Diff for /imach/src/imach.c between versions 1.1 and 1.51

version 1.1, 2000/12/28 18:49:56 version 1.51, 2002/07/19 12:22:25
Line 1 Line 1
       /* $Id$
 /*********************** Imach **************************************             Interpolated Markov Chain
   This program computes Healthy Life Expectancies from cross-longitudinal   
   data. Cross-longitudinal consist in a first survey ("cross") where     Short summary of the programme:
   individuals from different ages are interviewed on their health status   
   or degree of  disability. At least a second wave of interviews     This program computes Healthy Life Expectancies from
   ("longitudinal") should  measure each new individual health status.     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   Health expectancies are computed from the transistions observed between     first survey ("cross") where individuals from different ages are
   waves and are computed for each degree of severity of disability (number    interviewed on their health status or degree of disability (in the
   of life states). More degrees you consider, more time is necessary to    case of a health survey which is our main interest) -2- at least a
   reach the Maximum Likekilhood of the parameters involved in the model.    second wave of interviews ("longitudinal") which measure each change
   The simplest model is the multinomial logistic model where pij is    (if any) in individual health status.  Health expectancies are
   the probabibility to be observed in state j at the second wave conditional    computed from the time spent in each health state according to a
   to be observed in state i at the first wave. Therefore the model is:    model. More health states you consider, more time is necessary to reach the
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'     Maximum Likelihood of the parameters involved in the model.  The
   is a covariate. If you want to have a more complex model than "constant and    simplest model is the multinomial logistic model where pij is the
   age", you should modify the program where the markup     probability to be observed in state j at the second wave
     *Covariates have to be included here again* invites you to do it.    conditional to be observed in state i at the first wave. Therefore
   More covariates you add, less is the speed of the convergence.    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
     'age' is age and 'sex' is a covariate. If you want to have a more
   The advantage that this computer programme claims, comes from that if the     complex model than "constant and age", you should modify the program
   delay between waves is not identical for each individual, or if some     where the markup *Covariates have to be included here again* invites
   individual missed an interview, the information is not rounded or lost, but    you to do it.  More covariates you add, slower the
   taken into account using an interpolation or extrapolation.    convergence.
   hPijx is the probability to be  
   observed in state i at age x+h conditional to the observed state i at age     The advantage of this computer programme, compared to a simple
   x. The delay 'h' can be split into an exact number (nh*stepm) of     multinomial logistic model, is clear when the delay between waves is not
   unobserved intermediate  states. This elementary transition (by month or     identical for each individual. Also, if a individual missed an
   quarter trimester, semester or year) is model as a multinomial logistic.     intermediate interview, the information is lost, but taken into
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    account using an interpolation or extrapolation.  
   and the contribution of each individual to the likelihood is simply hPijx.  
     hPijx is the probability to be observed in state i at age x+h
   Also this programme outputs the covariance matrix of the parameters but also    conditional to the observed state i at age x. The delay 'h' can be
   of the life expectancies. It also computes the prevalence limits.     split into an exact number (nh*stepm) of unobserved intermediate
       states. This elementary transition (by month or quarter trimester,
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    semester or year) is model as a multinomial logistic.  The hPx
            Institut national d'études démographiques, Paris.    matrix is simply the matrix product of nh*stepm elementary matrices
   This software have been partly granted by Euro-REVES, a concerted action    and the contribution of each individual to the likelihood is simply
   from the European Union.    hPijx.
   It is copyrighted identically to a GNU software product, ie programme and  
   software can be distributed freely for non commercial use. Latest version    Also this programme outputs the covariance matrix of the parameters but also
   can be accessed at http://euroreves.ined.fr/imach .    of the life expectancies. It also computes the prevalence limits.
   **********************************************************************/   
      Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 #include <math.h>             Institut national d'études démographiques, Paris.
 #include <stdio.h>    This software have been partly granted by Euro-REVES, a concerted action
 #include <stdlib.h>    from the European Union.
 #include <unistd.h>    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
 #define MAXLINE 256    can be accessed at http://euroreves.ined.fr/imach .
 #define FILENAMELENGTH 80    **********************************************************************/
 /*#define DEBUG*/   
 /*#define win*/  #include <math.h>
   #include <stdio.h>
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  #include <stdlib.h>
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncov */  #include <unistd.h>
   
 #define NINTERVMAX 8  #define MAXLINE 256
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  #define GNUPLOTPROGRAM "gnuplot"
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 #define NCOVMAX 8 /* Maximum number of covariates */  #define FILENAMELENGTH 80
 #define MAXN 20000  /*#define DEBUG*/
 #define YEARM 12. /* Number of months per year */  #define windows
 #define AGESUP 130  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 #define AGEBASE 40  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
   #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 int nvar;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   
 int npar=NPARMAX;  #define NINTERVMAX 8
 int nlstate=2; /* Number of live states */  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 int ndeath=1; /* Number of dead states */  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 int ncov;     /* Total number of covariables including constant a12*1 +b12*x ncov=2 */  #define NCOVMAX 8 /* Maximum number of covariates */
   #define MAXN 20000
 int *wav; /* Number of waves for this individuual 0 is possible */  #define YEARM 12. /* Number of months per year */
 int maxwav; /* Maxim number of waves */  #define AGESUP 130
 int mle, weightopt;  #define AGEBASE 40
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  #ifdef windows
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  #define DIRSEPARATOR '\\'
 double **oldm, **newm, **savm; /* Working pointers to matrices */  #define ODIRSEPARATOR '/'
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  #else
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;  #define DIRSEPARATOR '/'
 FILE *ficgp, *fichtm;  #define ODIRSEPARATOR '\\'
   #endif
 #define NR_END 1  
 #define FREE_ARG char*  char version[80]="Imach version 0.8i, June 2002, INED-EUROREVES ";
 #define FTOL 1.0e-10  int erreur; /* Error number */
   int nvar;
 #define NRANSI   int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
 #define ITMAX 200   int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
 #define TOL 2.0e-4   int ndeath=1; /* Number of dead states */
   int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #define CGOLD 0.3819660   int popbased=0;
 #define ZEPS 1.0e-10   
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);   int *wav; /* Number of waves for this individuual 0 is possible */
   int maxwav; /* Maxim number of waves */
 #define GOLD 1.618034   int jmin, jmax; /* min, max spacing between 2 waves */
 #define GLIMIT 100.0   int mle, weightopt;
 #define TINY 1.0e-20   int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
 static double maxarg1,maxarg2;  double jmean; /* Mean space between 2 waves */
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  double **oldm, **newm, **savm; /* Working pointers to matrices */
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
    FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  FILE *ficlog;
 #define rint(a) floor(a+0.5)  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   FILE *ficresprobmorprev;
 static double sqrarg;  FILE *fichtm; /* Html File */
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  FILE *ficreseij;
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}   char filerese[FILENAMELENGTH];
   FILE  *ficresvij;
 int imx;   char fileresv[FILENAMELENGTH];
 int stepm;  FILE  *ficresvpl;
 /* Stepm, step in month: minimum step interpolation*/  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 int m,nb;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 int *num, firstpass=0, lastpass=2,*cod;  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   char filelog[FILENAMELENGTH]; /* Log file */
 double *weight;  char filerest[FILENAMELENGTH];
 int **s; /* Status */  char fileregp[FILENAMELENGTH];
 double *agedc, **covar, idx;  char popfile[FILENAMELENGTH];
   
   char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */  #define NR_END 1
   #define FREE_ARG char*
   #define FTOL 1.0e-10
 /******************************************/  
   #define NRANSI
 void replace(char *s, char*t)  #define ITMAX 200
 {  
   int i;  #define TOL 2.0e-4
   int lg=20;  
   i=0;  #define CGOLD 0.3819660
   lg=strlen(t);  #define ZEPS 1.0e-10
   for(i=0; i<= lg; i++) {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';  #define GOLD 1.618034
   }  #define GLIMIT 100.0
 }  #define TINY 1.0e-20
 void cut(char *u,char *v, char*t)  
 {  static double maxarg1,maxarg2;
   int i,lg,j,p;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   i=0;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   for(j=0; j<=strlen(t); j++) {   
     if(t[j]=='\\') p=j;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   }  #define rint(a) floor(a+0.5)
   
   lg=strlen(t);  static double sqrarg;
   for(j=0; j<p; j++) {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
     (u[j] = t[j]);  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}
     u[p]='\0';  
   }  int imx;
   int stepm;
   for(j=0; j<= lg; j++) {  /* Stepm, step in month: minimum step interpolation*/
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }  int estepm;
 }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
 /********************** nrerror ********************/  int m,nb;
   int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
 void nrerror(char error_text[])  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
 {  double **pmmij, ***probs, ***mobaverage;
   fprintf(stderr,"ERREUR ...\n");  double dateintmean=0;
   fprintf(stderr,"%s\n",error_text);  
   exit(1);  double *weight;
 }  int **s; /* Status */
 /*********************** vector *******************/  double *agedc, **covar, idx;
 double *vector(int nl, int nh)  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 {  
   double *v;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  double ftolhess; /* Tolerance for computing hessian */
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;  /**************** split *************************/
 }  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   {
 /************************ free vector ******************/     char *s;                             /* pointer */
 void free_vector(double*v, int nl, int nh)     int  l1, l2;                         /* length counters */
 {  
   free((FREE_ARG)(v+nl-NR_END));     l1 = strlen( path );                 /* length of path */
 }     if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
      s= strrchr( path, DIRSEPARATOR );            /* find last / */
 /************************ivector *******************************/     if ( s == NULL ) {                   /* no directory, so use current */
 int *ivector(long nl,long nh)       /*if(strrchr(path, ODIRSEPARATOR )==NULL)
 {         printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   int *v;  #if     defined(__bsd__)                /* get current working directory */
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));        extern char       *getwd( );
   if (!v) nrerror("allocation failure in ivector");  
   return v-nl+NR_END;        if ( getwd( dirc ) == NULL ) {
 }  #else
         extern char       *getcwd( );
 /******************free ivector **************************/  
 void free_ivector(int *v, long nl, long nh)        if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 {  #endif
   free((FREE_ARG)(v+nl-NR_END));           return( GLOCK_ERROR_GETCWD );
 }        }
         strcpy( name, path );             /* we've got it */
 /******************* imatrix *******************************/     } else {                             /* strip direcotry from path */
 int **imatrix(long nrl, long nrh, long ncl, long nch)         s++;                              /* after this, the filename */
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */         l2 = strlen( s );                 /* length of filename */
 {         if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;         strcpy( name, s );                /* save file name */
   int **m;         strncpy( dirc, path, l1 - l2 );   /* now the directory */
           dirc[l1-l2] = 0;                  /* add zero */
   /* allocate pointers to rows */      }
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));      l1 = strlen( dirc );                 /* length of directory */
   if (!m) nrerror("allocation failure 1 in matrix()");   #ifdef windows
   m += NR_END;      if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   m -= nrl;   #else
        if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
     #endif
   /* allocate rows and set pointers to them */      s = strrchr( name, '.' );            /* find last / */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));      s++;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");      strcpy(ext,s);                       /* save extension */
   m[nrl] += NR_END;      l1= strlen( name);
   m[nrl] -= ncl;      l2= strlen( s)+1;
        strncpy( finame, name, l1-l2);
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;      finame[l1-l2]= 0;
        return( 0 );                         /* we're done */
   /* return pointer to array of pointers to rows */   }
   return m;   
 }   
   /******************************************/
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)  void replace(char *s, char*t)
       int **m;  {
       long nch,ncl,nrh,nrl;     int i;
      /* free an int matrix allocated by imatrix() */     int lg=20;
 {     i=0;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));     lg=strlen(t);
   free((FREE_ARG) (m+nrl-NR_END));     for(i=0; i<= lg; i++) {
 }       (s[i] = t[i]);
       if (t[i]== '\\') s[i]='/';
 /******************* matrix *******************************/    }
 double **matrix(long nrl, long nrh, long ncl, long nch)  }
 {  
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  int nbocc(char *s, char occ)
   double **m;  {
     int i,j=0;
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    int lg=20;
   if (!m) nrerror("allocation failure 1 in matrix()");    i=0;
   m += NR_END;    lg=strlen(s);
   m -= nrl;    for(i=0; i<= lg; i++) {
     if  (s[i] == occ ) j++;
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    }
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    return j;
   m[nrl] += NR_END;  }
   m[nrl] -= ncl;  
   void cutv(char *u,char *v, char*t, char occ)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  {
   return m;    /* cuts string t into u and v where u is ended by char occ excluding it
 }       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
        gives u="abcedf" and v="ghi2j" */
 /*************************free matrix ************************/    int i,lg,j,p=0;
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    i=0;
 {    for(j=0; j<=strlen(t)-1; j++) {
   free((FREE_ARG)(m[nrl]+ncl-NR_END));      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   free((FREE_ARG)(m+nrl-NR_END));    }
 }  
     lg=strlen(t);
 /******************* ma3x *******************************/    for(j=0; j<p; j++) {
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)      (u[j] = t[j]);
 {    }
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;       u[p]='\0';
   double ***m;  
      for(j=0; j<= lg; j++) {
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));      if (j>=(p+1))(v[j-p-1] = t[j]);
   if (!m) nrerror("allocation failure 1 in matrix()");    }
   m += NR_END;  }
   m -= nrl;  
   /********************** nrerror ********************/
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  void nrerror(char error_text[])
   m[nrl] += NR_END;  {
   m[nrl] -= ncl;    fprintf(stderr,"ERREUR ...\n");
     fprintf(stderr,"%s\n",error_text);
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    exit(1);
   }
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  /*********************** vector *******************/
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  double *vector(int nl, int nh)
   m[nrl][ncl] += NR_END;  {
   m[nrl][ncl] -= nll;    double *v;
   for (j=ncl+1; j<=nch; j++)     v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     m[nrl][j]=m[nrl][j-1]+nlay;    if (!v) nrerror("allocation failure in vector");
       return v-nl+NR_END;
   for (i=nrl+1; i<=nrh; i++) {  }
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)   /************************ free vector ******************/
       m[i][j]=m[i][j-1]+nlay;  void free_vector(double*v, int nl, int nh)
   }  {
   return m;    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************************free ma3x ************************/  /************************ivector *******************************/
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  int *ivector(long nl,long nh)
 {  {
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    int *v;
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   free((FREE_ARG)(m+nrl-NR_END));    if (!v) nrerror("allocation failure in ivector");
 }    return v-nl+NR_END;
   }
 /***************** f1dim *************************/  
 extern int ncom;   /******************free ivector **************************/
 extern double *pcom,*xicom;  void free_ivector(int *v, long nl, long nh)
 extern double (*nrfunc)(double []);   {
      free((FREE_ARG)(v+nl-NR_END));
 double f1dim(double x)   }
 {   
   int j;   /******************* imatrix *******************************/
   double f;  int **imatrix(long nrl, long nrh, long ncl, long nch)
   double *xt;        /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
    {
   xt=vector(1,ncom);     long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];     int **m;
   f=(*nrfunc)(xt);    
   free_vector(xt,1,ncom);     /* allocate pointers to rows */
   return f;     m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
 }     if (!m) nrerror("allocation failure 1 in matrix()");
     m += NR_END;
 /*****************brent *************************/    m -= nrl;
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    
 {    
   int iter;     /* allocate rows and set pointers to them */
   double a,b,d,etemp;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));
   double fu,fv,fw,fx;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double ftemp;    m[nrl] += NR_END;
   double p,q,r,tol1,tol2,u,v,w,x,xm;     m[nrl] -= ncl;
   double e=0.0;    
      for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
   a=(ax < cx ? ax : cx);    
   b=(ax > cx ? ax : cx);     /* return pointer to array of pointers to rows */
   x=w=v=bx;     return m;
   fw=fv=fx=(*f)(x);   }
   for (iter=1;iter<=ITMAX;iter++) {   
     xm=0.5*(a+b);   /****************** free_imatrix *************************/
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);   void free_imatrix(m,nrl,nrh,ncl,nch)
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/        int **m;
     printf(".");fflush(stdout);        long nch,ncl,nrh,nrl;
 #ifdef DEBUG       /* free an int matrix allocated by imatrix() */
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  {
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    free((FREE_ARG) (m[nrl]+ncl-NR_END));
 #endif    free((FREE_ARG) (m+nrl-NR_END));
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){   }
       *xmin=x;   
       return fx;   /******************* matrix *******************************/
     }   double **matrix(long nrl, long nrh, long ncl, long nch)
     ftemp=fu;  {
     if (fabs(e) > tol1) {     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       r=(x-w)*(fx-fv);     double **m;
       q=(x-v)*(fx-fw);   
       p=(x-v)*q-(x-w)*r;     m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       q=2.0*(q-r);     if (!m) nrerror("allocation failure 1 in matrix()");
       if (q > 0.0) p = -p;     m += NR_END;
       q=fabs(q);     m -= nrl;
       etemp=e;   
       e=d;     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         d=CGOLD*(e=(x >= xm ? a-x : b-x));     m[nrl] += NR_END;
       else {     m[nrl] -= ncl;
         d=p/q;   
         u=x+d;     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         if (u-a < tol2 || b-u < tol2)     return m;
           d=SIGN(tol1,xm-x);   }
       }   
     } else {   /*************************free matrix ************************/
       d=CGOLD*(e=(x >= xm ? a-x : b-x));   void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     }   {
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));     free((FREE_ARG)(m[nrl]+ncl-NR_END));
     fu=(*f)(u);     free((FREE_ARG)(m+nrl-NR_END));
     if (fu <= fx) {   }
       if (u >= x) a=x; else b=x;   
       SHFT(v,w,x,u)   /******************* ma3x *******************************/
         SHFT(fv,fw,fx,fu)   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
         } else {   {
           if (u < x) a=u; else b=u;     long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
           if (fu <= fw || w == x) {     double ***m;
             v=w;   
             w=u;     m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
             fv=fw;     if (!m) nrerror("allocation failure 1 in matrix()");
             fw=fu;     m += NR_END;
           } else if (fu <= fv || v == x || v == w) {     m -= nrl;
             v=u;   
             fv=fu;     m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
           }     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         }     m[nrl] += NR_END;
   }     m[nrl] -= ncl;
   nrerror("Too many iterations in brent");   
   *xmin=x;     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   return fx;   
 }     m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
 /****************** mnbrak ***********************/    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,     for (j=ncl+1; j<=nch; j++)
             double (*func)(double))       m[nrl][j]=m[nrl][j-1]+nlay;
 {    
   double ulim,u,r,q, dum;    for (i=nrl+1; i<=nrh; i++) {
   double fu;       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
        for (j=ncl+1; j<=nch; j++)
   *fa=(*func)(*ax);         m[i][j]=m[i][j-1]+nlay;
   *fb=(*func)(*bx);     }
   if (*fb > *fa) {     return m;
     SHFT(dum,*ax,*bx,dum)   }
       SHFT(dum,*fb,*fa,dum)   
       }   /*************************free ma3x ************************/
   *cx=(*bx)+GOLD*(*bx-*ax);   void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   *fc=(*func)(*cx);   {
   while (*fb > *fc) {     free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     r=(*bx-*ax)*(*fb-*fc);     free((FREE_ARG)(m[nrl]+ncl-NR_END));
     q=(*bx-*cx)*(*fb-*fa);     free((FREE_ARG)(m+nrl-NR_END));
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/   }
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));   
     ulim=(*bx)+GLIMIT*(*cx-*bx);   /***************** f1dim *************************/
     if ((*bx-u)*(u-*cx) > 0.0) {   extern int ncom;
       fu=(*func)(u);   extern double *pcom,*xicom;
     } else if ((*cx-u)*(u-ulim) > 0.0) {   extern double (*nrfunc)(double []);
       fu=(*func)(u);    
       if (fu < *fc) {   double f1dim(double x)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))   {
           SHFT(*fb,*fc,fu,(*func)(u))     int j;
           }     double f;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {     double *xt;
       u=ulim;    
       fu=(*func)(u);     xt=vector(1,ncom);
     } else {     for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];
       u=(*cx)+GOLD*(*cx-*bx);     f=(*nrfunc)(xt);
       fu=(*func)(u);     free_vector(xt,1,ncom);
     }     return f;
     SHFT(*ax,*bx,*cx,u)   }
       SHFT(*fa,*fb,*fc,fu)   
       }   /*****************brent *************************/
 }   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)
   {
 /*************** linmin ************************/    int iter;
     double a,b,d,etemp;
 int ncom;     double fu,fv,fw,fx;
 double *pcom,*xicom;    double ftemp;
 double (*nrfunc)(double []);     double p,q,r,tol1,tol2,u,v,w,x,xm;
      double e=0.0;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    
 {     a=(ax < cx ? ax : cx);
   double brent(double ax, double bx, double cx,     b=(ax > cx ? ax : cx);
                double (*f)(double), double tol, double *xmin);     x=w=v=bx;
   double f1dim(double x);     fw=fv=fx=(*f)(x);
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,     for (iter=1;iter<=ITMAX;iter++) {
               double *fc, double (*func)(double));       xm=0.5*(a+b);
   int j;       tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
   double xx,xmin,bx,ax;       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   double fx,fb,fa;      printf(".");fflush(stdout);
        fprintf(ficlog,".");fflush(ficlog);
   ncom=n;   #ifdef DEBUG
   pcom=vector(1,n);       printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   xicom=vector(1,n);       fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   nrfunc=func;       /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   for (j=1;j<=n;j++) {   #endif
     pcom[j]=p[j];       if (fabs(x-xm) <= (tol2-0.5*(b-a))){
     xicom[j]=xi[j];         *xmin=x;
   }         return fx;
   ax=0.0;       }
   xx=1.0;       ftemp=fu;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);       if (fabs(e) > tol1) {
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);         r=(x-w)*(fx-fv);
 #ifdef DEBUG        q=(x-v)*(fx-fw);
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);        p=(x-v)*q-(x-w)*r;
 #endif        q=2.0*(q-r);
   for (j=1;j<=n;j++) {         if (q > 0.0) p = -p;
     xi[j] *= xmin;         q=fabs(q);
     p[j] += xi[j];         etemp=e;
   }         e=d;
   free_vector(xicom,1,n);         if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
   free_vector(pcom,1,n);           d=CGOLD*(e=(x >= xm ? a-x : b-x));
 }         else {
           d=p/q;
 /*************** powell ************************/          u=x+d;
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,           if (u-a < tol2 || b-u < tol2)
             double (*func)(double []))             d=SIGN(tol1,xm-x);
         }
 {       } else {
         d=CGOLD*(e=(x >= xm ? a-x : b-x));
       }
   void linmin(double p[], double xi[], int n, double *fret,       u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
               double (*func)(double []));       fu=(*f)(u);
   int i,ibig,j;       if (fu <= fx) {
   double del,t,*pt,*ptt,*xit;        if (u >= x) a=x; else b=x;
   double fp,fptt;        SHFT(v,w,x,u)
   double *xits;          SHFT(fv,fw,fx,fu)
   pt=vector(1,n);           } else {
   ptt=vector(1,n);             if (u < x) a=u; else b=u;
   xit=vector(1,n);             if (fu <= fw || w == x) {
   xits=vector(1,n);               v=w;
   *fret=(*func)(p);               w=u;
   for (j=1;j<=n;j++) pt[j]=p[j];               fv=fw;
   for (*iter=1;;++(*iter)) {               fw=fu;
     fp=(*fret);             } else if (fu <= fv || v == x || v == w) {
     ibig=0;               v=u;
     del=0.0;               fv=fu;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);            }
     for (i=1;i<=n;i++)           }
       printf(" %d %.12f",i, p[i]);    }
     printf("\n");    nrerror("Too many iterations in brent");
     for (i=1;i<=n;i++) {     *xmin=x;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];     return fx;
       fptt=(*fret);   }
 #ifdef DEBUG  
       printf("fret=%lf \n",*fret);  /****************** mnbrak ***********************/
 #endif  
       printf("%d",i);fflush(stdout);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,
       linmin(p,xit,n,fret,func);               double (*func)(double))
       if (fabs(fptt-(*fret)) > del) {   {
         del=fabs(fptt-(*fret));     double ulim,u,r,q, dum;
         ibig=i;     double fu;
       }    
 #ifdef DEBUG    *fa=(*func)(*ax);
       printf("%d %.12e",i,(*fret));    *fb=(*func)(*bx);
       for (j=1;j<=n;j++) {    if (*fb > *fa) {
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      SHFT(dum,*ax,*bx,dum)
         printf(" x(%d)=%.12e",j,xit[j]);        SHFT(dum,*fb,*fa,dum)
       }        }
       for(j=1;j<=n;j++)     *cx=(*bx)+GOLD*(*bx-*ax);
         printf(" p=%.12e",p[j]);    *fc=(*func)(*cx);
       printf("\n");    while (*fb > *fc) {
 #endif      r=(*bx-*ax)*(*fb-*fc);
     }       q=(*bx-*cx)*(*fb-*fa);
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/
 #ifdef DEBUG        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));
       int k[2],l;      ulim=(*bx)+GLIMIT*(*cx-*bx);
       k[0]=1;      if ((*bx-u)*(u-*cx) > 0.0) {
       k[1]=-1;        fu=(*func)(u);
       printf("Max: %.12e",(*func)(p));      } else if ((*cx-u)*(u-ulim) > 0.0) {
       for (j=1;j<=n;j++)         fu=(*func)(u);
         printf(" %.12e",p[j]);        if (fu < *fc) {
       printf("\n");          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))
       for(l=0;l<=1;l++) {            SHFT(*fb,*fc,fu,(*func)(u))
         for (j=1;j<=n;j++) {            }
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      } else if ((u-ulim)*(ulim-*cx) >= 0.0) {
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);        u=ulim;
         }        fu=(*func)(u);
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));      } else {
       }        u=(*cx)+GOLD*(*cx-*bx);
 #endif        fu=(*func)(u);
       }
       SHFT(*ax,*bx,*cx,u)
       free_vector(xit,1,n);         SHFT(*fa,*fb,*fc,fu)
       free_vector(xits,1,n);         }
       free_vector(ptt,1,n);   }
       free_vector(pt,1,n);   
       return;   /*************** linmin ************************/
     }   
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");   int ncom;
     for (j=1;j<=n;j++) {   double *pcom,*xicom;
       ptt[j]=2.0*p[j]-pt[j];   double (*nrfunc)(double []);
       xit[j]=p[j]-pt[j];    
       pt[j]=p[j];   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))
     }   {
     fptt=(*func)(ptt);     double brent(double ax, double bx, double cx,
     if (fptt < fp) {                  double (*f)(double), double tol, double *xmin);
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);     double f1dim(double x);
       if (t < 0.0) {     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,
         linmin(p,xit,n,fret,func);                 double *fc, double (*func)(double));
         for (j=1;j<=n;j++) {     int j;
           xi[j][ibig]=xi[j][n];     double xx,xmin,bx,ax;
           xi[j][n]=xit[j];     double fx,fb,fa;
         }   
 #ifdef DEBUG    ncom=n;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    pcom=vector(1,n);
         for(j=1;j<=n;j++)    xicom=vector(1,n);
           printf(" %.12e",xit[j]);    nrfunc=func;
         printf("\n");    for (j=1;j<=n;j++) {
 #endif      pcom[j]=p[j];
       }       xicom[j]=xi[j];
     }     }
   }     ax=0.0;
 }     xx=1.0;
     mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);
 /**** Prevalence limit ****************/    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);
   #ifdef DEBUG
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl)    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 {    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  #endif
      matrix by transitions matrix until convergence is reached */    for (j=1;j<=n;j++) {
       xi[j] *= xmin;
   int i, ii,j,k;      p[j] += xi[j];
   double min, max, maxmin, maxmax,sumnew=0.;    }
   double **matprod2();    free_vector(xicom,1,n);
   double **out, cov[NCOVMAX], **pmij();    free_vector(pcom,1,n);
   double **newm;  }
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /*************** powell ************************/
   for (ii=1;ii<=nlstate+ndeath;ii++)  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,
     for (j=1;j<=nlstate+ndeath;j++){              double (*func)(double []))
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  {
     }    void linmin(double p[], double xi[], int n, double *fret,
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */                double (*func)(double []));
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    int i,ibig,j;
     newm=savm;    double del,t,*pt,*ptt,*xit;
     /* Covariates have to be included here again */    double fp,fptt;
     cov[1]=1.;    double *xits;
     cov[2]=agefin;    pt=vector(1,n);
     out=matprod2(newm, pmij(pmmij,cov,ncov,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    ptt=vector(1,n);
 /*    printf("age=%f agefin=%f po=%f pn=%f\n",age,agefin,oldm[1][1],newm[1][1]);*/    xit=vector(1,n);
         xits=vector(1,n);
     savm=oldm;    *fret=(*func)(p);
     oldm=newm;    for (j=1;j<=n;j++) pt[j]=p[j];
     maxmax=0.;    for (*iter=1;;++(*iter)) {
     for(j=1;j<=nlstate;j++){      fp=(*fret);
       min=1.;      ibig=0;
       max=0.;      del=0.0;
       for(i=1; i<=nlstate; i++) {      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
         sumnew=0;      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];      for (i=1;i<=n;i++)
         prlim[i][j]= newm[i][j]/(1-sumnew);        printf(" %d %.12f",i, p[i]);
         max=FMAX(max,prlim[i][j]);      fprintf(ficlog," %d %.12f",i, p[i]);
         min=FMIN(min,prlim[i][j]);      printf("\n");
       }      fprintf(ficlog,"\n");
       maxmin=max-min;      for (i=1;i<=n;i++) {
       maxmax=FMAX(maxmax,maxmin);        for (j=1;j<=n;j++) xit[j]=xi[j][i];
     }        fptt=(*fret);
     if(maxmax < ftolpl){  #ifdef DEBUG
       return prlim;        printf("fret=%lf \n",*fret);
     }        fprintf(ficlog,"fret=%lf \n",*fret);
   }  #endif
 }        printf("%d",i);fflush(stdout);
         fprintf(ficlog,"%d",i);fflush(ficlog);
 /*************** transition probabilities **********/         linmin(p,xit,n,fret,func);
         if (fabs(fptt-(*fret)) > del) {
 double **pmij(double **ps, double *cov, int ncov, double *x, int nlstate )          del=fabs(fptt-(*fret));
 {          ibig=i;
   double s1, s2;        }
   /*double t34;*/  #ifdef DEBUG
   int i,j,j1, nc, ii, jj;        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
     for(i=1; i<= nlstate; i++){        for (j=1;j<=n;j++) {
     for(j=1; j<i;j++){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
       for (nc=1, s2=0.;nc <=ncov; nc++){          printf(" x(%d)=%.12e",j,xit[j]);
         /*s2 += param[i][j][nc]*cov[nc];*/          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         s2 += x[(i-1)*nlstate*ncov+(j-1)*ncov+nc+(i-1)*(ndeath-1)*ncov]*cov[nc];        }
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/        for(j=1;j<=n;j++) {
       }          printf(" p=%.12e",p[j]);
       ps[i][j]=s2;          fprintf(ficlog," p=%.12e",p[j]);
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/        }
     }        printf("\n");
     for(j=i+1; j<=nlstate+ndeath;j++){        fprintf(ficlog,"\n");
       for (nc=1, s2=0.;nc <=ncov; nc++){  #endif
         s2 += x[(i-1)*nlstate*ncov+(j-2)*ncov+nc+(i-1)*(ndeath-1)*ncov]*cov[nc];      }
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       }  #ifdef DEBUG
       ps[i][j]=s2;        int k[2],l;
     }        k[0]=1;
   }        k[1]=-1;
   for(i=1; i<= nlstate; i++){        printf("Max: %.12e",(*func)(p));
      s1=0;        fprintf(ficlog,"Max: %.12e",(*func)(p));
     for(j=1; j<i; j++)        for (j=1;j<=n;j++) {
       s1+=exp(ps[i][j]);          printf(" %.12e",p[j]);
     for(j=i+1; j<=nlstate+ndeath; j++)          fprintf(ficlog," %.12e",p[j]);
       s1+=exp(ps[i][j]);        }
     ps[i][i]=1./(s1+1.);        printf("\n");
     for(j=1; j<i; j++)        fprintf(ficlog,"\n");
       ps[i][j]= exp(ps[i][j])*ps[i][i];        for(l=0;l<=1;l++) {
     for(j=i+1; j<=nlstate+ndeath; j++)          for (j=1;j<=n;j++) {
       ps[i][j]= exp(ps[i][j])*ps[i][i];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   } /* end i */            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           }
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     for(jj=1; jj<= nlstate+ndeath; jj++){          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       ps[ii][jj]=0;        }
       ps[ii][ii]=1;  #endif
     }  
   }  
         free_vector(xit,1,n);
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){        free_vector(xits,1,n);
     for(jj=1; jj<= nlstate+ndeath; jj++){        free_vector(ptt,1,n);
      printf("%lf ",ps[ii][jj]);        free_vector(pt,1,n);
    }        return;
     printf("\n ");      }
     }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");
     printf("\n ");printf("%lf ",cov[2]);*/      for (j=1;j<=n;j++) {
 /*        ptt[j]=2.0*p[j]-pt[j];
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        xit[j]=p[j]-pt[j];
   goto end;*/        pt[j]=p[j];
     return ps;      }
 }      fptt=(*func)(ptt);
       if (fptt < fp) {
 /**************** Product of 2 matrices ******************/        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);
         if (t < 0.0) {
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)          linmin(p,xit,n,fret,func);
 {          for (j=1;j<=n;j++) {
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times            xi[j][ibig]=xi[j][n];
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */            xi[j][n]=xit[j];
   /* in, b, out are matrice of pointers which should have been initialized           }
      before: only the contents of out is modified. The function returns  #ifdef DEBUG
      a pointer to pointers identical to out */          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   long i, j, k;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   for(i=nrl; i<= nrh; i++)          for(j=1;j<=n;j++){
     for(k=ncolol; k<=ncoloh; k++)            printf(" %.12e",xit[j]);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)            fprintf(ficlog," %.12e",xit[j]);
         out[i][k] +=in[i][j]*b[j][k];          }
           printf("\n");
   return out;          fprintf(ficlog,"\n");
 }  #endif
         }
       }
 /************* Higher Matrix Product ***************/    }
   }
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm )  
 {  /**** Prevalence limit ****************/
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month   
      duration (i.e. until  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.   {
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step     /* Computes the prevalence limit in each live state at age x by left multiplying the unit
      (typically every 2 years instead of every month which is too big).       matrix by transitions matrix until convergence is reached */
      Model is determined by parameters x and covariates have to be   
      included manually here.     int i, ii,j,k;
     double min, max, maxmin, maxmax,sumnew=0.;
      */    double **matprod2();
     double **out, cov[NCOVMAX], **pmij();
   int i, j, d, h;    double **newm;
   double **out, cov[NCOVMAX];    double agefin, delaymax=50 ; /* Max number of years to converge */
   double **newm;  
     for (ii=1;ii<=nlstate+ndeath;ii++)
   /* Hstepm could be zero and should return the unit matrix */      for (j=1;j<=nlstate+ndeath;j++){
   for (i=1;i<=nlstate+ndeath;i++)        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (j=1;j<=nlstate+ndeath;j++){      }
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);     cov[1]=1.;
     }   
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   for(h=1; h <=nhstepm; h++){    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     for(d=1; d <=hstepm; d++){      newm=savm;
       newm=savm;      /* Covariates have to be included here again */
       /* Covariates have to be included here again */       cov[2]=agefin;
       cov[1]=1.;   
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        for (k=1; k<=cptcovn;k++) {
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,           /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
                    pmij(pmmij,cov,ncov,x,nlstate));        }
       savm=oldm;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       oldm=newm;        for (k=1; k<=cptcovprod;k++)
     }          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     for(i=1; i<=nlstate+ndeath; i++)  
       for(j=1;j<=nlstate+ndeath;j++) {        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         po[i][j][h]=newm[i][j];        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
          */      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
       }  
   } /* end h */      savm=oldm;
   return po;      oldm=newm;
 }      maxmax=0.;
       for(j=1;j<=nlstate;j++){
         min=1.;
 /*************** log-likelihood *************/        max=0.;
 double func( double *x)        for(i=1; i<=nlstate; i++) {
 {          sumnew=0;
   int i, ii, j, k, mi, d;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   double l, ll[NLSTATEMAX], cov[NCOVMAX];          prlim[i][j]= newm[i][j]/(1-sumnew);
   double **out;          max=FMAX(max,prlim[i][j]);
   double sw; /* Sum of weights */          min=FMIN(min,prlim[i][j]);
   double lli; /* Individual log likelihood */        }
   long ipmx;        maxmin=max-min;
   /*extern weight */        maxmax=FMAX(maxmax,maxmin);
   /* We are differentiating ll according to initial status */      }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      if(maxmax < ftolpl){
   /*for(i=1;i<imx;i++)         return prlim;
 printf(" %d\n",s[4][i]);      }
   */    }
   }
   for(k=1; k<=nlstate; k++) ll[k]=0.;  
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){  /*************** transition probabilities ***************/
        for(mi=1; mi<= wav[i]-1; mi++){  
       for (ii=1;ii<=nlstate+ndeath;ii++)  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  {
             for(d=0; d<dh[mi][i]; d++){    double s1, s2;
         newm=savm;    /*double t34;*/
           cov[1]=1.;    int i,j,j1, nc, ii, jj;
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      for(i=1; i<= nlstate; i++){
                        1,nlstate+ndeath,pmij(pmmij,cov,ncov,x,nlstate));      for(j=1; j<i;j++){
           savm=oldm;        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
           oldm=newm;          /*s2 += param[i][j][nc]*cov[nc];*/
           s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
           /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
       } /* end mult */        }
            ps[i][j]=s2;
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      }
       ipmx +=1;      for(j=i+1; j<=nlstate+ndeath;j++){
       sw += weight[i];        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     } /* end of wave */          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
   } /* end of individual */        }
         ps[i][j]=s2;
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      }
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    }
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */      /*ps[3][2]=1;*/
   return -l;  
 }    for(i=1; i<= nlstate; i++){
        s1=0;
       for(j=1; j<i; j++)
 /*********** Maximum Likelihood Estimation ***************/        s1+=exp(ps[i][j]);
       for(j=i+1; j<=nlstate+ndeath; j++)
 void mlikeli(FILE *ficres,double p[], int npar, int ncov, int nlstate, double ftol, double (*func)(double []))        s1+=exp(ps[i][j]);
 {      ps[i][i]=1./(s1+1.);
   int i,j, iter;      for(j=1; j<i; j++)
   double **xi,*delti;        ps[i][j]= exp(ps[i][j])*ps[i][i];
   double fret;      for(j=i+1; j<=nlstate+ndeath; j++)
   xi=matrix(1,npar,1,npar);        ps[i][j]= exp(ps[i][j])*ps[i][i];
   for (i=1;i<=npar;i++)      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     for (j=1;j<=npar;j++)    } /* end i */
       xi[i][j]=(i==j ? 1.0 : 0.0);  
   printf("Powell\n");    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   powell(p,xi,npar,ftol,&iter,&fret,func);      for(jj=1; jj<= nlstate+ndeath; jj++){
         ps[ii][jj]=0;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));        ps[ii][ii]=1;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));      }
     }
 }  
   
 /**** Computes Hessian and covariance matrix ***/    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      for(jj=1; jj<= nlstate+ndeath; jj++){
 {       printf("%lf ",ps[ii][jj]);
   double  **a,**y,*x,pd;     }
   double **hess;      printf("\n ");
   int i, j,jk;      }
   int *indx;      printf("\n ");printf("%lf ",cov[2]);*/
   /*
   double hessii(double p[], double delta, int theta, double delti[]);    for(i=1; i<= npar; i++) printf("%f ",x[i]);
   double hessij(double p[], double delti[], int i, int j);    goto end;*/
   void lubksb(double **a, int npar, int *indx, double b[]) ;      return ps;
   void ludcmp(double **a, int npar, int *indx, double *d) ;  }
   
   /**************** Product of 2 matrices ******************/
   hess=matrix(1,npar,1,npar);  
   double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   printf("\nCalculation of the hessian matrix. Wait...\n");  {
   for (i=1;i<=npar;i++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     printf("%d",i);fflush(stdout);       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     hess[i][i]=hessii(p,ftolhess,i,delti);    /* in, b, out are matrice of pointers which should have been initialized
     /*printf(" %f ",p[i]);*/       before: only the contents of out is modified. The function returns
   }       a pointer to pointers identical to out */
     long i, j, k;
   for (i=1;i<=npar;i++) {    for(i=nrl; i<= nrh; i++)
     for (j=1;j<=npar;j++)  {      for(k=ncolol; k<=ncoloh; k++)
       if (j>i) {         for(j=ncl,out[i][k]=0.; j<=nch; j++)
         printf(".%d%d",i,j);fflush(stdout);          out[i][k] +=in[i][j]*b[j][k];
         hess[i][j]=hessij(p,delti,i,j);  
         hess[j][i]=hess[i][j];    return out;
       }  }
     }  
   }  
   printf("\n");  /************* Higher Matrix Product ***************/
   
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     {
   a=matrix(1,npar,1,npar);    /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month
   y=matrix(1,npar,1,npar);       duration (i.e. until
   x=vector(1,npar);       age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.
   indx=ivector(1,npar);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step
   for (i=1;i<=npar;i++)       (typically every 2 years instead of every month which is too big).
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];       Model is determined by parameters x and covariates have to be
   ludcmp(a,npar,indx,&pd);       included manually here.
   
   for (j=1;j<=npar;j++) {       */
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;    int i, j, d, h, k;
     lubksb(a,npar,indx,x);    double **out, cov[NCOVMAX];
     for (i=1;i<=npar;i++){     double **newm;
       matcov[i][j]=x[i];  
     }    /* Hstepm could be zero and should return the unit matrix */
   }    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
   printf("\n#Hessian matrix#\n");        oldm[i][j]=(i==j ? 1.0 : 0.0);
   for (i=1;i<=npar;i++) {         po[i][j][0]=(i==j ? 1.0 : 0.0);
     for (j=1;j<=npar;j++) {       }
       printf("%.3e ",hess[i][j]);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     }    for(h=1; h <=nhstepm; h++){
     printf("\n");      for(d=1; d <=hstepm; d++){
   }        newm=savm;
         /* Covariates have to be included here again */
   /* Recompute Inverse */        cov[1]=1.;
   for (i=1;i<=npar;i++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   ludcmp(a,npar,indx,&pd);        for (k=1; k<=cptcovage;k++)
           cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   /*  printf("\n#Hessian matrix recomputed#\n");        for (k=1; k<=cptcovprod;k++)
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   for (j=1;j<=npar;j++) {  
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
     lubksb(a,npar,indx,x);        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
     for (i=1;i<=npar;i++){         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,
       y[i][j]=x[i];                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       printf("%.3e ",y[i][j]);        savm=oldm;
     }        oldm=newm;
     printf("\n");      }
   }      for(i=1; i<=nlstate+ndeath; i++)
   */        for(j=1;j<=nlstate+ndeath;j++) {
           po[i][j][h]=newm[i][j];
   free_matrix(a,1,npar,1,npar);          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
   free_matrix(y,1,npar,1,npar);           */
   free_vector(x,1,npar);        }
   free_ivector(indx,1,npar);    } /* end h */
   free_matrix(hess,1,npar,1,npar);    return po;
   }
   
 }  
   /*************** log-likelihood *************/
 /*************** hessian matrix ****************/  double func( double *x)
 double hessii( double x[], double delta, int theta, double delti[])  {
 {    int i, ii, j, k, mi, d, kk;
   int i;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
   int l=1, lmax=20;    double **out;
   double k1,k2;    double sw; /* Sum of weights */
   double p2[NPARMAX+1];    double lli; /* Individual log likelihood */
   double res;    long ipmx;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    /*extern weight */
   double fx;    /* We are differentiating ll according to initial status */
   int k=0,kmax=10;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   double l1;    /*for(i=1;i<imx;i++)
       printf(" %d\n",s[4][i]);
   fx=func(x);    */
   for (i=1;i<=npar;i++) p2[i]=x[i];    cov[1]=1.;
   for(l=0 ; l <=lmax; l++){  
     l1=pow(10,l);    for(k=1; k<=nlstate; k++) ll[k]=0.;
     delts=delt;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(k=1 ; k <kmax; k=k+1){      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       delt = delta*(l1*k);      for(mi=1; mi<= wav[i]-1; mi++){
       p2[theta]=x[theta] +delt;        for (ii=1;ii<=nlstate+ndeath;ii++)
       k1=func(p2)-fx;          for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       p2[theta]=x[theta]-delt;        for(d=0; d<dh[mi][i]; d++){
       k2=func(p2)-fx;          newm=savm;
       /*res= (k1-2.0*fx+k2)/delt/delt; */          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */          for (kk=1; kk<=cptcovage;kk++) {
                   cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 #ifdef DEBUG          }
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);         
 #endif          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          savm=oldm;
         k=kmax;          oldm=newm;
       }         
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */         
         k=kmax; l=lmax*10.;        } /* end mult */
       }       
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){         lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);
         delts=delt;        /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/
       }        ipmx +=1;
     }        sw += weight[i];
   }        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   delti[theta]=delts;      } /* end of wave */
   return res;    } /* end of individual */
     
 }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
 double hessij( double x[], double delti[], int thetai,int thetaj)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
 {    return -l;
   int i;  }
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;  
   double p2[NPARMAX+1];  /*********** Maximum Likelihood Estimation ***************/
   int k;  
   void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   fx=func(x);  {
   for (k=1; k<=2; k++) {    int i,j, iter;
     for (i=1;i<=npar;i++) p2[i]=x[i];    double **xi,*delti;
     p2[thetai]=x[thetai]+delti[thetai]/k;    double fret;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    xi=matrix(1,npar,1,npar);
     k1=func(p2)-fx;    for (i=1;i<=npar;i++)
         for (j=1;j<=npar;j++)
     p2[thetai]=x[thetai]+delti[thetai]/k;        xi[i][j]=(i==j ? 1.0 : 0.0);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     k2=func(p2)-fx;    powell(p,xi,npar,ftol,&iter,&fret,func);
     
     p2[thetai]=x[thetai]-delti[thetai]/k;     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    fprintf(ficlog,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     k3=func(p2)-fx;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     
     p2[thetai]=x[thetai]-delti[thetai]/k;  }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  
     k4=func(p2)-fx;  /**** Computes Hessian and covariance matrix ***/
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
 #ifdef DEBUG  {
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);    double  **a,**y,*x,pd;
 #endif    double **hess;
   }    int i, j,jk;
   return res;    int *indx;
 }  
     double hessii(double p[], double delta, int theta, double delti[]);
 /************** Inverse of matrix **************/    double hessij(double p[], double delti[], int i, int j);
 void ludcmp(double **a, int n, int *indx, double *d)     void lubksb(double **a, int npar, int *indx, double b[]) ;
 {     void ludcmp(double **a, int npar, int *indx, double *d) ;
   int i,imax,j,k;   
   double big,dum,sum,temp;     hess=matrix(1,npar,1,npar);
   double *vv;   
      printf("\nCalculation of the hessian matrix. Wait...\n");
   vv=vector(1,n);     fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   *d=1.0;     for (i=1;i<=npar;i++){
   for (i=1;i<=n;i++) {       printf("%d",i);fflush(stdout);
     big=0.0;       fprintf(ficlog,"%d",i);fflush(ficlog);
     for (j=1;j<=n;j++)       hess[i][i]=hessii(p,ftolhess,i,delti);
       if ((temp=fabs(a[i][j])) > big) big=temp;       /*printf(" %f ",p[i]);*/
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");       /*printf(" %lf ",hess[i][i]);*/
     vv[i]=1.0/big;     }
   }    
   for (j=1;j<=n;j++) {     for (i=1;i<=npar;i++) {
     for (i=1;i<j;i++) {       for (j=1;j<=npar;j++)  {
       sum=a[i][j];         if (j>i) {
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];           printf(".%d%d",i,j);fflush(stdout);
       a[i][j]=sum;           fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     }           hess[i][j]=hessij(p,delti,i,j);
     big=0.0;           hess[j][i]=hess[i][j];    
     for (i=j;i<=n;i++) {           /*printf(" %lf ",hess[i][j]);*/
       sum=a[i][j];         }
       for (k=1;k<j;k++)       }
         sum -= a[i][k]*a[k][j];     }
       a[i][j]=sum;     printf("\n");
       if ( (dum=vv[i]*fabs(sum)) >= big) {     fprintf(ficlog,"\n");
         big=dum;   
         imax=i;     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
       }     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     }    
     if (j != imax) {     a=matrix(1,npar,1,npar);
       for (k=1;k<=n;k++) {     y=matrix(1,npar,1,npar);
         dum=a[imax][k];     x=vector(1,npar);
         a[imax][k]=a[j][k];     indx=ivector(1,npar);
         a[j][k]=dum;     for (i=1;i<=npar;i++)
       }       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
       *d = -(*d);     ludcmp(a,npar,indx,&pd);
       vv[imax]=vv[j];   
     }     for (j=1;j<=npar;j++) {
     indx[j]=imax;       for (i=1;i<=npar;i++) x[i]=0;
     if (a[j][j] == 0.0) a[j][j]=TINY;       x[j]=1;
     if (j != n) {       lubksb(a,npar,indx,x);
       dum=1.0/(a[j][j]);       for (i=1;i<=npar;i++){
       for (i=j+1;i<=n;i++) a[i][j] *= dum;         matcov[i][j]=x[i];
     }       }
   }     }
   free_vector(vv,1,n);  /* Doesn't work */  
 ;    printf("\n#Hessian matrix#\n");
 }     fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) {
 void lubksb(double **a, int n, int *indx, double b[])       for (j=1;j<=npar;j++) {
 {         printf("%.3e ",hess[i][j]);
   int i,ii=0,ip,j;         fprintf(ficlog,"%.3e ",hess[i][j]);
   double sum;       }
        printf("\n");
   for (i=1;i<=n;i++) {       fprintf(ficlog,"\n");
     ip=indx[i];     }
     sum=b[ip];   
     b[ip]=b[i];     /* Recompute Inverse */
     if (ii)     for (i=1;i<=npar;i++)
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     else if (sum) ii=i;     ludcmp(a,npar,indx,&pd);
     b[i]=sum;   
   }     /*  printf("\n#Hessian matrix recomputed#\n");
   for (i=n;i>=1;i--) {   
     sum=b[i];     for (j=1;j<=npar;j++) {
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];       for (i=1;i<=npar;i++) x[i]=0;
     b[i]=sum/a[i][i];       x[j]=1;
   }       lubksb(a,npar,indx,x);
 }       for (i=1;i<=npar;i++){
         y[i][j]=x[i];
 /************ Frequencies ********************/        printf("%.3e ",y[i][j]);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx)        fprintf(ficlog,"%.3e ",y[i][j]);
 {  /* Some frequencies */      }
        printf("\n");
   int i, m, jk;      fprintf(ficlog,"\n");
   double ***freq; /* Frequencies */    }
   double *pp;    */
   double pos;  
   FILE *ficresp;    free_matrix(a,1,npar,1,npar);
   char fileresp[FILENAMELENGTH];    free_matrix(y,1,npar,1,npar);
     free_vector(x,1,npar);
   pp=vector(1,nlstate);    free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
   strcpy(fileresp,"p");  
   strcat(fileresp,fileres);  
   if((ficresp=fopen(fileresp,"w"))==NULL) {  }
     printf("Problem with prevalence resultfile: %s\n", fileresp);  
     exit(0);  /*************** hessian matrix ****************/
   }  double hessii( double x[], double delta, int theta, double delti[])
   {
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    int i;
   for (i=-1; i<=nlstate+ndeath; i++)      int l=1, lmax=20;
     for (jk=-1; jk<=nlstate+ndeath; jk++)      double k1,k2;
       for(m=agemin; m <= agemax+3; m++)    double p2[NPARMAX+1];
         freq[i][jk][m]=0;    double res;
     double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   for (i=1; i<=imx; i++)  {    double fx;
     for(m=firstpass; m<= lastpass-1; m++){    int k=0,kmax=10;
       if(agev[m][i]==0) agev[m][i]=agemax+1;    double l1;
       if(agev[m][i]==1) agev[m][i]=agemax+2;  
        freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    fx=func(x);
        freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    for (i=1;i<=npar;i++) p2[i]=x[i];
     }    for(l=0 ; l <=lmax; l++){
   }      l1=pow(10,l);
       delts=delt;
   fprintf(ficresp, "#");      for(k=1 ; k <kmax; k=k+1){
   for(i=1; i<=nlstate;i++)         delt = delta*(l1*k);
     fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        p2[theta]=x[theta] +delt;
 fprintf(ficresp, "\n");        k1=func(p2)-fx;
         p2[theta]=x[theta]-delt;
   for(i=(int)agemin; i <= (int)agemax+3; i++){        k2=func(p2)-fx;
     if(i==(int)agemax+3)        /*res= (k1-2.0*fx+k2)/delt/delt; */
       printf("Total");        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     else       
       printf("Age %d", i);  #ifdef DEBUG
     for(jk=1; jk <=nlstate ; jk++){        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         pp[jk] += freq[jk][m][i];  #endif
     }        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     for(jk=1; jk <=nlstate ; jk++){        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       for(m=-1, pos=0; m <=0 ; m++)          k=kmax;
         pos += freq[jk][m][i];        }
       if(pp[jk]>=1.e-10)        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          k=kmax; l=lmax*10.;
       else        }
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){
     }          delts=delt;
     for(jk=1; jk <=nlstate ; jk++){        }
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)      }
         pp[jk] += freq[jk][m][i];    }
     }    delti[theta]=delts;
     for(jk=1,pos=0; jk <=nlstate ; jk++)    return res;
       pos += pp[jk];   
     for(jk=1; jk <=nlstate ; jk++){  }
       if(pos>=1.e-5)  
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);  double hessij( double x[], double delti[], int thetai,int thetaj)
       else  {
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    int i;
       if( i <= (int) agemax){    int l=1, l1, lmax=20;
         if(pos>=1.e-5)    double k1,k2,k3,k4,res,fx;
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    double p2[NPARMAX+1];
       else    int k;
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  
       }    fx=func(x);
     }    for (k=1; k<=2; k++) {
     for(jk=-1; jk <=nlstate+ndeath; jk++)      for (i=1;i<=npar;i++) p2[i]=x[i];
       for(m=-1; m <=nlstate+ndeath; m++)      p2[thetai]=x[thetai]+delti[thetai]/k;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     if(i <= (int) agemax)      k1=func(p2)-fx;
       fprintf(ficresp,"\n");   
     printf("\n");      p2[thetai]=x[thetai]+delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k2=func(p2)-fx;
   fclose(ficresp);   
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      p2[thetai]=x[thetai]-delti[thetai]/k;
   free_vector(pp,1,nlstate);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k3=func(p2)-fx;
 }  /* End of Freq */   
       p2[thetai]=x[thetai]-delti[thetai]/k;
 /************* Waves Concatenation ***************/      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k4=func(p2)-fx;
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
 {  #ifdef DEBUG
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
      Death is a valid wave (if date is known).      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i  #endif
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    }
      and mw[mi+1][i]. dh depends on stepm.    return res;
      */  }
   
   int i, mi, m;  /************** Inverse of matrix **************/
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  void ludcmp(double **a, int n, int *indx, double *d)
 float sum=0.;  {
     int i,imax,j,k;
   for(i=1; i<=imx; i++){    double big,dum,sum,temp;
     mi=0;    double *vv;
     m=firstpass;   
     while(s[m][i] <= nlstate){    vv=vector(1,n);
       if(s[m][i]>=1)    *d=1.0;
         mw[++mi][i]=m;    for (i=1;i<=n;i++) {
       if(m >=lastpass)      big=0.0;
         break;      for (j=1;j<=n;j++)
       else        if ((temp=fabs(a[i][j])) > big) big=temp;
         m++;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
     }/* end while */      vv[i]=1.0/big;
     if (s[m][i] > nlstate){    }
       mi++;     /* Death is another wave */    for (j=1;j<=n;j++) {
       /* if(mi==0)  never been interviewed correctly before death */      for (i=1;i<j;i++) {
          /* Only death is a correct wave */        sum=a[i][j];
       mw[mi][i]=m;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];
     }        a[i][j]=sum;
       }
     wav[i]=mi;      big=0.0;
     if(mi==0)      for (i=j;i<=n;i++) {
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        sum=a[i][j];
   }        for (k=1;k<j;k++)
           sum -= a[i][k]*a[k][j];
   for(i=1; i<=imx; i++){        a[i][j]=sum;
     for(mi=1; mi<wav[i];mi++){        if ( (dum=vv[i]*fabs(sum)) >= big) {
       if (stepm <=0)          big=dum;
         dh[mi][i]=1;          imax=i;
       else{        }
         if (s[mw[mi+1][i]][i] > nlstate) {      }
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);       if (j != imax) {
           if(j=0) j=1;  /* Survives at least one month after exam */        for (k=1;k<=n;k++) {
         }          dum=a[imax][k];
         else{          a[imax][k]=a[j][k];
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          a[j][k]=dum;
           k=k+1;        }
           if (j >= jmax) jmax=j;        *d = -(*d);
           else if (j <= jmin)jmin=j;        vv[imax]=vv[j];
           sum=sum+j;      }
         }      indx[j]=imax;
         jk= j/stepm;      if (a[j][j] == 0.0) a[j][j]=TINY;
         jl= j -jk*stepm;      if (j != n) {
         ju= j -(jk+1)*stepm;        dum=1.0/(a[j][j]);
         if(jl <= -ju)        for (i=j+1;i<=n;i++) a[i][j] *= dum;
           dh[mi][i]=jk;      }
         else    }
           dh[mi][i]=jk+1;    free_vector(vv,1,n);  /* Doesn't work */
         if(dh[mi][i]==0)  ;
           dh[mi][i]=1; /* At least one step */  }
       }  
     }  void lubksb(double **a, int n, int *indx, double b[])
   }  {
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);    int i,ii=0,ip,j;
 }    double sum;
    
 /*********** Health Expectancies ****************/    for (i=1;i<=n;i++) {
       ip=indx[i];
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm)      sum=b[ip];
 {      b[ip]=b[i];
   /* Health expectancies */      if (ii)
   int i, j, nhstepm, hstepm, h;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];
   double age, agelim,hf;      else if (sum) ii=i;
   double ***p3mat;      b[i]=sum;
     }
   FILE  *ficreseij;    for (i=n;i>=1;i--) {
   char filerese[FILENAMELENGTH];      sum=b[i];
       for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];
   strcpy(filerese,"e");      b[i]=sum/a[i][i];
   strcat(filerese,fileres);    }
   if((ficreseij=fopen(filerese,"w"))==NULL) {  }
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);  
   }  /************ Frequencies ********************/
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);  void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)
   {  /* Some frequencies */
   fprintf(ficreseij,"# Health expectancies\n");   
   fprintf(ficreseij,"# Age");    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   for(i=1; i<=nlstate;i++)    int first;
     for(j=1; j<=nlstate;j++)    double ***freq; /* Frequencies */
       fprintf(ficreseij," %1d-%1d",i,j);    double *pp;
   fprintf(ficreseij,"\n");    double pos, k2, dateintsum=0,k2cpt=0;
     FILE *ficresp;
   hstepm=1*YEARM; /*  Every j years of age (in month) */    char fileresp[FILENAMELENGTH];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    
     pp=vector(1,nlstate);
   agelim=AGESUP;    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    strcpy(fileresp,"p");
     /* nhstepm age range expressed in number of stepm */    strcat(fileresp,fileres);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);     if((ficresp=fopen(fileresp,"w"))==NULL) {
     /* Typically if 20 years = 20*12/6=40 stepm */       printf("Problem with prevalence resultfile: %s\n", fileresp);
     if (stepm >= YEARM) hstepm=1;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      exit(0);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    }
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    j1=0;
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm);     
     j=cptcoveff;
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++)    first=1;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){  
           eij[i][j][(int)age] +=p3mat[i][j][h];    for(k1=1; k1<=j;k1++){
         }      for(i1=1; i1<=ncodemax[k1];i1++){
             j1++;
     hf=1;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
     if (stepm >= YEARM) hf=stepm/YEARM;          scanf("%d", i);*/
     fprintf(ficreseij,"%.0f",age );        for (i=-1; i<=nlstate+ndeath; i++)  
     for(i=1; i<=nlstate;i++)          for (jk=-1; jk<=nlstate+ndeath; jk++)  
       for(j=1; j<=nlstate;j++){            for(m=agemin; m <= agemax+3; m++)
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);              freq[i][jk][m]=0;
       }       
     fprintf(ficreseij,"\n");        dateintsum=0;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        k2cpt=0;
   }        for (i=1; i<=imx; i++) {
   fclose(ficreseij);          bool=1;
 }          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++)
 /************ Variance ******************/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl)                bool=0;
 {          }
   /* Variance of health expectancies */          if (bool==1) {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            for(m=firstpass; m<=lastpass; m++){
   double **newm;              k2=anint[m][i]+(mint[m][i]/12.);
   double **dnewm,**doldm;              if ((k2>=dateprev1) && (k2<=dateprev2)) {
   int i, j, nhstepm, hstepm, h;                if(agev[m][i]==0) agev[m][i]=agemax+1;
   int k;                if(agev[m][i]==1) agev[m][i]=agemax+2;
   FILE  *ficresvij;                if (m<lastpass) {
   char fileresv[FILENAMELENGTH];                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   double *xp;                  freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];
   double **gp, **gm;                }
   double ***gradg, ***trgradg;               
   double ***p3mat;                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {
   double age,agelim;                  dateintsum=dateintsum+k2;
   int theta;                  k2cpt++;
                 }
   strcpy(fileresv,"v");              }
   strcat(fileresv,fileres);            }
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          }
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);        }
   }         
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
   
         if  (cptcovn>0) {
   fprintf(ficresvij,"# Covariances of life expectancies\n");          fprintf(ficresp, "\n#********** Variable ");
   fprintf(ficresvij,"# Age");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   for(i=1; i<=nlstate;i++)          fprintf(ficresp, "**********\n#");
     for(j=1; j<=nlstate;j++)        }
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        for(i=1; i<=nlstate;i++)
   fprintf(ficresvij,"\n");          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
   xp=vector(1,npar);       
   dnewm=matrix(1,nlstate,1,npar);        for(i=(int)agemin; i <= (int)agemax+3; i++){
   doldm=matrix(1,nlstate,1,nlstate);          if(i==(int)agemax+3){
               fprintf(ficlog,"Total");
   hstepm=1*YEARM; /* Every year of age */          }else{
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */             if(first==1){
   agelim = AGESUP;              first=0;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              printf("See log file for details...\n");
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */             }
     if (stepm >= YEARM) hstepm=1;            fprintf(ficlog,"Age %d", i);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for(jk=1; jk <=nlstate ; jk++){
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     gp=matrix(0,nhstepm,1,nlstate);              pp[jk] += freq[jk][m][i];
     gm=matrix(0,nhstepm,1,nlstate);          }
           for(jk=1; jk <=nlstate ; jk++){
     for(theta=1; theta <=npar; theta++){            for(m=-1, pos=0; m <=0 ; m++)
       for(i=1; i<=npar; i++){ /* Computes gradient */              pos += freq[jk][m][i];
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            if(pp[jk]>=1.e-10){
       }              if(first==1){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);              }
       for(j=1; j<= nlstate; j++){              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
         for(h=0; h<=nhstepm; h++){            }else{
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)              if(first==1)
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
         }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       }            }
               }
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          for(jk=1; jk <=nlstate ; jk++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);              for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);              pp[jk] += freq[jk][m][i];
       for(j=1; j<= nlstate; j++){          }
         for(h=0; h<=nhstepm; h++){  
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          for(jk=1,pos=0; jk <=nlstate ; jk++)
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];            pos += pp[jk];
         }          for(jk=1; jk <=nlstate ; jk++){
       }            if(pos>=1.e-5){
       for(j=1; j<= nlstate; j++)              if(first==1)
         for(h=0; h<=nhstepm; h++){                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         }            }else{
     } /* End theta */              if(first==1)
                 printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }
     for(h=0; h<=nhstepm; h++)            if( i <= (int) agemax){
       for(j=1; j<=nlstate;j++)              if(pos>=1.e-5){
         for(theta=1; theta <=npar; theta++)                fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);
           trgradg[h][j][theta]=gradg[h][theta][j];                probs[i][jk][j1]= pp[jk]/pos;
                 /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     for(i=1;i<=nlstate;i++)              }
       for(j=1;j<=nlstate;j++)              else
         vareij[i][j][(int)age] =0.;                fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);
     for(h=0;h<=nhstepm;h++){            }
       for(k=0;k<=nhstepm;k++){          }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);         
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          for(jk=-1; jk <=nlstate+ndeath; jk++)
         for(i=1;i<=nlstate;i++)            for(m=-1; m <=nlstate+ndeath; m++)
           for(j=1;j<=nlstate;j++)              if(freq[jk][m][i] !=0 ) {
             vareij[i][j][(int)age] += doldm[i][j];              if(first==1)
       }                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     }                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     h=1;              }
     if (stepm >= YEARM) h=stepm/YEARM;          if(i <= (int) agemax)
     fprintf(ficresvij,"%.0f ",age );            fprintf(ficresp,"\n");
     for(i=1; i<=nlstate;i++)          if(first==1)
       for(j=1; j<=nlstate;j++){            printf("Others in log...\n");
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);          fprintf(ficlog,"\n");
       }        }
     fprintf(ficresvij,"\n");      }
     free_matrix(gp,0,nhstepm,1,nlstate);    }
     free_matrix(gm,0,nhstepm,1,nlstate);    dateintmean=dateintsum/k2cpt;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);   
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    fclose(ficresp);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
   } /* End age */    free_vector(pp,1,nlstate);
   fclose(ficresvij);   
   free_vector(xp,1,npar);    /* End of Freq */
   free_matrix(doldm,1,nlstate,1,npar);  }
   free_matrix(dnewm,1,nlstate,1,nlstate);  
   /************ Prevalence ********************/
 }  void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)
   {  /* Some frequencies */
 /************ Variance of prevlim ******************/   
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl)    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
 {    double ***freq; /* Frequencies */
   /* Variance of health expectancies */    double *pp;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    double pos, k2;
   double **newm;  
   double **dnewm,**doldm;    pp=vector(1,nlstate);
   int i, j, nhstepm, hstepm;    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   int k;   
   FILE  *ficresvpl;    freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
   char fileresvpl[FILENAMELENGTH];    j1=0;
   double *xp;   
   double *gp, *gm;    j=cptcoveff;
   double **gradg, **trgradg;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   double age,agelim;   
   int theta;    for(k1=1; k1<=j;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
   strcpy(fileresvpl,"vpl");        j1++;
   strcat(fileresvpl,fileres);       
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        for (i=-1; i<=nlstate+ndeath; i++)  
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          for (jk=-1; jk<=nlstate+ndeath; jk++)  
     exit(0);            for(m=agemin; m <= agemax+3; m++)
   }              freq[i][jk][m]=0;
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);       
         for (i=1; i<=imx; i++) {
           bool=1;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");          if  (cptcovn>0) {
   fprintf(ficresvpl,"# Age");            for (z1=1; z1<=cptcoveff; z1++)
   for(i=1; i<=nlstate;i++)              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])
       fprintf(ficresvpl," %1d-%1d",i,i);                bool=0;
   fprintf(ficresvpl,"\n");          }
           if (bool==1) {
   xp=vector(1,npar);            for(m=firstpass; m<=lastpass; m++){
   dnewm=matrix(1,nlstate,1,npar);              k2=anint[m][i]+(mint[m][i]/12.);
   doldm=matrix(1,nlstate,1,nlstate);              if ((k2>=dateprev1) && (k2<=dateprev2)) {
                   if(agev[m][i]==0) agev[m][i]=agemax+1;
   hstepm=1*YEARM; /* Every year of age */                if(agev[m][i]==1) agev[m][i]=agemax+2;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */                 if (m<lastpass) {
   agelim = AGESUP;                  if (calagedate>0)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                    freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */                   else
     if (stepm >= YEARM) hstepm=1;                    freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */                  freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];
     gradg=matrix(1,npar,1,nlstate);                }
     gp=vector(1,nlstate);              }
     gm=vector(1,nlstate);            }
           }
     for(theta=1; theta <=npar; theta++){        }
       for(i=1; i<=npar; i++){ /* Computes gradient */        for(i=(int)agemin; i <= (int)agemax+3; i++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          for(jk=1; jk <=nlstate ; jk++){
       }            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);              pp[jk] += freq[jk][m][i];
       for(i=1;i<=nlstate;i++)          }
         gp[i] = prlim[i][i];          for(jk=1; jk <=nlstate ; jk++){
                 for(m=-1, pos=0; m <=0 ; m++)
       for(i=1; i<=npar; i++) /* Computes gradient */              pos += freq[jk][m][i];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);         
       for(i=1;i<=nlstate;i++)          for(jk=1; jk <=nlstate ; jk++){
         gm[i] = prlim[i][i];            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
               pp[jk] += freq[jk][m][i];
       for(i=1;i<=nlstate;i++)          }
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];         
     } /* End theta */          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];
          
     trgradg =matrix(1,nlstate,1,npar);          for(jk=1; jk <=nlstate ; jk++){    
             if( i <= (int) agemax){
     for(j=1; j<=nlstate;j++)              if(pos>=1.e-5){
       for(theta=1; theta <=npar; theta++)                probs[i][jk][j1]= pp[jk]/pos;
         trgradg[j][theta]=gradg[theta][j];              }
             }
     for(i=1;i<=nlstate;i++)          }/* end jk */
       varpl[i][(int)age] =0.;        }/* end i */
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      } /* end i1 */
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    } /* end k1 */
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */   
     free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
     fprintf(ficresvpl,"%.0f ",age );    free_vector(pp,1,nlstate);
     for(i=1; i<=nlstate;i++)   
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));  }  /* End of Freq */
     fprintf(ficresvpl,"\n");  
     free_vector(gp,1,nlstate);  /************* Waves Concatenation ***************/
     free_vector(gm,1,nlstate);  
     free_matrix(gradg,1,npar,1,nlstate);  void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
     free_matrix(trgradg,1,nlstate,1,npar);  {
   } /* End age */    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   fclose(ficresvpl);       Death is a valid wave (if date is known).
   free_vector(xp,1,npar);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   free_matrix(doldm,1,nlstate,1,npar);       dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]
   free_matrix(dnewm,1,nlstate,1,nlstate);       and mw[mi+1][i]. dh depends on stepm.
        */
 }  
     int i, mi, m;
     /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
 /***********************************************/    int first;
 /**************** Main Program *****************/    int j, k=0,jk, ju, jl;
 /***********************************************/    double sum=0.;
     first=0;
 /*int main(int argc, char *argv[])*/    jmin=1e+5;
 int main()    jmax=-1;
 {    jmean=0.;
     for(i=1; i<=imx; i++){
   int i,j, k, n=MAXN,iter,m,size;      mi=0;
   double agedeb, agefin,hf;      m=firstpass;
   double agemin=1.e20, agemax=-1.e20;      while(s[m][i] <= nlstate){
         if(s[m][i]>=1)
   double fret;          mw[++mi][i]=m;
   double **xi,tmp,delta;        if(m >=lastpass)
           break;
   double dum; /* Dummy variable */        else
   double ***p3mat;          m++;
   int *indx;      }/* end while */
   char line[MAXLINE], linepar[MAXLINE];      if (s[m][i] > nlstate){
   char title[MAXLINE];        mi++;     /* Death is another wave */
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];        /* if(mi==0)  never been interviewed correctly before death */
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];           /* Only death is a correct wave */
   char filerest[FILENAMELENGTH];        mw[mi][i]=m;
   char fileregp[FILENAMELENGTH];      }
   char path[80],pathc[80],pathcd[80],pathtot[80];  
   int firstobs=1, lastobs=10;      wav[i]=mi;
   int sdeb, sfin; /* Status at beginning and end */      if(mi==0){
   int c,  h , cpt,l;        if(first==0){
   int ju,jl, mi;          printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);
   int i1,j1, k1,jk,aa,bb, stepsize;          first=1;
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        }
           if(first==1){
   int hstepm, nhstepm;          fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);
   double bage, fage, age, agelim, agebase;        }
   double ftolpl=FTOL;      } /* end mi==0 */
   double **prlim;    }
   double *severity;  
   double ***param; /* Matrix of parameters */    for(i=1; i<=imx; i++){
   double  *p;      for(mi=1; mi<wav[i];mi++){
   double **matcov; /* Matrix of covariance */        if (stepm <=0)
   double ***delti3; /* Scale */          dh[mi][i]=1;
   double *delti; /* Scale */        else{
   double ***eij, ***vareij;          if (s[mw[mi+1][i]][i] > nlstate) {
   double **varpl; /* Variances of prevalence limits by age */            if (agedc[i] < 2*AGESUP) {
   double *epj, vepp;            j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);
   char version[80]="Imach version 0.64, May 2000, INED-EUROREVES ";            if(j==0) j=1;  /* Survives at least one month after exam */
   char *alph[]={"a","a","b","c","d","e"}, str[4];            k=k+1;
   char z[1]="c";            if (j >= jmax) jmax=j;
 #include <sys/time.h>            if (j <= jmin) jmin=j;
 #include <time.h>            sum=sum+j;
             /*if (j<0) printf("j=%d num=%d \n",j,i); */
   /* long total_usecs;            }
   struct timeval start_time, end_time;          }
             else{
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
             k=k+1;
             if (j >= jmax) jmax=j;
   printf("\nIMACH, Version 0.64");            else if (j <= jmin)jmin=j;
   printf("\nEnter the parameter file name: ");            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
 #define windows 1            sum=sum+j;
 #ifdef windows          }
   scanf("%s",pathtot);          jk= j/stepm;
   getcwd(pathcd, size);          jl= j -jk*stepm;
   cut(path,optionfile,pathtot);          ju= j -(jk+1)*stepm;
   chdir(path);          if(jl <= -ju)
   replace(pathc,path);            dh[mi][i]=jk;
 #endif          else
 #ifdef unix            dh[mi][i]=jk+1;
   scanf("%s",optionfile);          if(dh[mi][i]==0)
 #endif            dh[mi][i]=1; /* At least one step */
         }
 /*-------- arguments in the command line --------*/      }
     }
   strcpy(fileres,"r");    jmean=sum/k;
   strcat(fileres, optionfile);    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
     fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
   /*---------arguments file --------*/   }
   
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  /*********** Tricode ****************************/
     printf("Problem with optionfile %s\n",optionfile);  void tricode(int *Tvar, int **nbcode, int imx)
     goto end;  {
   }    int Ndum[20],ij=1, k, j, i;
     int cptcode=0;
   strcpy(filereso,"o");    cptcoveff=0;
   strcat(filereso,fileres);   
   if((ficparo=fopen(filereso,"w"))==NULL) {    for (k=0; k<19; k++) Ndum[k]=0;
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    for (k=1; k<=7; k++) ncodemax[k]=0;
   }  
     for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
 /*--------- index.htm --------*/      for (i=1; i<=imx; i++) {
         ij=(int)(covar[Tvar[j]][i]);
   if((fichtm=fopen("index.htm","w"))==NULL)    {        Ndum[ij]++;
     printf("Problem with index.htm \n");goto end;        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
   }        if (ij > cptcode) cptcode=ij;
       }
  fprintf(fichtm,"<body><ul><li>Outputs files<br><br>\n  
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n      for (i=0; i<=cptcode; i++) {
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>        if(Ndum[i]!=0) ncodemax[j]++;
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      }
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      ij=1;
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>  
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>      for (i=1; i<=ncodemax[j]; i++) {
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>        for (k=0; k<=19; k++) {
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);          if (Ndum[k] != 0) {
             nbcode[Tvar[j]][ij]=k;
  fprintf(fichtm," <li>Graphs<br> <br>");           
              ij++;
 for(cpt=1; cpt<nlstate;cpt++)          }
    fprintf(fichtm,"- Prevalence of disability: p%s1.gif<br>          if (ij > ncodemax[j]) break;
 <img src=\"p%s1.gif\"><br>",strtok(optionfile, "."),strtok(optionfile, "."),cpt);        }  
  for(cpt=1; cpt<=nlstate;cpt++)      }
      fprintf(fichtm,"- Observed and stationary  prevalence (with confident    }  
 interval) in state (%d): v%s%d.gif <br>  
 <img src=\"v%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);   for (k=0; k<19; k++) Ndum[k]=0;
    
  for(cpt=1; cpt<=nlstate;cpt++)   for (i=1; i<=ncovmodel-2; i++) {
      fprintf(fichtm,"- Health life expectancies by age and initial health state (%d): exp%s%d.gif <br>     ij=Tvar[i];
 <img src=\"ex%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);     Ndum[ij]++;
       }
  fprintf(fichtm,"- Total life expectancy by age and  
         health expectancies in states (1) and (2): e%s.gif<br>   ij=1;
         <img src=\"e%s.gif\"></li> </ul></body>",strtok(optionfile, "."),strtok(optionfile, "."));   for (i=1; i<=10; i++) {
      if((Ndum[i]!=0) && (i<=ncovcol)){
        Tvaraff[ij]=i;
 fclose(fichtm);       ij++;
      }
   /* Reads comments: lines beginning with '#' */   }
   while((c=getc(ficpar))=='#' && c!= EOF){   
     ungetc(c,ficpar);   cptcoveff=ij-1;
     fgets(line, MAXLINE, ficpar);  }
     puts(line);  
     fputs(line,ficparo);  /*********** Health Expectancies ****************/
   }  
   ungetc(c,ficpar);  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )
   
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt);  {
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt);    /* Health expectancies */
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
       double age, agelim, hf;
   nvar=ncov-1; /* Suppressing age as a basic covariate */    double ***p3mat,***varhe;
       double **dnewm,**doldm;
   /* Read guess parameters */    double *xp;
   /* Reads comments: lines beginning with '#' */    double **gp, **gm;
   while((c=getc(ficpar))=='#' && c!= EOF){    double ***gradg, ***trgradg;
     ungetc(c,ficpar);    int theta;
     fgets(line, MAXLINE, ficpar);  
     puts(line);    varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);
     fputs(line,ficparo);    xp=vector(1,npar);
   }    dnewm=matrix(1,nlstate*2,1,npar);
   ungetc(c,ficpar);    doldm=matrix(1,nlstate*2,1,nlstate*2);
      
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);    fprintf(ficreseij,"# Health expectancies\n");
     for(i=1; i <=nlstate; i++)    fprintf(ficreseij,"# Age");
     for(j=1; j <=nlstate+ndeath-1; j++){    for(i=1; i<=nlstate;i++)
       fscanf(ficpar,"%1d%1d",&i1,&j1);      for(j=1; j<=nlstate;j++)
       fprintf(ficparo,"%1d%1d",i1,j1);        fprintf(ficreseij," %1d-%1d (SE)",i,j);
       printf("%1d%1d",i,j);    fprintf(ficreseij,"\n");
       for(k=1; k<=ncov;k++){  
         fscanf(ficpar," %lf",&param[i][j][k]);    if(estepm < stepm){
         printf(" %lf",param[i][j][k]);      printf ("Problem %d lower than %d\n",estepm, stepm);
         fprintf(ficparo," %lf",param[i][j][k]);    }
       }    else  hstepm=estepm;  
       fscanf(ficpar,"\n");    /* We compute the life expectancy from trapezoids spaced every estepm months
       printf("\n");     * This is mainly to measure the difference between two models: for example
       fprintf(ficparo,"\n");     * if stepm=24 months pijx are given only every 2 years and by summing them
     }     * we are calculating an estimate of the Life Expectancy assuming a linear
        * progression inbetween and thus overestimating or underestimating according
   npar= (nlstate+ndeath-1)*nlstate*ncov;     * to the curvature of the survival function. If, for the same date, we
   p=param[1][1];     * estimate the model with stepm=1 month, we can keep estepm to 24 months
        * to compare the new estimate of Life expectancy with the same linear
   /* Reads comments: lines beginning with '#' */     * hypothesis. A more precise result, taking into account a more precise
   while((c=getc(ficpar))=='#' && c!= EOF){     * curvature will be obtained if estepm is as small as stepm. */
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    /* For example we decided to compute the life expectancy with the smallest unit */
     puts(line);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.
     fputs(line,ficparo);       nhstepm is the number of hstepm from age to agelim
   }       nstepm is the number of stepm from age to agelin.
   ungetc(c,ficpar);       Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like estepm months */
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */       survival function given by stepm (the optimization length). Unfortunately it
   for(i=1; i <=nlstate; i++){       means that if the survival funtion is printed only each two years of age and if
     for(j=1; j <=nlstate+ndeath-1; j++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same
       fscanf(ficpar,"%1d%1d",&i1,&j1);       results. So we changed our mind and took the option of the best precision.
       printf("%1d%1d",i,j);    */
       fprintf(ficparo,"%1d%1d",i1,j1);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */
       for(k=1; k<=ncov;k++){  
         fscanf(ficpar,"%le",&delti3[i][j][k]);    agelim=AGESUP;
         printf(" %le",delti3[i][j][k]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         fprintf(ficparo," %le",delti3[i][j][k]);      /* nhstepm age range expressed in number of stepm */
       }      nstepm=(int) rint((agelim-age)*YEARM/stepm);
       fscanf(ficpar,"\n");      /* Typically if 20 years nstepm = 20*12/6=40 stepm */
       printf("\n");      /* if (stepm >= YEARM) hstepm=1;*/
       fprintf(ficparo,"\n");      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     }      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);
   delti=delti3[1][1];      gp=matrix(0,nhstepm,1,nlstate*2);
         gm=matrix(0,nhstepm,1,nlstate*2);
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     ungetc(c,ficpar);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
     fgets(line, MAXLINE, ficpar);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
     puts(line);   
     fputs(line,ficparo);  
   }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   ungetc(c,ficpar);  
         /* Computing Variances of health expectancies */
   matcov=matrix(1,npar,1,npar);  
   for(i=1; i <=npar; i++){       for(theta=1; theta <=npar; theta++){
     fscanf(ficpar,"%s",&str);        for(i=1; i<=npar; i++){
     printf("%s",str);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     fprintf(ficparo,"%s",str);        }
     for(j=1; j <=i; j++){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       fscanf(ficpar," %le",&matcov[i][j]);   
       printf(" %.5le",matcov[i][j]);        cptj=0;
       fprintf(ficparo," %.5le",matcov[i][j]);        for(j=1; j<= nlstate; j++){
     }          for(i=1; i<=nlstate; i++){
     fscanf(ficpar,"\n");            cptj=cptj+1;
     printf("\n");            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
     fprintf(ficparo,"\n");              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
   }            }
   for(i=1; i <=npar; i++)          }
     for(j=i+1;j<=npar;j++)        }
       matcov[i][j]=matcov[j][i];       
           
   printf("\n");        for(i=1; i<=npar; i++)
             xp[i] = x[i] - (i==theta ?delti[theta]:0);
           hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   if(mle==1){       
     /*-------- data file ----------*/        cptj=0;
     if((ficres =fopen(fileres,"w"))==NULL) {        for(j=1; j<= nlstate; j++){
       printf("Problem with resultfile: %s\n", fileres);goto end;          for(i=1;i<=nlstate;i++){
     }            cptj=cptj+1;
     fprintf(ficres,"#%s\n",version);            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
                   gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
     if((fic=fopen(datafile,"r"))==NULL)    {            }
       printf("Problem with datafile: %s\n", datafile);goto end;          }
     }        }
             for(j=1; j<= nlstate*2; j++)
     n= lastobs;          for(h=0; h<=nhstepm-1; h++){
     severity = vector(1,maxwav);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     outcome=imatrix(1,maxwav+1,1,n);          }
     num=ivector(1,n);       }
     moisnais=vector(1,n);     
     annais=vector(1,n);  /* End theta */
     moisdc=vector(1,n);  
     andc=vector(1,n);       trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);
     agedc=vector(1,n);  
     cod=ivector(1,n);       for(h=0; h<=nhstepm-1; h++)
     weight=vector(1,n);        for(j=1; j<=nlstate*2;j++)
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */          for(theta=1; theta <=npar; theta++)
     mint=matrix(1,maxwav,1,n);            trgradg[h][j][theta]=gradg[h][theta][j];
     anint=matrix(1,maxwav,1,n);       
     covar=matrix(1,NCOVMAX,1,n);  
     s=imatrix(1,maxwav+1,1,n);       for(i=1;i<=nlstate*2;i++)
     adl=imatrix(1,maxwav+1,1,n);            for(j=1;j<=nlstate*2;j++)
     tab=ivector(1,NCOVMAX);          varhe[i][j][(int)age] =0.;
     i=1;   
     while (fgets(line, MAXLINE, fic) != NULL)    {       printf("%d|",(int)age);fflush(stdout);
       if ((i >= firstobs) && (i <lastobs)) {       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
 sscanf(line,"%d %lf %lf %lf %lf/%lf %lf/%lf %lf/%lf %d %lf/%lf %d %lf/%lf %d %lf/%lf %d", &num[i], &covar[1][i], &covar[2][i],&weight[i],&moisnais[i],&annais[i],&moisdc[i],&andc[i], &mint[1][i], &anint[1][i], &s[1][i], &mint[2][i],&anint[2][i], &s[2][i],&mint[3][i],&anint[3][i], &s[3][i],&mint[4][i],&anint[4][i], &s[4][i]);       for(h=0;h<=nhstepm-1;h++){
         i=i+1;        for(k=0;k<=nhstepm-1;k++){
       }          matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);
     }           matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);
   imx=i-1; /* Number of individuals */          for(i=1;i<=nlstate*2;i++)
             for(j=1;j<=nlstate*2;j++)
     fclose(fic);              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
     if (weightopt != 1) { /* Maximisation without weights*/      }
       for(i=1;i<=n;i++) weight[i]=1.0;      /* Computing expectancies */
     }      for(i=1; i<=nlstate;i++)
     /*-calculation of age at interview from date of interview and age at death -*/        for(j=1; j<=nlstate;j++)
     agev=matrix(1,maxwav,1,imx);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
                 eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     for (i=1; i<=imx; i++)  {           
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
       for(m=1; (m<= maxwav); m++){  
         if(s[m][i] >0){          }
           if (s[m][i] == nlstate+1) {  
             if(agedc[i]>0)      fprintf(ficreseij,"%3.0f",age );
               agev[m][i]=agedc[i];      cptj=0;
             else{      for(i=1; i<=nlstate;i++)
               printf("Warning negative age at death: %d line:%d\n",num[i],i);        for(j=1; j<=nlstate;j++){
               agev[m][i]=-1;          cptj++;
             }          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
           }        }
           else if(s[m][i] !=9){ /* Should no more exist */      fprintf(ficreseij,"\n");
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);     
             if(mint[m][i]==99 || anint[m][i]==9999)      free_matrix(gm,0,nhstepm,1,nlstate*2);
               agev[m][i]=1;      free_matrix(gp,0,nhstepm,1,nlstate*2);
             else if(agev[m][i] <agemin){       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);
               agemin=agev[m][i];      free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             }    }
             else if(agev[m][i] >agemax){    printf("\n");
               agemax=agev[m][i];    fprintf(ficlog,"\n");
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/  
             }    free_vector(xp,1,npar);
             /*agev[m][i]=anint[m][i]-annais[i];*/    free_matrix(dnewm,1,nlstate*2,1,npar);
             /*   agev[m][i] = age[i]+2*m;*/    free_matrix(doldm,1,nlstate*2,1,nlstate*2);
           }    free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);
           else { /* =9 */  }
             agev[m][i]=1;  
             s[m][i]=-1;  /************ Variance ******************/
           }  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased)
         }  {
         else /*= 0 Unknown */    /* Variance of health expectancies */
           agev[m][i]=1;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
       }    /* double **newm;*/
         double **dnewm,**doldm;
     }    double **dnewmp,**doldmp;
     for (i=1; i<=imx; i++)  {    int i, j, nhstepm, hstepm, h, nstepm ;
       for(m=1; (m<= maxwav); m++){    int k, cptcode;
         if (s[m][i] > (nlstate+ndeath)) {    double *xp;
           printf("Error: Wrong value in nlstate or ndeath\n");      double **gp, **gm;  /* for var eij */
           goto end;    double ***gradg, ***trgradg; /*for var eij */
         }    double **gradgp, **trgradgp; /* for var p point j */
       }    double *gpp, *gmp; /* for var p point j */
     }    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    double age,agelim, hf;
     int theta;
     free_vector(severity,1,maxwav);    char digit[4];
     free_imatrix(outcome,1,maxwav+1,1,n);    char digitp[16];
     free_vector(moisnais,1,n);  
     free_vector(annais,1,n);    char fileresprobmorprev[FILENAMELENGTH];
     free_matrix(mint,1,maxwav,1,n);  
     free_matrix(anint,1,maxwav,1,n);    if(popbased==1)
     free_vector(moisdc,1,n);      strcpy(digitp,"-populbased-");
     free_vector(andc,1,n);    else
       strcpy(digitp,"-stablbased-");
      
     wav=ivector(1,imx);    strcpy(fileresprobmorprev,"prmorprev");
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    sprintf(digit,"%-d",ij);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
        strcat(fileresprobmorprev,digit); /* Tvar to be done */
     /* Concatenates waves */    strcat(fileresprobmorprev,digitp); /* Popbased or not */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    strcat(fileresprobmorprev,fileres);
         if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
    /* Calculates basic frequencies. Computes observed prevalence at single age      printf("Problem with resultfile: %s\n", fileresprobmorprev);
        and prints on file fileres'p'. */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
       freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx);     }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprobmorprev,"# probabilities of dying during a year and weighted mean w1*p1j+w2*p2j+... stand dev in()\n");
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      fprintf(ficresprobmorprev," p.%-d SE",j);
           for(i=1; i<=nlstate;i++)
     /* For Powell, parameters are in a vector p[] starting at p[1]        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    }  
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficresprobmorprev,"\n");
         if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
     mlikeli(ficres,p, npar, ncov, nlstate, ftol, func);      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
       fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
           exit(0);
     /*--------- results files --------------*/    }
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt);    else{
           fprintf(ficgp,"\n# Routine varevsij");
    jk=1;    }
    fprintf(ficres,"# Parameters\n");    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
    printf("# Parameters\n");      printf("Problem with html file: %s\n", optionfilehtm);
    for(i=1,jk=1; i <=nlstate; i++){      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
      for(k=1; k <=(nlstate+ndeath); k++){      exit(0);
        if (k != i)     }
          {    else{
            printf("%d%d ",i,k);      fprintf(fichtm,"\n<li><h4> Computing step probabilities of dying and weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
            fprintf(ficres,"%1d%1d ",i,k);    }
            for(j=1; j <=ncov; j++){    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
              printf("%f ",p[jk]);  
              fprintf(ficres,"%f ",p[jk]);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");
              jk++;     fprintf(ficresvij,"# Age");
            }    for(i=1; i<=nlstate;i++)
            printf("\n");      for(j=1; j<=nlstate;j++)
            fprintf(ficres,"\n");        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
          }    fprintf(ficresvij,"\n");
      }  
    }    xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     /* Computing hessian and covariance matrix */    doldm=matrix(1,nlstate,1,nlstate);
     ftolhess=ftol; /* Usually correct */    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     hesscov(matcov, p, npar, delti, ftolhess, func);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     fprintf(ficres,"# Scales\n");  
     printf("# Scales\n");    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
      for(i=1,jk=1; i <=nlstate; i++){    gpp=vector(nlstate+1,nlstate+ndeath);
       for(j=1; j <=nlstate+ndeath; j++){    gmp=vector(nlstate+1,nlstate+ndeath);
         if (j!=i) {    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
           fprintf(ficres,"%1d%1d",i,j);   
           printf("%1d%1d",i,j);    if(estepm < stepm){
           for(k=1; k<=ncov;k++){      printf ("Problem %d lower than %d\n",estepm, stepm);
             printf(" %.5e",delti[jk]);    }
             fprintf(ficres," %.5e",delti[jk]);    else  hstepm=estepm;  
             jk++;    /* For example we decided to compute the life expectancy with the smallest unit */
           }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.
           printf("\n");       nhstepm is the number of hstepm from age to agelim
           fprintf(ficres,"\n");       nstepm is the number of stepm from age to agelin.
         }       Look at hpijx to understand the reason of that which relies in memory size
       }       and note for a fixed period like k years */
       }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
            survival function given by stepm (the optimization length). Unfortunately it
     k=1;       means that if the survival funtion is printed only each two years of age and if
     fprintf(ficres,"# Covariance\n");       you sum them up and add 1 year (area under the trapezoids) you won't get the same
     printf("# Covariance\n");       results. So we changed our mind and took the option of the best precision.
     for(i=1;i<=npar;i++){    */
       /*  if (k>nlstate) k=1;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */
       i1=(i-1)/(ncov*nlstate)+1;     agelim = AGESUP;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       printf("%s%d%d",alph[k],i1,tab[i]);*/      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */
       fprintf(ficres,"%3d",i);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       printf("%3d",i);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       for(j=1; j<=i;j++){      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
         fprintf(ficres," %.5e",matcov[i][j]);      gp=matrix(0,nhstepm,1,nlstate);
         printf(" %.5e",matcov[i][j]);      gm=matrix(0,nhstepm,1,nlstate);
       }  
       fprintf(ficres,"\n");  
       printf("\n");      for(theta=1; theta <=npar; theta++){
       k++;        for(i=1; i<=npar; i++){ /* Computes gradient */
     }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
             }
     while((c=getc(ficpar))=='#' && c!= EOF){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       ungetc(c,ficpar);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       fgets(line, MAXLINE, ficpar);  
       puts(line);        if (popbased==1) {
       fputs(line,ficparo);          for(i=1; i<=nlstate;i++)
     }            prlim[i][i]=probs[(int)age][i][ij];
     ungetc(c,ficpar);        }
      
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        for(j=1; j<= nlstate; j++){
               for(h=0; h<=nhstepm; h++){
     if (fage <= 2) {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       bage = agemin;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       fage = agemax;          }
     }        }
         /* This for computing forces of mortality (h=1)as a weighted average */
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");        for(j=nlstate+1,gpp[j]=0.;j<=nlstate+ndeath;j++){
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);          for(i=1; i<= nlstate; i++)
 /*------------ gnuplot -------------*/            gpp[j] += prlim[i][i]*p3mat[i][j][1];
 chdir(pathcd);        }    
   if((ficgp=fopen("graph.gp","w"))==NULL) {        /* end force of mortality */
     printf("Problem with file graph.gp");goto end;  
   }        for(i=1; i<=npar; i++) /* Computes gradient */
 #ifdef windows          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   fprintf(ficgp,"cd \"%s\" \n",pathc);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 #endif        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    /* 1eme*/   
         if (popbased==1) {
   for (cpt=1; cpt<= nlstate ; cpt ++) {          for(i=1; i<=nlstate;i++)
 #ifdef windows            prlim[i][i]=probs[(int)age][i][ij];
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" u 1:%d \"\%%lf",agemin,fage,fileres,cpt*2);        }
 #endif  
 #ifdef unix        for(j=1; j<= nlstate; j++){
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:%d \"\%%lf",agemin,fage,fileres,cpt*2);          for(h=0; h<=nhstepm; h++){
 #endif            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" u 1:($%d+2*$%d) \"\%%lf",fileres,2*cpt,cpt*2+1);          }
     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");        }
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" u 1:($%d-2*$%d) \"\%%lf",fileres,2*cpt,2*cpt+1);         /* This for computing force of mortality (h=1)as a weighted average */
      for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");         for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" u 1:($%d) t\"Observed prevalence \" w l 2",fileres,2+4*(cpt-1));          for(i=1; i<= nlstate; i++)
 #ifdef unix            gmp[j] += prlim[i][i]*p3mat[i][j][1];
 fprintf(ficgp,"\nset ter gif small size 400,300");        }    
 #endif        /* end force of mortality */
 fprintf(ficgp,"\nset out \"v%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);  
          for(j=1; j<= nlstate; j++) /* vareij */
   }          for(h=0; h<=nhstepm; h++){
   /*2 eme*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
            }
   fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   for (i=1; i<= nlstate+1 ; i ++) {          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
 k=2*i;        }
     fprintf(ficgp,"\"t%s\" u 1:%d \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k);  
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");      } /* End theta */
     if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  
     else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     fprintf(ficgp,"\"t%s\" u 1:($%d-2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);  
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");      for(h=0; h<=nhstepm; h++) /* veij */
     fprintf(ficgp,"\" t\"\" w l 0,");        for(j=1; j<=nlstate;j++)
 fprintf(ficgp,"\"t%s\" u 1:($%d+2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);          for(theta=1; theta <=npar; theta++)
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");            trgradg[h][j][theta]=gradg[h][theta][j];
     if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  
 else fprintf(ficgp,"\" t\"\" w l 0,");      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   }         for(theta=1; theta <=npar; theta++)
   fprintf(ficgp,"\nset out \"e%s.gif\" \nreplot\n\n",strtok(optionfile, "."));          trgradgp[j][theta]=gradgp[theta][j];
   
   /*3eme*/      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 for (cpt=1; cpt<= nlstate ; cpt ++) {      for(i=1;i<=nlstate;i++)
   k=2+nlstate*(cpt-1);        for(j=1;j<=nlstate;j++)
     fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k,cpt);          vareij[i][j][(int)age] =0.;
 for (i=1; i< nlstate ; i ++) {  
 fprintf(ficgp,",\"e%s\" u 1:%d t \"e%d%d\" w l",fileres,k+1,cpt,i+1);      for(h=0;h<=nhstepm;h++){
 }         for(k=0;k<=nhstepm;k++){
 fprintf(ficgp,"\nset out \"ex%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
 }          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
            for(i=1;i<=nlstate;i++)
 /* CV preval stat */            for(j=1;j<=nlstate;j++)
 for (cpt=1; cpt<nlstate ; cpt ++) {              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
     k=3;        }
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u 2:($%d/($%d",agemin,agemax,fileres,k+cpt,k);      }
     for (i=1; i< nlstate ; i ++)  
       fprintf(ficgp,"+$%d",k+i);      /* pptj */
     fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
           matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
  l=3+(nlstate+ndeath)*cpt;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
    fprintf(ficgp,",\"pij%s\" u 2:($%d/($%d",fileres,l+cpt,l);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
            varppt[j][i]=doldmp[j][i];
    for (i=1; i< nlstate ; i ++) {      /* end ppptj */
    l=3+(nlstate+ndeath)*cpt;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     fprintf(ficgp,"+$%d",l+i);      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    }   
   fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      if (popbased==1) {
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
   fprintf(ficgp,"set out \"p%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);      }
   }      
       /* This for computing force of mortality (h=1)as a weighted average */
       for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){
   fclose(ficgp);        for(i=1; i<= nlstate; i++)
              gmp[j] += prlim[i][i]*p3mat[i][j][1];
 chdir(path);      }    
     free_matrix(agev,1,maxwav,1,imx);      /* end force of mortality */
     free_ivector(wav,1,imx);  
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
             fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
     free_imatrix(s,1,maxwav+1,1,n);        for(i=1; i<=nlstate;i++){
               fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
             }
     free_ivector(num,1,n);      }
     free_vector(agedc,1,n);      fprintf(ficresprobmorprev,"\n");
     free_vector(weight,1,n);  
     free_matrix(covar,1,NCOVMAX,1,n);      fprintf(ficresvij,"%.0f ",age );
     fclose(ficparo);      for(i=1; i<=nlstate;i++)
     fclose(ficres);        for(j=1; j<=nlstate;j++){
   }          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
   /*________fin mle=1_________*/      fprintf(ficresvij,"\n");
         free_matrix(gp,0,nhstepm,1,nlstate);
         free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   /* No more information from the sample is required now */      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
   /* Reads comments: lines beginning with '#' */      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   while((c=getc(ficpar))=='#' && c!= EOF){    } /* End age */
     ungetc(c,ficpar);    free_vector(gpp,nlstate+1,nlstate+ndeath);
     fgets(line, MAXLINE, ficpar);    free_vector(gmp,nlstate+1,nlstate+ndeath);
     puts(line);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     fputs(line,ficparo);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   }    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
   ungetc(c,ficpar);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
       fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm);
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm);
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm);
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
   /*--------------- Prevalence limit --------------*/    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
       fprintf(ficgp,"\nset out \"varmuptjgr%s%s.png\";replot;",digitp,digit);
   strcpy(filerespl,"pl");  
   strcat(filerespl,fileres);    free_vector(xp,1,npar);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    free_matrix(doldm,1,nlstate,1,nlstate);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    free_matrix(dnewm,1,nlstate,1,npar);
   }    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
   fprintf(ficrespl,"#Prevalence limit\n");    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   fprintf(ficrespl,"#Age ");    fclose(ficresprobmorprev);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    fclose(ficgp);
   fprintf(ficrespl,"\n");    fclose(fichtm);
     
   prlim=matrix(1,nlstate,1,nlstate);  }
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /************ Variance of prevlim ******************/
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  {
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    /* Variance of prevalence limit */
       /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   agebase=agemin;    double **newm;
   agelim=agemax;    double **dnewm,**doldm;
   ftolpl=1.e-10;    int i, j, nhstepm, hstepm;
   for (age=agebase; age<=agelim; age++){    int k, cptcode;
     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);    double *xp;
     fprintf(ficrespl,"%.0f",age );    double *gp, *gm;
     for(i=1; i<=nlstate;i++)    double **gradg, **trgradg;
       fprintf(ficrespl," %.5f", prlim[i][i]);    double age,agelim;
     fprintf(ficrespl,"\n");    int theta;
   }     
   fclose(ficrespl);    fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");
       fprintf(ficresvpl,"# Age");
   /*------------- h Pij x at various ages ------------*/    for(i=1; i<=nlstate;i++)
           fprintf(ficresvpl," %1d-%1d",i,i);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    fprintf(ficresvpl,"\n");
   if((ficrespij=fopen(filerespij,"w"))==NULL) {  
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    xp=vector(1,npar);
   }    dnewm=matrix(1,nlstate,1,npar);
   printf("Computing pij: result on file '%s' \n", filerespij);    doldm=matrix(1,nlstate,1,nlstate);
   stepsize=(int) (stepm+YEARM-1)/YEARM;   
   if (stepm<=24) stepsize=2;    hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */
   agelim=AGESUP;    agelim = AGESUP;
   hstepm=stepsize*YEARM; /* Every year of age */    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */
   for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      if (stepm >= YEARM) hstepm=1;
     nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      gradg=matrix(1,npar,1,nlstate);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      gp=vector(1,nlstate);
     oldm=oldms;savm=savms;      gm=vector(1,nlstate);
     hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm);    
     fprintf(ficrespij,"# Age");      for(theta=1; theta <=npar; theta++){
     for(i=1; i<=nlstate;i++)        for(i=1; i<=npar; i++){ /* Computes gradient */
       for(j=1; j<=nlstate+ndeath;j++)          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         fprintf(ficrespij," %1d-%1d",i,j);        }
     fprintf(ficrespij,"\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     for (h=0; h<=nhstepm; h++){        for(i=1;i<=nlstate;i++)
       fprintf(ficrespij,"%.0f %.0f",agedeb, agedeb+ h*hstepm/YEARM*stepm );          gp[i] = prlim[i][i];
       for(i=1; i<=nlstate;i++)     
         for(j=1; j<=nlstate+ndeath;j++)        for(i=1; i<=npar; i++) /* Computes gradient */
           fprintf(ficrespij," %.5f", p3mat[i][j][h]);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       fprintf(ficrespij,"\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     }        for(i=1;i<=nlstate;i++)
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          gm[i] = prlim[i][i];
     fprintf(ficrespij,"\n");  
   }        for(i=1;i<=nlstate;i++)
   fclose(ficrespij);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   /*---------- Health expectancies and variances ------------*/  
         trgradg =matrix(1,nlstate,1,npar);
   eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  
   oldm=oldms;savm=savms;      for(j=1; j<=nlstate;j++)
   evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm);        for(theta=1; theta <=npar; theta++)
             trgradg[j][theta]=gradg[theta][j];
   vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  
   oldm=oldms;savm=savms;      for(i=1;i<=nlstate;i++)
   varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);        varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
   strcpy(filerest,"t");      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
   strcat(filerest,fileres);      for(i=1;i<=nlstate;i++)
   if((ficrest=fopen(filerest,"w"))==NULL) {        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  
   }      fprintf(ficresvpl,"%.0f ",age );
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      for(i=1; i<=nlstate;i++)
   fprintf(ficrest,"#Total LEs with variances: e.. (std) ");        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
   for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);      fprintf(ficresvpl,"\n");
   fprintf(ficrest,"\n");      free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
   hf=1;      free_matrix(gradg,1,npar,1,nlstate);
   if (stepm >= YEARM) hf=stepm/YEARM;      free_matrix(trgradg,1,nlstate,1,npar);
   epj=vector(1,nlstate+1);    } /* End age */
   for(age=bage; age <=fage ;age++){  
     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);    free_vector(xp,1,npar);
     fprintf(ficrest," %.0f",age);    free_matrix(doldm,1,nlstate,1,npar);
     for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    free_matrix(dnewm,1,nlstate,1,nlstate);
       for(i=1, epj[j]=0.;i <=nlstate;i++) {  
         epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];  }
       }  
       epj[nlstate+1] +=epj[j];  /************ Variance of one-step probabilities  ******************/
     }  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
     for(i=1, vepp=0.;i <=nlstate;i++)  {
       for(j=1;j <=nlstate;j++)    int i, j=0,  i1, k1, l1, t, tj;
         vepp += vareij[i][j][(int)age];    int k2, l2, j1,  z1;
     fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    int k=0,l, cptcode;
     for(j=1;j <=nlstate;j++){    int first=1, first1;
       fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     }    double **dnewm,**doldm;
     fprintf(ficrest,"\n");    double *xp;
   }    double *gp, *gm;
   fclose(ficrest);    double **gradg, **trgradg;
   fclose(ficpar);    double **mu;
   free_vector(epj,1,nlstate+1);    double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
   /*------- Variance limit prevalence------*/       int theta;
     char fileresprob[FILENAMELENGTH];
   varpl=matrix(1,nlstate,(int) bage, (int) fage);    char fileresprobcov[FILENAMELENGTH];
   oldm=oldms;savm=savms;    char fileresprobcor[FILENAMELENGTH];
   varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);  
       double ***varpij;
     
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    strcpy(fileresprob,"prob");
       strcat(fileresprob,fileres);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      printf("Problem with resultfile: %s\n", fileresprob);
         fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
       }
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);    strcpy(fileresprobcov,"probcov");
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);    strcat(fileresprobcov,fileres);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);      printf("Problem with resultfile: %s\n", fileresprobcov);
         fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   free_matrix(matcov,1,npar,1,npar);    }
   free_vector(delti,1,npar);    strcpy(fileresprobcor,"probcor");
       strcat(fileresprobcor,fileres);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncov);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
   printf("End of Imach\n");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */    }
       printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   /*printf("Total time was %d uSec.\n", total_usecs);*/    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   /*------ End -----------*/    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
  end:    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
 #ifdef windows   
  chdir(pathcd);    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
 #endif     fprintf(ficresprob,"# Age");
  system("gnuplot graph.gp");    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
 #ifdef windows    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   while (z[0] != 'q') {    fprintf(ficresprobcov,"# Age");
     chdir(pathcd);   
     printf("\nType e to edit output files, c to start again, and q for exiting: ");  
     scanf("%s",z);    for(i=1; i<=nlstate;i++)
     if (z[0] == 'c') system("./imach");      for(j=1; j<=(nlstate+ndeath);j++){
     else if (z[0] == 'e') {        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
       chdir(path);        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       system("index.htm");        fprintf(ficresprobcor," p%1d-%1d ",i,j);
     }      }  
     else if (z[0] == 'q') exit(0);    fprintf(ficresprob,"\n");
   }    fprintf(ficresprobcov,"\n");
 #endif     fprintf(ficresprobcor,"\n");
 }    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
       fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
       exit(0);
     }
     else{
       fprintf(ficgp,"\n# Routine varprob");
     }
     if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
       fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
       exit(0);
     }
     else{
       fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
       fprintf(fichtm,"\n");
   
       fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
       fprintf(fichtm,"\nWe have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
       fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");
   
     }
   
    
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){
         j1++;
        
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable ");
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#");
           fprintf(ficresprobcov, "\n#********** Variable ");
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#");
          
           fprintf(ficgp, "\n#********** Variable ");
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#");
          
          
           fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable ");
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
          
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#");    
         }
        
         for (age=bage; age<=fage; age ++){
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
          
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
      
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:0);
            
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
            
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
            
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:0);
      
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)
               gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
          
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
          
           pmij(pmmij,cov,ncovmodel,x,nlstate);
          
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
        for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
          printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
          fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
        }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
         fprintf(ficgp,"\nset noparametric;unset label");
         fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
         fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
         fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
         fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
         fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
         fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
       free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
       free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
       free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
       free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
       free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
       free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
     }
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fclose(ficgp);
     fclose(fichtm);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
     /*char optionfilehtm[FILENAMELENGTH];*/
     if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
       fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);
     }
   
      fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n
    - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n
    - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n
    - Life expectancies by age and initial health status (estepm=%2d months):
      <a href=\"e%s\">e%s</a> <br>\n</li>", \
     jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++)
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>
   <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);    
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>
   <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);
          /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>
   <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>
   <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and
   health expectancies in states (1) and (2): e%s%d.png<br>
   <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n
    - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n
    - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n
    - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n
    - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n
    - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);
   
    if(popforecast==1) fprintf(fichtm,"\n
    - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n
    - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n
           <br>",fileres,fileres,fileres,fileres);
    else
      fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);
   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++)
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident
   interval) in state (%d): v%s%d%d.png <br>
   <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   fclose(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
       fprintf(ficlog,"Problem with file %s",optionfilegnuplot);
     }
   
   #ifdef windows
       fprintf(ficgp,"cd \"%s\" \n",pathc);
   #endif
   m=pow(2,cptcoveff);
    
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
   
   #ifdef windows
        fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);
   #endif
   #ifdef unix
   fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
   fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);
   #endif
   
   for (i=1; i<= nlstate ; i ++) {
     if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
     else fprintf(ficgp," \%%*lf (\%%*lf)");
   }
       fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);
       for (i=1; i<= nlstate ; i ++) {
     if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
     else fprintf(ficgp," \%%*lf (\%%*lf)");
   }
     fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
     if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
     else fprintf(ficgp," \%%*lf (\%%*lf)");
   }  
        fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));
   #ifdef unix
   fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");
   #endif
      }
     }
     /*2 eme*/
   
     for (k1=1; k1<= m ; k1 ++) {
       fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
      
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
     if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
     else fprintf(ficgp," \%%*lf (\%%*lf)");
   }  
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
   }  
         fprintf(ficgp,"\" t\"\" w l 0,");
        fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
     if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
     else fprintf(ficgp," \%%*lf (\%%*lf)");
   }  
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
    
     /*3eme*/
   
     for (k1=1; k1<= m ; k1 ++) {
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
         fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
    for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
   fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
   fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
    for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
   fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
   
   */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);
   
         }
       }
     }
    
     /* CV preval stat */
       for (k1=1; k1<= m ; k1 ++) {
       for (cpt=1; cpt<nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);
   
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
        
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);  
       }
     }  
    
     /* proba elementaires */
      for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++;
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){  
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fclose(ficgp);
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){
   
     int i, cpt, cptcod;
       for (agedeb=ageminpar; agedeb<=fage; agedeb++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)
             mobaverage[(int)agedeb][i][cptcod]=0.;
      
       for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){
         for (i=1; i<=nlstate;i++){
           for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
             for (cpt=0;cpt<=4;cpt++){
               mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];
             }
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;
           }
         }
       }
      
   }
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){
    
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     char fileresf[FILENAMELENGTH];
   
    agelim=AGESUP;
   calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;
   
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
    
    
     strcpy(fileresf,"f");
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav==1) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       movingaverage(agedeb, fage, ageminpar, mobaverage);
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
    
     agelim=AGESUP;
    
     hstepm=1;
     hstepm=hstepm/stepm;
     yp1=modf(dateintmean,&yp);
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
    
     fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);
    
     for(cptcov=1;cptcov<=i2;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# StartingAge FinalAge");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);
        
        
         for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);  
   
           for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);
             nhstepm = nhstepm/hstepm;
            
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
          
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedate+YEARM*cpt)) {
                 fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);
               }
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1)
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                  
                 }
                 if (h==(int)(calagedate+12*cpt)){
                   fprintf(ficresf," %.3f", kk1);
                          
                 }
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
       }
     }
          
     if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   /************** Forecasting ******************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
    
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
    
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
    
    
     strcpy(filerespop,"pop");
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav==1) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       movingaverage(agedeb, fage, ageminpar, mobaverage);
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
    
     agelim=AGESUP;
    
     hstepm=1;
     hstepm=hstepm/stepm;
    
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       }
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
      
       i=1;  
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
        
         for (cpt=0; cpt<=0;cpt++) {
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);  
          
           for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);
             nhstepm = nhstepm/hstepm;
            
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
          
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedate+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               }
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1)
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedate+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);  
           for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);
             nhstepm = nhstepm/hstepm;
            
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedate+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               }
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      }
     }
    
     if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   }
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   
     int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[80],pathc[80],pathcd[80],pathtot[80],model[80];
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;
    
   
     char *alph[]={"a","a","b","c","d","e"}, str[4];
   
   
     char z[1]="c", occ;
   #include <sys/time.h>
   #include <time.h>
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
    
     /* long total_usecs;
     struct timeval start_time, end_time;
    
     gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     getcwd(pathcd, size);
   
     printf("\n%s",version);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
      printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     replace(pathc,path);
   
   /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s",version);
     fprintf(ficlog,"\nEnter the parameter file name: ");
     fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     fflush(ficlog);
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       goto end;
     }
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) {
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
   while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
    
      
     covar=matrix(0,NCOVMAX,1,n);
     cptcovn=0;
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn;
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
    
     /* Read guess parameters */
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
    
     param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++)
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         fprintf(ficparo,"%1d%1d",i1,j1);
         if(mle==1)
           printf("%1d%1d",i,j);
         fprintf(ficlog,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar," %lf",&param[i][j][k]);
           if(mle==1){
             printf(" %lf",param[i][j][k]);
             fprintf(ficlog," %lf",param[i][j][k]);
           }
           else
             fprintf(ficlog," %lf",param[i][j][k]);
           fprintf(ficparo," %lf",param[i][j][k]);
         }
         fscanf(ficpar,"\n");
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
    
       npar= (nlstate+ndeath-1)*nlstate*ncovmodel;
   
     p=param[1][1];
    
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */
     for(i=1; i <=nlstate; i++){
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i1,j1);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar,"%le",&delti3[i][j][k]);
           printf(" %le",delti3[i][j][k]);
           fprintf(ficparo," %le",delti3[i][j][k]);
         }
         fscanf(ficpar,"\n");
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     delti=delti3[1][1];
    
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
    
     matcov=matrix(1,npar,1,npar);
     for(i=1; i <=npar; i++){
       fscanf(ficpar,"%s",&str);
       if(mle==1)
         printf("%s",str);
       fprintf(ficlog,"%s",str);
       fprintf(ficparo,"%s",str);
       for(j=1; j <=i; j++){
         fscanf(ficpar," %le",&matcov[i][j]);
         if(mle==1){
           printf(" %.5le",matcov[i][j]);
           fprintf(ficlog," %.5le",matcov[i][j]);
         }
         else
           fprintf(ficlog," %.5le",matcov[i][j]);
         fprintf(ficparo," %.5le",matcov[i][j]);
       }
       fscanf(ficpar,"\n");
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       fprintf(ficparo,"\n");
     }
     for(i=1; i <=npar; i++)
       for(j=i+1;j<=npar;j++)
         matcov[i][j]=matcov[j][i];
      
     if(mle==1)
       printf("\n");
     fprintf(ficlog,"\n");
   
   
       /*-------- Rewriting paramater file ----------*/
        strcpy(rfileres,"r");    /* "Rparameterfile */
        strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
        strcat(rfileres,".");    /* */
        strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
      
       /*-------- data file ----------*/
       if((fic=fopen(datafile,"r"))==NULL)    {
         printf("Problem with datafile: %s\n", datafile);goto end;
         fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
       }
   
       n= lastobs;
       severity = vector(1,maxwav);
       outcome=imatrix(1,maxwav+1,1,n);
       num=ivector(1,n);
       moisnais=vector(1,n);
       annais=vector(1,n);
       moisdc=vector(1,n);
       andc=vector(1,n);
       agedc=vector(1,n);
       cod=ivector(1,n);
       weight=vector(1,n);
       for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
       mint=matrix(1,maxwav,1,n);
       anint=matrix(1,maxwav,1,n);
       s=imatrix(1,maxwav+1,1,n);
       adl=imatrix(1,maxwav+1,1,n);    
       tab=ivector(1,NCOVMAX);
       ncodemax=ivector(1,8);
   
       i=1;
       while (fgets(line, MAXLINE, fic) != NULL)    {
         if ((i >= firstobs) && (i <=lastobs)) {
          
           for (j=maxwav;j>=1;j--){
             cutv(stra, strb,line,' '); s[j][i]=atoi(strb);
             strcpy(line,stra);
             cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
             cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           }
          
           cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);
   
           cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);
   
           cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);
           for (j=ncovcol;j>=1;j--){
             cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           }
           num[i]=atol(stra);
          
           /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
             printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
   
           i=i+1;
         }
       }
       /* printf("ii=%d", ij);
          scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1;
        printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
    
    
     /* Calculation of the number of parameter from char model*/
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15);
     Tvaraff=ivector(1,15);
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+');
       j1=nbocc(model,'*');
       cptcovn=j+1;
       cptcovprod=j1;
      
       strcpy(modelsav,model);
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
      
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyze it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2];
             for (k=1; k<=lastobs;k++)
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
    
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
     scanf("%d ",i);*/
       fclose(fic);
   
       /*  if(mle==1){*/
       if (weightopt != 1) { /* Maximisation without weights*/
         for(i=1;i<=n;i++) weight[i]=1.0;
       }
       /*-calculation of age at interview from date of interview and age at death -*/
       agev=matrix(1,maxwav,1,imx);
   
       for (i=1; i<=imx; i++) {
         for(m=2; (m<= maxwav); m++) {
          if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){
            anint[m][i]=9999;
            s[m][i]=-1;
          }
        if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;
         }
       }
   
       for (i=1; i<=imx; i++)  {
         agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
         for(m=1; (m<= maxwav); m++){
           if(s[m][i] >0){
             if (s[m][i] >= nlstate+1) {
               if(agedc[i]>0)
                 if(moisdc[i]!=99 && andc[i]!=9999)
                   agev[m][i]=agedc[i];
               /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
              else {
                 if (andc[i]!=9999){
                 printf("Warning negative age at death: %d line:%d\n",num[i],i);
                 fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);
                 agev[m][i]=-1;
                 }
               }
             }
             else if(s[m][i] !=9){ /* Should no more exist */
               agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
               if(mint[m][i]==99 || anint[m][i]==9999)
                 agev[m][i]=1;
               else if(agev[m][i] <agemin){
                 agemin=agev[m][i];
                 /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
               }
               else if(agev[m][i] >agemax){
                 agemax=agev[m][i];
                /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
               }
               /*agev[m][i]=anint[m][i]-annais[i];*/
               /*   agev[m][i] = age[i]+2*m;*/
             }
             else { /* =9 */
               agev[m][i]=1;
               s[m][i]=-1;
             }
           }
           else /*= 0 Unknown */
             agev[m][i]=1;
         }
      
       }
       for (i=1; i<=imx; i++)  {
         for(m=1; (m<= maxwav); m++){
           if (s[m][i] > (nlstate+ndeath)) {
             printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);  
             fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);  
             goto end;
           }
         }
       }
   
   printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
    fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
   
       free_vector(severity,1,maxwav);
       free_imatrix(outcome,1,maxwav+1,1,n);
       free_vector(moisnais,1,n);
       free_vector(annais,1,n);
       /* free_matrix(mint,1,maxwav,1,n);
          free_matrix(anint,1,maxwav,1,n);*/
       free_vector(moisdc,1,n);
       free_vector(andc,1,n);
   
      
       wav=ivector(1,imx);
       dh=imatrix(1,lastpass-firstpass+1,1,imx);
       mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
       /* Concatenates waves */
         concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
   
         Tcode=ivector(1,100);
         nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);
         ncodemax[1]=1;
         if (cptcovn > 0) tricode(Tvar,nbcode,imx);
        
      codtab=imatrix(1,100,1,10);
      h=0;
      m=pow(2,cptcoveff);
    
      for(k=1;k<=cptcoveff; k++){
        for(i=1; i <=(m/pow(2,k));i++){
          for(j=1; j <= ncodemax[k]; j++){
            for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
              h++;
              if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
              /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
            }
          }
        }
      }
      /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);
         codtab[1][2]=1;codtab[2][2]=2; */
      /* for(i=1; i <=m ;i++){
         for(k=1; k <=cptcovn; k++){
         printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
         }
         printf("\n");
         }
         scanf("%d",i);*/
      
      /* Calculates basic frequencies. Computes observed prevalence at single age
          and prints on file fileres'p'. */
   
      
      
       pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
        
       /* For Powell, parameters are in a vector p[] starting at p[1]
          so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
       p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
       if(mle==1){
       mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
      
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
    
   
      jk=1;
      fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
      printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
      fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
      for(i=1,jk=1; i <=nlstate; i++){
        for(k=1; k <=(nlstate+ndeath); k++){
          if (k != i)
            {
              printf("%d%d ",i,k);
              fprintf(ficlog,"%d%d ",i,k);
              fprintf(ficres,"%1d%1d ",i,k);
              for(j=1; j <=ncovmodel; j++){
                printf("%f ",p[jk]);
                fprintf(ficlog,"%f ",p[jk]);
                fprintf(ficres,"%f ",p[jk]);
                jk++;
              }
              printf("\n");
              fprintf(ficlog,"\n");
              fprintf(ficres,"\n");
            }
        }
      }
      if(mle==1){
        /* Computing hessian and covariance matrix */
        ftolhess=ftol; /* Usually correct */
        hesscov(matcov, p, npar, delti, ftolhess, func);
      }
      fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
      printf("# Scales (for hessian or gradient estimation)\n");
      fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
      for(i=1,jk=1; i <=nlstate; i++){
        for(j=1; j <=nlstate+ndeath; j++){
          if (j!=i) {
            fprintf(ficres,"%1d%1d",i,j);
            printf("%1d%1d",i,j);
            fprintf(ficlog,"%1d%1d",i,j);
            for(k=1; k<=ncovmodel;k++){
              printf(" %.5e",delti[jk]);
              fprintf(ficlog," %.5e",delti[jk]);
              fprintf(ficres," %.5e",delti[jk]);
              jk++;
            }
            printf("\n");
            fprintf(ficlog,"\n");
            fprintf(ficres,"\n");
          }
        }
      }
      
      k=1;
      fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
      if(mle==1)
        printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
      fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
      for(i=1;i<=npar;i++){
        /*  if (k>nlstate) k=1;
            i1=(i-1)/(ncovmodel*nlstate)+1;
            fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);
            printf("%s%d%d",alph[k],i1,tab[i]);*/
        fprintf(ficres,"%3d",i);
        if(mle==1)
          printf("%3d",i);
        fprintf(ficlog,"%3d",i);
        for(j=1; j<=i;j++){
          fprintf(ficres," %.5e",matcov[i][j]);
          if(mle==1)
            printf(" %.5e",matcov[i][j]);
          fprintf(ficlog," %.5e",matcov[i][j]);
        }
        fprintf(ficres,"\n");
        if(mle==1)
          printf("\n");
        fprintf(ficlog,"\n");
        k++;
      }
      
      while((c=getc(ficpar))=='#' && c!= EOF){
        ungetc(c,ficpar);
        fgets(line, MAXLINE, ficpar);
        puts(line);
        fputs(line,ficparo);
      }
      ungetc(c,ficpar);
      estepm=0;
      fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
      if (estepm==0 || estepm < stepm) estepm=stepm;
      if (fage <= 2) {
        bage = ageminpar;
        fage = agemaxpar;
      }
      
      fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
      fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
      fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
      
      while((c=getc(ficpar))=='#' && c!= EOF){
        ungetc(c,ficpar);
        fgets(line, MAXLINE, ficpar);
        puts(line);
        fputs(line,ficparo);
      }
      ungetc(c,ficpar);
    
      fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);
      fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
      fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
      
      while((c=getc(ficpar))=='#' && c!= EOF){
        ungetc(c,ficpar);
        fgets(line, MAXLINE, ficpar);
        puts(line);
        fputs(line,ficparo);
      }
      ungetc(c,ficpar);
    
   
      dateprev1=anprev1+mprev1/12.+jprev1/365.;
      dateprev2=anprev2+mprev2/12.+jprev2/365.;
   
     fscanf(ficpar,"pop_based=%d\n",&popbased);
     fprintf(ficparo,"pop_based=%d\n",popbased);  
     fprintf(ficres,"pop_based=%d\n",popbased);  
    
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);
   fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);
   fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);
   
   
   while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);
     fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);
     fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);
   
    freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
   
   /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     strcat(optionfilegnuplot,".gp");
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     fclose(ficgp);
    printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);
   /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfile);
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n
   \n
   Total number of observations=%d <br>\n
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n
   <hr  size=\"2\" color=\"#EC5E5E\">
    <ul><li><h4>Parameter files</h4>\n
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n
    - Log file of the run: <a href=\"%s\">%s</a><br>\n
    - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,filelog,filelog,optionfilegnuplot,optionfilegnuplot);
     fclose(fichtm);
   
    printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
    
   /*------------ free_vector  -------------*/
    chdir(path);
    
    free_ivector(wav,1,imx);
    free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
    free_imatrix(mw,1,lastpass-firstpass+1,1,imx);  
    free_ivector(num,1,n);
    free_vector(agedc,1,n);
    /*free_matrix(covar,1,NCOVMAX,1,n);*/
    fclose(ficparo);
    fclose(ficres);
   
   
     /*--------------- Prevalence limit --------------*/
    
     strcpy(filerespl,"pl");
     strcat(filerespl,fileres);
     if((ficrespl=fopen(filerespl,"w"))==NULL) {
       printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;
       fprintf(ficlog,"Problem with Prev limit resultfile: %s\n", filerespl);goto end;
     }
     printf("Computing prevalence limit: result on file '%s' \n", filerespl);
     fprintf(ficlog,"Computing prevalence limit: result on file '%s' \n", filerespl);
     fprintf(ficrespl,"#Prevalence limit\n");
     fprintf(ficrespl,"#Age ");
     for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
     fprintf(ficrespl,"\n");
    
     prlim=matrix(1,nlstate,1,nlstate);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
     k=0;
     agebase=ageminpar;
     agelim=agemaxpar;
     ftolpl=1.e-10;
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
   
     for(cptcov=1;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
          
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f",age );
             for(i=1; i<=nlstate;i++)
             fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
     fclose(ficrespl);
   
     /*------------- h Pij x at various ages ------------*/
    
     strcpy(filerespij,"pij");  strcat(filerespij,fileres);
     if((ficrespij=fopen(filerespij,"w"))==NULL) {
       printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
       fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
     }
     printf("Computing pij: result on file '%s' \n", filerespij);
     fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
    
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     /*if (stepm<=24) stepsize=2;*/
   
     agelim=AGESUP;
     hstepm=stepsize*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */
   
     /* hstepm=1;   aff par mois*/
   
     k=0;
     for(cptcov=1;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++)
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
          
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Age");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
              for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
                }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
       }
     }
   
     varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);
   
     fclose(ficrespij);
   
   
     /*---------- Forecasting ------------------*/
     if((stepm == 1) && (strcmp(model,".")==0)){
       prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);
       if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);
     }
     else{
       erreur=108;
       printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model);
       fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model);
     }
    
   
     /*---------- Health expectancies and variances ------------*/
   
     strcpy(filerest,"t");
     strcat(filerest,fileres);
     if((ficrest=fopen(filerest,"w"))==NULL) {
       printf("Problem with total LE resultfile: %s\n", filerest);goto end;
       fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
     }
     printf("Computing Total LEs with variances: file '%s' \n", filerest);
     fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest);
   
   
     strcpy(filerese,"e");
     strcat(filerese,fileres);
     if((ficreseij=fopen(filerese,"w"))==NULL) {
       printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
     }
     printf("Computing Health Expectancies: result on file '%s' \n", filerese);
     fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
     strcpy(fileresv,"v");
     strcat(fileresv,fileres);
     if((ficresvij=fopen(fileresv,"w"))==NULL) {
       printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
       fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
     }
     printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
     fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
     calagedate=-1;
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
   
     k=0;
     for(cptcov=1;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         fprintf(ficrest,"\n#****** ");
         for(j=1;j<=cptcoveff;j++)
           fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficrest,"******\n");
   
         fprintf(ficreseij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++)
           fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficreseij,"******\n");
   
         fprintf(ficresvij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++)
           fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficresvij,"******\n");
   
         eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;
         evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);  
    
         vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;
         varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0);
         if(popbased==1){
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased);
          }
   
    
         fprintf(ficrest,"#Total LEs with variances: e.. (std) ");
         for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
         fprintf(ficrest,"\n");
   
         epj=vector(1,nlstate+1);
         for(age=bage; age <=fage ;age++){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
           if (popbased==1) {
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][k];
           }
          
           fprintf(ficrest," %4.0f",age);
           for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
             for(i=1, epj[j]=0.;i <=nlstate;i++) {
               epj[j] += prlim[i][i]*eij[i][j][(int)age];
               /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
             }
             epj[nlstate+1] +=epj[j];
           }
   
           for(i=1, vepp=0.;i <=nlstate;i++)
             for(j=1;j <=nlstate;j++)
               vepp += vareij[i][j][(int)age];
           fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
           for(j=1;j <=nlstate;j++){
             fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
           }
           fprintf(ficrest,"\n");
         }
       }
     }
   free_matrix(mint,1,maxwav,1,n);
       free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);
       free_vector(weight,1,n);
     fclose(ficreseij);
     fclose(ficresvij);
     fclose(ficrest);
     fclose(ficpar);
     free_vector(epj,1,nlstate+1);
    
     /*------- Variance limit prevalence------*/  
   
     strcpy(fileresvpl,"vpl");
     strcat(fileresvpl,fileres);
     if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
       printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);
       exit(0);
     }
     printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);
   
     k=0;
     for(cptcov=1;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         fprintf(ficresvpl,"\n#****** ");
         for(j=1;j<=cptcoveff;j++)
           fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficresvpl,"******\n");
        
         varpl=matrix(1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;
        varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);
       }
    }
   
     fclose(ficresvpl);
   
     /*---------- End : free ----------------*/
     free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
    
     free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
     free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
    
    
     free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
     free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
     free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
     free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
    
     free_matrix(matcov,1,npar,1,npar);
     free_vector(delti,1,npar);
     free_matrix(agev,1,maxwav,1,imx);
     free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
     fprintf(fichtm,"\n</body>");
     fclose(fichtm);
     fclose(ficgp);
    
   
     if(erreur >0){
       printf("End of Imach with error or warning %d\n",erreur);
       fprintf(ficlog,"End of Imach with error or warning %d\n",erreur);
     }else{
      printf("End of Imach\n");
      fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     fclose(ficlog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
    
     /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/
     /*printf("Total time was %d uSec.\n", total_usecs);*/
     /*------ End -----------*/
   
   
    end:
   #ifdef windows
     /* chdir(pathcd);*/
   #endif
    /*system("wgnuplot graph.plt");*/
    /*system("../gp37mgw/wgnuplot graph.plt");*/
    /*system("cd ../gp37mgw");*/
    /* system("..\\gp37mgw\\wgnuplot graph.plt");*/
    strcpy(plotcmd,GNUPLOTPROGRAM);
    strcat(plotcmd," ");
    strcat(plotcmd,optionfilegnuplot);
    system(plotcmd);
   
   #ifdef windows
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");
       scanf("%s",z);
       if (z[0] == 'c') system("./imach");
       else if (z[0] == 'e') system(optionfilehtm);
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
   #endif
   }
   
   

Removed from v.1.1  
changed lines
  Added in v.1.51


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