Diff for /imach/src/imach.c between versions 1.6 and 1.68

version 1.6, 2001/05/02 17:47:10 version 1.68, 2003/02/04 12:40:59
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 Likelihood 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, quarter,
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    semester or year) is modelled 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 stable prevalence. 
   **********************************************************************/    
      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 windows  #include <math.h>
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */  #include <stdio.h>
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  #include <stdlib.h>
   #include <unistd.h>
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  #define MAXLINE 256
   #define GNUPLOTPROGRAM "gnuplot"
 #define NINTERVMAX 8  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  #define FILENAMELENGTH 80
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  /*#define DEBUG*/
 #define NCOVMAX 8 /* Maximum number of covariates */  #define windows
 #define MAXN 20000  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 #define YEARM 12. /* Number of months per year */  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 #define AGESUP 130  
 #define AGEBASE 40  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   
 int nvar;  #define NINTERVMAX 8
 static int cptcov;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 int cptcovn, cptcovage=0;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 int npar=NPARMAX;  #define NCOVMAX 8 /* Maximum number of covariates */
 int nlstate=2; /* Number of live states */  #define MAXN 20000
 int ndeath=1; /* Number of dead states */  #define YEARM 12. /* Number of months per year */
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  #define AGESUP 130
   #define AGEBASE 40
 int *wav; /* Number of waves for this individuual 0 is possible */  #ifdef windows
 int maxwav; /* Maxim number of waves */  #define DIRSEPARATOR '\\'
 int mle, weightopt;  #define ODIRSEPARATOR '/'
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  #else
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  #define DIRSEPARATOR '/'
 double **oldm, **newm, **savm; /* Working pointers to matrices */  #define ODIRSEPARATOR '\\'
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  #endif
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;  
 FILE *ficgp, *fichtm;  char version[80]="Imach version 0.91, November 2002, INED-EUROREVES ";
 FILE *ficreseij;  int erreur; /* Error number */
   char filerese[FILENAMELENGTH];  int nvar;
  FILE  *ficresvij;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   char fileresv[FILENAMELENGTH];  int npar=NPARMAX;
  FILE  *ficresvpl;  int nlstate=2; /* Number of live states */
   char fileresvpl[FILENAMELENGTH];  int ndeath=1; /* Number of dead states */
   int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #define NR_END 1  int popbased=0;
 #define FREE_ARG char*  
 #define FTOL 1.0e-10  int *wav; /* Number of waves for this individuual 0 is possible */
   int maxwav; /* Maxim number of waves */
 #define NRANSI  int jmin, jmax; /* min, max spacing between 2 waves */
 #define ITMAX 200  int mle, weightopt;
   int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 #define TOL 2.0e-4  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
 #define CGOLD 0.3819660             * wave mi and wave mi+1 is not an exact multiple of stepm. */
 #define ZEPS 1.0e-10  double jmean; /* Mean space between 2 waves */
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 #define GOLD 1.618034  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 #define GLIMIT 100.0  FILE *ficlog;
 #define TINY 1.0e-20  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   FILE *ficresprobmorprev;
 static double maxarg1,maxarg2;  FILE *fichtm; /* Html File */
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  FILE *ficreseij;
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  char filerese[FILENAMELENGTH];
    FILE  *ficresvij;
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  char fileresv[FILENAMELENGTH];
 #define rint(a) floor(a+0.5)  FILE  *ficresvpl;
   char fileresvpl[FILENAMELENGTH];
 static double sqrarg;  char title[MAXLINE];
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   
 int imx;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 int stepm;  char filelog[FILENAMELENGTH]; /* Log file */
 /* Stepm, step in month: minimum step interpolation*/  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 int m,nb;  char popfile[FILENAMELENGTH];
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
 double **pmmij;  
   #define NR_END 1
 double *weight;  #define FREE_ARG char*
 int **s; /* Status */  #define FTOL 1.0e-10
 double *agedc, **covar, idx;  
 int **nbcode, *Tcode, *Tvar, **codtab;  #define NRANSI 
   #define ITMAX 200 
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */  #define TOL 2.0e-4 
   
   #define CGOLD 0.3819660 
 static  int split( char *path, char *dirc, char *name )  #define ZEPS 1.0e-10 
 {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */  #define GOLD 1.618034 
   #define GLIMIT 100.0 
    l1 = strlen( path );                 /* length of path */  #define TINY 1.0e-20 
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  
    s = strrchr( path, '\\' );           /* find last / */  static double maxarg1,maxarg2;
    if ( s == NULL ) {                   /* no directory, so use current */  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 #if     defined(__bsd__)                /* get current working directory */  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
       extern char       *getwd( );    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
       if ( getwd( dirc ) == NULL ) {  #define rint(a) floor(a+0.5)
 #else  
       extern char       *getcwd( );  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 #endif  
          return( GLOCK_ERROR_GETCWD );  int imx; 
       }  int stepm;
       strcpy( name, path );             /* we've got it */  /* Stepm, step in month: minimum step interpolation*/
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */  int estepm;
       l2 = strlen( s );                 /* length of filename */  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );  
       strcpy( name, s );                /* save file name */  int m,nb;
       strncpy( dirc, path, l1 - l2 );   /* now the directory */  int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
       dirc[l1-l2] = 0;                  /* add zero */  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
    }  double **pmmij, ***probs;
    l1 = strlen( dirc );                 /* length of directory */  double dateintmean=0;
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
    return( 0 );                         /* we're done */  double *weight;
 }  int **s; /* Status */
   double *agedc, **covar, idx;
   int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 /******************************************/  
   double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 void replace(char *s, char*t)  double ftolhess; /* Tolerance for computing hessian */
 {  
   int i;  /**************** split *************************/
   int lg=20;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   i=0;  {
   lg=strlen(t);    char  *ss;                            /* pointer */
   for(i=0; i<= lg; i++) {    int   l1, l2;                         /* length counters */
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    l1 = strlen(path );                   /* length of path */
   }    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 }    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     if ( ss == NULL ) {                   /* no directory, so use current */
 int nbocc(char *s, char occ)      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
 {        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   int i,j=0;  #if     defined(__bsd__)                /* get current working directory */
   int lg=20;      extern char *getwd( );
   i=0;  
   lg=strlen(s);      if ( getwd( dirc ) == NULL ) {
   for(i=0; i<= lg; i++) {  #else
   if  (s[i] == occ ) j++;      extern char *getcwd( );
   }  
   return j;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 }  #endif
         return( GLOCK_ERROR_GETCWD );
 void cutv(char *u,char *v, char*t, char occ)      }
 {      strcpy( name, path );               /* we've got it */
   int i,lg,j,p=0;    } else {                              /* strip direcotry from path */
   i=0;      ss++;                               /* after this, the filename */
   for(j=0; j<=strlen(t)-1; j++) {      l2 = strlen( ss );                  /* length of filename */
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   }      strcpy( name, ss );         /* save file name */
       strncpy( dirc, path, l1 - l2 );     /* now the directory */
   lg=strlen(t);      dirc[l1-l2] = 0;                    /* add zero */
   for(j=0; j<p; j++) {    }
     (u[j] = t[j]);    l1 = strlen( dirc );                  /* length of directory */
   }  #ifdef windows
      u[p]='\0';    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   #else
    for(j=0; j<= lg; j++) {    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
     if (j>=(p+1))(v[j-p-1] = t[j]);  #endif
   }    ss = strrchr( name, '.' );            /* find last / */
 }    ss++;
     strcpy(ext,ss);                       /* save extension */
 /********************** nrerror ********************/    l1= strlen( name);
     l2= strlen(ss)+1;
 void nrerror(char error_text[])    strncpy( finame, name, l1-l2);
 {    finame[l1-l2]= 0;
   fprintf(stderr,"ERREUR ...\n");    return( 0 );                          /* we're done */
   fprintf(stderr,"%s\n",error_text);  }
   exit(1);  
 }  
 /*********************** vector *******************/  /******************************************/
 double *vector(int nl, int nh)  
 {  void replace(char *s, char*t)
   double *v;  {
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    int i;
   if (!v) nrerror("allocation failure in vector");    int lg=20;
   return v-nl+NR_END;    i=0;
 }    lg=strlen(t);
     for(i=0; i<= lg; i++) {
 /************************ free vector ******************/      (s[i] = t[i]);
 void free_vector(double*v, int nl, int nh)      if (t[i]== '\\') s[i]='/';
 {    }
   free((FREE_ARG)(v+nl-NR_END));  }
 }  
   int nbocc(char *s, char occ)
 /************************ivector *******************************/  {
 int *ivector(long nl,long nh)    int i,j=0;
 {    int lg=20;
   int *v;    i=0;
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    lg=strlen(s);
   if (!v) nrerror("allocation failure in ivector");    for(i=0; i<= lg; i++) {
   return v-nl+NR_END;    if  (s[i] == occ ) j++;
 }    }
     return j;
 /******************free ivector **************************/  }
 void free_ivector(int *v, long nl, long nh)  
 {  void cutv(char *u,char *v, char*t, char occ)
   free((FREE_ARG)(v+nl-NR_END));  {
 }    /* cuts string t into u and v where u is ended by char occ excluding it
        and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
 /******************* imatrix *******************************/       gives u="abcedf" and v="ghi2j" */
 int **imatrix(long nrl, long nrh, long ncl, long nch)    int i,lg,j,p=0;
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    i=0;
 {    for(j=0; j<=strlen(t)-1; j++) {
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   int **m;    }
    
   /* allocate pointers to rows */    lg=strlen(t);
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    for(j=0; j<p; j++) {
   if (!m) nrerror("allocation failure 1 in matrix()");      (u[j] = t[j]);
   m += NR_END;    }
   m -= nrl;       u[p]='\0';
    
       for(j=0; j<= lg; j++) {
   /* allocate rows and set pointers to them */      if (j>=(p+1))(v[j-p-1] = t[j]);
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    }
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  }
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /********************** nrerror ********************/
    
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  void nrerror(char error_text[])
    {
   /* return pointer to array of pointers to rows */    fprintf(stderr,"ERREUR ...\n");
   return m;    fprintf(stderr,"%s\n",error_text);
 }    exit(EXIT_FAILURE);
   }
 /****************** free_imatrix *************************/  /*********************** vector *******************/
 void free_imatrix(m,nrl,nrh,ncl,nch)  double *vector(int nl, int nh)
       int **m;  {
       long nch,ncl,nrh,nrl;    double *v;
      /* free an int matrix allocated by imatrix() */    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 {    if (!v) nrerror("allocation failure in vector");
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    return v-nl+NR_END;
   free((FREE_ARG) (m+nrl-NR_END));  }
 }  
   /************************ free vector ******************/
 /******************* matrix *******************************/  void free_vector(double*v, int nl, int nh)
 double **matrix(long nrl, long nrh, long ncl, long nch)  {
 {    free((FREE_ARG)(v+nl-NR_END));
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  }
   double **m;  
   /************************ivector *******************************/
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  int *ivector(long nl,long nh)
   if (!m) nrerror("allocation failure 1 in matrix()");  {
   m += NR_END;    int *v;
   m -= nrl;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    return v-nl+NR_END;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  }
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /******************free ivector **************************/
   void free_ivector(int *v, long nl, long nh)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  {
   return m;    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************************free matrix ************************/  /******************* imatrix *******************************/
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  int **imatrix(long nrl, long nrh, long ncl, long nch) 
 {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  { 
   free((FREE_ARG)(m+nrl-NR_END));    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
 }    int **m; 
     
 /******************* ma3x *******************************/    /* allocate pointers to rows */ 
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
 {    if (!m) nrerror("allocation failure 1 in matrix()"); 
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    m += NR_END; 
   double ***m;    m -= nrl; 
     
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    
   if (!m) nrerror("allocation failure 1 in matrix()");    /* allocate rows and set pointers to them */ 
   m += NR_END;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   m -= nrl;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     m[nrl] += NR_END; 
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    m[nrl] -= ncl; 
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    
   m[nrl] += NR_END;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   m[nrl] -= ncl;    
     /* return pointer to array of pointers to rows */ 
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    return m; 
   } 
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  /****************** free_imatrix *************************/
   m[nrl][ncl] += NR_END;  void free_imatrix(m,nrl,nrh,ncl,nch)
   m[nrl][ncl] -= nll;        int **m;
   for (j=ncl+1; j<=nch; j++)        long nch,ncl,nrh,nrl; 
     m[nrl][j]=m[nrl][j-1]+nlay;       /* free an int matrix allocated by imatrix() */ 
    { 
   for (i=nrl+1; i<=nrh; i++) {    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    free((FREE_ARG) (m+nrl-NR_END)); 
     for (j=ncl+1; j<=nch; j++)  } 
       m[i][j]=m[i][j-1]+nlay;  
   }  /******************* matrix *******************************/
   return m;  double **matrix(long nrl, long nrh, long ncl, long nch)
 }  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
 /*************************free ma3x ************************/    double **m;
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  
 {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    if (!m) nrerror("allocation failure 1 in matrix()");
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    m += NR_END;
   free((FREE_ARG)(m+nrl-NR_END));    m -= nrl;
 }  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 /***************** f1dim *************************/    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 extern int ncom;    m[nrl] += NR_END;
 extern double *pcom,*xicom;    m[nrl] -= ncl;
 extern double (*nrfunc)(double []);  
      for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 double f1dim(double x)    return m;
 {  }
   int j;  
   double f;  /*************************free matrix ************************/
   double *xt;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
    {
   xt=vector(1,ncom);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    free((FREE_ARG)(m+nrl-NR_END));
   f=(*nrfunc)(xt);  }
   free_vector(xt,1,ncom);  
   return f;  /******************* ma3x *******************************/
 }  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   {
 /*****************brent *************************/    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    double ***m;
 {  
   int iter;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double a,b,d,etemp;    if (!m) nrerror("allocation failure 1 in matrix()");
   double fu,fv,fw,fx;    m += NR_END;
   double ftemp;    m -= nrl;
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
      if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   a=(ax < cx ? ax : cx);    m[nrl] += NR_END;
   b=(ax > cx ? ax : cx);    m[nrl] -= ncl;
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    m[nrl][ncl] += NR_END;
     printf(".");fflush(stdout);    m[nrl][ncl] -= nll;
 #ifdef DEBUG    for (j=ncl+1; j<=nch; j++) 
     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);      m[nrl][j]=m[nrl][j-1]+nlay;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    
 #endif    for (i=nrl+1; i<=nrh; i++) {
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       *xmin=x;      for (j=ncl+1; j<=nch; j++) 
       return fx;        m[i][j]=m[i][j-1]+nlay;
     }    }
     ftemp=fu;    return m;
     if (fabs(e) > tol1) {  }
       r=(x-w)*(fx-fv);  
       q=(x-v)*(fx-fw);  /*************************free ma3x ************************/
       p=(x-v)*q-(x-w)*r;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       q=2.0*(q-r);  {
       if (q > 0.0) p = -p;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
       q=fabs(q);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       etemp=e;    free((FREE_ARG)(m+nrl-NR_END));
       e=d;  }
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  /***************** f1dim *************************/
       else {  extern int ncom; 
         d=p/q;  extern double *pcom,*xicom;
         u=x+d;  extern double (*nrfunc)(double []); 
         if (u-a < tol2 || b-u < tol2)   
           d=SIGN(tol1,xm-x);  double f1dim(double x) 
       }  { 
     } else {    int j; 
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    double f;
     }    double *xt; 
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));   
     fu=(*f)(u);    xt=vector(1,ncom); 
     if (fu <= fx) {    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       if (u >= x) a=x; else b=x;    f=(*nrfunc)(xt); 
       SHFT(v,w,x,u)    free_vector(xt,1,ncom); 
         SHFT(fv,fw,fx,fu)    return f; 
         } else {  } 
           if (u < x) a=u; else b=u;  
           if (fu <= fw || w == x) {  /*****************brent *************************/
             v=w;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
             w=u;  { 
             fv=fw;    int iter; 
             fw=fu;    double a,b,d,etemp;
           } else if (fu <= fv || v == x || v == w) {    double fu,fv,fw,fx;
             v=u;    double ftemp;
             fv=fu;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
           }    double e=0.0; 
         }   
   }    a=(ax < cx ? ax : cx); 
   nrerror("Too many iterations in brent");    b=(ax > cx ? ax : cx); 
   *xmin=x;    x=w=v=bx; 
   return fx;    fw=fv=fx=(*f)(x); 
 }    for (iter=1;iter<=ITMAX;iter++) { 
       xm=0.5*(a+b); 
 /****************** mnbrak ***********************/      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,      printf(".");fflush(stdout);
             double (*func)(double))      fprintf(ficlog,".");fflush(ficlog);
 {  #ifdef DEBUG
   double ulim,u,r,q, dum;      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 fu;      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
        /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   *fa=(*func)(*ax);  #endif
   *fb=(*func)(*bx);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   if (*fb > *fa) {        *xmin=x; 
     SHFT(dum,*ax,*bx,dum)        return fx; 
       SHFT(dum,*fb,*fa,dum)      } 
       }      ftemp=fu;
   *cx=(*bx)+GOLD*(*bx-*ax);      if (fabs(e) > tol1) { 
   *fc=(*func)(*cx);        r=(x-w)*(fx-fv); 
   while (*fb > *fc) {        q=(x-v)*(fx-fw); 
     r=(*bx-*ax)*(*fb-*fc);        p=(x-v)*q-(x-w)*r; 
     q=(*bx-*cx)*(*fb-*fa);        q=2.0*(q-r); 
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/        if (q > 0.0) p = -p; 
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));        q=fabs(q); 
     ulim=(*bx)+GLIMIT*(*cx-*bx);        etemp=e; 
     if ((*bx-u)*(u-*cx) > 0.0) {        e=d; 
       fu=(*func)(u);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     } else if ((*cx-u)*(u-ulim) > 0.0) {          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       fu=(*func)(u);        else { 
       if (fu < *fc) {          d=p/q; 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))          u=x+d; 
           SHFT(*fb,*fc,fu,(*func)(u))          if (u-a < tol2 || b-u < tol2) 
           }            d=SIGN(tol1,xm-x); 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {        } 
       u=ulim;      } else { 
       fu=(*func)(u);        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     } else {      } 
       u=(*cx)+GOLD*(*cx-*bx);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*func)(u);      fu=(*f)(u); 
     }      if (fu <= fx) { 
     SHFT(*ax,*bx,*cx,u)        if (u >= x) a=x; else b=x; 
       SHFT(*fa,*fb,*fc,fu)        SHFT(v,w,x,u) 
       }          SHFT(fv,fw,fx,fu) 
 }          } else { 
             if (u < x) a=u; else b=u; 
 /*************** linmin ************************/            if (fu <= fw || w == x) { 
               v=w; 
 int ncom;              w=u; 
 double *pcom,*xicom;              fv=fw; 
 double (*nrfunc)(double []);              fw=fu; 
              } else if (fu <= fv || v == x || v == w) { 
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))              v=u; 
 {              fv=fu; 
   double brent(double ax, double bx, double cx,            } 
                double (*f)(double), double tol, double *xmin);          } 
   double f1dim(double x);    } 
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    nrerror("Too many iterations in brent"); 
               double *fc, double (*func)(double));    *xmin=x; 
   int j;    return fx; 
   double xx,xmin,bx,ax;  } 
   double fx,fb,fa;  
    /****************** mnbrak ***********************/
   ncom=n;  
   pcom=vector(1,n);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   xicom=vector(1,n);              double (*func)(double)) 
   nrfunc=func;  { 
   for (j=1;j<=n;j++) {    double ulim,u,r,q, dum;
     pcom[j]=p[j];    double fu; 
     xicom[j]=xi[j];   
   }    *fa=(*func)(*ax); 
   ax=0.0;    *fb=(*func)(*bx); 
   xx=1.0;    if (*fb > *fa) { 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);      SHFT(dum,*ax,*bx,dum) 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);        SHFT(dum,*fb,*fa,dum) 
 #ifdef DEBUG        } 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    *cx=(*bx)+GOLD*(*bx-*ax); 
 #endif    *fc=(*func)(*cx); 
   for (j=1;j<=n;j++) {    while (*fb > *fc) { 
     xi[j] *= xmin;      r=(*bx-*ax)*(*fb-*fc); 
     p[j] += xi[j];      q=(*bx-*cx)*(*fb-*fa); 
   }      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   free_vector(xicom,1,n);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   free_vector(pcom,1,n);      ulim=(*bx)+GLIMIT*(*cx-*bx); 
 }      if ((*bx-u)*(u-*cx) > 0.0) { 
         fu=(*func)(u); 
 /*************** powell ************************/      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,        fu=(*func)(u); 
             double (*func)(double []))        if (fu < *fc) { 
 {          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   void linmin(double p[], double xi[], int n, double *fret,            SHFT(*fb,*fc,fu,(*func)(u)) 
               double (*func)(double []));            } 
   int i,ibig,j;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   double del,t,*pt,*ptt,*xit;        u=ulim; 
   double fp,fptt;        fu=(*func)(u); 
   double *xits;      } else { 
   pt=vector(1,n);        u=(*cx)+GOLD*(*cx-*bx); 
   ptt=vector(1,n);        fu=(*func)(u); 
   xit=vector(1,n);      } 
   xits=vector(1,n);      SHFT(*ax,*bx,*cx,u) 
   *fret=(*func)(p);        SHFT(*fa,*fb,*fc,fu) 
   for (j=1;j<=n;j++) pt[j]=p[j];        } 
   for (*iter=1;;++(*iter)) {  } 
     fp=(*fret);  
     ibig=0;  /*************** linmin ************************/
     del=0.0;  
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  int ncom; 
     for (i=1;i<=n;i++)  double *pcom,*xicom;
       printf(" %d %.12f",i, p[i]);  double (*nrfunc)(double []); 
     printf("\n");   
     for (i=1;i<=n;i++) {  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  { 
       fptt=(*fret);    double brent(double ax, double bx, double cx, 
 #ifdef DEBUG                 double (*f)(double), double tol, double *xmin); 
       printf("fret=%lf \n",*fret);    double f1dim(double x); 
 #endif    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       printf("%d",i);fflush(stdout);                double *fc, double (*func)(double)); 
       linmin(p,xit,n,fret,func);    int j; 
       if (fabs(fptt-(*fret)) > del) {    double xx,xmin,bx,ax; 
         del=fabs(fptt-(*fret));    double fx,fb,fa;
         ibig=i;   
       }    ncom=n; 
 #ifdef DEBUG    pcom=vector(1,n); 
       printf("%d %.12e",i,(*fret));    xicom=vector(1,n); 
       for (j=1;j<=n;j++) {    nrfunc=func; 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    for (j=1;j<=n;j++) { 
         printf(" x(%d)=%.12e",j,xit[j]);      pcom[j]=p[j]; 
       }      xicom[j]=xi[j]; 
       for(j=1;j<=n;j++)    } 
         printf(" p=%.12e",p[j]);    ax=0.0; 
       printf("\n");    xx=1.0; 
 #endif    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     }    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  #ifdef DEBUG
 #ifdef DEBUG    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       int k[2],l;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       k[0]=1;  #endif
       k[1]=-1;    for (j=1;j<=n;j++) { 
       printf("Max: %.12e",(*func)(p));      xi[j] *= xmin; 
       for (j=1;j<=n;j++)      p[j] += xi[j]; 
         printf(" %.12e",p[j]);    } 
       printf("\n");    free_vector(xicom,1,n); 
       for(l=0;l<=1;l++) {    free_vector(pcom,1,n); 
         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]);  /*************** powell ************************/
         }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));              double (*func)(double [])) 
       }  { 
 #endif    void linmin(double p[], double xi[], int n, double *fret, 
                 double (*func)(double [])); 
     int i,ibig,j; 
       free_vector(xit,1,n);    double del,t,*pt,*ptt,*xit;
       free_vector(xits,1,n);    double fp,fptt;
       free_vector(ptt,1,n);    double *xits;
       free_vector(pt,1,n);    pt=vector(1,n); 
       return;    ptt=vector(1,n); 
     }    xit=vector(1,n); 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    xits=vector(1,n); 
     for (j=1;j<=n;j++) {    *fret=(*func)(p); 
       ptt[j]=2.0*p[j]-pt[j];    for (j=1;j<=n;j++) pt[j]=p[j]; 
       xit[j]=p[j]-pt[j];    for (*iter=1;;++(*iter)) { 
       pt[j]=p[j];      fp=(*fret); 
     }      ibig=0; 
     fptt=(*func)(ptt);      del=0.0; 
     if (fptt < fp) {      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
       if (t < 0.0) {      for (i=1;i<=n;i++) 
         linmin(p,xit,n,fret,func);        printf(" %d %.12f",i, p[i]);
         for (j=1;j<=n;j++) {      fprintf(ficlog," %d %.12f",i, p[i]);
           xi[j][ibig]=xi[j][n];      printf("\n");
           xi[j][n]=xit[j];      fprintf(ficlog,"\n");
         }      for (i=1;i<=n;i++) { 
 #ifdef DEBUG        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);        fptt=(*fret); 
         for(j=1;j<=n;j++)  #ifdef DEBUG
           printf(" %.12e",xit[j]);        printf("fret=%lf \n",*fret);
         printf("\n");        fprintf(ficlog,"fret=%lf \n",*fret);
 #endif  #endif
       }        printf("%d",i);fflush(stdout);
     }        fprintf(ficlog,"%d",i);fflush(ficlog);
   }        linmin(p,xit,n,fret,func); 
 }        if (fabs(fptt-(*fret)) > del) { 
           del=fabs(fptt-(*fret)); 
 /**** Prevalence limit ****************/          ibig=i; 
         } 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  #ifdef DEBUG
 {        printf("%d %.12e",i,(*fret));
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit        fprintf(ficlog,"%d %.12e",i,(*fret));
      matrix by transitions matrix until convergence is reached */        for (j=1;j<=n;j++) {
           xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   int i, ii,j,k;          printf(" x(%d)=%.12e",j,xit[j]);
   double min, max, maxmin, maxmax,sumnew=0.;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   double **matprod2();        }
   double **out, cov[NCOVMAX], **pmij();        for(j=1;j<=n;j++) {
   double **newm;          printf(" p=%.12e",p[j]);
   double agefin, delaymax=50 ; /* Max number of years to converge */          fprintf(ficlog," p=%.12e",p[j]);
         }
   for (ii=1;ii<=nlstate+ndeath;ii++)        printf("\n");
     for (j=1;j<=nlstate+ndeath;j++){        fprintf(ficlog,"\n");
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  #endif
     }      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
    cov[1]=1.;  #ifdef DEBUG
          int k[2],l;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */        k[0]=1;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){        k[1]=-1;
     newm=savm;        printf("Max: %.12e",(*func)(p));
     /* Covariates have to be included here again */        fprintf(ficlog,"Max: %.12e",(*func)(p));
      cov[2]=agefin;        for (j=1;j<=n;j++) {
            printf(" %.12e",p[j]);
       for (k=1; k<=cptcovn;k++) {          fprintf(ficlog," %.12e",p[j]);
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];        }
         printf("\n");
 /*printf("Tcode[ij]=%d nbcode=%d\n",Tcode[ij],nbcode[k][Tcode[ij]]);*/        fprintf(ficlog,"\n");
       }        for(l=0;l<=1;l++) {
       for (k=1; k<=cptcovage;k++)          for (j=1;j<=n;j++) {
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];            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]);
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           }
     savm=oldm;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     oldm=newm;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     maxmax=0.;        }
     for(j=1;j<=nlstate;j++){  #endif
       min=1.;  
       max=0.;  
       for(i=1; i<=nlstate; i++) {        free_vector(xit,1,n); 
         sumnew=0;        free_vector(xits,1,n); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];        free_vector(ptt,1,n); 
         prlim[i][j]= newm[i][j]/(1-sumnew);        free_vector(pt,1,n); 
         max=FMAX(max,prlim[i][j]);        return; 
         min=FMIN(min,prlim[i][j]);      } 
       }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       maxmin=max-min;      for (j=1;j<=n;j++) { 
       maxmax=FMAX(maxmax,maxmin);        ptt[j]=2.0*p[j]-pt[j]; 
     }        xit[j]=p[j]-pt[j]; 
     if(maxmax < ftolpl){        pt[j]=p[j]; 
       return prlim;      } 
     }      fptt=(*func)(ptt); 
   }      if (fptt < fp) { 
 }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         if (t < 0.0) { 
 /*************** transition probabilities **********/          linmin(p,xit,n,fret,func); 
           for (j=1;j<=n;j++) { 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )            xi[j][ibig]=xi[j][n]; 
 {            xi[j][n]=xit[j]; 
   double s1, s2;          }
   /*double t34;*/  #ifdef DEBUG
   int i,j,j1, nc, ii, jj;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     for(i=1; i<= nlstate; i++){          for(j=1;j<=n;j++){
     for(j=1; j<i;j++){            printf(" %.12e",xit[j]);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){            fprintf(ficlog," %.12e",xit[j]);
         /*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("\n");
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/          fprintf(ficlog,"\n");
       }  #endif
       ps[i][j]=s2;        }
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/      } 
     }    } 
     for(j=i+1; j<=nlstate+ndeath;j++){  } 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  /**** Prevalence limit (stable prevalence)  ****************/
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       ps[i][j]=s2;  {
     }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   }       matrix by transitions matrix until convergence is reached */
   for(i=1; i<= nlstate; i++){  
      s1=0;    int i, ii,j,k;
     for(j=1; j<i; j++)    double min, max, maxmin, maxmax,sumnew=0.;
       s1+=exp(ps[i][j]);    double **matprod2();
     for(j=i+1; j<=nlstate+ndeath; j++)    double **out, cov[NCOVMAX], **pmij();
       s1+=exp(ps[i][j]);    double **newm;
     ps[i][i]=1./(s1+1.);    double agefin, delaymax=50 ; /* Max number of years to converge */
     for(j=1; j<i; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];    for (ii=1;ii<=nlstate+ndeath;ii++)
     for(j=i+1; j<=nlstate+ndeath; j++)      for (j=1;j<=nlstate+ndeath;j++){
       ps[i][j]= exp(ps[i][j])*ps[i][i];        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */      }
   } /* end i */  
      cov[1]=1.;
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){   
     for(jj=1; jj<= nlstate+ndeath; jj++){   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       ps[ii][jj]=0;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       ps[ii][ii]=1;      newm=savm;
     }      /* Covariates have to be included here again */
   }       cov[2]=agefin;
     
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){        for (k=1; k<=cptcovn;k++) {
     for(jj=1; jj<= nlstate+ndeath; jj++){          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
      printf("%lf ",ps[ii][jj]);          /*      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]]);*/
    }        }
     printf("\n ");        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     }        for (k=1; k<=cptcovprod;k++)
     printf("\n ");printf("%lf ",cov[2]);*/          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
 /*  
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   goto end;*/        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
     return ps;        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
 }      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   
 /**************** Product of 2 matrices ******************/      savm=oldm;
       oldm=newm;
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      maxmax=0.;
 {      for(j=1;j<=nlstate;j++){
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        min=1.;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */        max=0.;
   /* in, b, out are matrice of pointers which should have been initialized        for(i=1; i<=nlstate; i++) {
      before: only the contents of out is modified. The function returns          sumnew=0;
      a pointer to pointers identical to out */          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   long i, j, k;          prlim[i][j]= newm[i][j]/(1-sumnew);
   for(i=nrl; i<= nrh; i++)          max=FMAX(max,prlim[i][j]);
     for(k=ncolol; k<=ncoloh; k++)          min=FMIN(min,prlim[i][j]);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        }
         out[i][k] +=in[i][j]*b[j][k];        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
   return out;      }
 }      if(maxmax < ftolpl){
         return prlim;
       }
 /************* Higher Matrix Product ***************/    }
   }
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  
 {  /*************** transition probabilities ***************/ 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
      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 s1, s2;
      (typically every 2 years instead of every month which is too big).    /*double t34;*/
      Model is determined by parameters x and covariates have to be    int i,j,j1, nc, ii, jj;
      included manually here.  
       for(i=1; i<= nlstate; i++){
      */      for(j=1; j<i;j++){
         for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   int i, j, d, h, k;          /*s2 += param[i][j][nc]*cov[nc];*/
   double **out, cov[NCOVMAX];          s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   double **newm;          /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
         }
   /* Hstepm could be zero and should return the unit matrix */        ps[i][j]=s2;
   for (i=1;i<=nlstate+ndeath;i++)        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
     for (j=1;j<=nlstate+ndeath;j++){      }
       oldm[i][j]=(i==j ? 1.0 : 0.0);      for(j=i+1; j<=nlstate+ndeath;j++){
       po[i][j][0]=(i==j ? 1.0 : 0.0);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     }          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
   for(h=1; h <=nhstepm; h++){        }
     for(d=1; d <=hstepm; d++){        ps[i][j]=s2;
       newm=savm;      }
       /* Covariates have to be included here again */    }
       cov[1]=1.;      /*ps[3][2]=1;*/
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  
       if (cptcovn>0){    for(i=1; i<= nlstate; i++){
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];       s1=0;
     }      for(j=1; j<i; j++)
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/        s1+=exp(ps[i][j]);
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/      for(j=i+1; j<=nlstate+ndeath; j++)
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,        s1+=exp(ps[i][j]);
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      ps[i][i]=1./(s1+1.);
       savm=oldm;      for(j=1; j<i; j++)
       oldm=newm;        ps[i][j]= exp(ps[i][j])*ps[i][i];
     }      for(j=i+1; j<=nlstate+ndeath; j++)
     for(i=1; i<=nlstate+ndeath; i++)        ps[i][j]= exp(ps[i][j])*ps[i][i];
       for(j=1;j<=nlstate+ndeath;j++) {      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         po[i][j][h]=newm[i][j];    } /* end i */
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  
          */    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       }      for(jj=1; jj<= nlstate+ndeath; jj++){
   } /* end h */        ps[ii][jj]=0;
   return po;        ps[ii][ii]=1;
 }      }
     }
   
 /*************** log-likelihood *************/  
 double func( double *x)    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
 {      for(jj=1; jj<= nlstate+ndeath; jj++){
   int i, ii, j, k, mi, d, kk;       printf("%lf ",ps[ii][jj]);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];     }
   double **out;      printf("\n ");
   double sw; /* Sum of weights */      }
   double lli; /* Individual log likelihood */      printf("\n ");printf("%lf ",cov[2]);*/
   long ipmx;  /*
   /*extern weight */    for(i=1; i<= npar; i++) printf("%f ",x[i]);
   /* We are differentiating ll according to initial status */    goto end;*/
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      return ps;
   /*for(i=1;i<imx;i++)  }
 printf(" %d\n",s[4][i]);  
   */  /**************** Product of 2 matrices ******************/
   cov[1]=1.;  
   double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   for(k=1; k<=nlstate; k++) ll[k]=0.;  {
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
        for(mi=1; mi<= wav[i]-1; mi++){    /* in, b, out are matrice of pointers which should have been initialized 
       for (ii=1;ii<=nlstate+ndeath;ii++)       before: only the contents of out is modified. The function returns
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);       a pointer to pointers identical to out */
             for(d=0; d<dh[mi][i]; d++){    long i, j, k;
               newm=savm;    for(i=nrl; i<= nrh; i++)
               cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      for(k=ncolol; k<=ncoloh; k++)
               for (kk=1; kk<=cptcovage;kk++) {        for(j=ncl,out[i][k]=0.; j<=nch; j++)
                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];          out[i][k] +=in[i][j]*b[j][k];
                  /*printf("%d %d",kk,Tage[kk]);*/  
               }    return out;
               /*cov[4]=covar[1][i]*cov[2];scanf("%d", i);*/  }
               /*cov[3]=pow(cov[2],2)/1000.;*/  
   
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  /************* Higher Matrix Product ***************/
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  
           savm=oldm;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
           oldm=newm;  {
     /* Computes the transition matrix starting at age 'age' over 
        'nhstepm*hstepm*stepm' months (i.e. until
       } /* end mult */       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
           nhstepm*hstepm matrices. 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/       (typically every 2 years instead of every month which is too big 
       ipmx +=1;       for the memory).
       sw += weight[i];       Model is determined by parameters x and covariates have to be 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;       included manually here. 
     } /* end of wave */  
   } /* end of individual */       */
   
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    int i, j, d, h, k;
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    double **out, cov[NCOVMAX];
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    double **newm;
   return -l;  
 }    /* Hstepm could be zero and should return the unit matrix */
     for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
 /*********** Maximum Likelihood Estimation ***************/        oldm[i][j]=(i==j ? 1.0 : 0.0);
         po[i][j][0]=(i==j ? 1.0 : 0.0);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      }
 {    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   int i,j, iter;    for(h=1; h <=nhstepm; h++){
   double **xi,*delti;      for(d=1; d <=hstepm; d++){
   double fret;        newm=savm;
   xi=matrix(1,npar,1,npar);        /* Covariates have to be included here again */
   for (i=1;i<=npar;i++)        cov[1]=1.;
     for (j=1;j<=npar;j++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
       xi[i][j]=(i==j ? 1.0 : 0.0);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   printf("Powell\n");        for (k=1; k<=cptcovage;k++)
   powell(p,xi,npar,ftol,&iter,&fret,func);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         for (k=1; k<=cptcovprod;k++)
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));  
   
 }        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
         /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
 /**** Computes Hessian and covariance matrix ***/        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))                     pmij(pmmij,cov,ncovmodel,x,nlstate));
 {        savm=oldm;
   double  **a,**y,*x,pd;        oldm=newm;
   double **hess;      }
   int i, j,jk;      for(i=1; i<=nlstate+ndeath; i++)
   int *indx;        for(j=1;j<=nlstate+ndeath;j++) {
           po[i][j][h]=newm[i][j];
   double hessii(double p[], double delta, int theta, double delti[]);          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
   double hessij(double p[], double delti[], int i, int j);           */
   void lubksb(double **a, int npar, int *indx, double b[]) ;        }
   void ludcmp(double **a, int npar, int *indx, double *d) ;    } /* end h */
     return po;
   }
   hess=matrix(1,npar,1,npar);  
   
   printf("\nCalculation of the hessian matrix. Wait...\n");  /*************** log-likelihood *************/
   for (i=1;i<=npar;i++){  double func( double *x)
     printf("%d",i);fflush(stdout);  {
     hess[i][i]=hessii(p,ftolhess,i,delti);    int i, ii, j, k, mi, d, kk;
     /*printf(" %f ",p[i]);*/    double l, ll[NLSTATEMAX], cov[NCOVMAX];
   }    double **out;
     double sw; /* Sum of weights */
   for (i=1;i<=npar;i++) {    double lli; /* Individual log likelihood */
     for (j=1;j<=npar;j++)  {    int s1, s2;
       if (j>i) {    double bbh, survp;
         printf(".%d%d",i,j);fflush(stdout);    long ipmx;
         hess[i][j]=hessij(p,delti,i,j);    /*extern weight */
         hess[j][i]=hess[i][j];    /* We are differentiating ll according to initial status */
       }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     }    /*for(i=1;i<imx;i++) 
   }      printf(" %d\n",s[4][i]);
   printf("\n");    */
     cov[1]=1.;
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  
      for(k=1; k<=nlstate; k++) ll[k]=0.;
   a=matrix(1,npar,1,npar);  
   y=matrix(1,npar,1,npar);    if(mle==1){
   x=vector(1,npar);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   indx=ivector(1,npar);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   for (i=1;i<=npar;i++)        for(mi=1; mi<= wav[i]-1; mi++){
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          for (ii=1;ii<=nlstate+ndeath;ii++)
   ludcmp(a,npar,indx,&pd);            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (j=1;j<=npar;j++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=1;i<=npar;i++) x[i]=0;            }
     x[j]=1;          for(d=0; d<dh[mi][i]; d++){
     lubksb(a,npar,indx,x);            newm=savm;
     for (i=1;i<=npar;i++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       matcov[i][j]=x[i];            for (kk=1; kk<=cptcovage;kk++) {
     }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   }            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   printf("\n#Hessian matrix#\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   for (i=1;i<=npar;i++) {            savm=oldm;
     for (j=1;j<=npar;j++) {            oldm=newm;
       printf("%.3e ",hess[i][j]);          } /* end mult */
     }        
     printf("\n");          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   }          /* But now since version 0.9 we anticipate for bias and large stepm.
            * If stepm is larger than one month (smallest stepm) and if the exact delay 
   /* Recompute Inverse */           * (in months) between two waves is not a multiple of stepm, we rounded to 
   for (i=1;i<=npar;i++)           * the nearest (and in case of equal distance, to the lowest) interval but now
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   ludcmp(a,npar,indx,&pd);           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
            * probability in order to take into account the bias as a fraction of the way
   /*  printf("\n#Hessian matrix recomputed#\n");           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
            * -stepm/2 to stepm/2 .
   for (j=1;j<=npar;j++) {           * For stepm=1 the results are the same as for previous versions of Imach.
     for (i=1;i<=npar;i++) x[i]=0;           * For stepm > 1 the results are less biased than in previous versions. 
     x[j]=1;           */
     lubksb(a,npar,indx,x);          s1=s[mw[mi][i]][i];
     for (i=1;i<=npar;i++){          s2=s[mw[mi+1][i]][i];
       y[i][j]=x[i];          bbh=(double)bh[mi][i]/(double)stepm; 
       printf("%.3e ",y[i][j]);          /* bias is positive if real duration
     }           * is higher than the multiple of stepm and negative otherwise.
     printf("\n");           */
   }          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   */          /* if s2=-2 lli=out[1][1]+out[1][2];*/
           if (s2==-2) {
   free_matrix(a,1,npar,1,npar);            for (j=1,survp=0. ; j<=nlstate; j++) 
   free_matrix(y,1,npar,1,npar);              survp += out[s1][j];
   free_vector(x,1,npar);            lli= survp;
   free_ivector(indx,1,npar);          }
   free_matrix(hess,1,npar,1,npar);  
           else
           lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));  /* linear interpolation */
 }          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
           /*if(lli ==000.0)*/
 /*************** hessian matrix ****************/          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
 double hessii( double x[], double delta, int theta, double delti[])          ipmx +=1;
 {          sw += weight[i];
   int i;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int l=1, lmax=20;        } /* end of wave */
   double k1,k2;      } /* end of individual */
   double p2[NPARMAX+1];    }  else if(mle==2){
   double res;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double fx;        for(mi=1; mi<= wav[i]-1; mi++){
   int k=0,kmax=10;          for (ii=1;ii<=nlstate+ndeath;ii++)
   double l1;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   fx=func(x);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (i=1;i<=npar;i++) p2[i]=x[i];            }
   for(l=0 ; l <=lmax; l++){          for(d=0; d<=dh[mi][i]; d++){
     l1=pow(10,l);            newm=savm;
     delts=delt;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(k=1 ; k <kmax; k=k+1){            for (kk=1; kk<=cptcovage;kk++) {
       delt = delta*(l1*k);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       p2[theta]=x[theta] +delt;            }
       k1=func(p2)-fx;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       p2[theta]=x[theta]-delt;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       k2=func(p2)-fx;            savm=oldm;
       /*res= (k1-2.0*fx+k2)/delt/delt; */            oldm=newm;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */          } /* end mult */
              
 #ifdef DEBUG          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       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);          /* But now since version 0.9 we anticipate for bias and large stepm.
 #endif           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */           * (in months) between two waves is not a multiple of stepm, we rounded to 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){           * the nearest (and in case of equal distance, to the lowest) interval but now
         k=kmax;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       }           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */           * probability in order to take into account the bias as a fraction of the way
         k=kmax; l=lmax*10.;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
       }           * -stepm/2 to stepm/2 .
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){           * For stepm=1 the results are the same as for previous versions of Imach.
         delts=delt;           * For stepm > 1 the results are less biased than in previous versions. 
       }           */
     }          s1=s[mw[mi][i]][i];
   }          s2=s[mw[mi+1][i]][i];
   delti[theta]=delts;          bbh=(double)bh[mi][i]/(double)stepm; 
   return res;          /* bias is positive if real duration
             * is higher than the multiple of stepm and negative otherwise.
 }           */
           lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
 double hessij( double x[], double delti[], int thetai,int thetaj)          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
 {          /*lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.-+bh)*out[s1][s2])); */ /* exponential interpolation */
   int i;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   int l=1, l1, lmax=20;          /*if(lli ==000.0)*/
   double k1,k2,k3,k4,res,fx;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
   double p2[NPARMAX+1];          ipmx +=1;
   int k;          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fx=func(x);        } /* end of wave */
   for (k=1; k<=2; k++) {      } /* end of individual */
     for (i=1;i<=npar;i++) p2[i]=x[i];    }  else if(mle==3){  /* exponential inter-extrapolation */
     p2[thetai]=x[thetai]+delti[thetai]/k;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     k1=func(p2)-fx;        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
     p2[thetai]=x[thetai]+delti[thetai]/k;            for (j=1;j<=nlstate+ndeath;j++){
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     k2=func(p2)-fx;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
     p2[thetai]=x[thetai]-delti[thetai]/k;          for(d=0; d<dh[mi][i]; d++){
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;            newm=savm;
     k3=func(p2)-fx;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
     p2[thetai]=x[thetai]-delti[thetai]/k;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            }
     k4=func(p2)-fx;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 #ifdef DEBUG            savm=oldm;
     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);            oldm=newm;
 #endif          } /* end mult */
   }        
   return res;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
 }          /* But now since version 0.9 we anticipate for bias and large stepm.
            * If stepm is larger than one month (smallest stepm) and if the exact delay 
 /************** Inverse of matrix **************/           * (in months) between two waves is not a multiple of stepm, we rounded to 
 void ludcmp(double **a, int n, int *indx, double *d)           * the nearest (and in case of equal distance, to the lowest) interval but now
 {           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   int i,imax,j,k;           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
   double big,dum,sum,temp;           * probability in order to take into account the bias as a fraction of the way
   double *vv;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
             * -stepm/2 to stepm/2 .
   vv=vector(1,n);           * For stepm=1 the results are the same as for previous versions of Imach.
   *d=1.0;           * For stepm > 1 the results are less biased than in previous versions. 
   for (i=1;i<=n;i++) {           */
     big=0.0;          s1=s[mw[mi][i]][i];
     for (j=1;j<=n;j++)          s2=s[mw[mi+1][i]][i];
       if ((temp=fabs(a[i][j])) > big) big=temp;          bbh=(double)bh[mi][i]/(double)stepm; 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          /* bias is positive if real duration
     vv[i]=1.0/big;           * is higher than the multiple of stepm and negative otherwise.
   }           */
   for (j=1;j<=n;j++) {          /* lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); */ /* linear interpolation */
     for (i=1;i<j;i++) {          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       sum=a[i][j];          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          /*if(lli ==000.0)*/
       a[i][j]=sum;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
     }          ipmx +=1;
     big=0.0;          sw += weight[i];
     for (i=j;i<=n;i++) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       sum=a[i][j];        } /* end of wave */
       for (k=1;k<j;k++)      } /* end of individual */
         sum -= a[i][k]*a[k][j];    }else{  /* ml=4 no inter-extrapolation */
       a[i][j]=sum;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       if ( (dum=vv[i]*fabs(sum)) >= big) {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         big=dum;        for(mi=1; mi<= wav[i]-1; mi++){
         imax=i;          for (ii=1;ii<=nlstate+ndeath;ii++)
       }            for (j=1;j<=nlstate+ndeath;j++){
     }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     if (j != imax) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for (k=1;k<=n;k++) {            }
         dum=a[imax][k];          for(d=0; d<dh[mi][i]; d++){
         a[imax][k]=a[j][k];            newm=savm;
         a[j][k]=dum;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
       *d = -(*d);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       vv[imax]=vv[j];            }
     }          
     indx[j]=imax;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     if (a[j][j] == 0.0) a[j][j]=TINY;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     if (j != n) {            savm=oldm;
       dum=1.0/(a[j][j]);            oldm=newm;
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          } /* end mult */
     }        
   }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   free_vector(vv,1,n);  /* Doesn't work */          ipmx +=1;
 ;          sw += weight[i];
 }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
 void lubksb(double **a, int n, int *indx, double b[])      } /* end of individual */
 {    } /* End of if */
   int i,ii=0,ip,j;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   double sum;    /* 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<=n;i++) {    return -l;
     ip=indx[i];  }
     sum=b[ip];  
     b[ip]=b[i];  
     if (ii)  /*********** Maximum Likelihood Estimation ***************/
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  
     else if (sum) ii=i;  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     b[i]=sum;  {
   }    int i,j, iter;
   for (i=n;i>=1;i--) {    double **xi,*delti;
     sum=b[i];    double fret;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    xi=matrix(1,npar,1,npar);
     b[i]=sum/a[i][i];    for (i=1;i<=npar;i++)
   }      for (j=1;j<=npar;j++)
 }        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
 /************ Frequencies ********************/    powell(p,xi,npar,ftol,&iter,&fret,func);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)  
 {  /* Some frequencies */     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
      fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   double ***freq; /* Frequencies */  
   double *pp;  }
   double pos;  
   FILE *ficresp;  /**** Computes Hessian and covariance matrix ***/
   char fileresp[FILENAMELENGTH];  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   {
   pp=vector(1,nlstate);    double  **a,**y,*x,pd;
     double **hess;
   strcpy(fileresp,"p");    int i, j,jk;
   strcat(fileresp,fileres);    int *indx;
   if((ficresp=fopen(fileresp,"w"))==NULL) {  
     printf("Problem with prevalence resultfile: %s\n", fileresp);    double hessii(double p[], double delta, int theta, double delti[]);
     exit(0);    double hessij(double p[], double delti[], int i, int j);
   }    void lubksb(double **a, int npar, int *indx, double b[]) ;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    void ludcmp(double **a, int npar, int *indx, double *d) ;
   j1=0;  
     hess=matrix(1,npar,1,npar);
   j=cptcovn;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    printf("\nCalculation of the hessian matrix. Wait...\n");
     fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   for(k1=1; k1<=j;k1++){    for (i=1;i<=npar;i++){
    for(i1=1; i1<=ncodemax[k1];i1++){      printf("%d",i);fflush(stdout);
        j1++;      fprintf(ficlog,"%d",i);fflush(ficlog);
       hess[i][i]=hessii(p,ftolhess,i,delti);
         for (i=-1; i<=nlstate+ndeath; i++)        /*printf(" %f ",p[i]);*/
          for (jk=-1; jk<=nlstate+ndeath; jk++)        /*printf(" %lf ",hess[i][i]);*/
            for(m=agemin; m <= agemax+3; m++)    }
              freq[i][jk][m]=0;    
            for (i=1;i<=npar;i++) {
        for (i=1; i<=imx; i++) {      for (j=1;j<=npar;j++)  {
          bool=1;        if (j>i) { 
          if  (cptcovn>0) {          printf(".%d%d",i,j);fflush(stdout);
            for (z1=1; z1<=cptcovn; z1++)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;          hess[i][j]=hessij(p,delti,i,j);
          }          hess[j][i]=hess[i][j];    
           if (bool==1) {          /*printf(" %lf ",hess[i][j]);*/
            for(m=firstpass; m<=lastpass-1; m++){        }
              if(agev[m][i]==0) agev[m][i]=agemax+1;      }
              if(agev[m][i]==1) agev[m][i]=agemax+2;    }
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    printf("\n");
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    fprintf(ficlog,"\n");
            }  
          }    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
        }    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
         if  (cptcovn>0) {    
          fprintf(ficresp, "\n#Variable");    a=matrix(1,npar,1,npar);
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);    y=matrix(1,npar,1,npar);
        }    x=vector(1,npar);
        fprintf(ficresp, "\n#");    indx=ivector(1,npar);
        for(i=1; i<=nlstate;i++)    for (i=1;i<=npar;i++)
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
        fprintf(ficresp, "\n");    ludcmp(a,npar,indx,&pd);
          
   for(i=(int)agemin; i <= (int)agemax+3; i++){    for (j=1;j<=npar;j++) {
     if(i==(int)agemax+3)      for (i=1;i<=npar;i++) x[i]=0;
       printf("Total");      x[j]=1;
     else      lubksb(a,npar,indx,x);
       printf("Age %d", i);      for (i=1;i<=npar;i++){ 
     for(jk=1; jk <=nlstate ; jk++){        matcov[i][j]=x[i];
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      }
         pp[jk] += freq[jk][m][i];    }
     }  
     for(jk=1; jk <=nlstate ; jk++){    printf("\n#Hessian matrix#\n");
       for(m=-1, pos=0; m <=0 ; m++)    fprintf(ficlog,"\n#Hessian matrix#\n");
         pos += freq[jk][m][i];    for (i=1;i<=npar;i++) { 
       if(pp[jk]>=1.e-10)      for (j=1;j<=npar;j++) { 
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        printf("%.3e ",hess[i][j]);
       else        fprintf(ficlog,"%.3e ",hess[i][j]);
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);      }
     }      printf("\n");
     for(jk=1; jk <=nlstate ; jk++){      fprintf(ficlog,"\n");
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)    }
         pp[jk] += freq[jk][m][i];  
     }    /* Recompute Inverse */
     for(jk=1,pos=0; jk <=nlstate ; jk++)    for (i=1;i<=npar;i++)
       pos += pp[jk];      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     for(jk=1; jk <=nlstate ; jk++){    ludcmp(a,npar,indx,&pd);
       if(pos>=1.e-5)  
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    /*  printf("\n#Hessian matrix recomputed#\n");
       else  
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    for (j=1;j<=npar;j++) {
       if( i <= (int) agemax){      for (i=1;i<=npar;i++) x[i]=0;
         if(pos>=1.e-5)      x[j]=1;
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      lubksb(a,npar,indx,x);
       else      for (i=1;i<=npar;i++){ 
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        y[i][j]=x[i];
       }        printf("%.3e ",y[i][j]);
     }        fprintf(ficlog,"%.3e ",y[i][j]);
     for(jk=-1; jk <=nlstate+ndeath; jk++)      }
       for(m=-1; m <=nlstate+ndeath; m++)      printf("\n");
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      fprintf(ficlog,"\n");
     if(i <= (int) agemax)    }
       fprintf(ficresp,"\n");    */
     printf("\n");  
     }    free_matrix(a,1,npar,1,npar);
     }    free_matrix(y,1,npar,1,npar);
  }    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
   fclose(ficresp);    free_matrix(hess,1,npar,1,npar);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  
   free_vector(pp,1,nlstate);  
   }
 }  /* End of Freq */  
   /*************** hessian matrix ****************/
 /************* Waves Concatenation ***************/  double hessii( double x[], double delta, int theta, double delti[])
   {
 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 i;
 {    int l=1, lmax=20;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    double k1,k2;
      Death is a valid wave (if date is known).    double p2[NPARMAX+1];
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    double res;
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
      and mw[mi+1][i]. dh depends on stepm.    double fx;
      */    int k=0,kmax=10;
     double l1;
   int i, mi, m;  
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    fx=func(x);
 float sum=0.;    for (i=1;i<=npar;i++) p2[i]=x[i];
     for(l=0 ; l <=lmax; l++){
   for(i=1; i<=imx; i++){      l1=pow(10,l);
     mi=0;      delts=delt;
     m=firstpass;      for(k=1 ; k <kmax; k=k+1){
     while(s[m][i] <= nlstate){        delt = delta*(l1*k);
       if(s[m][i]>=1)        p2[theta]=x[theta] +delt;
         mw[++mi][i]=m;        k1=func(p2)-fx;
       if(m >=lastpass)        p2[theta]=x[theta]-delt;
         break;        k2=func(p2)-fx;
       else        /*res= (k1-2.0*fx+k2)/delt/delt; */
         m++;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     }/* end while */        
     if (s[m][i] > nlstate){  #ifdef DEBUG
       mi++;     /* Death is another wave */        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);
       /* if(mi==0)  never been interviewed correctly before death */        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
          /* Only death is a correct wave */  #endif
       mw[mi][i]=m;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
     wav[i]=mi;        }
     if(mi==0)        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          k=kmax; l=lmax*10.;
   }        }
         else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   for(i=1; i<=imx; i++){          delts=delt;
     for(mi=1; mi<wav[i];mi++){        }
       if (stepm <=0)      }
         dh[mi][i]=1;    }
       else{    delti[theta]=delts;
         if (s[mw[mi+1][i]][i] > nlstate) {    return res; 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);    
           if(j=0) j=1;  /* Survives at least one month after exam */  }
         }  
         else{  double hessij( double x[], double delti[], int thetai,int thetaj)
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  {
           k=k+1;    int i;
           if (j >= jmax) jmax=j;    int l=1, l1, lmax=20;
           else if (j <= jmin)jmin=j;    double k1,k2,k3,k4,res,fx;
           sum=sum+j;    double p2[NPARMAX+1];
         }    int k;
         jk= j/stepm;  
         jl= j -jk*stepm;    fx=func(x);
         ju= j -(jk+1)*stepm;    for (k=1; k<=2; k++) {
         if(jl <= -ju)      for (i=1;i<=npar;i++) p2[i]=x[i];
           dh[mi][i]=jk;      p2[thetai]=x[thetai]+delti[thetai]/k;
         else      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           dh[mi][i]=jk+1;      k1=func(p2)-fx;
         if(dh[mi][i]==0)    
           dh[mi][i]=1; /* At least one step */      p2[thetai]=x[thetai]+delti[thetai]/k;
       }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     }      k2=func(p2)-fx;
   }    
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);      p2[thetai]=x[thetai]-delti[thetai]/k;
 }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
 /*********** Tricode ****************************/      k3=func(p2)-fx;
 void tricode(int *Tvar, int **nbcode, int imx)    
 {      p2[thetai]=x[thetai]-delti[thetai]/k;
   int Ndum[80],ij=1, k, j, i, Ntvar[20];      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   int cptcode=0;      k4=func(p2)-fx;
   for (k=0; k<79; k++) Ndum[k]=0;      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   for (k=1; k<=7; k++) ncodemax[k]=0;  #ifdef DEBUG
       printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   for (j=1; j<=cptcovn; j++) {      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
     for (i=1; i<=imx; i++) {  #endif
       ij=(int)(covar[Tvar[j]][i]);    }
       Ndum[ij]++;    return res;
       if (ij > cptcode) cptcode=ij;  }
     }  
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/  /************** Inverse of matrix **************/
     for (i=0; i<=cptcode; i++) {  void ludcmp(double **a, int n, int *indx, double *d) 
       if(Ndum[i]!=0) ncodemax[j]++;  { 
     }    int i,imax,j,k; 
      double big,dum,sum,temp; 
     ij=1;    double *vv; 
     for (i=1; i<=ncodemax[j]; i++) {   
       for (k=0; k<=79; k++) {    vv=vector(1,n); 
         if (Ndum[k] != 0) {    *d=1.0; 
           nbcode[Tvar[j]][ij]=k;    for (i=1;i<=n;i++) { 
           ij++;      big=0.0; 
         }      for (j=1;j<=n;j++) 
         if (ij > ncodemax[j]) break;        if ((temp=fabs(a[i][j])) > big) big=temp; 
       }        if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     }      vv[i]=1.0/big; 
   }      } 
      for (j=1;j<=n;j++) { 
 }      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
 /*********** Health Expectancies ****************/        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)      } 
 {      big=0.0; 
   /* Health expectancies */      for (i=j;i<=n;i++) { 
   int i, j, nhstepm, hstepm, h;        sum=a[i][j]; 
   double age, agelim,hf;        for (k=1;k<j;k++) 
   double ***p3mat;          sum -= a[i][k]*a[k][j]; 
          a[i][j]=sum; 
   fprintf(ficreseij,"# Health expectancies\n");        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   fprintf(ficreseij,"# Age");          big=dum; 
   for(i=1; i<=nlstate;i++)          imax=i; 
     for(j=1; j<=nlstate;j++)        } 
       fprintf(ficreseij," %1d-%1d",i,j);      } 
   fprintf(ficreseij,"\n");      if (j != imax) { 
         for (k=1;k<=n;k++) { 
   hstepm=1*YEARM; /*  Every j years of age (in month) */          dum=a[imax][k]; 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          a[imax][k]=a[j][k]; 
           a[j][k]=dum; 
   agelim=AGESUP;        } 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        *d = -(*d); 
     /* nhstepm age range expressed in number of stepm */        vv[imax]=vv[j]; 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);      } 
     /* Typically if 20 years = 20*12/6=40 stepm */      indx[j]=imax; 
     if (stepm >= YEARM) hstepm=1;      if (a[j][j] == 0.0) a[j][j]=TINY; 
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      if (j != n) { 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        dum=1.0/(a[j][j]); 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      } 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      } 
     free_vector(vv,1,n);  /* Doesn't work */
   ;
     for(i=1; i<=nlstate;i++)  } 
       for(j=1; j<=nlstate;j++)  
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){  void lubksb(double **a, int n, int *indx, double b[]) 
           eij[i][j][(int)age] +=p3mat[i][j][h];  { 
         }    int i,ii=0,ip,j; 
        double sum; 
     hf=1;   
     if (stepm >= YEARM) hf=stepm/YEARM;    for (i=1;i<=n;i++) { 
     fprintf(ficreseij,"%.0f",age );      ip=indx[i]; 
     for(i=1; i<=nlstate;i++)      sum=b[ip]; 
       for(j=1; j<=nlstate;j++){      b[ip]=b[i]; 
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);      if (ii) 
       }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     fprintf(ficreseij,"\n");      else if (sum) ii=i; 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      b[i]=sum; 
   }    } 
 }    for (i=n;i>=1;i--) { 
       sum=b[i]; 
 /************ Variance ******************/      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[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)      b[i]=sum/a[i][i]; 
 {    } 
   /* Variance of health expectancies */  } 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  
   double **newm;  /************ Frequencies ********************/
   double **dnewm,**doldm;  void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)
   int i, j, nhstepm, hstepm, h;  {  /* Some frequencies */
   int k, cptcode;    
    double *xp;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   double **gp, **gm;    int first;
   double ***gradg, ***trgradg;    double ***freq; /* Frequencies */
   double ***p3mat;    double *pp;
   double age,agelim;    double pos, k2, dateintsum=0,k2cpt=0;
   int theta;    FILE *ficresp;
     char fileresp[FILENAMELENGTH];
    fprintf(ficresvij,"# Covariances of life expectancies\n");    
   fprintf(ficresvij,"# Age");    pp=vector(1,nlstate);
   for(i=1; i<=nlstate;i++)    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     for(j=1; j<=nlstate;j++)    strcpy(fileresp,"p");
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    strcat(fileresp,fileres);
   fprintf(ficresvij,"\n");    if((ficresp=fopen(fileresp,"w"))==NULL) {
       printf("Problem with prevalence resultfile: %s\n", fileresp);
   xp=vector(1,npar);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   dnewm=matrix(1,nlstate,1,npar);      exit(0);
   doldm=matrix(1,nlstate,1,nlstate);    }
      freq= ma3x(-2,nlstate+ndeath,-2,nlstate+ndeath,agemin,agemax+3);
   hstepm=1*YEARM; /* Every year of age */    j1=0;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    
   agelim = AGESUP;    j=cptcoveff;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     if (stepm >= YEARM) hstepm=1;    first=1;
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(k1=1; k1<=j;k1++){
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);      for(i1=1; i1<=ncodemax[k1];i1++){
     gp=matrix(0,nhstepm,1,nlstate);        j1++;
     gm=matrix(0,nhstepm,1,nlstate);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           scanf("%d", i);*/
     for(theta=1; theta <=npar; theta++){        for (i=-1; i<=nlstate+ndeath; i++)  
       for(i=1; i<=npar; i++){ /* Computes gradient */          for (jk=-1; jk<=nlstate+ndeath; jk++)  
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            for(m=agemin; m <= agemax+3; m++)
       }              freq[i][jk][m]=0;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        dateintsum=0;
       for(j=1; j<= nlstate; j++){        k2cpt=0;
         for(h=0; h<=nhstepm; h++){        for (i=1; i<=imx; i++) {
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          bool=1;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          if  (cptcovn>0) {
         }            for (z1=1; z1<=cptcoveff; z1++) 
       }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                    bool=0;
       for(i=1; i<=npar; i++) /* Computes gradient */          }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          if (bool==1){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              for(m=firstpass; m<=lastpass; m++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);              k2=anint[m][i]+(mint[m][i]/12.);
       for(j=1; j<= nlstate; j++){              if ((k2>=dateprev1) && (k2<=dateprev2)) {
         for(h=0; h<=nhstepm; h++){                if(agev[m][i]==0) agev[m][i]=agemax+1;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)                if(agev[m][i]==1) agev[m][i]=agemax+2;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];                if (m<lastpass) {
         }                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
       }                  freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];
       for(j=1; j<= nlstate; j++)                }
         for(h=0; h<=nhstepm; h++){                
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {
         }                  dateintsum=dateintsum+k2;
     } /* End theta */                  k2cpt++;
                 }
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);              }
             }
     for(h=0; h<=nhstepm; h++)          }
       for(j=1; j<=nlstate;j++)        }
         for(theta=1; theta <=npar; theta++)         
           trgradg[h][j][theta]=gradg[h][theta][j];        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
   
     for(i=1;i<=nlstate;i++)        if  (cptcovn>0) {
       for(j=1;j<=nlstate;j++)          fprintf(ficresp, "\n#********** Variable "); 
         vareij[i][j][(int)age] =0.;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(h=0;h<=nhstepm;h++){          fprintf(ficresp, "**********\n#");
       for(k=0;k<=nhstepm;k++){        }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);        for(i=1; i<=nlstate;i++) 
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         for(i=1;i<=nlstate;i++)        fprintf(ficresp, "\n");
           for(j=1;j<=nlstate;j++)        
             vareij[i][j][(int)age] += doldm[i][j];        for(i=(int)agemin; i <= (int)agemax+3; i++){
       }          if(i==(int)agemax+3){
     }            fprintf(ficlog,"Total");
     h=1;          }else{
     if (stepm >= YEARM) h=stepm/YEARM;            if(first==1){
     fprintf(ficresvij,"%.0f ",age );              first=0;
     for(i=1; i<=nlstate;i++)              printf("See log file for details...\n");
       for(j=1; j<=nlstate;j++){            }
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);            fprintf(ficlog,"Age %d", i);
       }          }
     fprintf(ficresvij,"\n");          for(jk=1; jk <=nlstate ; jk++){
     free_matrix(gp,0,nhstepm,1,nlstate);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     free_matrix(gm,0,nhstepm,1,nlstate);              pp[jk] += freq[jk][m][i]; 
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);          }
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);          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++)
   } /* End age */              pos += freq[jk][m][i];
              if(pp[jk]>=1.e-10){
   free_vector(xp,1,npar);              if(first==1){
   free_matrix(doldm,1,nlstate,1,npar);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   free_matrix(dnewm,1,nlstate,1,nlstate);              }
               fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 }            }else{
               if(first==1)
 /************ Variance of prevlim ******************/                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 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)              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 {            }
   /* Variance of prevalence limit */          }
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  
   double **newm;          for(jk=1; jk <=nlstate ; jk++){
   double **dnewm,**doldm;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   int i, j, nhstepm, hstepm;              pp[jk] += freq[jk][m][i];
   int k, cptcode;          }
   double *xp;  
   double *gp, *gm;          for(jk=1,pos=0; jk <=nlstate ; jk++)
   double **gradg, **trgradg;            pos += pp[jk];
   double age,agelim;          for(jk=1; jk <=nlstate ; jk++){
   int theta;            if(pos>=1.e-5){
                  if(first==1)
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   fprintf(ficresvpl,"# Age");              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   for(i=1; i<=nlstate;i++)            }else{
       fprintf(ficresvpl," %1d-%1d",i,i);              if(first==1)
   fprintf(ficresvpl,"\n");                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   xp=vector(1,npar);            }
   dnewm=matrix(1,nlstate,1,npar);            if( i <= (int) agemax){
   doldm=matrix(1,nlstate,1,nlstate);              if(pos>=1.e-5){
                  fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);
   hstepm=1*YEARM; /* Every year of age */                probs[i][jk][j1]= pp[jk]/pos;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   agelim = AGESUP;              }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              else
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */                fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);
     if (stepm >= YEARM) hstepm=1;            }
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          }
     gradg=matrix(1,npar,1,nlstate);          
     gp=vector(1,nlstate);          for(jk=-2; jk <=nlstate+ndeath; jk++)
     gm=vector(1,nlstate);            for(m=-2; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
     for(theta=1; theta <=npar; theta++){              if(first==1)
       for(i=1; i<=npar; i++){ /* Computes gradient */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
       }              }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          if(i <= (int) agemax)
       for(i=1;i<=nlstate;i++)            fprintf(ficresp,"\n");
         gp[i] = prlim[i][i];          if(first==1)
                printf("Others in log...\n");
       for(i=1; i<=npar; i++) /* Computes gradient */          fprintf(ficlog,"\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++)    }
         gm[i] = prlim[i][i];    dateintmean=dateintsum/k2cpt; 
    
       for(i=1;i<=nlstate;i++)    fclose(ficresp);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    free_ma3x(freq,-2,nlstate+ndeath,-2,nlstate+ndeath,(int) agemin,(int) agemax+3);
     } /* End theta */    free_vector(pp,1,nlstate);
     
     trgradg =matrix(1,nlstate,1,npar);    /* End of Freq */
   }
     for(j=1; j<=nlstate;j++)  
       for(theta=1; theta <=npar; theta++)  /************ Prevalence ********************/
         trgradg[j][theta]=gradg[theta][j];  void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)
   {  /* Some frequencies */
     for(i=1;i<=nlstate;i++)   
       varpl[i][(int)age] =0.;    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    double ***freq; /* Frequencies */
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    double *pp;
     for(i=1;i<=nlstate;i++)    double pos, k2;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  
     pp=vector(1,nlstate);
     fprintf(ficresvpl,"%.0f ",age );    
     for(i=1; i<=nlstate;i++)    freq=ma3x(-2,nlstate+ndeath,-2,nlstate+ndeath,agemin,agemax+3);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    j1=0;
     fprintf(ficresvpl,"\n");    
     free_vector(gp,1,nlstate);    j=cptcoveff;
     free_vector(gm,1,nlstate);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_matrix(gradg,1,npar,1,nlstate);    
     free_matrix(trgradg,1,nlstate,1,npar);    for(k1=1; k1<=j;k1++){
   } /* End age */      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
   free_vector(xp,1,npar);        
   free_matrix(doldm,1,nlstate,1,npar);        for (i=-2; i<=nlstate+ndeath; i++)  
   free_matrix(dnewm,1,nlstate,1,nlstate);          for (jk=-2; jk<=nlstate+ndeath; jk++)  
             for(m=agemin; m <= agemax+3; m++)
 }              freq[i][jk][m]=0;
        
         for (i=1; i<=imx; i++) {
           bool=1;
 /***********************************************/          if  (cptcovn>0) {
 /**************** Main Program *****************/            for (z1=1; z1<=cptcoveff; z1++) 
 /***********************************************/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
 /*int main(int argc, char *argv[])*/          } 
 int main()          if (bool==1) { 
 {            for(m=firstpass; m<=lastpass; m++){
               k2=anint[m][i]+(mint[m][i]/12.);
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;              if ((k2>=dateprev1) && (k2<=dateprev2)) {
   double agedeb, agefin,hf;                if(agev[m][i]==0) agev[m][i]=agemax+1;
   double agemin=1.e20, agemax=-1.e20;                if(agev[m][i]==1) agev[m][i]=agemax+2;
                 if (m<lastpass) {
   double fret;                  if (calagedate>0) 
   double **xi,tmp,delta;                    freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];
                   else
   double dum; /* Dummy variable */                    freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   double ***p3mat;                  freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i]; 
   int *indx;                }
   char line[MAXLINE], linepar[MAXLINE];              }
   char title[MAXLINE];            }
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];          }
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];        }
   char filerest[FILENAMELENGTH];        for(i=(int)agemin; i <= (int)agemax+3; i++){ 
   char fileregp[FILENAMELENGTH];          for(jk=1; jk <=nlstate ; jk++){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   int firstobs=1, lastobs=10;              pp[jk] += freq[jk][m][i]; 
   int sdeb, sfin; /* Status at beginning and end */          }
   int c,  h , cpt,l;          for(jk=1; jk <=nlstate ; jk++){
   int ju,jl, mi;            for(m=-1, pos=0; m <=0 ; m++)
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize;              pos += freq[jk][m][i];
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          }
            
   int hstepm, nhstepm;          for(jk=1; jk <=nlstate ; jk++){
   double bage, fage, age, agelim, agebase;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   double ftolpl=FTOL;              pp[jk] += freq[jk][m][i];
   double **prlim;          }
   double *severity;          
   double ***param; /* Matrix of parameters */          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];
   double  *p;          
   double **matcov; /* Matrix of covariance */          for(jk=1; jk <=nlstate ; jk++){    
   double ***delti3; /* Scale */            if( i <= (int) agemax){
   double *delti; /* Scale */              if(pos>=1.e-5){
   double ***eij, ***vareij;                probs[i][jk][j1]= pp[jk]/pos;
   double **varpl; /* Variances of prevalence limits by age */              }
   double *epj, vepp;            }
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";          }/* end jk */
   char *alph[]={"a","a","b","c","d","e"}, str[4];        }/* end i */
       } /* end i1 */
   char z[1]="c", occ;    } /* end k1 */
 #include <sys/time.h>  
 #include <time.h>    
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    free_ma3x(freq,-2,nlstate+ndeath,-2,nlstate+ndeath,(int) agemin,(int) agemax+3);
   /* long total_usecs;    free_vector(pp,1,nlstate);
   struct timeval start_time, end_time;    
    }  /* End of Freq */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   /************* Waves Concatenation ***************/
   
   printf("\nIMACH, Version 0.64a");  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
   printf("\nEnter the parameter file name: ");  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
 #ifdef windows       Death is a valid wave (if date is known).
   scanf("%s",pathtot);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   getcwd(pathcd, size);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
   /*cygwin_split_path(pathtot,path,optionfile);       and mw[mi+1][i]. dh depends on stepm.
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/       */
   /* cutv(path,optionfile,pathtot,'\\');*/  
     int i, mi, m;
 split(pathtot, path,optionfile);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
   chdir(path);       double sum=0., jmean=0.;*/
   replace(pathc,path);    int first;
 #endif    int j, k=0,jk, ju, jl;
 #ifdef unix    double sum=0.;
   scanf("%s",optionfile);    first=0;
 #endif    jmin=1e+5;
     jmax=-1;
 /*-------- arguments in the command line --------*/    jmean=0.;
     for(i=1; i<=imx; i++){
   strcpy(fileres,"r");      mi=0;
   strcat(fileres, optionfile);      m=firstpass;
       while(s[m][i] <= nlstate){
   /*---------arguments file --------*/        if(s[m][i]>=1 || s[m][i]==-2)
           mw[++mi][i]=m;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        if(m >=lastpass)
     printf("Problem with optionfile %s\n",optionfile);          break;
     goto end;        else
   }          m++;
       }/* end while */
   strcpy(filereso,"o");      if (s[m][i] > nlstate){
   strcat(filereso,fileres);        mi++;     /* Death is another wave */
   if((ficparo=fopen(filereso,"w"))==NULL) {        /* if(mi==0)  never been interviewed correctly before death */
     printf("Problem with Output resultfile: %s\n", filereso);goto end;           /* Only death is a correct wave */
   }        mw[mi][i]=m;
       }
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){      wav[i]=mi;
     ungetc(c,ficpar);      if(mi==0){
     fgets(line, MAXLINE, ficpar);        if(first==0){
     puts(line);          printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);
     fputs(line,ficparo);          first=1;
   }        }
   ungetc(c,ficpar);        if(first==1){
           fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);
   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\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);        }
   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\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);      } /* end mi==0 */
   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\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);    }
   
   covar=matrix(0,NCOVMAX,1,n);        for(i=1; i<=imx; i++){
   if (strlen(model)<=1) cptcovn=0;      for(mi=1; mi<wav[i];mi++){
   else {        if (stepm <=0)
     j=0;          dh[mi][i]=1;
     j=nbocc(model,'+');        else{
     cptcovn=j+1;          if (s[mw[mi+1][i]][i] > nlstate) {
   }            if (agedc[i] < 2*AGESUP) {
             j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   ncovmodel=2+cptcovn;            if(j==0) j=1;  /* Survives at least one month after exam */
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */            k=k+1;
              if (j >= jmax) jmax=j;
   /* Read guess parameters */            if (j <= jmin) jmin=j;
   /* Reads comments: lines beginning with '#' */            sum=sum+j;
   while((c=getc(ficpar))=='#' && c!= EOF){            /*if (j<0) printf("j=%d num=%d \n",j,i); */
     ungetc(c,ficpar);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     fgets(line, MAXLINE, ficpar);            }
     puts(line);          }
     fputs(line,ficparo);          else{
   }            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   ungetc(c,ficpar);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
              k=k+1;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);            if (j >= jmax) jmax=j;
     for(i=1; i <=nlstate; i++)            else if (j <= jmin)jmin=j;
     for(j=1; j <=nlstate+ndeath-1; j++){            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       fscanf(ficpar,"%1d%1d",&i1,&j1);            sum=sum+j;
       fprintf(ficparo,"%1d%1d",i1,j1);          }
       printf("%1d%1d",i,j);          jk= j/stepm;
       for(k=1; k<=ncovmodel;k++){          jl= j -jk*stepm;
         fscanf(ficpar," %lf",&param[i][j][k]);          ju= j -(jk+1)*stepm;
         printf(" %lf",param[i][j][k]);          if(mle <=1){ 
         fprintf(ficparo," %lf",param[i][j][k]);            if(jl==0){
       }              dh[mi][i]=jk;
       fscanf(ficpar,"\n");              bh[mi][i]=0;
       printf("\n");            }else{ /* We want a negative bias in order to only have interpolation ie
       fprintf(ficparo,"\n");                    * at the price of an extra matrix product in likelihood */
     }              dh[mi][i]=jk+1;
                bh[mi][i]=ju;
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;            }
   p=param[1][1];          }else{
              if(jl <= -ju){
   /* Reads comments: lines beginning with '#' */              dh[mi][i]=jk;
   while((c=getc(ficpar))=='#' && c!= EOF){              bh[mi][i]=jl;       /* bias is positive if real duration
     ungetc(c,ficpar);                                   * is higher than the multiple of stepm and negative otherwise.
     fgets(line, MAXLINE, ficpar);                                   */
     puts(line);            }
     fputs(line,ficparo);            else{
   }              dh[mi][i]=jk+1;
   ungetc(c,ficpar);              bh[mi][i]=ju;
             }
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);            if(dh[mi][i]==0){
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */              dh[mi][i]=1; /* At least one step */
   for(i=1; i <=nlstate; i++){              bh[mi][i]=ju; /* At least one step */
     for(j=1; j <=nlstate+ndeath-1; j++){              printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);
       fscanf(ficpar,"%1d%1d",&i1,&j1);            }
       printf("%1d%1d",i,j);          }
       fprintf(ficparo,"%1d%1d",i1,j1);        } /* end if mle */
       for(k=1; k<=ncovmodel;k++){      } /* end wave */
         fscanf(ficpar,"%le",&delti3[i][j][k]);    }
         printf(" %le",delti3[i][j][k]);    jmean=sum/k;
         fprintf(ficparo," %le",delti3[i][j][k]);    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       }    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       fscanf(ficpar,"\n");   }
       printf("\n");  
       fprintf(ficparo,"\n");  /*********** Tricode ****************************/
     }  void tricode(int *Tvar, int **nbcode, int imx)
   }  {
   delti=delti3[1][1];    
      int Ndum[20],ij=1, k, j, i, maxncov=19;
   /* Reads comments: lines beginning with '#' */    int cptcode=0;
   while((c=getc(ficpar))=='#' && c!= EOF){    cptcoveff=0; 
     ungetc(c,ficpar);   
     fgets(line, MAXLINE, ficpar);    for (k=0; k<maxncov; k++) Ndum[k]=0;
     puts(line);    for (k=1; k<=7; k++) ncodemax[k]=0;
     fputs(line,ficparo);  
   }    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
   ungetc(c,ficpar);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
                                   modality*/ 
   matcov=matrix(1,npar,1,npar);        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
   for(i=1; i <=npar; i++){        Ndum[ij]++; /*store the modality */
     fscanf(ficpar,"%s",&str);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     printf("%s",str);        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
     fprintf(ficparo,"%s",str);                                         Tvar[j]. If V=sex and male is 0 and 
     for(j=1; j <=i; j++){                                         female is 1, then  cptcode=1.*/
       fscanf(ficpar," %le",&matcov[i][j]);      }
       printf(" %.5le",matcov[i][j]);  
       fprintf(ficparo," %.5le",matcov[i][j]);      for (i=0; i<=cptcode; i++) {
     }        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
     fscanf(ficpar,"\n");      }
     printf("\n");  
     fprintf(ficparo,"\n");      ij=1; 
   }      for (i=1; i<=ncodemax[j]; i++) {
   for(i=1; i <=npar; i++)        for (k=0; k<= maxncov; k++) {
     for(j=i+1;j<=npar;j++)          if (Ndum[k] != 0) {
       matcov[i][j]=matcov[j][i];            nbcode[Tvar[j]][ij]=k; 
                /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   printf("\n");            
             ij++;
           }
     /*-------- data file ----------*/          if (ij > ncodemax[j]) break; 
     if((ficres =fopen(fileres,"w"))==NULL) {        }  
       printf("Problem with resultfile: %s\n", fileres);goto end;      } 
     }    }  
     fprintf(ficres,"#%s\n",version);  
       for (k=0; k< maxncov; k++) Ndum[k]=0;
     if((fic=fopen(datafile,"r"))==NULL)    {  
       printf("Problem with datafile: %s\n", datafile);goto end;   for (i=1; i<=ncovmodel-2; i++) { 
     }     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
      ij=Tvar[i];
     n= lastobs;     Ndum[ij]++;
     severity = vector(1,maxwav);   }
     outcome=imatrix(1,maxwav+1,1,n);  
     num=ivector(1,n);   ij=1;
     moisnais=vector(1,n);   for (i=1; i<= maxncov; i++) {
     annais=vector(1,n);     if((Ndum[i]!=0) && (i<=ncovcol)){
     moisdc=vector(1,n);       Tvaraff[ij]=i; /*For printing */
     andc=vector(1,n);       ij++;
     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 */   cptcoveff=ij-1; /*Number of simple covariates*/
     mint=matrix(1,maxwav,1,n);  }
     anint=matrix(1,maxwav,1,n);  
     s=imatrix(1,maxwav+1,1,n);  /*********** Health Expectancies ****************/
     adl=imatrix(1,maxwav+1,1,n);      
     tab=ivector(1,NCOVMAX);  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 )
     ncodemax=ivector(1,8);  
   {
     i=1;    /* Health expectancies */
     while (fgets(line, MAXLINE, fic) != NULL)    {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
       if ((i >= firstobs) && (i <=lastobs)) {    double age, agelim, hf;
            double ***p3mat,***varhe;
         for (j=maxwav;j>=1;j--){    double **dnewm,**doldm;
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    double *xp;
           strcpy(line,stra);    double **gp, **gm;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    double ***gradg, ***trgradg;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int theta;
         }  
            varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    xp=vector(1,npar);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    dnewm=matrix(1,nlstate*2,1,npar);
     doldm=matrix(1,nlstate*2,1,nlstate*2);
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficreseij,"# Health expectancies\n");
     fprintf(ficreseij,"# Age");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    for(i=1; i<=nlstate;i++)
         for (j=ncov;j>=1;j--){      for(j=1; j<=nlstate;j++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        fprintf(ficreseij," %1d-%1d (SE)",i,j);
         }    fprintf(ficreseij,"\n");
         num[i]=atol(stra);  
     if(estepm < stepm){
         /*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]));*/      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
         i=i+1;    else  hstepm=estepm;   
       }    /* We compute the life expectancy from trapezoids spaced every estepm months
     }     * This is mainly to measure the difference between two models: for example
      * if stepm=24 months pijx are given only every 2 years and by summing them
     /*scanf("%d",i);*/     * we are calculating an estimate of the Life Expectancy assuming a linear 
   imx=i-1; /* Number of individuals */     * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
   /* Calculation of the number of parameter from char model*/     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   Tvar=ivector(1,15);         * to compare the new estimate of Life expectancy with the same linear 
   Tage=ivector(1,15);           * hypothesis. A more precise result, taking into account a more precise
         * curvature will be obtained if estepm is as small as stepm. */
   if (strlen(model) >1){  
     j=0, j1=0;    /* For example we decided to compute the life expectancy with the smallest unit */
     j=nbocc(model,'+');    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     j1=nbocc(model,'*');       nhstepm is the number of hstepm from age to agelim 
     cptcovn=j+1;       nstepm is the number of stepm from age to agelin. 
           Look at hpijx to understand the reason of that which relies in memory size
     strcpy(modelsav,model);       and note for a fixed period like estepm months */
     if (j==0) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       if (j1==0){       survival function given by stepm (the optimization length). Unfortunately it
        cutv(stra,strb,modelsav,'V');       means that if the survival funtion is printed only each two years of age and if
        Tvar[1]=atoi(strb);       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.
       else if (j1==1) {    */
        cutv(stra,strb,modelsav,'*');    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
        /*      printf("stra=%s strb=%s modelsav=%s ",stra,strb,modelsav);*/  
        Tage[1]=1; cptcovage++;    agelim=AGESUP;
        if (strcmp(stra,"age")==0) {    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
          cutv(strd,strc,strb,'V');      /* nhstepm age range expressed in number of stepm */
          Tvar[1]=atoi(strc);      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
        }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
        else if (strcmp(strb,"age")==0) {      /* if (stepm >= YEARM) hstepm=1;*/
          cutv(strd,strc,stra,'V');      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
          Tvar[1]=atoi(strc);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);
        else {printf("Error"); exit(0);}      gp=matrix(0,nhstepm,1,nlstate*2);
       }      gm=matrix(0,nhstepm,1,nlstate*2);
     }  
     else {      /* Computed by stepm unit matrices, product of hstepm matrices, stored
       for(i=j; i>=1;i--){         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
         cutv(stra,strb,modelsav,'+');      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
         /*printf("%s %s %s\n", stra,strb,modelsav);*/   
         if (strchr(strb,'*')) {  
           cutv(strd,strc,strb,'*');      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
           if (strcmp(strc,"age")==0) {  
             cutv(strb,stre,strd,'V');      /* Computing Variances of health expectancies */
             Tvar[i+1]=atoi(stre);  
             cptcovage++;       for(theta=1; theta <=npar; theta++){
             Tage[cptcovage]=i+1;        for(i=1; i<=npar; i++){ 
             printf("stre=%s ", stre);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           }        }
           else if (strcmp(strd,"age")==0) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             cutv(strb,stre,strc,'V');    
             Tvar[i+1]=atoi(stre);        cptj=0;
             cptcovage++;        for(j=1; j<= nlstate; j++){
             Tage[cptcovage]=i+1;          for(i=1; i<=nlstate; i++){
           }            cptj=cptj+1;
           else {            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
             cutv(strb,stre,strc,'V');              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
             Tvar[i+1]=ncov+1;            }
             cutv(strb,strc,strd,'V');          }
             for (k=1; k<=lastobs;k++)        }
               covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];       
           }       
         }        for(i=1; i<=npar; i++) 
         else {          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           cutv(strd,strc,strb,'V');        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           /* printf("%s %s %s", strd,strc,strb);*/        
         cptj=0;
         Tvar[i+1]=atoi(strc);        for(j=1; j<= nlstate; j++){
         }          for(i=1;i<=nlstate;i++){
         strcpy(modelsav,stra);              cptj=cptj+1;
       }            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
       cutv(strd,strc,stra,'V');              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
       Tvar[1]=atoi(strc);            }
     }          }
   }        }
         for(j=1; j<= nlstate*2; j++)
   /* printf("tvar=%d %d cptcovage=%d %d",Tvar[1],Tvar[2],cptcovage,Tage[1]);          for(h=0; h<=nhstepm-1; h++){
      scanf("%d ",i);*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     fclose(fic);          }
        } 
    if(mle==1){     
     if (weightopt != 1) { /* Maximisation without weights*/  /* End theta */
       for(i=1;i<=n;i++) weight[i]=1.0;  
     }       trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);
     /*-calculation of age at interview from date of interview and age at death -*/  
     agev=matrix(1,maxwav,1,imx);       for(h=0; h<=nhstepm-1; h++)
            for(j=1; j<=nlstate*2;j++)
     for (i=1; i<=imx; i++)  {          for(theta=1; theta <=npar; theta++)
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);            trgradg[h][j][theta]=gradg[h][theta][j];
       for(m=1; (m<= maxwav); m++){       
         if(s[m][i] >0){  
           if (s[m][i] == nlstate+1) {       for(i=1;i<=nlstate*2;i++)
             if(agedc[i]>0)        for(j=1;j<=nlstate*2;j++)
               if(moisdc[i]!=99 && andc[i]!=9999)          varhe[i][j][(int)age] =0.;
               agev[m][i]=agedc[i];  
             else{       printf("%d|",(int)age);fflush(stdout);
               printf("Warning negative age at death: %d line:%d\n",num[i],i);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
               agev[m][i]=-1;       for(h=0;h<=nhstepm-1;h++){
             }        for(k=0;k<=nhstepm-1;k++){
           }          matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);
           else if(s[m][i] !=9){ /* Should no more exist */          matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          for(i=1;i<=nlstate*2;i++)
             if(mint[m][i]==99 || anint[m][i]==9999)            for(j=1;j<=nlstate*2;j++)
               agev[m][i]=1;              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
             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);*/      /* Computing expectancies */
             }      for(i=1; i<=nlstate;i++)
             else if(agev[m][i] >agemax){        for(j=1; j<=nlstate;j++)
               agemax=agev[m][i];          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             }            
             /*agev[m][i]=anint[m][i]-annais[i];*/  /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
             /*   agev[m][i] = age[i]+2*m;*/  
           }          }
           else { /* =9 */  
             agev[m][i]=1;      fprintf(ficreseij,"%3.0f",age );
             s[m][i]=-1;      cptj=0;
           }      for(i=1; i<=nlstate;i++)
         }        for(j=1; j<=nlstate;j++){
         else /*= 0 Unknown */          cptj++;
           agev[m][i]=1;          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
       }        }
          fprintf(ficreseij,"\n");
     }     
     for (i=1; i<=imx; i++)  {      free_matrix(gm,0,nhstepm,1,nlstate*2);
       for(m=1; (m<= maxwav); m++){      free_matrix(gp,0,nhstepm,1,nlstate*2);
         if (s[m][i] > (nlstate+ndeath)) {      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);
           printf("Error: Wrong value in nlstate or ndeath\n");        free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);
           goto end;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         }    }
       }    printf("\n");
     }    fprintf(ficlog,"\n");
   
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*2,1,npar);
     free_vector(severity,1,maxwav);    free_matrix(doldm,1,nlstate*2,1,nlstate*2);
     free_imatrix(outcome,1,maxwav+1,1,n);    free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);
     free_vector(moisnais,1,n);  }
     free_vector(annais,1,n);  
     free_matrix(mint,1,maxwav,1,n);  /************ Variance ******************/
     free_matrix(anint,1,maxwav,1,n);  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav)
     free_vector(moisdc,1,n);  {
     free_vector(andc,1,n);    /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
        /* double **newm;*/
     wav=ivector(1,imx);    double **dnewm,**doldm;
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    double **dnewmp,**doldmp;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    int i, j, nhstepm, hstepm, h, nstepm ;
        int k, cptcode;
     /* Concatenates waves */    double *xp;
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
       Tcode=ivector(1,100);    double *gpp, *gmp; /* for var p point j */
    nbcode=imatrix(1,nvar,1,8);      double **varppt; /* for var p point j nlstate to nlstate+ndeath */
    ncodemax[1]=1;    double ***p3mat;
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);    double age,agelim, hf;
      double ***mobaverage;
    codtab=imatrix(1,100,1,10);    int theta;
    h=0;    char digit[4];
    m=pow(2,cptcovn);    char digitp[25];
    
    for(k=1;k<=cptcovn; k++){    char fileresprobmorprev[FILENAMELENGTH];
      for(i=1; i <=(m/pow(2,k));i++){  
        for(j=1; j <= ncodemax[k]; j++){    if(popbased==1){
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){      if(mobilav!=0)
            h++;        strcpy(digitp,"-populbased-mobilav-");
            if (h>m) h=1;codtab[h][k]=j;      else strcpy(digitp,"-populbased-nomobil-");
          }    }
        }    else 
      }      strcpy(digitp,"-stablbased-");
    }  
     if (mobilav!=0) {
    /* for(i=1; i <=m ;i++){      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
      for(k=1; k <=cptcovn; k++){      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
      }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
      printf("\n");      }
    }    }
    scanf("%d",i);*/  
        strcpy(fileresprobmorprev,"prmorprev"); 
    /* Calculates basic frequencies. Computes observed prevalence at single age    sprintf(digit,"%-d",ij);
        and prints on file fileres'p'. */    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
    freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    strcat(fileresprobmorprev,fileres);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    }
        printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     /* For Powell, parameters are in a vector p[] starting at p[1]    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
        for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
            fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     /*--------- 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\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);    fprintf(ficresprobmorprev,"\n");
        if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
    jk=1;      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
    fprintf(ficres,"# Parameters\n");      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
    printf("# Parameters\n");      exit(0);
    for(i=1,jk=1; i <=nlstate; i++){    }
      for(k=1; k <=(nlstate+ndeath); k++){    else{
        if (k != i)      fprintf(ficgp,"\n# Routine varevsij");
          {    }
            printf("%d%d ",i,k);    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
            fprintf(ficres,"%1d%1d ",i,k);      printf("Problem with html file: %s\n", optionfilehtm);
            for(j=1; j <=ncovmodel; j++){      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
              printf("%f ",p[jk]);      exit(0);
              fprintf(ficres,"%f ",p[jk]);    }
              jk++;    else{
            }      fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
            printf("\n");      fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
            fprintf(ficres,"\n");    }
          }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
      }  
    }    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");
     /* Computing hessian and covariance matrix */    for(i=1; i<=nlstate;i++)
     ftolhess=ftol; /* Usually correct */      for(j=1; j<=nlstate;j++)
     hesscov(matcov, p, npar, delti, ftolhess, func);        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
     fprintf(ficres,"# Scales\n");    fprintf(ficresvij,"\n");
     printf("# Scales\n");  
      for(i=1,jk=1; i <=nlstate; i++){    xp=vector(1,npar);
       for(j=1; j <=nlstate+ndeath; j++){    dnewm=matrix(1,nlstate,1,npar);
         if (j!=i) {    doldm=matrix(1,nlstate,1,nlstate);
           fprintf(ficres,"%1d%1d",i,j);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
           printf("%1d%1d",i,j);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           for(k=1; k<=ncovmodel;k++){  
             printf(" %.5e",delti[jk]);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
             fprintf(ficres," %.5e",delti[jk]);    gpp=vector(nlstate+1,nlstate+ndeath);
             jk++;    gmp=vector(nlstate+1,nlstate+ndeath);
           }    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
           printf("\n");    
           fprintf(ficres,"\n");    if(estepm < stepm){
         }      printf ("Problem %d lower than %d\n",estepm, stepm);
       }    }
       }    else  hstepm=estepm;   
        /* For example we decided to compute the life expectancy with the smallest unit */
     k=1;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     fprintf(ficres,"# Covariance\n");       nhstepm is the number of hstepm from age to agelim 
     printf("# Covariance\n");       nstepm is the number of stepm from age to agelin. 
     for(i=1;i<=npar;i++){       Look at hpijx to understand the reason of that which relies in memory size
       /*  if (k>nlstate) k=1;       and note for a fixed period like k years */
       i1=(i-1)/(ncovmodel*nlstate)+1;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);       survival function given by stepm (the optimization length). Unfortunately it
       printf("%s%d%d",alph[k],i1,tab[i]);*/       means that if the survival funtion is printed every two years of age and if
       fprintf(ficres,"%3d",i);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       printf("%3d",i);       results. So we changed our mind and took the option of the best precision.
       for(j=1; j<=i;j++){    */
         fprintf(ficres," %.5e",matcov[i][j]);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         printf(" %.5e",matcov[i][j]);    agelim = AGESUP;
       }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       fprintf(ficres,"\n");      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       printf("\n");      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       k++;      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
          gp=matrix(0,nhstepm,1,nlstate);
     while((c=getc(ficpar))=='#' && c!= EOF){      gm=matrix(0,nhstepm,1,nlstate);
       ungetc(c,ficpar);  
       fgets(line, MAXLINE, ficpar);  
       puts(line);      for(theta=1; theta <=npar; theta++){
       fputs(line,ficparo);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     ungetc(c,ficpar);        }
          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
      
     if (fage <= 2) {        if (popbased==1) {
       bage = agemin;          if(mobilav ==0){
       fage = agemax;            for(i=1; i<=nlstate;i++)
     }              prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");            for(i=1; i<=nlstate;i++)
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);              prlim[i][i]=mobaverage[(int)age][i][ij];
 /*------------ gnuplot -------------*/          }
 chdir(pathcd);        }
   if((ficgp=fopen("graph.plt","w"))==NULL) {    
     printf("Problem with file graph.gp");goto end;        for(j=1; j<= nlstate; j++){
   }          for(h=0; h<=nhstepm; h++){
 #ifdef windows            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
   fprintf(ficgp,"cd \"%s\" \n",pathc);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
 #endif          }
 m=pow(2,cptcovn);        }
          /* This for computing probability of death (h=1 means
  /* 1eme*/           computed over hstepm matrices product = hstepm*stepm months) 
   for (cpt=1; cpt<= nlstate ; cpt ++) {           as a weighted average of prlim.
    for (k1=1; k1<= m ; k1 ++) {        */
         for(j=nlstate+1,gpp[j]=0.;j<=nlstate+ndeath;j++){
 #ifdef windows          for(i=1,gpp[j]=0.; i<= nlstate; i++)
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
 #endif        }    
 #ifdef unix        /* end probability of death */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);  
 #endif        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
 for (i=1; i<= nlstate ; i ++) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   else fprintf(ficgp," \%%*lf (\%%*lf)");   
 }        if (popbased==1) {
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);          if(mobilav ==0){
     for (i=1; i<= nlstate ; i ++) {            for(i=1; i<=nlstate;i++)
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              prlim[i][i]=probs[(int)age][i][ij];
   else fprintf(ficgp," \%%*lf (\%%*lf)");          }else{ /* mobilav */ 
 }            for(i=1; i<=nlstate;i++)
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);              prlim[i][i]=mobaverage[(int)age][i][ij];
      for (i=1; i<= nlstate ; i ++) {          }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }          for(j=1; j<= nlstate; j++){
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          for(h=0; h<=nhstepm; h++){
 #ifdef unix            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
 fprintf(ficgp,"\nset ter gif small size 400,300");              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
 #endif          }
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        }
    }        /* This for computing probability of death (h=1 means
   }           computed over hstepm matrices product = hstepm*stepm months) 
   /*2 eme*/           as a weighted average of prlim.
         */
   for (k1=1; k1<= m ; k1 ++) {        for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
               gmp[j] += prlim[i][i]*p3mat[i][j][1];
     for (i=1; i<= nlstate+1 ; i ++) {        }    
       k=2*i;        /* end probability of death */
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {        for(j=1; j<= nlstate; j++) /* vareij */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          for(h=0; h<=nhstepm; h++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 }            }
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
       for (j=1; j<= nlstate+1 ; j ++) {        }
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
         else fprintf(ficgp," \%%*lf (\%%*lf)");      } /* End theta */
 }    
       fprintf(ficgp,"\" t\"\" w l 0,");      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
      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 ++) {      for(h=0; h<=nhstepm; h++) /* veij */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        for(j=1; j<=nlstate;j++)
   else fprintf(ficgp," \%%*lf (\%%*lf)");          for(theta=1; theta <=npar; theta++)
 }              trgradg[h][j][theta]=gradg[h][theta][j];
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  
       else fprintf(ficgp,"\" t\"\" w l 0,");      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     }        for(theta=1; theta <=npar; theta++) {
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);          trgradgp[j][theta]=gradgp[theta][j];
   }        }
    
   /*3eme*/      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
   for (k1=1; k1<= m ; k1 ++) {        for(j=1;j<=nlstate;j++)
     for (cpt=1; cpt<= nlstate ; cpt ++) {          vareij[i][j][(int)age] =0.;
       k=2+nlstate*(cpt-1);  
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);      for(h=0;h<=nhstepm;h++){
       for (i=1; i< nlstate ; i ++) {        for(k=0;k<=nhstepm;k++){
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
       }          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          for(i=1;i<=nlstate;i++)
     }            for(j=1;j<=nlstate;j++)
   }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
          }
   /* CV preval stat */      }
   for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {      /* pptj */
       k=3;      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for (i=1; i< nlstate ; i ++)   
         fprintf(ficgp,"+$%d",k+i+1);     for(j=nlstate+1;j<=nlstate+ndeath;j++)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);       for(i=nlstate+1;i<=nlstate+ndeath;i++){
                varppt[j][i]=doldmp[j][i];
       l=3+(nlstate+ndeath)*cpt;       }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  
       for (i=1; i< nlstate ; i ++) {      /* end ppptj */
         l=3+(nlstate+ndeath)*cpt;      /*  x centered again */
         fprintf(ficgp,"+$%d",l+i+1);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       }      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);     
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      if (popbased==1) {
     }        if(mobilav ==0){
   }          for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
   /* proba elementaires */        }else{ /* mobilav */ 
    for(i=1,jk=1; i <=nlstate; i++){          for(i=1; i<=nlstate;i++)
     for(k=1; k <=(nlstate+ndeath); k++){            prlim[i][i]=mobaverage[(int)age][i][ij];
       if (k != i) {        }
         for(j=1; j <=ncovmodel; j++){      }
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/      
           /*fprintf(ficgp,"%s",alph[1]);*/      /* This for computing probability of death (h=1 means
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
           jk++;         as a weighted average of prlim.
           fprintf(ficgp,"\n");      */
         }      for(j=nlstate+1;j<=nlstate+ndeath;j++){
       }        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     }          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     }      }    
       /* end probability of death */
   for(jk=1; jk <=m; jk++) {  
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
    i=1;      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
    for(k2=1; k2<=nlstate; k2++) {        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
      k3=i;        for(i=1; i<=nlstate;i++){
      for(k=1; k<=(nlstate+ndeath); k++) {          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
        if (k != k2){        }
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);      } 
       fprintf(ficresprobmorprev,"\n");
         for(j=3; j <=ncovmodel; j++)  
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      fprintf(ficresvij,"%.0f ",age );
         fprintf(ficgp,")/(1");      for(i=1; i<=nlstate;i++)
                for(j=1; j<=nlstate;j++){
         for(k1=1; k1 <=nlstate; k1++){            fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);        }
           for(j=3; j <=ncovmodel; j++)      fprintf(ficresvij,"\n");
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      free_matrix(gp,0,nhstepm,1,nlstate);
           fprintf(ficgp,")");      free_matrix(gm,0,nhstepm,1,nlstate);
         }      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         i=i+ncovmodel;    } /* End age */
        }    free_vector(gpp,nlstate+1,nlstate+ndeath);
      }    free_vector(gmp,nlstate+1,nlstate+ndeath);
    }    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   }    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
        /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
   fclose(ficgp);    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
      /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
 chdir(path);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
     free_matrix(agev,1,maxwav,1,imx);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     free_ivector(wav,1,imx);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",fileresprobmorprev);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",fileresprobmorprev);
        fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
     free_imatrix(s,1,maxwav+1,1,n);    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", estepm,digitp,digit);
        /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
      */
     free_ivector(num,1,n);    fprintf(ficgp,"\nset out \"varmuptjgr%s%s.png\";replot;",digitp,digit);
     free_vector(agedc,1,n);  
     free_vector(weight,1,n);    free_vector(xp,1,npar);
     /*free_matrix(covar,1,NCOVMAX,1,n);*/    free_matrix(doldm,1,nlstate,1,nlstate);
     fclose(ficparo);    free_matrix(dnewm,1,nlstate,1,npar);
     fclose(ficres);    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
    }    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
        free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
    /*________fin mle=1_________*/    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
        fclose(ficresprobmorprev);
     fclose(ficgp);
      fclose(fichtm);
     /* No more information from the sample is required now */  }
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){  /************ Variance of prevlim ******************/
     ungetc(c,ficpar);  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)
     fgets(line, MAXLINE, ficpar);  {
     puts(line);    /* Variance of prevalence limit */
     fputs(line,ficparo);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   }    double **newm;
   ungetc(c,ficpar);    double **dnewm,**doldm;
      int i, j, nhstepm, hstepm;
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    int k, cptcode;
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    double *xp;
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    double *gp, *gm;
 /*--------- index.htm --------*/    double **gradg, **trgradg;
     double age,agelim;
   if((fichtm=fopen("index.htm","w"))==NULL)    {    int theta;
     printf("Problem with index.htm \n");goto end;     
   }    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
     fprintf(ficresvpl,"# Age");
  fprintf(fichtm,"<body><ul> Imach, Version 0.64a<hr> <li>Outputs files<br><br>\n    for(i=1; i<=nlstate;i++)
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        fprintf(ficresvpl," %1d-%1d",i,i);
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>    fprintf(ficresvpl,"\n");
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>  
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    xp=vector(1,npar);
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    dnewm=matrix(1,nlstate,1,npar);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    doldm=matrix(1,nlstate,1,nlstate);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    hstepm=1*YEARM; /* Every year of age */
         - 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);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
  fprintf(fichtm," <li>Graphs</li>\n<p>");    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
  m=cptcovn;      if (stepm >= YEARM) hstepm=1;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
  j1=0;      gp=vector(1,nlstate);
  for(k1=1; k1<=m;k1++){      gm=vector(1,nlstate);
    for(i1=1; i1<=ncodemax[k1];i1++){  
        j1++;      for(theta=1; theta <=npar; theta++){
        if (cptcovn > 0) {        for(i=1; i<=npar; i++){ /* Computes gradient */
          fprintf(fichtm,"<hr>************ Results for covariates");          xp[i] = x[i] + (i==theta ?delti[theta]:0);
          for (cpt=1; cpt<=cptcovn;cpt++)        }
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
          fprintf(fichtm," ************\n<hr>");        for(i=1;i<=nlstate;i++)
        }          gp[i] = prlim[i][i];
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);            for(i=1; i<=npar; i++) /* Computes gradient */
        for(cpt=1; cpt<nlstate;cpt++){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        for(i=1;i<=nlstate;i++)
        }          gm[i] = prlim[i][i];
     for(cpt=1; cpt<=nlstate;cpt++) {  
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident        for(i=1;i<=nlstate;i++)
 interval) in state (%d): v%s%d%d.gif <br>          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        } /* End theta */
      }  
      for(cpt=1; cpt<=nlstate;cpt++) {      trgradg =matrix(1,nlstate,1,npar);
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>  
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      for(j=1; j<=nlstate;j++)
      }        for(theta=1; theta <=npar; theta++)
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          trgradg[j][theta]=gradg[theta][j];
 health expectancies in states (1) and (2): e%s%d.gif<br>  
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);      for(i=1;i<=nlstate;i++)
 fprintf(fichtm,"\n</body>");        varpl[i][(int)age] =0.;
    }      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
  }      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
 fclose(fichtm);      for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   /*--------------- Prevalence limit --------------*/  
        fprintf(ficresvpl,"%.0f ",age );
   strcpy(filerespl,"pl");      for(i=1; i<=nlstate;i++)
   strcat(filerespl,fileres);        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      fprintf(ficresvpl,"\n");
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      free_vector(gp,1,nlstate);
   }      free_vector(gm,1,nlstate);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);      free_matrix(gradg,1,npar,1,nlstate);
   fprintf(ficrespl,"#Prevalence limit\n");      free_matrix(trgradg,1,nlstate,1,npar);
   fprintf(ficrespl,"#Age ");    } /* End age */
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");    free_vector(xp,1,npar);
      free_matrix(doldm,1,nlstate,1,npar);
   prlim=matrix(1,nlstate,1,nlstate);    free_matrix(dnewm,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 */  /************ Variance of one-step probabilities  ******************/
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   k=0;  {
   agebase=agemin;    int i, j=0,  i1, k1, l1, t, tj;
   agelim=agemax;    int k2, l2, j1,  z1;
   ftolpl=1.e-10;    int k=0,l, cptcode;
   i1=cptcovn;    int first=1, first1;
   if (cptcovn < 1){i1=1;}    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
   for(cptcov=1;cptcov<=i1;cptcov++){    double *xp;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double *gp, *gm;
         k=k+1;    double **gradg, **trgradg;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    double **mu;
         fprintf(ficrespl,"\n#******");    double age,agelim, cov[NCOVMAX];
         for(j=1;j<=cptcovn;j++)    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
           fprintf(ficrespl," V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    int theta;
         fprintf(ficrespl,"******\n");    char fileresprob[FILENAMELENGTH];
            char fileresprobcov[FILENAMELENGTH];
         for (age=agebase; age<=agelim; age++){    char fileresprobcor[FILENAMELENGTH];
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  
           fprintf(ficrespl,"%.0f",age );    double ***varpij;
           for(i=1; i<=nlstate;i++)  
           fprintf(ficrespl," %.5f", prlim[i][i]);    strcpy(fileresprob,"prob"); 
           fprintf(ficrespl,"\n");    strcat(fileresprob,fileres);
         }    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       }      printf("Problem with resultfile: %s\n", fileresprob);
     }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
   fclose(ficrespl);    }
   /*------------- h Pij x at various ages ------------*/    strcpy(fileresprobcov,"probcov"); 
      strcat(fileresprobcov,fileres);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      printf("Problem with resultfile: %s\n", fileresprobcov);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   }    }
   printf("Computing pij: result on file '%s' \n", filerespij);    strcpy(fileresprobcor,"probcor"); 
      strcat(fileresprobcor,fileres);
   stepsize=(int) (stepm+YEARM-1)/YEARM;    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
   if (stepm<=24) stepsize=2;      printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   agelim=AGESUP;    }
   hstepm=stepsize*YEARM; /* Every year of age */    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
      printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   k=0;    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   for(cptcov=1;cptcov<=i1;cptcov++){    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
       k=k+1;    
         fprintf(ficrespij,"\n#****** ");    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
         for(j=1;j<=cptcovn;j++)    fprintf(ficresprob,"# Age");
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
         fprintf(ficrespij,"******\n");    fprintf(ficresprobcov,"# Age");
            fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    fprintf(ficresprobcov,"# Age");
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(i=1; i<=nlstate;i++)
           oldm=oldms;savm=savms;      for(j=1; j<=(nlstate+ndeath);j++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          fprintf(ficresprob," p%1d-%1d (SE)",i,j);
           fprintf(ficrespij,"# Age");        fprintf(ficresprobcov," p%1d-%1d ",i,j);
           for(i=1; i<=nlstate;i++)        fprintf(ficresprobcor," p%1d-%1d ",i,j);
             for(j=1; j<=nlstate+ndeath;j++)      }  
               fprintf(ficrespij," %1d-%1d",i,j);    fprintf(ficresprob,"\n");
           fprintf(ficrespij,"\n");    fprintf(ficresprobcov,"\n");
           for (h=0; h<=nhstepm; h++){    fprintf(ficresprobcor,"\n");
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    xp=vector(1,npar);
             for(i=1; i<=nlstate;i++)    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
               for(j=1; j<=nlstate+ndeath;j++)    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
             fprintf(ficrespij,"\n");    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
           }    first=1;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
           fprintf(ficrespij,"\n");      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
         }      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
     }      exit(0);
   }    }
     else{
   fclose(ficrespij);      fprintf(ficgp,"\n# Routine varprob");
     }
   /*---------- Health expectancies and variances ------------*/    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
   strcpy(filerest,"t");      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
   strcat(filerest,fileres);      exit(0);
   if((ficrest=fopen(filerest,"w"))==NULL) {    }
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    else{
   }      fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      fprintf(fichtm,"\n");
   
       fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
   strcpy(filerese,"e");      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");
   strcat(filerese,fileres);      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");
   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);    cov[1]=1;
     tj=cptcoveff;
  strcpy(fileresv,"v");    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   strcat(fileresv,fileres);    j1=0;
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    for(t=1; t<=tj;t++){
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      for(i1=1; i1<=ncodemax[t];i1++){ 
   }        j1++;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);        if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
   k=0;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   for(cptcov=1;cptcov<=i1;cptcov++){          fprintf(ficresprob, "**********\n#");
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          fprintf(ficresprobcov, "\n#********** Variable "); 
       k=k+1;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       fprintf(ficrest,"\n#****** ");          fprintf(ficresprobcov, "**********\n#");
       for(j=1;j<=cptcovn;j++)          
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);          fprintf(ficgp, "\n#********** Variable "); 
       fprintf(ficrest,"******\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#");
       fprintf(ficreseij,"\n#****** ");          
       for(j=1;j<=cptcovn;j++)          
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);          fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
       fprintf(ficreseij,"******\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
       fprintf(ficresvij,"\n#****** ");          
       for(j=1;j<=cptcovn;j++)          fprintf(ficresprobcor, "\n#********** Variable ");    
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       fprintf(ficresvij,"******\n");          fprintf(ficgp, "**********\n#");    
         }
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        
       oldm=oldms;savm=savms;        for (age=bage; age<=fage; age ++){ 
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);            cov[2]=age;
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          for (k=1; k<=cptcovn;k++) {
       oldm=oldms;savm=savms;            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);          }
                for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          for (k=1; k<=cptcovprod;k++)
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       fprintf(ficrest,"\n");          
                  gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
       hf=1;          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
       if (stepm >= YEARM) hf=stepm/YEARM;          gp=vector(1,(nlstate)*(nlstate+ndeath));
       epj=vector(1,nlstate+1);          gm=vector(1,(nlstate)*(nlstate+ndeath));
       for(age=bage; age <=fage ;age++){      
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);          for(theta=1; theta <=npar; theta++){
         fprintf(ficrest," %.0f",age);            for(i=1; i<=npar; i++)
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){              xp[i] = x[i] + (i==theta ?delti[theta]:0);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {            
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];            pmij(pmmij,cov,ncovmodel,xp,nlstate);
           }            
           epj[nlstate+1] +=epj[j];            k=0;
         }            for(i=1; i<= (nlstate); i++){
         for(i=1, vepp=0.;i <=nlstate;i++)              for(j=1; j<=(nlstate+ndeath);j++){
           for(j=1;j <=nlstate;j++)                k=k+1;
             vepp += vareij[i][j][(int)age];                gp[k]=pmmij[i][j];
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));              }
         for(j=1;j <=nlstate;j++){            }
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));            
         }            for(i=1; i<=npar; i++)
         fprintf(ficrest,"\n");              xp[i] = x[i] - (i==theta ?delti[theta]:0);
       }      
     }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   }            k=0;
                    for(i=1; i<=(nlstate); i++){
  fclose(ficreseij);              for(j=1; j<=(nlstate+ndeath);j++){
  fclose(ficresvij);                k=k+1;
   fclose(ficrest);                gm[k]=pmmij[i][j];
   fclose(ficpar);              }
   free_vector(epj,1,nlstate+1);            }
   /*  scanf("%d ",i); */       
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
   /*------- Variance limit prevalence------*/                gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];  
           }
 strcpy(fileresvpl,"vpl");  
   strcat(fileresvpl,fileres);          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {            for(theta=1; theta <=npar; theta++)
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);              trgradg[j][theta]=gradg[theta][j];
     exit(0);          
   }          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
  k=0;          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
  for(cptcov=1;cptcov<=i1;cptcov++){          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
      k=k+1;  
      fprintf(ficresvpl,"\n#****** ");          pmij(pmmij,cov,ncovmodel,x,nlstate);
      for(j=1;j<=cptcovn;j++)          
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);          k=0;
      fprintf(ficresvpl,"******\n");          for(i=1; i<=(nlstate); i++){
                  for(j=1; j<=(nlstate+ndeath);j++){
      varpl=matrix(1,nlstate,(int) bage, (int) fage);              k=k+1;
      oldm=oldms;savm=savms;              mu[k][(int) age]=pmmij[i][j];
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);            }
    }          }
  }          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
   fclose(ficresvpl);              varpij[i][j][(int)age] = doldm[i][j];
   
   /*---------- End : free ----------------*/          /*printf("\n%d ",(int)age);
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
              printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);            }*/
    
            fprintf(ficresprob,"\n%d ",(int)age);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficresprobcov,"\n%d ",(int)age);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficresprobcor,"\n%d ",(int)age);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
              fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
   free_matrix(matcov,1,npar,1,npar);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   free_vector(delti,1,npar);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
              fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          }
           i=0;
   printf("End of Imach\n");          for (k=1; k<=(nlstate);k++){
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */            for (l=1; l<=(nlstate+ndeath);l++){ 
                i=i++;
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
   /*printf("Total time was %d uSec.\n", total_usecs);*/              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
   /*------ End -----------*/              for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
  end:                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
 #ifdef windows              }
  chdir(pathcd);            }
 #endif          }/* end of loop for state */
  system("wgnuplot graph.plt");        } /* end of loop for age */
   
 #ifdef windows        /* Confidence intervalle of pij  */
   while (z[0] != 'q') {        /*
     chdir(pathcd);          fprintf(ficgp,"\nset noparametric;unset label");
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
     scanf("%s",z);          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
     if (z[0] == 'c') system("./imach");          fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
     else if (z[0] == 'e') {          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
       chdir(path);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
       system("index.htm");          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
     }        */
     else if (z[0] == 'q') exit(0);  
   }        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
 #endif        first1=1;
 }        for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtm," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fclose(ficgp);
     fclose(fichtm);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
     /*char optionfilehtm[FILENAMELENGTH];*/
     if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
       fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);
     }
   
      fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n
    - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n
    - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n
    - Life expectancies by age and initial health status (estepm=%2d months): 
      <a href=\"e%s\">e%s</a> <br>\n</li>", \
     jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>
   <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>
   <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1); 
          /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>
   <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>
   <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and
   health expectancies in states (1) and (2): e%s%d.png<br>
   <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n
    - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n
    - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n
    - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n 
    - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n
    - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);
   
    if(popforecast==1) fprintf(fichtm,"\n
    - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n
    - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n
           <br>",fileres,fileres,fileres,fileres);
    else 
      fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);
   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident
   interval) in state (%d): v%s%d%d.png <br>
   <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   fclose(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
       fprintf(ficlog,"Problem with file %s",optionfilegnuplot);
     }
   
     /*#ifdef windows */
       fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   m=pow(2,cptcoveff);
     
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        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);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Stable 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));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
         fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);
           
         } 
       }
     }
     
     /* CV preval stat */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fclose(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** 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;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
    agelim=AGESUP;
    calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;
   
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
    
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     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!=0) 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;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedate+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedate+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedate+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1); 
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) 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 movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     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;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[80],pathc[80],pathcd[80],pathtot[80],model[80];
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;
   
     char *alph[]={"a","a","b","c","d","e"}, str[4];
   
   
     char z[1]="c", occ;
   #include <sys/time.h>
   #include <time.h>
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
    
     /* long total_usecs;
        struct timeval start_time, end_time;
     
        gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     getcwd(pathcd, size);
   
     printf("\n%s",version);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     replace(pathc,path);
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s",version);
     fprintf(ficlog,"\nEnter the parameter file name: ");
     fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     fflush(ficlog);
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       goto end;
     }
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) {
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     
     /* Read guess parameters */
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
     param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     for(i=1; i <=nlstate; i++)
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         fprintf(ficparo,"%1d%1d",i1,j1);
         if(mle==1)
           printf("%1d%1d",i,j);
         fprintf(ficlog,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar," %lf",&param[i][j][k]);
           if(mle==1){
             printf(" %lf",param[i][j][k]);
             fprintf(ficlog," %lf",param[i][j][k]);
           }
           else
             fprintf(ficlog," %lf",param[i][j][k]);
           fprintf(ficparo," %lf",param[i][j][k]);
         }
         fscanf(ficpar,"\n");
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
     
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     p=param[1][1];
     
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */
     for(i=1; i <=nlstate; i++){
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i1,j1);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar,"%le",&delti3[i][j][k]);
           printf(" %le",delti3[i][j][k]);
           fprintf(ficparo," %le",delti3[i][j][k]);
         }
         fscanf(ficpar,"\n");
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     delti=delti3[1][1];
     
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
     matcov=matrix(1,npar,1,npar);
     for(i=1; i <=npar; i++){
       fscanf(ficpar,"%s",&str);
       if(mle==1)
         printf("%s",str);
       fprintf(ficlog,"%s",str);
       fprintf(ficparo,"%s",str);
       for(j=1; j <=i; j++){
         fscanf(ficpar," %le",&matcov[i][j]);
         if(mle==1){
           printf(" %.5le",matcov[i][j]);
           fprintf(ficlog," %.5le",matcov[i][j]);
         }
         else
           fprintf(ficlog," %.5le",matcov[i][j]);
         fprintf(ficparo," %.5le",matcov[i][j]);
       }
       fscanf(ficpar,"\n");
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       fprintf(ficparo,"\n");
     }
     for(i=1; i <=npar; i++)
       for(j=i+1;j<=npar;j++)
         matcov[i][j]=matcov[j][i];
      
     if(mle==1)
       printf("\n");
     fprintf(ficlog,"\n");
   
   
     /*-------- Rewriting paramater file ----------*/
     strcpy(rfileres,"r");    /* "Rparameterfile */
     strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
     strcat(rfileres,".");    /* */
     strcat(rfileres,optionfilext);    /* Other files have txt extension */
     if((ficres =fopen(rfileres,"w"))==NULL) {
       printf("Problem writing new parameter file: %s\n", fileres);goto end;
       fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
     }
     fprintf(ficres,"#%s\n",version);
       
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=ivector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     while (fgets(line, MAXLINE, fic) != NULL)    {
       if ((i >= firstobs) && (i <=lastobs)) {
           
         for (j=maxwav;j>=1;j--){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb); 
           strcpy(line,stra);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         }
           
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);
         for (j=ncovcol;j>=1;j--){
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         } 
         num[i]=atol(stra);
           
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
   
         i=i+1;
       }
     }
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
    
     /* Calculation of the number of parameter from char model*/
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);
     fclose(fic);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=1; (m<= maxwav); m++){
         if(s[m][i] >0 || s[m][i]==-2){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if(moisdc[i]!=99 && andc[i]!=9999) agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if (andc[i]!=9999){
                   printf("Warning negative age at death: %d line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Should no more exist */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if(mint[m][i]==99 || anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=1; (m<= maxwav); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
     
   
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     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); /* Cross tabulation to get the order of 
                                    the estimations*/
     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){ /* Could be 1 or 2 */
       mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
     }
       
     /*--------- results files --------------*/
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
     
   
     jk=1;
     fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) 
           {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%f ",p[jk]);
               fprintf(ficlog,"%f ",p[jk]);
               fprintf(ficres,"%f ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
       }
     }
     if(mle==1){
       /* Computing hessian and covariance matrix */
       ftolhess=ftol; /* Usually correct */
       hesscov(matcov, p, npar, delti, ftolhess, func);
     }
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
     for(i=1,jk=1; i <=nlstate; i++){
       for(j=1; j <=nlstate+ndeath; j++){
         if (j!=i) {
           fprintf(ficres,"%1d%1d",i,j);
           printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             printf(" %.5e",delti[jk]);
             fprintf(ficlog," %.5e",delti[jk]);
             fprintf(ficres," %.5e",delti[jk]);
             jk++;
           }
           printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficres,"\n");
         }
       }
     }
      
     fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
     if(mle==1)
       printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
     fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
     for(i=1,k=1;i<=npar;i++){
       /*  if (k>nlstate) k=1;
           i1=(i-1)/(ncovmodel*nlstate)+1; 
           fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);
           printf("%s%d%d",alph[k],i1,tab[i]);
       */
       fprintf(ficres,"%3d",i);
       if(mle==1)
         printf("%3d",i);
       fprintf(ficlog,"%3d",i);
       for(j=1; j<=i;j++){
         fprintf(ficres," %.5e",matcov[i][j]);
         if(mle==1)
           printf(" %.5e",matcov[i][j]);
         fprintf(ficlog," %.5e",matcov[i][j]);
       }
       fprintf(ficres,"\n");
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       k++;
     }
      
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     estepm=0;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
     if (estepm==0 || estepm < stepm) estepm=stepm;
     if (fage <= 2) {
       bage = ageminpar;
       fage = agemaxpar;
     }
      
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
      
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
     fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
     fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
     fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
      
     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\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2);
     fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);
     fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);
   
   
     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,Tvaraff,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);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     fclose(ficgp);
     printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfile);
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n
   \n
   Total number of observations=%d <br>\n
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n
   <hr  size=\"2\" color=\"#EC5E5E\">
    <ul><li><h4>Parameter files</h4>\n
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n
    - Log file of the run: <a href=\"%s\">%s</a><br>\n
    - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,filelog,filelog,optionfilegnuplot,optionfilegnuplot);
     fclose(fichtm);
   
     printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
    
     /*------------ free_vector  -------------*/
     chdir(path);
    
     free_ivector(wav,1,imx);
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
     free_imatrix(bh,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,0,NCOVMAX,1,n);*/
     /*free_matrix(covar,1,NCOVMAX,1,n);*/
     fclose(ficparo);
     fclose(ficres);
   
   
     /*--------------- Prevalence limit  (stable prevalence) --------------*/
     
     strcpy(filerespl,"pl");
     strcat(filerespl,fileres);
     if((ficrespl=fopen(filerespl,"w"))==NULL) {
       printf("Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
       fprintf(ficlog,"Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
     }
     printf("Computing stable prevalence: result on file '%s' \n", filerespl);
     fprintf(ficlog,"Computing stable prevalence: result on file '%s' \n", filerespl);
     fprintf(ficrespl,"#Stable prevalence \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);
   
     agebase=ageminpar;
     agelim=agemaxpar;
     ftolpl=1.e-10;
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
   
     for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
         fprintf(ficrespl,"\n#******");
         printf("\n#******");
         fprintf(ficlog,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespl,"******\n");
         printf("******\n");
         fprintf(ficlog,"******\n");
           
         for (age=agebase; age<=agelim; age++){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
           fprintf(ficrespl,"%.0f",age );
           for(i=1; i<=nlstate;i++)
             fprintf(ficrespl," %.5f", prlim[i][i]);
           fprintf(ficrespl,"\n");
         }
       }
     }
     fclose(ficrespl);
   
     /*------------- h Pij x at various ages ------------*/
     
     strcpy(filerespij,"pij");  strcat(filerespij,fileres);
     if((ficrespij=fopen(filerespij,"w"))==NULL) {
       printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
       fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
     }
     printf("Computing pij: result on file '%s' \n", filerespij);
     fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     /*if (stepm<=24) stepsize=2;*/
   
     agelim=AGESUP;
     hstepm=stepsize*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
     /* hstepm=1;   aff par mois*/
   
     for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         fprintf(ficrespij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficrespij,"******\n");
           
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
           /*        nhstepm=nhstepm*YEARM; aff par mois*/
   
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           oldm=oldms;savm=savms;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           fprintf(ficrespij,"# Age");
           for(i=1; i<=nlstate;i++)
             for(j=1; j<=nlstate+ndeath;j++)
               fprintf(ficrespij," %1d-%1d",i,j);
           fprintf(ficrespij,"\n");
           for (h=0; h<=nhstepm; h++){
             fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);
             fprintf(ficrespij,"\n");
           }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"\n");
         }
       }
     }
   
     varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);
   
     fclose(ficrespij);
   
   
     /*---------- Forecasting ------------------*/
      if((stepm == 1) && (strcmp(model,".")==0)){
       prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);
       if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);
     } 
     else{
       erreur=108;
       printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model);
       fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model);
       }
     
   
     /*---------- Health expectancies and variances ------------*/
   
     strcpy(filerest,"t");
     strcat(filerest,fileres);
     if((ficrest=fopen(filerest,"w"))==NULL) {
       printf("Problem with total LE resultfile: %s\n", filerest);goto end;
       fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
     }
     printf("Computing Total LEs with variances: file '%s' \n", filerest); 
     fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest); 
   
   
     strcpy(filerese,"e");
     strcat(filerese,fileres);
     if((ficreseij=fopen(filerese,"w"))==NULL) {
       printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
     }
     printf("Computing Health Expectancies: result on file '%s' \n", filerese);
     fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
   
     strcpy(fileresv,"v");
     strcat(fileresv,fileres);
     if((ficresvij=fopen(fileresv,"w"))==NULL) {
       printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
       fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
     }
     printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
     fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
     calagedate=-1;
   
     prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1; 
         fprintf(ficrest,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficrest,"******\n");
   
         fprintf(ficreseij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficreseij,"******\n");
   
         fprintf(ficresvij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficresvij,"******\n");
   
         eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;
         evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);  
    
         vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;
         varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav);
         if(popbased==1){
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav);
         }
   
    
         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) {
             if(mobilav ==0){
               for(i=1; i<=nlstate;i++)
                 prlim[i][i]=probs[(int)age][i][k];
             }else{ /* mobilav */ 
               for(i=1; i<=nlstate;i++)
                 prlim[i][i]=mobaverage[(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_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         free_vector(epj,1,nlstate+1);
       }
     }
     free_vector(weight,1,n);
     free_imatrix(Tvard,1,15,1,2);
     free_imatrix(s,1,maxwav+1,1,n);
     free_matrix(anint,1,maxwav,1,n); 
     free_matrix(mint,1,maxwav,1,n);
     free_ivector(cod,1,n);
     free_ivector(tab,1,NCOVMAX);
     fclose(ficreseij);
     fclose(ficresvij);
     fclose(ficrest);
     fclose(ficpar);
     
     /*------- Variance of stable prevalence------*/   
   
     strcpy(fileresvpl,"vpl");
     strcat(fileresvpl,fileres);
     if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
       printf("Problem with variance of stable prevalence  resultfile: %s\n", fileresvpl);
       exit(0);
     }
     printf("Computing Variance-covariance of stable prevalence: file '%s' \n", fileresvpl);
   
     for(cptcov=1,k=0;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);
         free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
       }
     }
   
     fclose(ficresvpl);
   
     /*---------- End : free ----------------*/
     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(covar,0,NCOVMAX,1,n);
     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);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ivector(ncodemax,1,8);
     free_ivector(Tvar,1,15);
     free_ivector(Tprod,1,15);
     free_ivector(Tvaraff,1,15);
     free_ivector(Tage,1,15);
     free_ivector(Tcode,1,100);
   
     fprintf(fichtm,"\n</body>");
     fclose(fichtm);
     fclose(ficgp);
     
   
     if(erreur >0){
       printf("End of Imach with error or warning %d\n",erreur);
       fprintf(ficlog,"End of Imach with error or warning %d\n",erreur);
     }else{
      printf("End of Imach\n");
      fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     fclose(ficlog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     
     /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/
     /*printf("Total time was %d uSec.\n", total_usecs);*/
     /*------ End -----------*/
   
     end:
   #ifdef windows
     /* chdir(pathcd);*/
   #endif 
    /*system("wgnuplot graph.plt");*/
    /*system("../gp37mgw/wgnuplot graph.plt");*/
    /*system("cd ../gp37mgw");*/
    /* system("..\\gp37mgw\\wgnuplot graph.plt");*/
     strcpy(plotcmd,GNUPLOTPROGRAM);
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting: %s\n",plotcmd);fflush(stdout);
     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 */
   }
   
   

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changed lines
  Added in v.1.68


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