Diff for /imach/src/imach.c between versions 1.1.1.1 and 1.49

version 1.1.1.1, 2000/12/28 18:49:56 version 1.49, 2002/06/20 14:03:39
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 */  #else
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  #define DIRSEPARATOR '/'
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;  #endif
 FILE *ficgp, *fichtm;  
   char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";
 #define NR_END 1  int erreur; /* Error number */
 #define FREE_ARG char*  int nvar;
 #define FTOL 1.0e-10  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int npar=NPARMAX;
 #define NRANSI   int nlstate=2; /* Number of live states */
 #define ITMAX 200   int ndeath=1; /* Number of dead states */
   int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #define TOL 2.0e-4   int popbased=0;
   
 #define CGOLD 0.3819660   int *wav; /* Number of waves for this individuual 0 is possible */
 #define ZEPS 1.0e-10   int maxwav; /* Maxim number of waves */
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);   int jmin, jmax; /* min, max spacing between 2 waves */
   int mle, weightopt;
 #define GOLD 1.618034   int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 #define GLIMIT 100.0   int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
 #define TINY 1.0e-20   double jmean; /* Mean space between 2 waves */
   double **oldm, **newm, **savm; /* Working pointers to matrices */
 static double maxarg1,maxarg2;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
    FILE *fichtm; /* Html File */
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  FILE *ficreseij;
 #define rint(a) floor(a+0.5)  char filerese[FILENAMELENGTH];
   FILE  *ficresvij;
 static double sqrarg;  char fileresv[FILENAMELENGTH];
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  FILE  *ficresvpl;
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}   char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 int imx;   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 int stepm;  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
 /* Stepm, step in month: minimum step interpolation*/  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 int m,nb;  
 int *num, firstpass=0, lastpass=2,*cod;  char filerest[FILENAMELENGTH];
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  char fileregp[FILENAMELENGTH];
 double **pmmij;  char popfile[FILENAMELENGTH];
   
 double *weight;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
 int **s; /* Status */  
 double *agedc, **covar, idx;  #define NR_END 1
   #define FREE_ARG char*
   #define FTOL 1.0e-10
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */  #define NRANSI
   #define ITMAX 200
   
 /******************************************/  #define TOL 2.0e-4
   
 void replace(char *s, char*t)  #define CGOLD 0.3819660
 {  #define ZEPS 1.0e-10
   int i;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
   int lg=20;  
   i=0;  #define GOLD 1.618034
   lg=strlen(t);  #define GLIMIT 100.0
   for(i=0; i<= lg; i++) {  #define TINY 1.0e-20
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';  static double maxarg1,maxarg2;
   }  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 void cut(char *u,char *v, char*t)   
 {  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   int i,lg,j,p;  #define rint(a) floor(a+0.5)
   i=0;  
   for(j=0; j<=strlen(t); j++) {  static double sqrarg;
     if(t[j]=='\\') p=j;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}
   
   lg=strlen(t);  int imx;
   for(j=0; j<p; j++) {  int stepm;
     (u[j] = t[j]);  /* Stepm, step in month: minimum step interpolation*/
     u[p]='\0';  
   }  int estepm;
   /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);  int m,nb;
   }  int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
 }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double **pmmij, ***probs, ***mobaverage;
 /********************** nrerror ********************/  double dateintmean=0;
   
 void nrerror(char error_text[])  double *weight;
 {  int **s; /* Status */
   fprintf(stderr,"ERREUR ...\n");  double *agedc, **covar, idx;
   fprintf(stderr,"%s\n",error_text);  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   exit(1);  
 }  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 /*********************** vector *******************/  double ftolhess; /* Tolerance for computing hessian */
 double *vector(int nl, int nh)  
 {  /**************** split *************************/
   double *v;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  {
   if (!v) nrerror("allocation failure in vector");     char *s;                             /* pointer */
   return v-nl+NR_END;     int  l1, l2;                         /* length counters */
 }  
      l1 = strlen( path );                 /* length of path */
 /************************ free vector ******************/     if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 void free_vector(double*v, int nl, int nh)     s = strrchr( path,  DIRSEPARATOR );          /* find last / */
 {     if ( s == NULL ) {                   /* no directory, so use current */
   free((FREE_ARG)(v+nl-NR_END));  #if     defined(__bsd__)                /* get current working directory */
 }        extern char       *getwd( );
   
 /************************ivector *******************************/        if ( getwd( dirc ) == NULL ) {
 int *ivector(long nl,long nh)  #else
 {        extern char       *getcwd( );
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));        if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   if (!v) nrerror("allocation failure in ivector");  #endif
   return v-nl+NR_END;           return( GLOCK_ERROR_GETCWD );
 }        }
         strcpy( name, path );             /* we've got it */
 /******************free ivector **************************/     } else {                             /* strip direcotry from path */
 void free_ivector(int *v, long nl, long nh)        s++;                              /* after this, the filename */
 {        l2 = strlen( s );                 /* length of filename */
   free((FREE_ARG)(v+nl-NR_END));        if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 }        strcpy( name, s );                /* save file name */
         strncpy( dirc, path, l1 - l2 );   /* now the directory */
 /******************* imatrix *******************************/        dirc[l1-l2] = 0;                  /* add zero */
 int **imatrix(long nrl, long nrh, long ncl, long nch)      }
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */      l1 = strlen( dirc );                 /* length of directory */
 {   #ifdef windows
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;      if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   int **m;   #else
        if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   /* allocate pointers to rows */   #endif
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));      s = strrchr( name, '.' );            /* find last / */
   if (!m) nrerror("allocation failure 1 in matrix()");      s++;
   m += NR_END;      strcpy(ext,s);                       /* save extension */
   m -= nrl;      l1= strlen( name);
        l2= strlen( s)+1;
        strncpy( finame, name, l1-l2);
   /* allocate rows and set pointers to them */      finame[l1-l2]= 0;
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));      return( 0 );                         /* we're done */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");   }
   m[nrl] += NR_END;   
   m[nrl] -= ncl;   
     /******************************************/
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;   
     void replace(char *s, char*t)
   /* return pointer to array of pointers to rows */   {
   return m;     int i;
 }     int lg=20;
     i=0;
 /****************** free_imatrix *************************/    lg=strlen(t);
 void free_imatrix(m,nrl,nrh,ncl,nch)    for(i=0; i<= lg; i++) {
       int **m;      (s[i] = t[i]);
       long nch,ncl,nrh,nrl;       if (t[i]== '\\') s[i]='/';
      /* free an int matrix allocated by imatrix() */     }
 {   }
   free((FREE_ARG) (m[nrl]+ncl-NR_END));   
   free((FREE_ARG) (m+nrl-NR_END));   int nbocc(char *s, char occ)
 }   {
     int i,j=0;
 /******************* matrix *******************************/    int lg=20;
 double **matrix(long nrl, long nrh, long ncl, long nch)    i=0;
 {    lg=strlen(s);
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    for(i=0; i<= lg; i++) {
   double **m;    if  (s[i] == occ ) j++;
     }
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    return j;
   if (!m) nrerror("allocation failure 1 in matrix()");  }
   m += NR_END;  
   m -= nrl;  void cutv(char *u,char *v, char*t, char occ)
   {
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    int i,lg,j,p=0;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    i=0;
   m[nrl] += NR_END;    for(j=0; j<=strlen(t)-1; j++) {
   m[nrl] -= ncl;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     }
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   return m;    lg=strlen(t);
 }    for(j=0; j<p; j++) {
       (u[j] = t[j]);
 /*************************free matrix ************************/    }
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)       u[p]='\0';
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));     for(j=0; j<= lg; j++) {
   free((FREE_ARG)(m+nrl-NR_END));      if (j>=(p+1))(v[j-p-1] = t[j]);
 }    }
   }
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  /********************** nrerror ********************/
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  void nrerror(char error_text[])
   double ***m;  {
     fprintf(stderr,"ERREUR ...\n");
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    fprintf(stderr,"%s\n",error_text);
   if (!m) nrerror("allocation failure 1 in matrix()");    exit(1);
   m += NR_END;  }
   m -= nrl;  /*********************** vector *******************/
   double *vector(int nl, int nh)
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  {
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    double *v;
   m[nrl] += NR_END;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   m[nrl] -= ncl;    if (!v) nrerror("allocation failure in vector");
     return v-nl+NR_END;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  }
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  /************************ free vector ******************/
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  void free_vector(double*v, int nl, int nh)
   m[nrl][ncl] += NR_END;  {
   m[nrl][ncl] -= nll;    free((FREE_ARG)(v+nl-NR_END));
   for (j=ncl+1; j<=nch; j++)   }
     m[nrl][j]=m[nrl][j-1]+nlay;  
     /************************ivector *******************************/
   for (i=nrl+1; i<=nrh; i++) {  int *ivector(long nl,long nh)
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  {
     for (j=ncl+1; j<=nch; j++)     int *v;
       m[i][j]=m[i][j-1]+nlay;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   }    if (!v) nrerror("allocation failure in ivector");
   return m;    return v-nl+NR_END;
 }  }
   
 /*************************free ma3x ************************/  /******************free ivector **************************/
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  void free_ivector(int *v, long nl, long nh)
 {  {
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    free((FREE_ARG)(v+nl-NR_END));
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  }
   free((FREE_ARG)(m+nrl-NR_END));  
 }  /******************* imatrix *******************************/
   int **imatrix(long nrl, long nrh, long ncl, long nch)
 /***************** f1dim *************************/       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
 extern int ncom;   {
 extern double *pcom,*xicom;    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
 extern double (*nrfunc)(double []);     int **m;
     
 double f1dim(double x)     /* allocate pointers to rows */
 {     m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
   int j;     if (!m) nrerror("allocation failure 1 in matrix()");
   double f;    m += NR_END;
   double *xt;     m -= nrl;
     
   xt=vector(1,ncom);    
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];     /* allocate rows and set pointers to them */
   f=(*nrfunc)(xt);     m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));
   free_vector(xt,1,ncom);     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   return f;     m[nrl] += NR_END;
 }     m[nrl] -= ncl;
    
 /*****************brent *************************/    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    
 {     /* return pointer to array of pointers to rows */
   int iter;     return m;
   double a,b,d,etemp;  }
   double fu,fv,fw,fx;  
   double ftemp;  /****************** free_imatrix *************************/
   double p,q,r,tol1,tol2,u,v,w,x,xm;   void free_imatrix(m,nrl,nrh,ncl,nch)
   double e=0.0;         int **m;
          long nch,ncl,nrh,nrl;
   a=(ax < cx ? ax : cx);        /* free an int matrix allocated by imatrix() */
   b=(ax > cx ? ax : cx);   {
   x=w=v=bx;     free((FREE_ARG) (m[nrl]+ncl-NR_END));
   fw=fv=fx=(*f)(x);     free((FREE_ARG) (m+nrl-NR_END));
   for (iter=1;iter<=ITMAX;iter++) {   }
     xm=0.5*(a+b);   
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);   /******************* matrix *******************************/
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  double **matrix(long nrl, long nrh, long ncl, long nch)
     printf(".");fflush(stdout);  {
 #ifdef DEBUG    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     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);    double **m;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){     if (!m) nrerror("allocation failure 1 in matrix()");
       *xmin=x;     m += NR_END;
       return fx;     m -= nrl;
     }   
     ftemp=fu;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (fabs(e) > tol1) {     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       r=(x-w)*(fx-fv);     m[nrl] += NR_END;
       q=(x-v)*(fx-fw);     m[nrl] -= ncl;
       p=(x-v)*q-(x-w)*r;   
       q=2.0*(q-r);     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       if (q > 0.0) p = -p;     return m;
       q=fabs(q);   }
       etemp=e;   
       e=d;   /*************************free matrix ************************/
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))   void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         d=CGOLD*(e=(x >= xm ? a-x : b-x));   {
       else {     free((FREE_ARG)(m[nrl]+ncl-NR_END));
         d=p/q;     free((FREE_ARG)(m+nrl-NR_END));
         u=x+d;   }
         if (u-a < tol2 || b-u < tol2)   
           d=SIGN(tol1,xm-x);   /******************* ma3x *******************************/
       }   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     } else {   {
       d=CGOLD*(e=(x >= xm ? a-x : b-x));     long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     }     double ***m;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));   
     fu=(*f)(u);     m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (fu <= fx) {     if (!m) nrerror("allocation failure 1 in matrix()");
       if (u >= x) a=x; else b=x;     m += NR_END;
       SHFT(v,w,x,u)     m -= nrl;
         SHFT(fv,fw,fx,fu)   
         } else {     m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
           if (u < x) a=u; else b=u;     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
           if (fu <= fw || w == x) {     m[nrl] += NR_END;
             v=w;     m[nrl] -= ncl;
             w=u;   
             fv=fw;     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
             fw=fu;   
           } else if (fu <= fv || v == x || v == w) {     m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
             v=u;     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
             fv=fu;     m[nrl][ncl] += NR_END;
           }     m[nrl][ncl] -= nll;
         }     for (j=ncl+1; j<=nch; j++)
   }       m[nrl][j]=m[nrl][j-1]+nlay;
   nrerror("Too many iterations in brent");    
   *xmin=x;     for (i=nrl+1; i<=nrh; i++) {
   return fx;       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
 }       for (j=ncl+1; j<=nch; j++)
         m[i][j]=m[i][j-1]+nlay;
 /****************** mnbrak ***********************/    }
     return m;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,   }
             double (*func)(double))   
 {   /*************************free ma3x ************************/
   double ulim,u,r,q, dum;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   double fu;   {
      free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   *fa=(*func)(*ax);     free((FREE_ARG)(m[nrl]+ncl-NR_END));
   *fb=(*func)(*bx);     free((FREE_ARG)(m+nrl-NR_END));
   if (*fb > *fa) {   }
     SHFT(dum,*ax,*bx,dum)   
       SHFT(dum,*fb,*fa,dum)   /***************** f1dim *************************/
       }   extern int ncom;
   *cx=(*bx)+GOLD*(*bx-*ax);   extern double *pcom,*xicom;
   *fc=(*func)(*cx);   extern double (*nrfunc)(double []);
   while (*fb > *fc) {    
     r=(*bx-*ax)*(*fb-*fc);   double f1dim(double x)
     q=(*bx-*cx)*(*fb-*fa);   {
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/     int j;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));     double f;
     ulim=(*bx)+GLIMIT*(*cx-*bx);     double *xt;
     if ((*bx-u)*(u-*cx) > 0.0) {    
       fu=(*func)(u);     xt=vector(1,ncom);
     } else if ((*cx-u)*(u-ulim) > 0.0) {     for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];
       fu=(*func)(u);     f=(*nrfunc)(xt);
       if (fu < *fc) {     free_vector(xt,1,ncom);
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))     return f;
           SHFT(*fb,*fc,fu,(*func)(u))   }
           }   
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {   /*****************brent *************************/
       u=ulim;   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)
       fu=(*func)(u);   {
     } else {     int iter;
       u=(*cx)+GOLD*(*cx-*bx);     double a,b,d,etemp;
       fu=(*func)(u);     double fu,fv,fw,fx;
     }     double ftemp;
     SHFT(*ax,*bx,*cx,u)     double p,q,r,tol1,tol2,u,v,w,x,xm;
       SHFT(*fa,*fb,*fc,fu)     double e=0.0;
       }    
 }     a=(ax < cx ? ax : cx);
     b=(ax > cx ? ax : cx);
 /*************** linmin ************************/    x=w=v=bx;
     fw=fv=fx=(*f)(x);
 int ncom;     for (iter=1;iter<=ITMAX;iter++) {
 double *pcom,*xicom;      xm=0.5*(a+b);
 double (*nrfunc)(double []);       tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
        /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))       printf(".");fflush(stdout);
 {   #ifdef DEBUG
   double brent(double ax, double bx, double cx,       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);
                double (*f)(double), double tol, double *xmin);       /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   double f1dim(double x);   #endif
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,       if (fabs(x-xm) <= (tol2-0.5*(b-a))){
               double *fc, double (*func)(double));         *xmin=x;
   int j;         return fx;
   double xx,xmin,bx,ax;       }
   double fx,fb,fa;      ftemp=fu;
        if (fabs(e) > tol1) {
   ncom=n;         r=(x-w)*(fx-fv);
   pcom=vector(1,n);         q=(x-v)*(fx-fw);
   xicom=vector(1,n);         p=(x-v)*q-(x-w)*r;
   nrfunc=func;         q=2.0*(q-r);
   for (j=1;j<=n;j++) {         if (q > 0.0) p = -p;
     pcom[j]=p[j];         q=fabs(q);
     xicom[j]=xi[j];         etemp=e;
   }         e=d;
   ax=0.0;         if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
   xx=1.0;           d=CGOLD*(e=(x >= xm ? a-x : b-x));
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);         else {
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);           d=p/q;
 #ifdef DEBUG          u=x+d;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);          if (u-a < tol2 || b-u < tol2)
 #endif            d=SIGN(tol1,xm-x);
   for (j=1;j<=n;j++) {         }
     xi[j] *= xmin;       } else {
     p[j] += xi[j];         d=CGOLD*(e=(x >= xm ? a-x : b-x));
   }       }
   free_vector(xicom,1,n);       u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
   free_vector(pcom,1,n);       fu=(*f)(u);
 }       if (fu <= fx) {
         if (u >= x) a=x; else b=x;
 /*************** powell ************************/        SHFT(v,w,x,u)
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,           SHFT(fv,fw,fx,fu)
             double (*func)(double []))           } else {
             if (u < x) a=u; else b=u;
 {             if (fu <= fw || w == x) {
               v=w;
               w=u;
   void linmin(double p[], double xi[], int n, double *fret,               fv=fw;
               double (*func)(double []));               fw=fu;
   int i,ibig,j;             } else if (fu <= fv || v == x || v == w) {
   double del,t,*pt,*ptt,*xit;              v=u;
   double fp,fptt;              fv=fu;
   double *xits;            }
   pt=vector(1,n);           }
   ptt=vector(1,n);     }
   xit=vector(1,n);     nrerror("Too many iterations in brent");
   xits=vector(1,n);     *xmin=x;
   *fret=(*func)(p);     return fx;
   for (j=1;j<=n;j++) pt[j]=p[j];   }
   for (*iter=1;;++(*iter)) {   
     fp=(*fret);   /****************** mnbrak ***********************/
     ibig=0;   
     del=0.0;   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);              double (*func)(double))
     for (i=1;i<=n;i++)   {
       printf(" %d %.12f",i, p[i]);    double ulim,u,r,q, dum;
     printf("\n");    double fu;
     for (i=1;i<=n;i++) {    
       for (j=1;j<=n;j++) xit[j]=xi[j][i];     *fa=(*func)(*ax);
       fptt=(*fret);     *fb=(*func)(*bx);
 #ifdef DEBUG    if (*fb > *fa) {
       printf("fret=%lf \n",*fret);      SHFT(dum,*ax,*bx,dum)
 #endif        SHFT(dum,*fb,*fa,dum)
       printf("%d",i);fflush(stdout);        }
       linmin(p,xit,n,fret,func);     *cx=(*bx)+GOLD*(*bx-*ax);
       if (fabs(fptt-(*fret)) > del) {     *fc=(*func)(*cx);
         del=fabs(fptt-(*fret));     while (*fb > *fc) {
         ibig=i;       r=(*bx-*ax)*(*fb-*fc);
       }       q=(*bx-*cx)*(*fb-*fa);
 #ifdef DEBUG      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/
       printf("%d %.12e",i,(*fret));        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));
       for (j=1;j<=n;j++) {      ulim=(*bx)+GLIMIT*(*cx-*bx);
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      if ((*bx-u)*(u-*cx) > 0.0) {
         printf(" x(%d)=%.12e",j,xit[j]);        fu=(*func)(u);
       }      } else if ((*cx-u)*(u-ulim) > 0.0) {
       for(j=1;j<=n;j++)         fu=(*func)(u);
         printf(" p=%.12e",p[j]);        if (fu < *fc) {
       printf("\n");          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))
 #endif            SHFT(*fb,*fc,fu,(*func)(u))
     }             }
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      } else if ((u-ulim)*(ulim-*cx) >= 0.0) {
 #ifdef DEBUG        u=ulim;
       int k[2],l;        fu=(*func)(u);
       k[0]=1;      } else {
       k[1]=-1;        u=(*cx)+GOLD*(*cx-*bx);
       printf("Max: %.12e",(*func)(p));        fu=(*func)(u);
       for (j=1;j<=n;j++)       }
         printf(" %.12e",p[j]);      SHFT(*ax,*bx,*cx,u)
       printf("\n");        SHFT(*fa,*fb,*fc,fu)
       for(l=0;l<=1;l++) {        }
         for (j=1;j<=n;j++) {  }
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  /*************** linmin ************************/
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  int ncom;
       }  double *pcom,*xicom;
 #endif  double (*nrfunc)(double []);
    
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))
       free_vector(xit,1,n);   {
       free_vector(xits,1,n);     double brent(double ax, double bx, double cx,
       free_vector(ptt,1,n);                  double (*f)(double), double tol, double *xmin);
       free_vector(pt,1,n);     double f1dim(double x);
       return;     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,
     }                 double *fc, double (*func)(double));
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");     int j;
     for (j=1;j<=n;j++) {     double xx,xmin,bx,ax;
       ptt[j]=2.0*p[j]-pt[j];     double fx,fb,fa;
       xit[j]=p[j]-pt[j];    
       pt[j]=p[j];     ncom=n;
     }     pcom=vector(1,n);
     fptt=(*func)(ptt);     xicom=vector(1,n);
     if (fptt < fp) {     nrfunc=func;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);     for (j=1;j<=n;j++) {
       if (t < 0.0) {       pcom[j]=p[j];
         linmin(p,xit,n,fret,func);       xicom[j]=xi[j];
         for (j=1;j<=n;j++) {     }
           xi[j][ibig]=xi[j][n];     ax=0.0;
           xi[j][n]=xit[j];     xx=1.0;
         }    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);
 #ifdef DEBUG    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  #ifdef DEBUG
         for(j=1;j<=n;j++)    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
           printf(" %.12e",xit[j]);  #endif
         printf("\n");    for (j=1;j<=n;j++) {
 #endif      xi[j] *= xmin;
       }       p[j] += xi[j];
     }     }
   }     free_vector(xicom,1,n);
 }     free_vector(pcom,1,n);
   }
 /**** Prevalence limit ****************/  
   /*************** powell ************************/
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl)  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,
 {              double (*func)(double []))
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  {
      matrix by transitions matrix until convergence is reached */    void linmin(double p[], double xi[], int n, double *fret,
                 double (*func)(double []));
   int i, ii,j,k;    int i,ibig,j;
   double min, max, maxmin, maxmax,sumnew=0.;    double del,t,*pt,*ptt,*xit;
   double **matprod2();    double fp,fptt;
   double **out, cov[NCOVMAX], **pmij();    double *xits;
   double **newm;    pt=vector(1,n);
   double agefin, delaymax=50 ; /* Max number of years to converge */    ptt=vector(1,n);
     xit=vector(1,n);
   for (ii=1;ii<=nlstate+ndeath;ii++)    xits=vector(1,n);
     for (j=1;j<=nlstate+ndeath;j++){    *fret=(*func)(p);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    for (j=1;j<=n;j++) pt[j]=p[j];
     }    for (*iter=1;;++(*iter)) {
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */      fp=(*fret);
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){      ibig=0;
     newm=savm;      del=0.0;
     /* Covariates have to be included here again */      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
     cov[1]=1.;      for (i=1;i<=n;i++)
     cov[2]=agefin;        printf(" %d %.12f",i, p[i]);
     out=matprod2(newm, pmij(pmmij,cov,ncov,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);      printf("\n");
 /*    printf("age=%f agefin=%f po=%f pn=%f\n",age,agefin,oldm[1][1],newm[1][1]);*/      for (i=1;i<=n;i++) {
             for (j=1;j<=n;j++) xit[j]=xi[j][i];
     savm=oldm;        fptt=(*fret);
     oldm=newm;  #ifdef DEBUG
     maxmax=0.;        printf("fret=%lf \n",*fret);
     for(j=1;j<=nlstate;j++){  #endif
       min=1.;        printf("%d",i);fflush(stdout);
       max=0.;        linmin(p,xit,n,fret,func);
       for(i=1; i<=nlstate; i++) {        if (fabs(fptt-(*fret)) > del) {
         sumnew=0;          del=fabs(fptt-(*fret));
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];          ibig=i;
         prlim[i][j]= newm[i][j]/(1-sumnew);        }
         max=FMAX(max,prlim[i][j]);  #ifdef DEBUG
         min=FMIN(min,prlim[i][j]);        printf("%d %.12e",i,(*fret));
       }        for (j=1;j<=n;j++) {
       maxmin=max-min;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
       maxmax=FMAX(maxmax,maxmin);          printf(" x(%d)=%.12e",j,xit[j]);
     }        }
     if(maxmax < ftolpl){        for(j=1;j<=n;j++)
       return prlim;          printf(" p=%.12e",p[j]);
     }        printf("\n");
   }  #endif
 }      }
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
 /*************** transition probabilities **********/   #ifdef DEBUG
         int k[2],l;
 double **pmij(double **ps, double *cov, int ncov, double *x, int nlstate )        k[0]=1;
 {        k[1]=-1;
   double s1, s2;        printf("Max: %.12e",(*func)(p));
   /*double t34;*/        for (j=1;j<=n;j++)
   int i,j,j1, nc, ii, jj;          printf(" %.12e",p[j]);
         printf("\n");
     for(i=1; i<= nlstate; i++){        for(l=0;l<=1;l++) {
     for(j=1; j<i;j++){          for (j=1;j<=n;j++) {
       for (nc=1, s2=0.;nc <=ncov; nc++){            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
         /*s2 += param[i][j][nc]*cov[nc];*/            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[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);*/          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       }        }
       ps[i][j]=s2;  #endif
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  
     }  
     for(j=i+1; j<=nlstate+ndeath;j++){        free_vector(xit,1,n);
       for (nc=1, s2=0.;nc <=ncov; nc++){        free_vector(xits,1,n);
         s2 += x[(i-1)*nlstate*ncov+(j-2)*ncov+nc+(i-1)*(ndeath-1)*ncov]*cov[nc];        free_vector(ptt,1,n);
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/        free_vector(pt,1,n);
       }        return;
       ps[i][j]=s2;      }
     }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");
   }      for (j=1;j<=n;j++) {
   for(i=1; i<= nlstate; i++){        ptt[j]=2.0*p[j]-pt[j];
      s1=0;        xit[j]=p[j]-pt[j];
     for(j=1; j<i; j++)        pt[j]=p[j];
       s1+=exp(ps[i][j]);      }
     for(j=i+1; j<=nlstate+ndeath; j++)      fptt=(*func)(ptt);
       s1+=exp(ps[i][j]);      if (fptt < fp) {
     ps[i][i]=1./(s1+1.);        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);
     for(j=1; j<i; j++)        if (t < 0.0) {
       ps[i][j]= exp(ps[i][j])*ps[i][i];          linmin(p,xit,n,fret,func);
     for(j=i+1; j<=nlstate+ndeath; j++)          for (j=1;j<=n;j++) {
       ps[i][j]= exp(ps[i][j])*ps[i][i];            xi[j][ibig]=xi[j][n];
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */            xi[j][n]=xit[j];
   } /* end i */          }
   #ifdef DEBUG
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     for(jj=1; jj<= nlstate+ndeath; jj++){          for(j=1;j<=n;j++)
       ps[ii][jj]=0;            printf(" %.12e",xit[j]);
       ps[ii][ii]=1;          printf("\n");
     }  #endif
   }        }
       }
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    }
     for(jj=1; jj<= nlstate+ndeath; jj++){  }
      printf("%lf ",ps[ii][jj]);  
    }  /**** Prevalence limit ****************/
     printf("\n ");  
     }  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
     printf("\n ");printf("%lf ",cov[2]);*/  {
 /*    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   for(i=1; i<= npar; i++) printf("%f ",x[i]);       matrix by transitions matrix until convergence is reached */
   goto end;*/  
     return ps;    int i, ii,j,k;
 }    double min, max, maxmin, maxmax,sumnew=0.;
     double **matprod2();
 /**************** Product of 2 matrices ******************/    double **out, cov[NCOVMAX], **pmij();
     double **newm;
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    double agefin, delaymax=50 ; /* Max number of years to converge */
 {  
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    for (ii=1;ii<=nlstate+ndeath;ii++)
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */      for (j=1;j<=nlstate+ndeath;j++){
   /* in, b, out are matrice of pointers which should have been initialized         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      before: only the contents of out is modified. The function returns      }
      a pointer to pointers identical to out */  
   long i, j, k;     cov[1]=1.;
   for(i=nrl; i<= nrh; i++)   
     for(k=ncolol; k<=ncoloh; k++)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
         out[i][k] +=in[i][j]*b[j][k];      newm=savm;
       /* Covariates have to be included here again */
   return out;       cov[2]=agefin;
 }   
         for (k=1; k<=cptcovn;k++) {
           cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
 /************* Higher Matrix Product ***************/          /*      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]]);*/
         }
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm )        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 {        for (k=1; k<=cptcovprod;k++)
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.         /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step         /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
      (typically every 2 years instead of every month which is too big).        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
      Model is determined by parameters x and covariates have to be       out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
      included manually here.   
       savm=oldm;
      */      oldm=newm;
       maxmax=0.;
   int i, j, d, h;      for(j=1;j<=nlstate;j++){
   double **out, cov[NCOVMAX];        min=1.;
   double **newm;        max=0.;
         for(i=1; i<=nlstate; i++) {
   /* Hstepm could be zero and should return the unit matrix */          sumnew=0;
   for (i=1;i<=nlstate+ndeath;i++)          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     for (j=1;j<=nlstate+ndeath;j++){          prlim[i][j]= newm[i][j]/(1-sumnew);
       oldm[i][j]=(i==j ? 1.0 : 0.0);          max=FMAX(max,prlim[i][j]);
       po[i][j][0]=(i==j ? 1.0 : 0.0);          min=FMIN(min,prlim[i][j]);
     }        }
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        maxmin=max-min;
   for(h=1; h <=nhstepm; h++){        maxmax=FMAX(maxmax,maxmin);
     for(d=1; d <=hstepm; d++){      }
       newm=savm;      if(maxmax < ftolpl){
       /* Covariates have to be included here again */        return prlim;
       cov[1]=1.;      }
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    }
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  }
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,   
                    pmij(pmmij,cov,ncov,x,nlstate));  /*************** transition probabilities ***************/
       savm=oldm;  
       oldm=newm;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
     }  {
     for(i=1; i<=nlstate+ndeath; i++)    double s1, s2;
       for(j=1;j<=nlstate+ndeath;j++) {    /*double t34;*/
         po[i][j][h]=newm[i][j];    int i,j,j1, nc, ii, jj;
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  
          */      for(i=1; i<= nlstate; i++){
       }      for(j=1; j<i;j++){
   } /* end h */        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   return po;          /*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);*/
         }
 /*************** log-likelihood *************/        ps[i][j]=s2;
 double func( double *x)        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
 {      }
   int i, ii, j, k, mi, d;      for(j=i+1; j<=nlstate+ndeath;j++){
   double l, ll[NLSTATEMAX], cov[NCOVMAX];        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   double **out;          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   double sw; /* Sum of weights */          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
   double lli; /* Individual log likelihood */        }
   long ipmx;        ps[i][j]=s2;
   /*extern weight */      }
   /* We are differentiating ll according to initial status */    }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      /*ps[3][2]=1;*/
   /*for(i=1;i<imx;i++)   
 printf(" %d\n",s[4][i]);    for(i=1; i<= nlstate; i++){
   */       s1=0;
       for(j=1; j<i; j++)
   for(k=1; k<=nlstate; k++) ll[k]=0.;        s1+=exp(ps[i][j]);
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      for(j=i+1; j<=nlstate+ndeath; j++)
        for(mi=1; mi<= wav[i]-1; mi++){        s1+=exp(ps[i][j]);
       for (ii=1;ii<=nlstate+ndeath;ii++)      ps[i][i]=1./(s1+1.);
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      for(j=1; j<i; j++)
             for(d=0; d<dh[mi][i]; d++){        ps[i][j]= exp(ps[i][j])*ps[i][i];
         newm=savm;      for(j=i+1; j<=nlstate+ndeath; j++)
           cov[1]=1.;        ps[i][j]= exp(ps[i][j])*ps[i][i];
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    } /* end i */
                        1,nlstate+ndeath,pmij(pmmij,cov,ncov,x,nlstate));  
           savm=oldm;    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
           oldm=newm;      for(jj=1; jj<= nlstate+ndeath; jj++){
         ps[ii][jj]=0;
         ps[ii][ii]=1;
       } /* end mult */      }
        }
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  
       ipmx +=1;    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
       sw += weight[i];      for(jj=1; jj<= nlstate+ndeath; jj++){
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;       printf("%lf ",ps[ii][jj]);
     } /* end of wave */     }
   } /* end of individual */      printf("\n ");
       }
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      printf("\n ");printf("%lf ",cov[2]);*/
   /* 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 */    for(i=1; i<= npar; i++) printf("%f ",x[i]);
   return -l;    goto end;*/
 }      return ps;
   }
   
 /*********** Maximum Likelihood Estimation ***************/  /**************** Product of 2 matrices ******************/
   
 void mlikeli(FILE *ficres,double p[], int npar, int ncov, int nlstate, double ftol, double (*func)(double []))  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
 {  {
   int i,j, iter;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   double **xi,*delti;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   double fret;    /* in, b, out are matrice of pointers which should have been initialized
   xi=matrix(1,npar,1,npar);       before: only the contents of out is modified. The function returns
   for (i=1;i<=npar;i++)       a pointer to pointers identical to out */
     for (j=1;j<=npar;j++)    long i, j, k;
       xi[i][j]=(i==j ? 1.0 : 0.0);    for(i=nrl; i<= nrh; i++)
   printf("Powell\n");      for(k=ncolol; k<=ncoloh; k++)
   powell(p,xi,npar,ftol,&iter,&fret,func);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    return out;
   }
 }  
   
 /**** Computes Hessian and covariance matrix ***/  /************* Higher Matrix Product ***************/
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  
 {  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   double  **a,**y,*x,pd;  {
   double **hess;    /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month
   int i, j,jk;       duration (i.e. until
   int *indx;       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
   double hessii(double p[], double delta, int theta, double delti[]);       (typically every 2 years instead of every month which is too big).
   double hessij(double p[], double delti[], int i, int j);       Model is determined by parameters x and covariates have to be
   void lubksb(double **a, int npar, int *indx, double b[]) ;       included manually here.
   void ludcmp(double **a, int npar, int *indx, double *d) ;  
        */
   
   hess=matrix(1,npar,1,npar);    int i, j, d, h, k;
     double **out, cov[NCOVMAX];
   printf("\nCalculation of the hessian matrix. Wait...\n");    double **newm;
   for (i=1;i<=npar;i++){  
     printf("%d",i);fflush(stdout);    /* Hstepm could be zero and should return the unit matrix */
     hess[i][i]=hessii(p,ftolhess,i,delti);    for (i=1;i<=nlstate+ndeath;i++)
     /*printf(" %f ",p[i]);*/      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);
   for (i=1;i<=npar;i++) {      }
     for (j=1;j<=npar;j++)  {    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       if (j>i) {     for(h=1; h <=nhstepm; h++){
         printf(".%d%d",i,j);fflush(stdout);      for(d=1; d <=hstepm; d++){
         hess[i][j]=hessij(p,delti,i,j);        newm=savm;
         hess[j][i]=hess[i][j];        /* Covariates have to be included here again */
       }        cov[1]=1.;
     }        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   }        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   printf("\n");        for (k=1; k<=cptcovage;k++)
           cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   printf("\nInverting the hessian to get the covariance matrix. Wait...\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]]];
   a=matrix(1,npar,1,npar);  
   y=matrix(1,npar,1,npar);  
   x=vector(1,npar);        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   indx=ivector(1,npar);        /*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,
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   ludcmp(a,npar,indx,&pd);        savm=oldm;
         oldm=newm;
   for (j=1;j<=npar;j++) {      }
     for (i=1;i<=npar;i++) x[i]=0;      for(i=1; i<=nlstate+ndeath; i++)
     x[j]=1;        for(j=1;j<=nlstate+ndeath;j++) {
     lubksb(a,npar,indx,x);          po[i][j][h]=newm[i][j];
     for (i=1;i<=npar;i++){           /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       matcov[i][j]=x[i];           */
     }        }
   }    } /* end h */
     return po;
   printf("\n#Hessian matrix#\n");  }
   for (i=1;i<=npar;i++) {   
     for (j=1;j<=npar;j++) {   
       printf("%.3e ",hess[i][j]);  /*************** log-likelihood *************/
     }  double func( double *x)
     printf("\n");  {
   }    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX], cov[NCOVMAX];
   /* Recompute Inverse */    double **out;
   for (i=1;i<=npar;i++)    double sw; /* Sum of weights */
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    double lli; /* Individual log likelihood */
   ludcmp(a,npar,indx,&pd);    long ipmx;
     /*extern weight */
   /*  printf("\n#Hessian matrix recomputed#\n");    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   for (j=1;j<=npar;j++) {    /*for(i=1;i<imx;i++)
     for (i=1;i<=npar;i++) x[i]=0;      printf(" %d\n",s[4][i]);
     x[j]=1;    */
     lubksb(a,npar,indx,x);    cov[1]=1.;
     for (i=1;i<=npar;i++){   
       y[i][j]=x[i];    for(k=1; k<=nlstate; k++) ll[k]=0.;
       printf("%.3e ",y[i][j]);    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     printf("\n");      for(mi=1; mi<= wav[i]-1; mi++){
   }        for (ii=1;ii<=nlstate+ndeath;ii++)
   */          for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(d=0; d<dh[mi][i]; d++){
   free_matrix(a,1,npar,1,npar);          newm=savm;
   free_matrix(y,1,npar,1,npar);          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   free_vector(x,1,npar);          for (kk=1; kk<=cptcovage;kk++) {
   free_ivector(indx,1,npar);            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   free_matrix(hess,1,npar,1,npar);          }
          
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 }                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           savm=oldm;
 /*************** hessian matrix ****************/          oldm=newm;
 double hessii( double x[], double delta, int theta, double delti[])         
 {         
   int i;        } /* end mult */
   int l=1, lmax=20;       
   double k1,k2;        lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);
   double p2[NPARMAX+1];        /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/
   double res;        ipmx +=1;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        sw += weight[i];
   double fx;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int k=0,kmax=10;      } /* end of wave */
   double l1;    } /* end of individual */
   
   fx=func(x);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   for (i=1;i<=npar;i++) p2[i]=x[i];    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   for(l=0 ; l <=lmax; l++){    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     l1=pow(10,l);    return -l;
     delts=delt;  }
     for(k=1 ; k <kmax; k=k+1){  
       delt = delta*(l1*k);  
       p2[theta]=x[theta] +delt;  /*********** Maximum Likelihood Estimation ***************/
       k1=func(p2)-fx;  
       p2[theta]=x[theta]-delt;  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       k2=func(p2)-fx;  {
       /*res= (k1-2.0*fx+k2)/delt/delt; */    int i,j, iter;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    double **xi,*delti;
           double fret;
 #ifdef DEBUG    xi=matrix(1,npar,1,npar);
       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 (i=1;i<=npar;i++)
 #endif      for (j=1;j<=npar;j++)
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        xi[i][j]=(i==j ? 1.0 : 0.0);
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    printf("Powell\n");
         k=kmax;    powell(p,xi,npar,ftol,&iter,&fret,func);
       }  
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         k=kmax; l=lmax*10.;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       }  
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){   }
         delts=delt;  
       }  /**** Computes Hessian and covariance matrix ***/
     }  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   }  {
   delti[theta]=delts;    double  **a,**y,*x,pd;
   return res;    double **hess;
       int i, j,jk;
 }    int *indx;
   
 double hessij( double x[], double delti[], int thetai,int thetaj)    double hessii(double p[], double delta, int theta, double delti[]);
 {    double hessij(double p[], double delti[], int i, int j);
   int i;    void lubksb(double **a, int npar, int *indx, double b[]) ;
   int l=1, l1, lmax=20;    void ludcmp(double **a, int npar, int *indx, double *d) ;
   double k1,k2,k3,k4,res,fx;  
   double p2[NPARMAX+1];    hess=matrix(1,npar,1,npar);
   int k;  
     printf("\nCalculation of the hessian matrix. Wait...\n");
   fx=func(x);    for (i=1;i<=npar;i++){
   for (k=1; k<=2; k++) {      printf("%d",i);fflush(stdout);
     for (i=1;i<=npar;i++) p2[i]=x[i];      hess[i][i]=hessii(p,ftolhess,i,delti);
     p2[thetai]=x[thetai]+delti[thetai]/k;      /*printf(" %f ",p[i]);*/
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      /*printf(" %lf ",hess[i][i]);*/
     k1=func(p2)-fx;    }
      
     p2[thetai]=x[thetai]+delti[thetai]/k;    for (i=1;i<=npar;i++) {
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      for (j=1;j<=npar;j++)  {
     k2=func(p2)-fx;        if (j>i) {
             printf(".%d%d",i,j);fflush(stdout);
     p2[thetai]=x[thetai]-delti[thetai]/k;          hess[i][j]=hessij(p,delti,i,j);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          hess[j][i]=hess[i][j];    
     k3=func(p2)-fx;          /*printf(" %lf ",hess[i][j]);*/
           }
     p2[thetai]=x[thetai]-delti[thetai]/k;      }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    }
     k4=func(p2)-fx;    printf("\n");
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  
 #ifdef DEBUG    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     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);   
 #endif    a=matrix(1,npar,1,npar);
   }    y=matrix(1,npar,1,npar);
   return res;    x=vector(1,npar);
 }    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
 /************** Inverse of matrix **************/      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
 void ludcmp(double **a, int n, int *indx, double *d)     ludcmp(a,npar,indx,&pd);
 {   
   int i,imax,j,k;     for (j=1;j<=npar;j++) {
   double big,dum,sum,temp;       for (i=1;i<=npar;i++) x[i]=0;
   double *vv;       x[j]=1;
        lubksb(a,npar,indx,x);
   vv=vector(1,n);       for (i=1;i<=npar;i++){
   *d=1.0;         matcov[i][j]=x[i];
   for (i=1;i<=n;i++) {       }
     big=0.0;     }
     for (j=1;j<=n;j++)   
       if ((temp=fabs(a[i][j])) > big) big=temp;     printf("\n#Hessian matrix#\n");
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");     for (i=1;i<=npar;i++) {
     vv[i]=1.0/big;       for (j=1;j<=npar;j++) {
   }         printf("%.3e ",hess[i][j]);
   for (j=1;j<=n;j++) {       }
     for (i=1;i<j;i++) {       printf("\n");
       sum=a[i][j];     }
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];   
       a[i][j]=sum;     /* Recompute Inverse */
     }     for (i=1;i<=npar;i++)
     big=0.0;       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     for (i=j;i<=n;i++) {     ludcmp(a,npar,indx,&pd);
       sum=a[i][j];   
       for (k=1;k<j;k++)     /*  printf("\n#Hessian matrix recomputed#\n");
         sum -= a[i][k]*a[k][j];   
       a[i][j]=sum;     for (j=1;j<=npar;j++) {
       if ( (dum=vv[i]*fabs(sum)) >= big) {       for (i=1;i<=npar;i++) x[i]=0;
         big=dum;       x[j]=1;
         imax=i;       lubksb(a,npar,indx,x);
       }       for (i=1;i<=npar;i++){
     }         y[i][j]=x[i];
     if (j != imax) {         printf("%.3e ",y[i][j]);
       for (k=1;k<=n;k++) {       }
         dum=a[imax][k];       printf("\n");
         a[imax][k]=a[j][k];     }
         a[j][k]=dum;     */
       }   
       *d = -(*d);     free_matrix(a,1,npar,1,npar);
       vv[imax]=vv[j];     free_matrix(y,1,npar,1,npar);
     }     free_vector(x,1,npar);
     indx[j]=imax;     free_ivector(indx,1,npar);
     if (a[j][j] == 0.0) a[j][j]=TINY;     free_matrix(hess,1,npar,1,npar);
     if (j != n) {   
       dum=1.0/(a[j][j]);   
       for (i=j+1;i<=n;i++) a[i][j] *= dum;   }
     }   
   }   /*************** hessian matrix ****************/
   free_vector(vv,1,n);  /* Doesn't work */  double hessii( double x[], double delta, int theta, double delti[])
 ;  {
 }     int i;
     int l=1, lmax=20;
 void lubksb(double **a, int n, int *indx, double b[])     double k1,k2;
 {     double p2[NPARMAX+1];
   int i,ii=0,ip,j;     double res;
   double sum;     double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
      double fx;
   for (i=1;i<=n;i++) {     int k=0,kmax=10;
     ip=indx[i];     double l1;
     sum=b[ip];   
     b[ip]=b[i];     fx=func(x);
     if (ii)     for (i=1;i<=npar;i++) p2[i]=x[i];
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];     for(l=0 ; l <=lmax; l++){
     else if (sum) ii=i;       l1=pow(10,l);
     b[i]=sum;       delts=delt;
   }       for(k=1 ; k <kmax; k=k+1){
   for (i=n;i>=1;i--) {         delt = delta*(l1*k);
     sum=b[i];         p2[theta]=x[theta] +delt;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];         k1=func(p2)-fx;
     b[i]=sum/a[i][i];         p2[theta]=x[theta]-delt;
   }         k2=func(p2)-fx;
 }         /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
 /************ Frequencies ********************/       
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx)  #ifdef DEBUG
 {  /* Some frequencies */        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
   int i, m, jk;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   double ***freq; /* Frequencies */        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   double *pp;          k=kmax;
   double pos;        }
   FILE *ficresp;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   char fileresp[FILENAMELENGTH];          k=kmax; l=lmax*10.;
         }
   pp=vector(1,nlstate);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){
           delts=delt;
   strcpy(fileresp,"p");        }
   strcat(fileresp,fileres);      }
   if((ficresp=fopen(fileresp,"w"))==NULL) {    }
     printf("Problem with prevalence resultfile: %s\n", fileresp);    delti[theta]=delts;
     exit(0);    return res;
   }   
   }
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  
   for (i=-1; i<=nlstate+ndeath; i++)    double hessij( double x[], double delti[], int thetai,int thetaj)
     for (jk=-1; jk<=nlstate+ndeath; jk++)    {
       for(m=agemin; m <= agemax+3; m++)    int i;
         freq[i][jk][m]=0;    int l=1, l1, lmax=20;
     double k1,k2,k3,k4,res,fx;
   for (i=1; i<=imx; i++)  {    double p2[NPARMAX+1];
     for(m=firstpass; m<= lastpass-1; m++){    int k;
       if(agev[m][i]==0) agev[m][i]=agemax+1;  
       if(agev[m][i]==1) agev[m][i]=agemax+2;    fx=func(x);
        freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    for (k=1; k<=2; k++) {
        freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      for (i=1;i<=npar;i++) p2[i]=x[i];
     }      p2[thetai]=x[thetai]+delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k1=func(p2)-fx;
   fprintf(ficresp, "#");   
   for(i=1; i<=nlstate;i++)       p2[thetai]=x[thetai]+delti[thetai]/k;
     fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
 fprintf(ficresp, "\n");      k2=func(p2)-fx;
    
   for(i=(int)agemin; i <= (int)agemax+3; i++){      p2[thetai]=x[thetai]-delti[thetai]/k;
     if(i==(int)agemax+3)      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       printf("Total");      k3=func(p2)-fx;
     else   
       printf("Age %d", i);      p2[thetai]=x[thetai]-delti[thetai]/k;
     for(jk=1; jk <=nlstate ; jk++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      k4=func(p2)-fx;
         pp[jk] += freq[jk][m][i];      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     }  #ifdef DEBUG
     for(jk=1; jk <=nlstate ; jk++){      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);
       for(m=-1, pos=0; m <=0 ; m++)  #endif
         pos += freq[jk][m][i];    }
       if(pp[jk]>=1.e-10)    return res;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  }
       else  
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  /************** Inverse of matrix **************/
     }  void ludcmp(double **a, int n, int *indx, double *d)
     for(jk=1; jk <=nlstate ; jk++){  {
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)    int i,imax,j,k;
         pp[jk] += freq[jk][m][i];    double big,dum,sum,temp;
     }    double *vv;
     for(jk=1,pos=0; jk <=nlstate ; jk++)   
       pos += pp[jk];    vv=vector(1,n);
     for(jk=1; jk <=nlstate ; jk++){    *d=1.0;
       if(pos>=1.e-5)    for (i=1;i<=n;i++) {
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);      big=0.0;
       else      for (j=1;j<=n;j++)
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        if ((temp=fabs(a[i][j])) > big) big=temp;
       if( i <= (int) agemax){      if (big == 0.0) nrerror("Singular matrix in routine ludcmp");
         if(pos>=1.e-5)      vv[i]=1.0/big;
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    }
       else    for (j=1;j<=n;j++) {
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      for (i=1;i<j;i++) {
       }        sum=a[i][j];
     }        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];
     for(jk=-1; jk <=nlstate+ndeath; jk++)        a[i][j]=sum;
       for(m=-1; m <=nlstate+ndeath; m++)      }
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      big=0.0;
     if(i <= (int) agemax)      for (i=j;i<=n;i++) {
       fprintf(ficresp,"\n");        sum=a[i][j];
     printf("\n");        for (k=1;k<j;k++)
   }          sum -= a[i][k]*a[k][j];
         a[i][j]=sum;
   fclose(ficresp);        if ( (dum=vv[i]*fabs(sum)) >= big) {
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          big=dum;
   free_vector(pp,1,nlstate);          imax=i;
         }
 }  /* End of Freq */      }
       if (j != imax) {
 /************* Waves Concatenation ***************/        for (k=1;k<=n;k++) {
           dum=a[imax][k];
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          a[imax][k]=a[j][k];
 {          a[j][k]=dum;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        }
      Death is a valid wave (if date is known).        *d = -(*d);
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        vv[imax]=vv[j];
      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.      indx[j]=imax;
      */      if (a[j][j] == 0.0) a[j][j]=TINY;
       if (j != n) {
   int i, mi, m;        dum=1.0/(a[j][j]);
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        for (i=j+1;i<=n;i++) a[i][j] *= dum;
 float sum=0.;      }
     }
   for(i=1; i<=imx; i++){    free_vector(vv,1,n);  /* Doesn't work */
     mi=0;  ;
     m=firstpass;  }
     while(s[m][i] <= nlstate){  
       if(s[m][i]>=1)  void lubksb(double **a, int n, int *indx, double b[])
         mw[++mi][i]=m;  {
       if(m >=lastpass)    int i,ii=0,ip,j;
         break;    double sum;
       else   
         m++;    for (i=1;i<=n;i++) {
     }/* end while */      ip=indx[i];
     if (s[m][i] > nlstate){      sum=b[ip];
       mi++;     /* Death is another wave */      b[ip]=b[i];
       /* if(mi==0)  never been interviewed correctly before death */      if (ii)
          /* Only death is a correct wave */        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];
       mw[mi][i]=m;      else if (sum) ii=i;
     }      b[i]=sum;
     }
     wav[i]=mi;    for (i=n;i>=1;i--) {
     if(mi==0)      sum=b[i];
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];
   }      b[i]=sum/a[i][i];
     }
   for(i=1; i<=imx; i++){  }
     for(mi=1; mi<wav[i];mi++){  
       if (stepm <=0)  /************ Frequencies ********************/
         dh[mi][i]=1;  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)
       else{  {  /* Some frequencies */
         if (s[mw[mi+1][i]][i] > nlstate) {   
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);     int i, m, jk, k1,i1, j1, bool, z1,z2,j;
           if(j=0) j=1;  /* Survives at least one month after exam */    double ***freq; /* Frequencies */
         }    double *pp;
         else{    double pos, k2, dateintsum=0,k2cpt=0;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    FILE *ficresp;
           k=k+1;    char fileresp[FILENAMELENGTH];
           if (j >= jmax) jmax=j;   
           else if (j <= jmin)jmin=j;    pp=vector(1,nlstate);
           sum=sum+j;    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
         }    strcpy(fileresp,"p");
         jk= j/stepm;    strcat(fileresp,fileres);
         jl= j -jk*stepm;    if((ficresp=fopen(fileresp,"w"))==NULL) {
         ju= j -(jk+1)*stepm;      printf("Problem with prevalence resultfile: %s\n", fileresp);
         if(jl <= -ju)      exit(0);
           dh[mi][i]=jk;    }
         else    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
           dh[mi][i]=jk+1;    j1=0;
         if(dh[mi][i]==0)   
           dh[mi][i]=1; /* At least one step */    j=cptcoveff;
       }    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     }   
   }    for(k1=1; k1<=j;k1++){
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);      for(i1=1; i1<=ncodemax[k1];i1++){
 }        j1++;
         /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
 /*********** Health Expectancies ****************/          scanf("%d", i);*/
         for (i=-1; i<=nlstate+ndeath; i++)  
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm)          for (jk=-1; jk<=nlstate+ndeath; jk++)  
 {            for(m=agemin; m <= agemax+3; m++)
   /* Health expectancies */              freq[i][jk][m]=0;
   int i, j, nhstepm, hstepm, h;       
   double age, agelim,hf;        dateintsum=0;
   double ***p3mat;        k2cpt=0;
         for (i=1; i<=imx; i++) {
   FILE  *ficreseij;          bool=1;
   char filerese[FILENAMELENGTH];          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++)
   strcpy(filerese,"e");              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])
   strcat(filerese,fileres);                bool=0;
   if((ficreseij=fopen(filerese,"w"))==NULL) {          }
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          if (bool==1) {
   }            for(m=firstpass; m<=lastpass; m++){
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);              k2=anint[m][i]+(mint[m][i]/12.);
               if ((k2>=dateprev1) && (k2<=dateprev2)) {
   fprintf(ficreseij,"# Health expectancies\n");                if(agev[m][i]==0) agev[m][i]=agemax+1;
   fprintf(ficreseij,"# Age");                if(agev[m][i]==1) agev[m][i]=agemax+2;
   for(i=1; i<=nlstate;i++)                if (m<lastpass) {
     for(j=1; j<=nlstate;j++)                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
       fprintf(ficreseij," %1d-%1d",i,j);                  freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];
   fprintf(ficreseij,"\n");                }
                
   hstepm=1*YEARM; /*  Every j years of age (in month) */                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */                   dateintsum=dateintsum+k2;
                   k2cpt++;
   agelim=AGESUP;                }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              }
     /* nhstepm age range expressed in number of stepm */            }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);           }
     /* Typically if 20 years = 20*12/6=40 stepm */         }
     if (stepm >= YEARM) hstepm=1;         
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        if  (cptcovn>0) {
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          fprintf(ficresp, "\n#********** Variable ");
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm);            for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresp, "**********\n#");
         }
     for(i=1; i<=nlstate;i++)        for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){        fprintf(ficresp, "\n");
           eij[i][j][(int)age] +=p3mat[i][j][h];       
         }        for(i=(int)agemin; i <= (int)agemax+3; i++){
               if(i==(int)agemax+3)
     hf=1;            printf("Total");
     if (stepm >= YEARM) hf=stepm/YEARM;          else
     fprintf(ficreseij,"%.0f",age );            printf("Age %d", i);
     for(i=1; i<=nlstate;i++)          for(jk=1; jk <=nlstate ; jk++){
       for(j=1; j<=nlstate;j++){            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);              pp[jk] += freq[jk][m][i];
       }          }
     fprintf(ficreseij,"\n");          for(jk=1; jk <=nlstate ; jk++){
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for(m=-1, pos=0; m <=0 ; m++)
   }              pos += freq[jk][m][i];
   fclose(ficreseij);            if(pp[jk]>=1.e-10)
 }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             else
 /************ Variance ******************/              printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 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)          }
 {  
   /* Variance of health expectancies */          for(jk=1; jk <=nlstate ; jk++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   double **newm;              pp[jk] += freq[jk][m][i];
   double **dnewm,**doldm;          }
   int i, j, nhstepm, hstepm, h;  
   int k;          for(jk=1,pos=0; jk <=nlstate ; jk++)
   FILE  *ficresvij;            pos += pp[jk];
   char fileresv[FILENAMELENGTH];          for(jk=1; jk <=nlstate ; jk++){
   double *xp;            if(pos>=1.e-5)
   double **gp, **gm;              printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   double ***gradg, ***trgradg;            else
   double ***p3mat;              printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   double age,agelim;            if( i <= (int) agemax){
   int theta;              if(pos>=1.e-5){
                 fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);
   strcpy(fileresv,"v");                probs[i][jk][j1]= pp[jk]/pos;
   strcat(fileresv,fileres);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   if((ficresvij=fopen(fileresv,"w"))==NULL) {              }
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);              else
   }                fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);            }
           }
          
   fprintf(ficresvij,"# Covariances of life expectancies\n");          for(jk=-1; jk <=nlstate+ndeath; jk++)
   fprintf(ficresvij,"# Age");            for(m=-1; m <=nlstate+ndeath; m++)
   for(i=1; i<=nlstate;i++)              if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     for(j=1; j<=nlstate;j++)          if(i <= (int) agemax)
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);            fprintf(ficresp,"\n");
   fprintf(ficresvij,"\n");          printf("\n");
         }
   xp=vector(1,npar);      }
   dnewm=matrix(1,nlstate,1,npar);    }
   doldm=matrix(1,nlstate,1,nlstate);    dateintmean=dateintsum/k2cpt;
      
   hstepm=1*YEARM; /* Every year of age */    fclose(ficresp);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */     free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
   agelim = AGESUP;    free_vector(pp,1,nlstate);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */   
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */     /* End of Freq */
     if (stepm >= YEARM) hstepm=1;  }
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  /************ Prevalence ********************/
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  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)
     gp=matrix(0,nhstepm,1,nlstate);  {  /* Some frequencies */
     gm=matrix(0,nhstepm,1,nlstate);   
     int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     for(theta=1; theta <=npar; theta++){    double ***freq; /* Frequencies */
       for(i=1; i<=npar; i++){ /* Computes gradient */    double *pp;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    double pos, k2;
       }  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);      pp=vector(1,nlstate);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(j=1; j<= nlstate; j++){   
         for(h=0; h<=nhstepm; h++){    freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    j1=0;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];   
         }    j=cptcoveff;
       }    if (cptcovn<1) {j=1;ncodemax[1]=1;}
        
       for(i=1; i<=npar; i++) /* Computes gradient */    for(k1=1; k1<=j;k1++){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      for(i1=1; i1<=ncodemax[k1];i1++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);          j1++;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);       
       for(j=1; j<= nlstate; j++){        for (i=-1; i<=nlstate+ndeath; i++)  
         for(h=0; h<=nhstepm; h++){          for (jk=-1; jk<=nlstate+ndeath; jk++)  
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)            for(m=agemin; m <= agemax+3; m++)
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];              freq[i][jk][m]=0;
         }       
       }        for (i=1; i<=imx; i++) {
       for(j=1; j<= nlstate; j++)          bool=1;
         for(h=0; h<=nhstepm; h++){          if  (cptcovn>0) {
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];            for (z1=1; z1<=cptcoveff; z1++)
         }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])
     } /* End theta */                bool=0;
           }
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          if (bool==1) {
             for(m=firstpass; m<=lastpass; m++){
     for(h=0; h<=nhstepm; h++)              k2=anint[m][i]+(mint[m][i]/12.);
       for(j=1; j<=nlstate;j++)              if ((k2>=dateprev1) && (k2<=dateprev2)) {
         for(theta=1; theta <=npar; theta++)                if(agev[m][i]==0) agev[m][i]=agemax+1;
           trgradg[h][j][theta]=gradg[h][theta][j];                if(agev[m][i]==1) agev[m][i]=agemax+2;
                 if (m<lastpass) {
     for(i=1;i<=nlstate;i++)                  if (calagedate>0)
       for(j=1;j<=nlstate;j++)                    freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];
         vareij[i][j][(int)age] =0.;                  else
     for(h=0;h<=nhstepm;h++){                    freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
       for(k=0;k<=nhstepm;k++){                  freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];
         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++)            }
           for(j=1;j<=nlstate;j++)          }
             vareij[i][j][(int)age] += doldm[i][j];        }
       }        for(i=(int)agemin; i <= (int)agemax+3; i++){
     }          for(jk=1; jk <=nlstate ; jk++){
     h=1;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     if (stepm >= YEARM) h=stepm/YEARM;              pp[jk] += freq[jk][m][i];
     fprintf(ficresvij,"%.0f ",age );          }
     for(i=1; i<=nlstate;i++)          for(jk=1; jk <=nlstate ; jk++){
       for(j=1; j<=nlstate;j++){            for(m=-1, pos=0; m <=0 ; m++)
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);              pos += freq[jk][m][i];
       }          }
     fprintf(ficresvij,"\n");         
     free_matrix(gp,0,nhstepm,1,nlstate);          for(jk=1; jk <=nlstate ; jk++){
     free_matrix(gm,0,nhstepm,1,nlstate);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);              pp[jk] += freq[jk][m][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);          }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         
   } /* End age */          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];
   fclose(ficresvij);         
   free_vector(xp,1,npar);          for(jk=1; jk <=nlstate ; jk++){    
   free_matrix(doldm,1,nlstate,1,npar);            if( i <= (int) agemax){
   free_matrix(dnewm,1,nlstate,1,nlstate);              if(pos>=1.e-5){
                 probs[i][jk][j1]= pp[jk]/pos;
 }              }
             }
 /************ 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)         
 {        }
   /* Variance of health expectancies */      }
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;  
   double **dnewm,**doldm;   
   int i, j, nhstepm, hstepm;    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
   int k;    free_vector(pp,1,nlstate);
   FILE  *ficresvpl;   
   char fileresvpl[FILENAMELENGTH];  }  /* End of Freq */
   double *xp;  
   double *gp, *gm;  /************* Waves Concatenation ***************/
   double **gradg, **trgradg;  
   double age,agelim;  void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
   int theta;  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   strcpy(fileresvpl,"vpl");       Death is a valid wave (if date is known).
   strcat(fileresvpl,fileres);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {       dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);       and mw[mi+1][i]. dh depends on stepm.
     exit(0);       */
   }  
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    int i, mi, m;
     /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  
   fprintf(ficresvpl,"# Age");    int j, k=0,jk, ju, jl;
   for(i=1; i<=nlstate;i++)    double sum=0.;
       fprintf(ficresvpl," %1d-%1d",i,i);    jmin=1e+5;
   fprintf(ficresvpl,"\n");    jmax=-1;
     jmean=0.;
   xp=vector(1,npar);    for(i=1; i<=imx; i++){
   dnewm=matrix(1,nlstate,1,npar);      mi=0;
   doldm=matrix(1,nlstate,1,nlstate);      m=firstpass;
         while(s[m][i] <= nlstate){
   hstepm=1*YEARM; /* Every year of age */        if(s[m][i]>=1)
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */           mw[++mi][i]=m;
   agelim = AGESUP;        if(m >=lastpass)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          break;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */         else
     if (stepm >= YEARM) hstepm=1;          m++;
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      }/* end while */
     gradg=matrix(1,npar,1,nlstate);      if (s[m][i] > nlstate){
     gp=vector(1,nlstate);        mi++;     /* Death is another wave */
     gm=vector(1,nlstate);        /* if(mi==0)  never been interviewed correctly before death */
            /* Only death is a correct wave */
     for(theta=1; theta <=npar; theta++){        mw[mi][i]=m;
       for(i=1; i<=npar; i++){ /* Computes gradient */      }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }      wav[i]=mi;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);      if(mi==0)
       for(i=1;i<=nlstate;i++)        printf("Warning, no any valid information for:%d line=%d\n",num[i],i);
         gp[i] = prlim[i][i];    }
       
       for(i=1; i<=npar; i++) /* Computes gradient */    for(i=1; i<=imx; i++){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      for(mi=1; mi<wav[i];mi++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);        if (stepm <=0)
       for(i=1;i<=nlstate;i++)          dh[mi][i]=1;
         gm[i] = prlim[i][i];        else{
           if (s[mw[mi+1][i]][i] > nlstate) {
       for(i=1;i<=nlstate;i++)            if (agedc[i] < 2*AGESUP) {
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];            j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);
     } /* End theta */            if(j==0) j=1;  /* Survives at least one month after exam */
             k=k+1;
     trgradg =matrix(1,nlstate,1,npar);            if (j >= jmax) jmax=j;
             if (j <= jmin) jmin=j;
     for(j=1; j<=nlstate;j++)            sum=sum+j;
       for(theta=1; theta <=npar; theta++)            /*if (j<0) printf("j=%d num=%d \n",j,i); */
         trgradg[j][theta]=gradg[theta][j];            }
           }
     for(i=1;i<=nlstate;i++)          else{
       varpl[i][(int)age] =0.;            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);            k=k+1;
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);            if (j >= jmax) jmax=j;
     for(i=1;i<=nlstate;i++)            else if (j <= jmin)jmin=j;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             sum=sum+j;
     fprintf(ficresvpl,"%.0f ",age );          }
     for(i=1; i<=nlstate;i++)          jk= j/stepm;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          jl= j -jk*stepm;
     fprintf(ficresvpl,"\n");          ju= j -(jk+1)*stepm;
     free_vector(gp,1,nlstate);          if(jl <= -ju)
     free_vector(gm,1,nlstate);            dh[mi][i]=jk;
     free_matrix(gradg,1,npar,1,nlstate);          else
     free_matrix(trgradg,1,nlstate,1,npar);            dh[mi][i]=jk+1;
   } /* End age */          if(dh[mi][i]==0)
   fclose(ficresvpl);            dh[mi][i]=1; /* At least one step */
   free_vector(xp,1,npar);        }
   free_matrix(doldm,1,nlstate,1,npar);      }
   free_matrix(dnewm,1,nlstate,1,nlstate);    }
     jmean=sum/k;
 }    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
    }
   /*********** Tricode ****************************/
   void tricode(int *Tvar, int **nbcode, int imx)
 /***********************************************/  {
 /**************** Main Program *****************/    int Ndum[20],ij=1, k, j, i;
 /***********************************************/    int cptcode=0;
     cptcoveff=0;
 /*int main(int argc, char *argv[])*/   
 int main()    for (k=0; k<19; k++) Ndum[k]=0;
 {    for (k=1; k<=7; k++) ncodemax[k]=0;
   
   int i,j, k, n=MAXN,iter,m,size;    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
   double agedeb, agefin,hf;      for (i=1; i<=imx; i++) {
   double agemin=1.e20, agemax=-1.e20;        ij=(int)(covar[Tvar[j]][i]);
         Ndum[ij]++;
   double fret;        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
   double **xi,tmp,delta;        if (ij > cptcode) cptcode=ij;
       }
   double dum; /* Dummy variable */  
   double ***p3mat;      for (i=0; i<=cptcode; i++) {
   int *indx;        if(Ndum[i]!=0) ncodemax[j]++;
   char line[MAXLINE], linepar[MAXLINE];      }
   char title[MAXLINE];      ij=1;
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];  
   char filerest[FILENAMELENGTH];      for (i=1; i<=ncodemax[j]; i++) {
   char fileregp[FILENAMELENGTH];        for (k=0; k<=19; k++) {
   char path[80],pathc[80],pathcd[80],pathtot[80];          if (Ndum[k] != 0) {
   int firstobs=1, lastobs=10;            nbcode[Tvar[j]][ij]=k;
   int sdeb, sfin; /* Status at beginning and end */           
   int c,  h , cpt,l;            ij++;
   int ju,jl, mi;          }
   int i1,j1, k1,jk,aa,bb, stepsize;          if (ij > ncodemax[j]) break;
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        }  
         }
   int hstepm, nhstepm;    }  
   double bage, fage, age, agelim, agebase;  
   double ftolpl=FTOL;   for (k=0; k<19; k++) Ndum[k]=0;
   double **prlim;  
   double *severity;   for (i=1; i<=ncovmodel-2; i++) {
   double ***param; /* Matrix of parameters */        ij=Tvar[i];
   double  *p;        Ndum[ij]++;
   double **matcov; /* Matrix of covariance */      }
   double ***delti3; /* Scale */  
   double *delti; /* Scale */   ij=1;
   double ***eij, ***vareij;   for (i=1; i<=10; i++) {
   double **varpl; /* Variances of prevalence limits by age */     if((Ndum[i]!=0) && (i<=ncovcol)){
   double *epj, vepp;       Tvaraff[ij]=i;
   char version[80]="Imach version 0.64, May 2000, INED-EUROREVES ";       ij++;
   char *alph[]={"a","a","b","c","d","e"}, str[4];     }
   char z[1]="c";   }
 #include <sys/time.h>   
 #include <time.h>      cptcoveff=ij-1;
   }
   /* long total_usecs;  
   struct timeval start_time, end_time;  /*********** Health Expectancies ****************/
     
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  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 )
   
   {
   printf("\nIMACH, Version 0.64");    /* Health expectancies */
   printf("\nEnter the parameter file name: ");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
 #define windows 1    double age, agelim, hf;
 #ifdef windows    double ***p3mat,***varhe;
   scanf("%s",pathtot);    double **dnewm,**doldm;
   getcwd(pathcd, size);    double *xp;
   cut(path,optionfile,pathtot);    double **gp, **gm;
   chdir(path);    double ***gradg, ***trgradg;
   replace(pathc,path);    int theta;
 #endif  
 #ifdef unix    varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);
   scanf("%s",optionfile);    xp=vector(1,npar);
 #endif    dnewm=matrix(1,nlstate*2,1,npar);
     doldm=matrix(1,nlstate*2,1,nlstate*2);
 /*-------- arguments in the command line --------*/   
     fprintf(ficreseij,"# Health expectancies\n");
   strcpy(fileres,"r");    fprintf(ficreseij,"# Age");
   strcat(fileres, optionfile);    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
   /*---------arguments file --------*/        fprintf(ficreseij," %1d-%1d (SE)",i,j);
     fprintf(ficreseij,"\n");
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  
     printf("Problem with optionfile %s\n",optionfile);    if(estepm < stepm){
     goto end;      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
     else  hstepm=estepm;  
   strcpy(filereso,"o");    /* We compute the life expectancy from trapezoids spaced every estepm months
   strcat(filereso,fileres);     * This is mainly to measure the difference between two models: for example
   if((ficparo=fopen(filereso,"w"))==NULL) {     * if stepm=24 months pijx are given only every 2 years and by summing them
     printf("Problem with Output resultfile: %s\n", filereso);goto end;     * we are calculating an estimate of the Life Expectancy assuming a linear
   }     * progression inbetween and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we
 /*--------- index.htm --------*/     * 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
   if((fichtm=fopen("index.htm","w"))==NULL)    {     * hypothesis. A more precise result, taking into account a more precise
     printf("Problem with index.htm \n");goto end;     * curvature will be obtained if estepm is as small as stepm. */
   }  
     /* For example we decided to compute the life expectancy with the smallest unit */
  fprintf(fichtm,"<body><ul><li>Outputs files<br><br>\n    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n       nhstepm is the number of hstepm from age to agelim
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>       nstepm is the number of stepm from age to agelin.
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>       Look at hpijx to understand the reason of that which relies in memory size
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>       and note for a fixed period like estepm months */
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>       survival function given by stepm (the optimization length). Unfortunately it
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>       means that if the survival funtion is printed only each two years of age and if
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>       you sum them up and add 1 year (area under the trapezoids) you won't get the same
         - 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);       results. So we changed our mind and took the option of the best precision.
     */
  fprintf(fichtm," <li>Graphs<br> <br>");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */
    
 for(cpt=1; cpt<nlstate;cpt++)    agelim=AGESUP;
    fprintf(fichtm,"- Prevalence of disability: p%s1.gif<br>    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
 <img src=\"p%s1.gif\"><br>",strtok(optionfile, "."),strtok(optionfile, "."),cpt);      /* nhstepm age range expressed in number of stepm */
  for(cpt=1; cpt<=nlstate;cpt++)      nstepm=(int) rint((agelim-age)*YEARM/stepm);
      fprintf(fichtm,"- Observed and stationary  prevalence (with confident      /* Typically if 20 years nstepm = 20*12/6=40 stepm */
 interval) in state (%d): v%s%d.gif <br>      /* if (stepm >= YEARM) hstepm=1;*/
 <img src=\"v%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  for(cpt=1; cpt<=nlstate;cpt++)      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);
      fprintf(fichtm,"- Health life expectancies by age and initial health state (%d): exp%s%d.gif <br>      gp=matrix(0,nhstepm,1,nlstate*2);
 <img src=\"ex%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);      gm=matrix(0,nhstepm,1,nlstate*2);
      
  fprintf(fichtm,"- Total life expectancy by age and      /* Computed by stepm unit matrices, product of hstepm matrices, stored
         health expectancies in states (1) and (2): e%s.gif<br>         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
         <img src=\"e%s.gif\"></li> </ul></body>",strtok(optionfile, "."),strtok(optionfile, "."));      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
    
   
 fclose(fichtm);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
   /* Reads comments: lines beginning with '#' */      /* Computing Variances of health expectancies */
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);       for(theta=1; theta <=npar; theta++){
     fgets(line, MAXLINE, ficpar);        for(i=1; i<=npar; i++){
     puts(line);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     fputs(line,ficparo);        }
   }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   ungetc(c,ficpar);   
         cptj=0;
   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);        for(j=1; j<= nlstate; j++){
   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);          for(i=1; i<=nlstate; i++){
   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);            cptj=cptj+1;
               for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
   nvar=ncov-1; /* Suppressing age as a basic covariate */              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
               }
   /* Read guess parameters */          }
   /* Reads comments: lines beginning with '#' */        }
   while((c=getc(ficpar))=='#' && c!= EOF){       
     ungetc(c,ficpar);       
     fgets(line, MAXLINE, ficpar);        for(i=1; i<=npar; i++)
     puts(line);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     fputs(line,ficparo);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   }       
   ungetc(c,ficpar);        cptj=0;
           for(j=1; j<= nlstate; j++){
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);          for(i=1;i<=nlstate;i++){
     for(i=1; i <=nlstate; i++)            cptj=cptj+1;
     for(j=1; j <=nlstate+ndeath-1; j++){            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
       fscanf(ficpar,"%1d%1d",&i1,&j1);              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
       fprintf(ficparo,"%1d%1d",i1,j1);            }
       printf("%1d%1d",i,j);          }
       for(k=1; k<=ncov;k++){        }
         fscanf(ficpar," %lf",&param[i][j][k]);        for(j=1; j<= nlstate*2; j++)
         printf(" %lf",param[i][j][k]);          for(h=0; h<=nhstepm-1; h++){
         fprintf(ficparo," %lf",param[i][j][k]);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       }          }
       fscanf(ficpar,"\n");       }
       printf("\n");     
       fprintf(ficparo,"\n");  /* End theta */
     }  
          trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);
   npar= (nlstate+ndeath-1)*nlstate*ncov;  
   p=param[1][1];       for(h=0; h<=nhstepm-1; h++)
           for(j=1; j<=nlstate*2;j++)
   /* Reads comments: lines beginning with '#' */          for(theta=1; theta <=npar; theta++)
   while((c=getc(ficpar))=='#' && c!= EOF){            trgradg[h][j][theta]=gradg[h][theta][j];
     ungetc(c,ficpar);       
     fgets(line, MAXLINE, ficpar);  
     puts(line);       for(i=1;i<=nlstate*2;i++)
     fputs(line,ficparo);        for(j=1;j<=nlstate*2;j++)
   }          varhe[i][j][(int)age] =0.;
   ungetc(c,ficpar);  
        printf("%d|",(int)age);fflush(stdout);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);       for(h=0;h<=nhstepm-1;h++){
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        for(k=0;k<=nhstepm-1;k++){
   for(i=1; i <=nlstate; i++){          matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);
     for(j=1; j <=nlstate+ndeath-1; j++){          matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);
       fscanf(ficpar,"%1d%1d",&i1,&j1);          for(i=1;i<=nlstate*2;i++)
       printf("%1d%1d",i,j);            for(j=1;j<=nlstate*2;j++)
       fprintf(ficparo,"%1d%1d",i1,j1);              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
       for(k=1; k<=ncov;k++){        }
         fscanf(ficpar,"%le",&delti3[i][j][k]);      }
         printf(" %le",delti3[i][j][k]);      /* Computing expectancies */
         fprintf(ficparo," %le",delti3[i][j][k]);      for(i=1; i<=nlstate;i++)
       }        for(j=1; j<=nlstate;j++)
       fscanf(ficpar,"\n");          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       printf("\n");            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
       fprintf(ficparo,"\n");           
     }  /* 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]);*/
   }  
   delti=delti3[1][1];          }
     
   /* Reads comments: lines beginning with '#' */      fprintf(ficreseij,"%3.0f",age );
   while((c=getc(ficpar))=='#' && c!= EOF){      cptj=0;
     ungetc(c,ficpar);      for(i=1; i<=nlstate;i++)
     fgets(line, MAXLINE, ficpar);        for(j=1; j<=nlstate;j++){
     puts(line);          cptj++;
     fputs(line,ficparo);          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
   }        }
   ungetc(c,ficpar);      fprintf(ficreseij,"\n");
        
   matcov=matrix(1,npar,1,npar);      free_matrix(gm,0,nhstepm,1,nlstate*2);
   for(i=1; i <=npar; i++){      free_matrix(gp,0,nhstepm,1,nlstate*2);
     fscanf(ficpar,"%s",&str);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);
     printf("%s",str);      free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);
     fprintf(ficparo,"%s",str);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for(j=1; j <=i; j++){    }
       fscanf(ficpar," %le",&matcov[i][j]);    printf("\n");
       printf(" %.5le",matcov[i][j]);  
       fprintf(ficparo," %.5le",matcov[i][j]);    free_vector(xp,1,npar);
     }    free_matrix(dnewm,1,nlstate*2,1,npar);
     fscanf(ficpar,"\n");    free_matrix(doldm,1,nlstate*2,1,nlstate*2);
     printf("\n");    free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);
     fprintf(ficparo,"\n");  }
   }  
   for(i=1; i <=npar; i++)  /************ Variance ******************/
     for(j=i+1;j<=npar;j++)  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, int ij, int estepm)
       matcov[i][j]=matcov[j][i];  {
        /* Variance of health expectancies */
   printf("\n");    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
       double **newm;
       double **dnewm,**doldm;
   if(mle==1){    int i, j, nhstepm, hstepm, h, nstepm ;
     /*-------- data file ----------*/    int k, cptcode;
     if((ficres =fopen(fileres,"w"))==NULL) {    double *xp;
       printf("Problem with resultfile: %s\n", fileres);goto end;    double **gp, **gm;
     }    double ***gradg, ***trgradg;
     fprintf(ficres,"#%s\n",version);    double ***p3mat;
         double age,agelim, hf;
     if((fic=fopen(datafile,"r"))==NULL)    {    int theta;
       printf("Problem with datafile: %s\n", datafile);goto end;  
     }    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");
         fprintf(ficresvij,"# Age");
     n= lastobs;    for(i=1; i<=nlstate;i++)
     severity = vector(1,maxwav);      for(j=1; j<=nlstate;j++)
     outcome=imatrix(1,maxwav+1,1,n);        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
     num=ivector(1,n);    fprintf(ficresvij,"\n");
     moisnais=vector(1,n);  
     annais=vector(1,n);    xp=vector(1,npar);
     moisdc=vector(1,n);    dnewm=matrix(1,nlstate,1,npar);
     andc=vector(1,n);    doldm=matrix(1,nlstate,1,nlstate);
     agedc=vector(1,n);   
     cod=ivector(1,n);    if(estepm < stepm){
     weight=vector(1,n);      printf ("Problem %d lower than %d\n",estepm, stepm);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    }
     mint=matrix(1,maxwav,1,n);    else  hstepm=estepm;  
     anint=matrix(1,maxwav,1,n);    /* For example we decided to compute the life expectancy with the smallest unit */
     covar=matrix(1,NCOVMAX,1,n);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.
     s=imatrix(1,maxwav+1,1,n);       nhstepm is the number of hstepm from age to agelim
     adl=imatrix(1,maxwav+1,1,n);           nstepm is the number of stepm from age to agelin.
     tab=ivector(1,NCOVMAX);       Look at hpijx to understand the reason of that which relies in memory size
     i=1;        and note for a fixed period like k years */
     while (fgets(line, MAXLINE, fic) != NULL)    {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       if ((i >= firstobs) && (i <lastobs)) {       survival function given by stepm (the optimization length). Unfortunately it
 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]);       means that if the survival funtion is printed only each two years of age and if
         i=i+1;       you sum them up and add 1 year (area under the trapezoids) you won't get the same
       }       results. So we changed our mind and took the option of the best precision.
     }     */
   imx=i-1; /* Number of individuals */    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */
     agelim = AGESUP;
     fclose(fic);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */
     if (weightopt != 1) { /* Maximisation without weights*/      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       for(i=1;i<=n;i++) weight[i]=1.0;      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
     /*-calculation of age at interview from date of interview and age at death -*/      gp=matrix(0,nhstepm,1,nlstate);
     agev=matrix(1,maxwav,1,imx);      gm=matrix(0,nhstepm,1,nlstate);
       
     for (i=1; i<=imx; i++)  {      for(theta=1; theta <=npar; theta++){
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        for(i=1; i<=npar; i++){ /* Computes gradient */
       for(m=1; (m<= maxwav); m++){          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         if(s[m][i] >0){        }
           if (s[m][i] == nlstate+1) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             if(agedc[i]>0)        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
               agev[m][i]=agedc[i];  
             else{        if (popbased==1) {
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          for(i=1; i<=nlstate;i++)
               agev[m][i]=-1;            prlim[i][i]=probs[(int)age][i][ij];
             }        }
           }   
           else if(s[m][i] !=9){ /* Should no more exist */        for(j=1; j<= nlstate; j++){
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          for(h=0; h<=nhstepm; h++){
             if(mint[m][i]==99 || anint[m][i]==9999)            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               agev[m][i]=1;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
             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);*/     
             }        for(i=1; i<=npar; i++) /* Computes gradient */
             else if(agev[m][i] >agemax){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
               agemax=agev[m][i];        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
             }   
             /*agev[m][i]=anint[m][i]-annais[i];*/        if (popbased==1) {
             /*   agev[m][i] = age[i]+2*m;*/          for(i=1; i<=nlstate;i++)
           }            prlim[i][i]=probs[(int)age][i][ij];
           else { /* =9 */        }
             agev[m][i]=1;  
             s[m][i]=-1;        for(j=1; j<= nlstate; j++){
           }          for(h=0; h<=nhstepm; h++){
         }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
         else /*= 0 Unknown */              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           agev[m][i]=1;          }
       }        }
       
     }        for(j=1; j<= nlstate; j++)
     for (i=1; i<=imx; i++)  {          for(h=0; h<=nhstepm; h++){
       for(m=1; (m<= maxwav); m++){            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
         if (s[m][i] > (nlstate+ndeath)) {          }
           printf("Error: Wrong value in nlstate or ndeath\n");        } /* End theta */
           goto end;  
         }      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);
       }  
     }      for(h=0; h<=nhstepm; h++)
         for(j=1; j<=nlstate;j++)
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);          for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
     free_vector(severity,1,maxwav);  
     free_imatrix(outcome,1,maxwav+1,1,n);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     free_vector(moisnais,1,n);      for(i=1;i<=nlstate;i++)
     free_vector(annais,1,n);        for(j=1;j<=nlstate;j++)
     free_matrix(mint,1,maxwav,1,n);          vareij[i][j][(int)age] =0.;
     free_matrix(anint,1,maxwav,1,n);  
     free_vector(moisdc,1,n);      for(h=0;h<=nhstepm;h++){
     free_vector(andc,1,n);        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]);
     wav=ivector(1,imx);          for(i=1;i<=nlstate;i++)
     dh=imatrix(1,lastpass-firstpass+1,1,imx);            for(j=1;j<=nlstate;j++)
     mw=imatrix(1,lastpass-firstpass+1,1,imx);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
            }
     /* Concatenates waves */      }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  
           fprintf(ficresvij,"%.0f ",age );
    /* Calculates basic frequencies. Computes observed prevalence at single age      for(i=1; i<=nlstate;i++)
        and prints on file fileres'p'. */        for(j=1; j<=nlstate;j++){
       freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx);           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresvij,"\n");
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_matrix(gp,0,nhstepm,1,nlstate);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_matrix(gm,0,nhstepm,1,nlstate);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     /* For Powell, parameters are in a vector p[] starting at p[1]    } /* End age */
        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) */    free_vector(xp,1,npar);
         free_matrix(doldm,1,nlstate,1,npar);
     mlikeli(ficres,p, npar, ncov, nlstate, ftol, func);    free_matrix(dnewm,1,nlstate,1,nlstate);
   
       }
     /*--------- 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);  /************ 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 ij)
    jk=1;  {
    fprintf(ficres,"# Parameters\n");    /* Variance of prevalence limit */
    printf("# Parameters\n");    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
    for(i=1,jk=1; i <=nlstate; i++){    double **newm;
      for(k=1; k <=(nlstate+ndeath); k++){    double **dnewm,**doldm;
        if (k != i)     int i, j, nhstepm, hstepm;
          {    int k, cptcode;
            printf("%d%d ",i,k);    double *xp;
            fprintf(ficres,"%1d%1d ",i,k);    double *gp, *gm;
            for(j=1; j <=ncov; j++){    double **gradg, **trgradg;
              printf("%f ",p[jk]);    double age,agelim;
              fprintf(ficres,"%f ",p[jk]);    int theta;
              jk++;      
            }    fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");
            printf("\n");    fprintf(ficresvpl,"# Age");
            fprintf(ficres,"\n");    for(i=1; i<=nlstate;i++)
          }        fprintf(ficresvpl," %1d-%1d",i,i);
      }    fprintf(ficresvpl,"\n");
    }  
     xp=vector(1,npar);
     /* Computing hessian and covariance matrix */    dnewm=matrix(1,nlstate,1,npar);
     ftolhess=ftol; /* Usually correct */    doldm=matrix(1,nlstate,1,nlstate);
     hesscov(matcov, p, npar, delti, ftolhess, func);   
     fprintf(ficres,"# Scales\n");    hstepm=1*YEARM; /* Every year of age */
     printf("# Scales\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */
      for(i=1,jk=1; i <=nlstate; i++){    agelim = AGESUP;
       for(j=1; j <=nlstate+ndeath; j++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         if (j!=i) {      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */
           fprintf(ficres,"%1d%1d",i,j);      if (stepm >= YEARM) hstepm=1;
           printf("%1d%1d",i,j);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
           for(k=1; k<=ncov;k++){      gradg=matrix(1,npar,1,nlstate);
             printf(" %.5e",delti[jk]);      gp=vector(1,nlstate);
             fprintf(ficres," %.5e",delti[jk]);      gm=vector(1,nlstate);
             jk++;  
           }      for(theta=1; theta <=npar; theta++){
           printf("\n");        for(i=1; i<=npar; i++){ /* Computes gradient */
           fprintf(ficres,"\n");          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }        }
       }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       }        for(i=1;i<=nlstate;i++)
               gp[i] = prlim[i][i];
     k=1;     
     fprintf(ficres,"# Covariance\n");        for(i=1; i<=npar; i++) /* Computes gradient */
     printf("# Covariance\n");          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     for(i=1;i<=npar;i++){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       /*  if (k>nlstate) k=1;        for(i=1;i<=nlstate;i++)
       i1=(i-1)/(ncov*nlstate)+1;           gm[i] = prlim[i][i];
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);  
       printf("%s%d%d",alph[k],i1,tab[i]);*/        for(i=1;i<=nlstate;i++)
       fprintf(ficres,"%3d",i);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       printf("%3d",i);      } /* End theta */
       for(j=1; j<=i;j++){  
         fprintf(ficres," %.5e",matcov[i][j]);      trgradg =matrix(1,nlstate,1,npar);
         printf(" %.5e",matcov[i][j]);  
       }      for(j=1; j<=nlstate;j++)
       fprintf(ficres,"\n");        for(theta=1; theta <=npar; theta++)
       printf("\n");          trgradg[j][theta]=gradg[theta][j];
       k++;  
     }      for(i=1;i<=nlstate;i++)
             varpl[i][(int)age] =0.;
     while((c=getc(ficpar))=='#' && c!= EOF){      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       ungetc(c,ficpar);      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       fgets(line, MAXLINE, ficpar);      for(i=1;i<=nlstate;i++)
       puts(line);        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
       fputs(line,ficparo);  
     }      fprintf(ficresvpl,"%.0f ",age );
     ungetc(c,ficpar);      for(i=1; i<=nlstate;i++)
           fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      fprintf(ficresvpl,"\n");
           free_vector(gp,1,nlstate);
     if (fage <= 2) {      free_vector(gm,1,nlstate);
       bage = agemin;      free_matrix(gradg,1,npar,1,nlstate);
       fage = agemax;      free_matrix(trgradg,1,nlstate,1,npar);
     }    } /* End age */
   
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    free_vector(xp,1,npar);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    free_matrix(doldm,1,nlstate,1,npar);
 /*------------ gnuplot -------------*/    free_matrix(dnewm,1,nlstate,1,nlstate);
 chdir(pathcd);  
   if((ficgp=fopen("graph.gp","w"))==NULL) {  }
     printf("Problem with file graph.gp");goto end;  
   }  /************ Variance of one-step probabilities  ******************/
 #ifdef windows  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   fprintf(ficgp,"cd \"%s\" \n",pathc);  {
 #endif    int i, j=0,  i1, k1, l1, t, tj;
    /* 1eme*/    int k2, l2, j1,  z1;
     int k=0,l, cptcode;
   for (cpt=1; cpt<= nlstate ; cpt ++) {    int first=1;
 #ifdef windows    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;
     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);    double **dnewm,**doldm;
 #endif    double *xp;
 #ifdef unix    double *gp, *gm;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:%d \"\%%lf",agemin,fage,fileres,cpt*2);    double **gradg, **trgradg;
 #endif    double **mu;
     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");    double age,agelim, cov[NCOVMAX];
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" u 1:($%d+2*$%d) \"\%%lf",fileres,2*cpt,cpt*2+1);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");    int theta;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" u 1:($%d-2*$%d) \"\%%lf",fileres,2*cpt,2*cpt+1);     char fileresprob[FILENAMELENGTH];
      for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");     char fileresprobcov[FILENAMELENGTH];
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" u 1:($%d) t\"Observed prevalence \" w l 2",fileres,2+4*(cpt-1));    char fileresprobcor[FILENAMELENGTH];
 #ifdef unix  
 fprintf(ficgp,"\nset ter gif small size 400,300");    double ***varpij;
 #endif  
 fprintf(ficgp,"\nset out \"v%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);    strcpy(fileresprob,"prob");
      strcat(fileresprob,fileres);
   }    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   /*2 eme*/      printf("Problem with resultfile: %s\n", fileresprob);
      }
   fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    strcpy(fileresprobcov,"probcov");
   for (i=1; i<= nlstate+1 ; i ++) {    strcat(fileresprobcov,fileres);
 k=2*i;    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
     fprintf(ficgp,"\"t%s\" u 1:%d \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k);      printf("Problem with resultfile: %s\n", fileresprobcov);
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");    }
     if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    strcpy(fileresprobcor,"probcor");
     else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    strcat(fileresprobcor,fileres);
     fprintf(ficgp,"\"t%s\" u 1:($%d-2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");      printf("Problem with resultfile: %s\n", fileresprobcor);
     fprintf(ficgp,"\" t\"\" w l 0,");    }
 fprintf(ficgp,"\"t%s\" u 1:($%d+2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
 else fprintf(ficgp,"\" t\"\" w l 0,");   
   }     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   fprintf(ficgp,"\nset out \"e%s.gif\" \nreplot\n\n",strtok(optionfile, "."));    fprintf(ficresprob,"# Age");
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   /*3eme*/    fprintf(ficresprobcov,"# Age");
 for (cpt=1; cpt<= nlstate ; cpt ++) {    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   k=2+nlstate*(cpt-1);    fprintf(ficresprobcov,"# Age");
     fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k,cpt);  
 for (i=1; i< nlstate ; i ++) {  
 fprintf(ficgp,",\"e%s\" u 1:%d t \"e%d%d\" w l",fileres,k+1,cpt,i+1);    for(i=1; i<=nlstate;i++)
 }       for(j=1; j<=(nlstate+ndeath);j++){
 fprintf(ficgp,"\nset out \"ex%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
 }        fprintf(ficresprobcov," p%1d-%1d ",i,j);
          fprintf(ficresprobcor," p%1d-%1d ",i,j);
 /* CV preval stat */      }  
 for (cpt=1; cpt<nlstate ; cpt ++) {    fprintf(ficresprob,"\n");
     k=3;    fprintf(ficresprobcov,"\n");
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u 2:($%d/($%d",agemin,agemax,fileres,k+cpt,k);    fprintf(ficresprobcor,"\n");
     for (i=1; i< nlstate ; i ++)    xp=vector(1,npar);
       fprintf(ficgp,"+$%d",k+i);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
         mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
  l=3+(nlstate+ndeath)*cpt;    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
    fprintf(ficgp,",\"pij%s\" u 2:($%d/($%d",fileres,l+cpt,l);    first=1;
      if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
    for (i=1; i< nlstate ; i ++) {      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
    l=3+(nlstate+ndeath)*cpt;      exit(0);
     fprintf(ficgp,"+$%d",l+i);    }
    }    else{
   fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      fprintf(ficgp,"\n# Routine varprob");
       }
       if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
   fprintf(ficgp,"set out \"p%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);      printf("Problem with html file: %s\n", optionfilehtm);
   }       exit(0);
     }
     else{
   fclose(ficgp);      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");
 chdir(path);      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");
     free_matrix(agev,1,maxwav,1,imx);  
     free_ivector(wav,1,imx);    }
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);  
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
         cov[1]=1;
     free_imatrix(s,1,maxwav+1,1,n);    tj=cptcoveff;
         if (cptcovn<1) {tj=1;ncodemax[1]=1;}
         j1=0;
     free_ivector(num,1,n);    for(t=1; t<=tj;t++){
     free_vector(agedc,1,n);      for(i1=1; i1<=ncodemax[t];i1++){
     free_vector(weight,1,n);        j1++;
     free_matrix(covar,1,NCOVMAX,1,n);       
     fclose(ficparo);        if  (cptcovn>0) {
     fclose(ficres);          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#");
   /*________fin mle=1_________*/          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#");
          
   /* No more information from the sample is required now */          fprintf(ficgp, "\n#********** Variable ");
   /* Reads comments: lines beginning with '#' */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   while((c=getc(ficpar))=='#' && c!= EOF){          fprintf(ficgp, "**********\n#");
     ungetc(c,ficpar);         
     fgets(line, MAXLINE, ficpar);         
     puts(line);          fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable ");
     fputs(line,ficparo);          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\">");
   ungetc(c,ficpar);         
             fprintf(ficresprobcor, "\n#********** Variable ");    
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);          fprintf(ficgp, "**********\n#");    
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        }
        
   /*--------------- Prevalence limit --------------*/        for (age=bage; age<=fage; age ++){
             cov[2]=age;
   strcpy(filerespl,"pl");          for (k=1; k<=cptcovn;k++) {
   strcat(filerespl,fileres);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   if((ficrespl=fopen(filerespl,"w"))==NULL) {          }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   }          for (k=1; k<=cptcovprod;k++)
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   fprintf(ficrespl,"#Prevalence limit\n");         
   fprintf(ficrespl,"#Age ");          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   fprintf(ficrespl,"\n");          gp=vector(1,(nlstate)*(nlstate+ndeath));
             gm=vector(1,(nlstate)*(nlstate+ndeath));
   prlim=matrix(1,nlstate,1,nlstate);     
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(theta=1; theta <=npar; theta++){
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for(i=1; i<=npar; i++)
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              xp[i] = x[i] + (i==theta ?delti[theta]:0);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            pmij(pmmij,cov,ncovmodel,xp,nlstate);
              
   agebase=agemin;            k=0;
   agelim=agemax;            for(i=1; i<= (nlstate); i++){
   ftolpl=1.e-10;              for(j=1; j<=(nlstate+ndeath);j++){
   for (age=agebase; age<=agelim; age++){                k=k+1;
     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);                gp[k]=pmmij[i][j];
     fprintf(ficrespl,"%.0f",age );              }
     for(i=1; i<=nlstate;i++)            }
       fprintf(ficrespl," %.5f", prlim[i][i]);           
     fprintf(ficrespl,"\n");            for(i=1; i<=npar; i++)
   }              xp[i] = x[i] - (i==theta ?delti[theta]:0);
   fclose(ficrespl);     
               pmij(pmmij,cov,ncovmodel,xp,nlstate);
   /*------------- h Pij x at various ages ------------*/            k=0;
               for(i=1; i<=(nlstate); i++){
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);              for(j=1; j<=(nlstate+ndeath);j++){
   if((ficrespij=fopen(filerespij,"w"))==NULL) {                k=k+1;
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;                gm[k]=pmmij[i][j];
   }              }
   printf("Computing pij: result on file '%s' \n", filerespij);            }
   stepsize=(int) (stepm+YEARM-1)/YEARM;       
   if (stepm<=24) stepsize=2;            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)
               gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];  
   agelim=AGESUP;          }
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */            for(theta=1; theta <=npar; theta++)
     nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */               trgradg[j][theta]=gradg[theta][j];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */         
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);
     oldm=oldms;savm=savms;          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
     hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm);           
     fprintf(ficrespij,"# Age");          pmij(pmmij,cov,ncovmodel,x,nlstate);
     for(i=1; i<=nlstate;i++)         
       for(j=1; j<=nlstate+ndeath;j++)          k=0;
         fprintf(ficrespij," %1d-%1d",i,j);          for(i=1; i<=(nlstate); i++){
     fprintf(ficrespij,"\n");            for(j=1; j<=(nlstate+ndeath);j++){
     for (h=0; h<=nhstepm; h++){              k=k+1;
       fprintf(ficrespij,"%.0f %.0f",agedeb, agedeb+ h*hstepm/YEARM*stepm );              mu[k][(int) age]=pmmij[i][j];
       for(i=1; i<=nlstate;i++)            }
         for(j=1; j<=nlstate+ndeath;j++)          }
           fprintf(ficrespij," %.5f", p3mat[i][j][h]);          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
       fprintf(ficrespij,"\n");            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
     }              varpij[i][j][(int)age] = doldm[i][j];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
     fprintf(ficrespij,"\n");          /*printf("\n%d ",(int)age);
   }       for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   fclose(ficrespij);         printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
        }*/
   /*---------- Health expectancies and variances ------------*/  
             fprintf(ficresprob,"\n%d ",(int)age);
   eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          fprintf(ficresprobcov,"\n%d ",(int)age);
   oldm=oldms;savm=savms;          fprintf(ficresprobcor,"\n%d ",(int)age);
   evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm);  
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
   vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
   oldm=oldms;savm=savms;          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   strcpy(filerest,"t");          }
   strcat(filerest,fileres);          i=0;
   if((ficrest=fopen(filerest,"w"))==NULL) {          for (k=1; k<=(nlstate);k++){
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;            for (l=1; l<=(nlstate+ndeath);l++){
   }              i=i++;
   printf("Computing Total LEs with variances: file '%s' \n", filerest);              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
   fprintf(ficrest,"#Total LEs with variances: e.. (std) ");              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
   for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);              for (j=1; j<=i;j++){
   fprintf(ficrest,"\n");                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]));
   hf=1;              }
   if (stepm >= YEARM) hf=stepm/YEARM;            }
   epj=vector(1,nlstate+1);          }/* end of loop for state */
   for(age=bage; age <=fage ;age++){        } /* end of loop for age */
     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);          /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
     fprintf(ficrest," %.0f",age);        for (k1=1; k1<=(nlstate);k1++){
     for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){          for (l1=1; l1<=(nlstate+ndeath);l1++){
       for(i=1, epj[j]=0.;i <=nlstate;i++) {            if(l1==k1) continue;
         epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];            i=(k1-1)*(nlstate+ndeath)+l1;
       }            for (k2=1; k2<=(nlstate);k2++){
       epj[nlstate+1] +=epj[j];              for (l2=1; l2<=(nlstate+ndeath);l2++){
     }                if(l2==k2) continue;
     for(i=1, vepp=0.;i <=nlstate;i++)                j=(k2-1)*(nlstate+ndeath)+l2;
       for(j=1;j <=nlstate;j++)                if(j<=i) continue;
         vepp += vareij[i][j][(int)age];                for (age=bage; age<=fage; age ++){
     fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));                  if ((int)age %5==0){
     for(j=1;j <=nlstate;j++){                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
       fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
     }                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
     fprintf(ficrest,"\n");                    mu1=mu[i][(int) age]/stepm*YEARM ;
   }                    mu2=mu[j][(int) age]/stepm*YEARM;
   fclose(ficrest);                    /* Computing eigen value of matrix of covariance */
   fclose(ficpar);                    lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));
   free_vector(epj,1,nlstate+1);                    lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));
                     printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);
   /*------- Variance limit prevalence------*/                       /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
   varpl=matrix(1,nlstate,(int) bage, (int) fage);                    v21=sqrt(1.-v11*v11);
   oldm=oldms;savm=savms;                    v12=-v21;
   varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);                    v22=v11;
                       /*printf(fignu*/
                       /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);                    /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */
                       if(first==1){
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                      first=0;
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);                      fprintf(ficgp,"\nset parametric;set nolabel");
                         fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1);
                         fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);                      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>, ",k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);                      fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k2,l2,k1,l1);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);                      fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k2,l2,k1,l1);
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);
                         fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);
   free_matrix(matcov,1,npar,1,npar);                      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)) t \"%d\"",\
   free_vector(delti,1,npar);                              mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \
                                 mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncov);                    }else{
                       first=0;
   printf("End of Imach\n");                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);
                         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)) t \"%d\"",\
   /* 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);*/                              mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \
   /*printf("Total time was %d uSec.\n", total_usecs);*/                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);
   /*------ End -----------*/                    }/* if first */
                   } /* age mod 5 */
  end:                } /* end loop age */
 #ifdef windows                fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k2,l2,k1,l1);
  chdir(pathcd);                first=1;
 #endif               } /*l12 */
  system("gnuplot graph.gp");            } /* k12 */
           } /*l1 */
 #ifdef windows        }/* k1 */
   while (z[0] != 'q') {      } /* loop covariates */
     chdir(pathcd);       free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     printf("\nType e to edit output files, c to start again, and q for exiting: ");      free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
     scanf("%s",z);      free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
     if (z[0] == 'c') system("./imach");      free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     else if (z[0] == 'e') {      free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
       chdir(path);      free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
       system("index.htm");    }
     }    free_vector(xp,1,npar);
     else if (z[0] == 'q') exit(0);    fclose(ficresprob);
   }    fclose(ficresprobcov);
 #endif     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(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<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," <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,"<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);  
        }
        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);
      }
    }
   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);
     }
   
   #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;
              }
            }
          }
        }
      }
      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);
     }
     printf("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);
     }
     printf("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);
       }
       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[20];
     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 --------*/
   
     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);
       goto end;
     }
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) {
       printf("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\nmodel=%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);
         printf("%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar," %lf",&param[i][j][k]);
           printf(" %lf",param[i][j][k]);
           fprintf(ficparo," %lf",param[i][j][k]);
         }
         fscanf(ficpar,"\n");
         printf("\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);
       printf("%s",str);
       fprintf(ficparo,"%s",str);
       for(j=1; j <=i; j++){
         fscanf(ficpar," %le",&matcov[i][j]);
         printf(" %.5le",matcov[i][j]);
         fprintf(ficparo," %.5le",matcov[i][j]);
       }
       fscanf(ficpar,"\n");
       printf("\n");
       fprintf(ficparo,"\n");
     }
     for(i=1; i <=npar; i++)
       for(j=i+1;j<=npar;j++)
         matcov[i][j]=matcov[j][i];
      
     printf("\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(ficres,"#%s\n",version);
      
       /*-------- data file ----------*/
       if((fic=fopen(datafile,"r"))==NULL)    {
         printf("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);
     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);
         goto end;
       }
      
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+');
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {
           cutv(strd,strc,strb,'*');
           if (strcmp(strc,"age")==0) {
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) {
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {
             cutv(strb,stre,strc,'V');
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V');
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc);
             Tvard[k1][2]=atoi(stre);
             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 {
           /*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);*/
       }
   }
    
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("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);
                 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: Wrong value in nlstate or ndeath\n");  
             goto end;
           }
         }
       }
   
   printf("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");
      for(i=1,jk=1; i <=nlstate; i++){
        for(k=1; k <=(nlstate+ndeath); k++){
          if (k != i)
            {
              printf("%d%d ",i,k);
              fprintf(ficres,"%1d%1d ",i,k);
              for(j=1; j <=ncovmodel; j++){
                printf("%f ",p[jk]);
                fprintf(ficres,"%f ",p[jk]);
                jk++;
              }
              printf("\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");
        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);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\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");
       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");
       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);
         printf("%3d",i);
         for(j=1; j<=i;j++){
           fprintf(ficres," %.5e",matcov[i][j]);
           printf(" %.5e",matcov[i][j]);
         }
         fprintf(ficres,"\n");
         printf("\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
    - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,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;
     }
     printf("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#******");
           for(j=1;j<=cptcoveff;j++)
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespl,"******\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;
     }
     printf("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);
     }
    
   
     /*---------- 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;
     }
     printf("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);
     }
     printf("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);
     }
     printf("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(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);
      
   
    
         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);
     else   printf("End of Imach\n");
     /*  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.1.1.1.1  
changed lines
  Added in v.1.49


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