NULL);
- }
- }
- else {
- file=fopen(outfile,"w");
- if (verbosity&VER_INPUT)
- fprintf(stderr,"Opened %s for output\n",outfile);
- if (arimaset) {
- fprintf(file,"#convergence of residuals in arima fit\n");
- for (i=0;i<realiter;i++) {
- fprintf(file,"#iteration %ld ",i+1);
- for (j=0;j<dim;j++)
- fprintf(file,"%e ",xdiff[i][j]);
- fprintf(file,"%e",diffcoeff[i]);
- fprintf(file,"\n");
- }
- }
- avpm=pm[0]*pm[0];
- loglikelihood= -log(pm[0]);
- for (i=1;i<dim;i++) {
- avpm += pm[i]*pm[i];
- loglikelihood -= log(pm[i]);
- }
- loglikelihood *= ((double)length);
- loglikelihood += -((double)length)*
- ((1.0+log(2.*M_PI))*dim)/2.0;
- avpm=sqrt(avpm/dim);
- fprintf(file,"#average forcast error= %e\n",avpm);
- fprintf(file,"#individual forecast errors: ");
- for (i=0;i<dim;i++)
- fprintf(file,"%e ",pm[i]);
- fprintf(file,"\n");
- if (arimaset)
- aic=2.0*(arpoles+mapoles)-2.0*loglikelihood;
- else
- aic=2.0*poles-2.0*loglikelihood;
- fprintf(file,"#Log-Likelihood= %e\t AIC= %e\n",loglikelihood,aic);
- for (i=0;i<size;i++) {
- id=aindex[0][i];
- is=aindex[1][i];
- if (id < dim)
- fprintf(file,"#x_%u(n-%u) ",id+1,is);
- else
- fprintf(file,"#e_%u(n-%u) ",id+1-dim,is);
- for (j=0;j<dim;j++)
- fprintf(file,"%e ",coeff[j][i]);
- fprintf(file,"\n");
- }
- if (!run_model || (verbosity&VER_USR1)) {
- for (i=poles;i<length;i++) {
- if (run_model)
- fprintf(file,"#");
- for (j=0;j<dim;j++)
- if (verbosity&VER_USR2)
- fprintf(file,"%e %e ",series[j][i]+my_average[j],diff[j][i]);
- else
- fprintf(file,"%e ",diff[j][i]);
- fprintf(file,"\n");
- }
- }
- if (run_model && (ilength > 0)) {
- if (!arimaset)
- iterate_model(coeff,pm,diff,file);
- else
- iterate_arima_model(coeff,pm,diff,file);
- }
- fclose(file);
- }
- if (outfile != NULL)
- free(outfile);
- if (infile != NULL)
- free(infile);
- for (i=0;i<dim;i++) {
- free(coeff[i]);
- free(diff[i]);
- free(series[i]);
- if (arimaset)
- free(series[i+dim]);
- }
- free(coeff);
- free(diff);
- free(series);
-
- free(pm);
-
- return 0;
-}