Diff for /imach/src/imach.c between versions 1.4 and 1.72

version 1.4, 2001/05/02 17:34:41 version 1.72, 2003/03/28 13:33:56
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>
   #include <stdio.h>
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  #include <stdlib.h>
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  #include <unistd.h>
   
 #define NINTERVMAX 8  #define MAXLINE 256
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  #define GNUPLOTPROGRAM "gnuplot"
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 #define NCOVMAX 8 /* Maximum number of covariates */  #define FILENAMELENGTH 80
 #define MAXN 20000  /*#define DEBUG*/
 #define YEARM 12. /* Number of months per year */  #define windows
 #define AGESUP 130  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 #define AGEBASE 40  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
   #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 int nvar;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 static int cptcov;  
 int cptcovn;  #define NINTERVMAX 8
 int npar=NPARMAX;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 int nlstate=2; /* Number of live states */  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 int ndeath=1; /* Number of dead states */  #define NCOVMAX 8 /* Maximum number of covariates */
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  #define MAXN 20000
   #define YEARM 12. /* Number of months per year */
 int *wav; /* Number of waves for this individuual 0 is possible */  #define AGESUP 130
 int maxwav; /* Maxim number of waves */  #define AGEBASE 40
 int mle, weightopt;  #ifdef windows
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  #define DIRSEPARATOR '\\'
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  #define ODIRSEPARATOR '/'
 double **oldm, **newm, **savm; /* Working pointers to matrices */  #else
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  #define DIRSEPARATOR '/'
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;  #define ODIRSEPARATOR '\\'
 FILE *ficgp, *fichtm;  #endif
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];  char version[80]="Imach version 0.93, February 2003, INED-EUROREVES ";
  FILE  *ficresvij;  int erreur; /* Error number */
   char fileresv[FILENAMELENGTH];  int nvar;
  FILE  *ficresvpl;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   char fileresvpl[FILENAMELENGTH];  int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
   int ndeath=1; /* Number of dead states */
   int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   int popbased=0;
 #define NR_END 1  
 #define FREE_ARG char*  int *wav; /* Number of waves for this individuual 0 is possible */
 #define FTOL 1.0e-10  int maxwav; /* Maxim number of waves */
   int jmin, jmax; /* min, max spacing between 2 waves */
 #define NRANSI  int mle, weightopt;
 #define ITMAX 200  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
 #define TOL 2.0e-4  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
              * wave mi and wave mi+1 is not an exact multiple of stepm. */
 #define CGOLD 0.3819660  double jmean; /* Mean space between 2 waves */
 #define ZEPS 1.0e-10  double **oldm, **newm, **savm; /* Working pointers to matrices */
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 #define GOLD 1.618034  FILE *ficlog;
 #define GLIMIT 100.0  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 #define TINY 1.0e-20  FILE *ficresprobmorprev;
   FILE *fichtm; /* Html File */
 static double maxarg1,maxarg2;  FILE *ficreseij;
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  char filerese[FILENAMELENGTH];
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  FILE  *ficresvij;
    char fileresv[FILENAMELENGTH];
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  FILE  *ficresvpl;
 #define rint(a) floor(a+0.5)  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 static double sqrarg;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 int imx;  char filelog[FILENAMELENGTH]; /* Log file */
 int stepm;  char filerest[FILENAMELENGTH];
 /* Stepm, step in month: minimum step interpolation*/  char fileregp[FILENAMELENGTH];
   char popfile[FILENAMELENGTH];
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij;  #define NR_END 1
   #define FREE_ARG char*
 double *weight;  #define FTOL 1.0e-10
 int **s; /* Status */  
 double *agedc, **covar, idx;  #define NRANSI 
 int **nbcode, *Tcode, *Tvar, **codtab;  #define ITMAX 200 
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  #define TOL 2.0e-4 
 double ftolhess; /* Tolerance for computing hessian */  
   #define CGOLD 0.3819660 
   #define ZEPS 1.0e-10 
 /******************************************/  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   
 void replace(char *s, char*t)  #define GOLD 1.618034 
 {  #define GLIMIT 100.0 
   int i;  #define TINY 1.0e-20 
   int lg=20;  
   i=0;  static double maxarg1,maxarg2;
   lg=strlen(t);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   for(i=0; i<= lg; i++) {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     (s[i] = t[i]);    
     if (t[i]== '\\') s[i]='/';  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   }  #define rint(a) floor(a+0.5)
 }  
   static double sqrarg;
 int nbocc(char *s, char occ)  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int i,j=0;  
   int lg=20;  int imx; 
   i=0;  int stepm;
   lg=strlen(s);  /* Stepm, step in month: minimum step interpolation*/
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;  int estepm;
   }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   return j;  
 }  int m,nb;
   int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
 void cutv(char *u,char *v, char*t, char occ)  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
 {  double **pmmij, ***probs;
   int i,lg,j,p;  double dateintmean=0;
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {  double *weight;
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  int **s; /* Status */
   }  double *agedc, **covar, idx;
   int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   lg=strlen(t);  
   for(j=0; j<p; j++) {  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
     (u[j] = t[j]);  double ftolhess; /* Tolerance for computing hessian */
     u[p]='\0';  
   }  /**************** split *************************/
   static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
    for(j=0; j<= lg; j++) {  {
     if (j>=(p+1))(v[j-p-1] = t[j]);    char  *ss;                            /* pointer */
   }    int   l1, l2;                         /* length counters */
 }  
     l1 = strlen(path );                   /* length of path */
 /********************** nrerror ********************/    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 void nrerror(char error_text[])    if ( ss == NULL ) {                   /* no directory, so use current */
 {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   fprintf(stderr,"ERREUR ...\n");        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   fprintf(stderr,"%s\n",error_text);  #if     defined(__bsd__)                /* get current working directory */
   exit(1);      extern char *getwd( );
 }  
 /*********************** vector *******************/      if ( getwd( dirc ) == NULL ) {
 double *vector(int nl, int nh)  #else
 {      extern char *getcwd( );
   double *v;  
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   if (!v) nrerror("allocation failure in vector");  #endif
   return v-nl+NR_END;        return( GLOCK_ERROR_GETCWD );
 }      }
       strcpy( name, path );               /* we've got it */
 /************************ free vector ******************/    } else {                              /* strip direcotry from path */
 void free_vector(double*v, int nl, int nh)      ss++;                               /* after this, the filename */
 {      l2 = strlen( ss );                  /* length of filename */
   free((FREE_ARG)(v+nl-NR_END));      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 }      strcpy( name, ss );         /* save file name */
       strncpy( dirc, path, l1 - l2 );     /* now the directory */
 /************************ivector *******************************/      dirc[l1-l2] = 0;                    /* add zero */
 int *ivector(long nl,long nh)    }
 {    l1 = strlen( dirc );                  /* length of directory */
   int *v;  #ifdef windows
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   if (!v) nrerror("allocation failure in ivector");  #else
   return v-nl+NR_END;    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
 }  #endif
     ss = strrchr( name, '.' );            /* find last / */
 /******************free ivector **************************/    ss++;
 void free_ivector(int *v, long nl, long nh)    strcpy(ext,ss);                       /* save extension */
 {    l1= strlen( name);
   free((FREE_ARG)(v+nl-NR_END));    l2= strlen(ss)+1;
 }    strncpy( finame, name, l1-l2);
     finame[l1-l2]= 0;
 /******************* imatrix *******************************/    return( 0 );                          /* we're done */
 int **imatrix(long nrl, long nrh, long ncl, long nch)  }
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  /******************************************/
   int **m;  
    void replace(char *s, char*t)
   /* allocate pointers to rows */  {
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    int i;
   if (!m) nrerror("allocation failure 1 in matrix()");    int lg=20;
   m += NR_END;    i=0;
   m -= nrl;    lg=strlen(t);
      for(i=0; i<= lg; i++) {
        (s[i] = t[i]);
   /* allocate rows and set pointers to them */      if (t[i]== '\\') s[i]='/';
   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;  int nbocc(char *s, char occ)
    {
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    int i,j=0;
      int lg=20;
   /* return pointer to array of pointers to rows */    i=0;
   return m;    lg=strlen(s);
 }    for(i=0; i<= lg; i++) {
     if  (s[i] == occ ) j++;
 /****************** free_imatrix *************************/    }
 void free_imatrix(m,nrl,nrh,ncl,nch)    return j;
       int **m;  }
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */  void cutv(char *u,char *v, char*t, char occ)
 {  {
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    /* cuts string t into u and v where u is ended by char occ excluding it
   free((FREE_ARG) (m+nrl-NR_END));       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
 }       gives u="abcedf" and v="ghi2j" */
     int i,lg,j,p=0;
 /******************* matrix *******************************/    i=0;
 double **matrix(long nrl, long nrh, long ncl, long nch)    for(j=0; j<=strlen(t)-1; j++) {
 {      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    }
   double **m;  
     lg=strlen(t);
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    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';
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));     for(j=0; j<= lg; j++) {
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");      if (j>=(p+1))(v[j-p-1] = t[j]);
   m[nrl] += NR_END;    }
   m[nrl] -= ncl;  }
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  /********************** nrerror ********************/
   return m;  
 }  void nrerror(char error_text[])
   {
 /*************************free matrix ************************/    fprintf(stderr,"ERREUR ...\n");
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    fprintf(stderr,"%s\n",error_text);
 {    exit(EXIT_FAILURE);
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  }
   free((FREE_ARG)(m+nrl-NR_END));  /*********************** vector *******************/
 }  double *vector(int nl, int nh)
   {
 /******************* ma3x *******************************/    double *v;
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 {    if (!v) nrerror("allocation failure in vector");
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    return v-nl+NR_END;
   double ***m;  }
   
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  /************************ free vector ******************/
   if (!m) nrerror("allocation failure 1 in matrix()");  void free_vector(double*v, int nl, int nh)
   m += NR_END;  {
   m -= nrl;    free((FREE_ARG)(v+nl-NR_END));
   }
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /************************ivector *******************************/
   m[nrl] += NR_END;  int *ivector(long nl,long nh)
   m[nrl] -= ncl;  {
     int *v;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    return v-nl+NR_END;
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  }
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  /******************free ivector **************************/
   for (j=ncl+1; j<=nch; j++)  void free_ivector(int *v, long nl, long nh)
     m[nrl][j]=m[nrl][j-1]+nlay;  {
      free((FREE_ARG)(v+nl-NR_END));
   for (i=nrl+1; i<=nrh; i++) {  }
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  /******************* imatrix *******************************/
       m[i][j]=m[i][j-1]+nlay;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   }       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   return m;  { 
 }    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     int **m; 
 /*************************free ma3x ************************/    
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    /* allocate pointers to rows */ 
 {    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   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; 
 }    
     
 /***************** f1dim *************************/    /* allocate rows and set pointers to them */ 
 extern int ncom;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
 extern double *pcom,*xicom;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 extern double (*nrfunc)(double []);    m[nrl] += NR_END; 
      m[nrl] -= ncl; 
 double f1dim(double x)    
 {    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   int j;    
   double f;    /* return pointer to array of pointers to rows */ 
   double *xt;    return m; 
    } 
   xt=vector(1,ncom);  
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  /****************** free_imatrix *************************/
   f=(*nrfunc)(xt);  void free_imatrix(m,nrl,nrh,ncl,nch)
   free_vector(xt,1,ncom);        int **m;
   return f;        long nch,ncl,nrh,nrl; 
 }       /* free an int matrix allocated by imatrix() */ 
   { 
 /*****************brent *************************/    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    free((FREE_ARG) (m+nrl-NR_END)); 
 {  } 
   int iter;  
   double a,b,d,etemp;  /******************* matrix *******************************/
   double fu,fv,fw,fx;  double **matrix(long nrl, long nrh, long ncl, long nch)
   double ftemp;  {
   double p,q,r,tol1,tol2,u,v,w,x,xm;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   double e=0.0;    double **m;
    
   a=(ax < cx ? ax : cx);    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   b=(ax > cx ? ax : cx);    if (!m) nrerror("allocation failure 1 in matrix()");
   x=w=v=bx;    m += NR_END;
   fw=fv=fx=(*f)(x);    m -= nrl;
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    m[nrl] += NR_END;
     printf(".");fflush(stdout);    m[nrl] -= ncl;
 #ifdef DEBUG  
     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);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    return m;
 #endif  }
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;  /*************************free matrix ************************/
       return fx;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     }  {
     ftemp=fu;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     if (fabs(e) > tol1) {    free((FREE_ARG)(m+nrl-NR_END));
       r=(x-w)*(fx-fv);  }
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;  /******************* ma3x *******************************/
       q=2.0*(q-r);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       if (q > 0.0) p = -p;  {
       q=fabs(q);    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       etemp=e;    double ***m;
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    if (!m) nrerror("allocation failure 1 in matrix()");
       else {    m += NR_END;
         d=p/q;    m -= nrl;
         u=x+d;  
         if (u-a < tol2 || b-u < tol2)    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
           d=SIGN(tol1,xm-x);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       }    m[nrl] += NR_END;
     } else {    m[nrl] -= ncl;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  
     }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  
     fu=(*f)(u);    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (fu <= fx) {    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       if (u >= x) a=x; else b=x;    m[nrl][ncl] += NR_END;
       SHFT(v,w,x,u)    m[nrl][ncl] -= nll;
         SHFT(fv,fw,fx,fu)    for (j=ncl+1; j<=nch; j++) 
         } else {      m[nrl][j]=m[nrl][j-1]+nlay;
           if (u < x) a=u; else b=u;    
           if (fu <= fw || w == x) {    for (i=nrl+1; i<=nrh; i++) {
             v=w;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
             w=u;      for (j=ncl+1; j<=nch; j++) 
             fv=fw;        m[i][j]=m[i][j-1]+nlay;
             fw=fu;    }
           } else if (fu <= fv || v == x || v == w) {    return m;
             v=u;  }
             fv=fu;  
           }  /*************************free ma3x ************************/
         }  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   }  {
   nrerror("Too many iterations in brent");    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   *xmin=x;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   return fx;    free((FREE_ARG)(m+nrl-NR_END));
 }  }
   
 /****************** mnbrak ***********************/  /***************** f1dim *************************/
   extern int ncom; 
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  extern double *pcom,*xicom;
             double (*func)(double))  extern double (*nrfunc)(double []); 
 {   
   double ulim,u,r,q, dum;  double f1dim(double x) 
   double fu;  { 
      int j; 
   *fa=(*func)(*ax);    double f;
   *fb=(*func)(*bx);    double *xt; 
   if (*fb > *fa) {   
     SHFT(dum,*ax,*bx,dum)    xt=vector(1,ncom); 
       SHFT(dum,*fb,*fa,dum)    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       }    f=(*nrfunc)(xt); 
   *cx=(*bx)+GOLD*(*bx-*ax);    free_vector(xt,1,ncom); 
   *fc=(*func)(*cx);    return f; 
   while (*fb > *fc) {  } 
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  /*****************brent *************************/
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  { 
     ulim=(*bx)+GLIMIT*(*cx-*bx);    int iter; 
     if ((*bx-u)*(u-*cx) > 0.0) {    double a,b,d,etemp;
       fu=(*func)(u);    double fu,fv,fw,fx;
     } else if ((*cx-u)*(u-ulim) > 0.0) {    double ftemp;
       fu=(*func)(u);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       if (fu < *fc) {    double e=0.0; 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))   
           SHFT(*fb,*fc,fu,(*func)(u))    a=(ax < cx ? ax : cx); 
           }    b=(ax > cx ? ax : cx); 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    x=w=v=bx; 
       u=ulim;    fw=fv=fx=(*f)(x); 
       fu=(*func)(u);    for (iter=1;iter<=ITMAX;iter++) { 
     } else {      xm=0.5*(a+b); 
       u=(*cx)+GOLD*(*cx-*bx);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       fu=(*func)(u);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     }      printf(".");fflush(stdout);
     SHFT(*ax,*bx,*cx,u)      fprintf(ficlog,".");fflush(ficlog);
       SHFT(*fa,*fb,*fc,fu)  #ifdef DEBUG
       }      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);
 }      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)))) { */
 /*************** linmin ************************/  #endif
       if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
 int ncom;        *xmin=x; 
 double *pcom,*xicom;        return fx; 
 double (*nrfunc)(double []);      } 
        ftemp=fu;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))      if (fabs(e) > tol1) { 
 {        r=(x-w)*(fx-fv); 
   double brent(double ax, double bx, double cx,        q=(x-v)*(fx-fw); 
                double (*f)(double), double tol, double *xmin);        p=(x-v)*q-(x-w)*r; 
   double f1dim(double x);        q=2.0*(q-r); 
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,        if (q > 0.0) p = -p; 
               double *fc, double (*func)(double));        q=fabs(q); 
   int j;        etemp=e; 
   double xx,xmin,bx,ax;        e=d; 
   double fx,fb,fa;        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)); 
   ncom=n;        else { 
   pcom=vector(1,n);          d=p/q; 
   xicom=vector(1,n);          u=x+d; 
   nrfunc=func;          if (u-a < tol2 || b-u < tol2) 
   for (j=1;j<=n;j++) {            d=SIGN(tol1,xm-x); 
     pcom[j]=p[j];        } 
     xicom[j]=xi[j];      } else { 
   }        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   ax=0.0;      } 
   xx=1.0;      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);      fu=(*f)(u); 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);      if (fu <= fx) { 
 #ifdef DEBUG        if (u >= x) a=x; else b=x; 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);        SHFT(v,w,x,u) 
 #endif          SHFT(fv,fw,fx,fu) 
   for (j=1;j<=n;j++) {          } else { 
     xi[j] *= xmin;            if (u < x) a=u; else b=u; 
     p[j] += xi[j];            if (fu <= fw || w == x) { 
   }              v=w; 
   free_vector(xicom,1,n);              w=u; 
   free_vector(pcom,1,n);              fv=fw; 
 }              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
 /*************** powell ************************/              v=u; 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,              fv=fu; 
             double (*func)(double []))            } 
 {          } 
   void linmin(double p[], double xi[], int n, double *fret,    } 
               double (*func)(double []));    nrerror("Too many iterations in brent"); 
   int i,ibig,j;    *xmin=x; 
   double del,t,*pt,*ptt,*xit;    return fx; 
   double fp,fptt;  } 
   double *xits;  
   pt=vector(1,n);  /****************** mnbrak ***********************/
   ptt=vector(1,n);  
   xit=vector(1,n);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   xits=vector(1,n);              double (*func)(double)) 
   *fret=(*func)(p);  { 
   for (j=1;j<=n;j++) pt[j]=p[j];    double ulim,u,r,q, dum;
   for (*iter=1;;++(*iter)) {    double fu; 
     fp=(*fret);   
     ibig=0;    *fa=(*func)(*ax); 
     del=0.0;    *fb=(*func)(*bx); 
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    if (*fb > *fa) { 
     for (i=1;i<=n;i++)      SHFT(dum,*ax,*bx,dum) 
       printf(" %d %.12f",i, p[i]);        SHFT(dum,*fb,*fa,dum) 
     printf("\n");        } 
     for (i=1;i<=n;i++) {    *cx=(*bx)+GOLD*(*bx-*ax); 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    *fc=(*func)(*cx); 
       fptt=(*fret);    while (*fb > *fc) { 
 #ifdef DEBUG      r=(*bx-*ax)*(*fb-*fc); 
       printf("fret=%lf \n",*fret);      q=(*bx-*cx)*(*fb-*fa); 
 #endif      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       printf("%d",i);fflush(stdout);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       linmin(p,xit,n,fret,func);      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if (fabs(fptt-(*fret)) > del) {      if ((*bx-u)*(u-*cx) > 0.0) { 
         del=fabs(fptt-(*fret));        fu=(*func)(u); 
         ibig=i;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
       }        fu=(*func)(u); 
 #ifdef DEBUG        if (fu < *fc) { 
       printf("%d %.12e",i,(*fret));          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       for (j=1;j<=n;j++) {            SHFT(*fb,*fc,fu,(*func)(u)) 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);            } 
         printf(" x(%d)=%.12e",j,xit[j]);      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       }        u=ulim; 
       for(j=1;j<=n;j++)        fu=(*func)(u); 
         printf(" p=%.12e",p[j]);      } else { 
       printf("\n");        u=(*cx)+GOLD*(*cx-*bx); 
 #endif        fu=(*func)(u); 
     }      } 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      SHFT(*ax,*bx,*cx,u) 
 #ifdef DEBUG        SHFT(*fa,*fb,*fc,fu) 
       int k[2],l;        } 
       k[0]=1;  } 
       k[1]=-1;  
       printf("Max: %.12e",(*func)(p));  /*************** linmin ************************/
       for (j=1;j<=n;j++)  
         printf(" %.12e",p[j]);  int ncom; 
       printf("\n");  double *pcom,*xicom;
       for(l=0;l<=1;l++) {  double (*nrfunc)(double []); 
         for (j=1;j<=n;j++) {   
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  { 
         }    double brent(double ax, double bx, double cx, 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));                 double (*f)(double), double tol, double *xmin); 
       }    double f1dim(double x); 
 #endif    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
                 double *fc, double (*func)(double)); 
     int j; 
       free_vector(xit,1,n);    double xx,xmin,bx,ax; 
       free_vector(xits,1,n);    double fx,fb,fa;
       free_vector(ptt,1,n);   
       free_vector(pt,1,n);    ncom=n; 
       return;    pcom=vector(1,n); 
     }    xicom=vector(1,n); 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    nrfunc=func; 
     for (j=1;j<=n;j++) {    for (j=1;j<=n;j++) { 
       ptt[j]=2.0*p[j]-pt[j];      pcom[j]=p[j]; 
       xit[j]=p[j]-pt[j];      xicom[j]=xi[j]; 
       pt[j]=p[j];    } 
     }    ax=0.0; 
     fptt=(*func)(ptt);    xx=1.0; 
     if (fptt < fp) {    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       if (t < 0.0) {  #ifdef DEBUG
         linmin(p,xit,n,fret,func);    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         for (j=1;j<=n;j++) {    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
           xi[j][ibig]=xi[j][n];  #endif
           xi[j][n]=xit[j];    for (j=1;j<=n;j++) { 
         }      xi[j] *= xmin; 
 #ifdef DEBUG      p[j] += xi[j]; 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    } 
         for(j=1;j<=n;j++)    free_vector(xicom,1,n); 
           printf(" %.12e",xit[j]);    free_vector(pcom,1,n); 
         printf("\n");  } 
 #endif  
       }  /*************** powell ************************/
     }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   }              double (*func)(double [])) 
 }  { 
     void linmin(double p[], double xi[], int n, double *fret, 
 /**** Prevalence limit ****************/                double (*func)(double [])); 
     int i,ibig,j; 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    double del,t,*pt,*ptt,*xit;
 {    double fp,fptt;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    double *xits;
      matrix by transitions matrix until convergence is reached */    pt=vector(1,n); 
     ptt=vector(1,n); 
   int i, ii,j,k;    xit=vector(1,n); 
   double min, max, maxmin, maxmax,sumnew=0.;    xits=vector(1,n); 
   double **matprod2();    *fret=(*func)(p); 
   double **out, cov[NCOVMAX], **pmij();    for (j=1;j<=n;j++) pt[j]=p[j]; 
   double **newm;    for (*iter=1;;++(*iter)) { 
   double agefin, delaymax=50 ; /* Max number of years to converge */      fp=(*fret); 
       ibig=0; 
   for (ii=1;ii<=nlstate+ndeath;ii++)      del=0.0; 
     for (j=1;j<=nlstate+ndeath;j++){      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
     }      for (i=1;i<=n;i++) 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        printf(" %d %.12f",i, p[i]);
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){      fprintf(ficlog," %d %.12f",i, p[i]);
     newm=savm;      printf("\n");
     /* Covariates have to be included here again */      fprintf(ficlog,"\n");
     cov[1]=1.;      for (i=1;i<=n;i++) { 
     cov[2]=agefin;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     if (cptcovn>0){        fptt=(*fret); 
       for (k=1; k<=cptcovn;k++) {cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];/*printf("Tcode[ij]=%d nbcode=%d\n",Tcode[ij],nbcode[k][Tcode[ij]]);*/}  #ifdef DEBUG
     }        printf("fret=%lf \n",*fret);
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);        fprintf(ficlog,"fret=%lf \n",*fret);
   #endif
     savm=oldm;        printf("%d",i);fflush(stdout);
     oldm=newm;        fprintf(ficlog,"%d",i);fflush(ficlog);
     maxmax=0.;        linmin(p,xit,n,fret,func); 
     for(j=1;j<=nlstate;j++){        if (fabs(fptt-(*fret)) > del) { 
       min=1.;          del=fabs(fptt-(*fret)); 
       max=0.;          ibig=i; 
       for(i=1; i<=nlstate; i++) {        } 
         sumnew=0;  #ifdef DEBUG
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];        printf("%d %.12e",i,(*fret));
         prlim[i][j]= newm[i][j]/(1-sumnew);        fprintf(ficlog,"%d %.12e",i,(*fret));
         max=FMAX(max,prlim[i][j]);        for (j=1;j<=n;j++) {
         min=FMIN(min,prlim[i][j]);          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
       }          printf(" x(%d)=%.12e",j,xit[j]);
       maxmin=max-min;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
       maxmax=FMAX(maxmax,maxmin);        }
     }        for(j=1;j<=n;j++) {
     if(maxmax < ftolpl){          printf(" p=%.12e",p[j]);
       return prlim;          fprintf(ficlog," p=%.12e",p[j]);
     }        }
   }        printf("\n");
 }        fprintf(ficlog,"\n");
   #endif
 /*************** transition probabilities **********/      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  #ifdef DEBUG
 {        int k[2],l;
   double s1, s2;        k[0]=1;
   /*double t34;*/        k[1]=-1;
   int i,j,j1, nc, ii, jj;        printf("Max: %.12e",(*func)(p));
         fprintf(ficlog,"Max: %.12e",(*func)(p));
     for(i=1; i<= nlstate; i++){        for (j=1;j<=n;j++) {
     for(j=1; j<i;j++){          printf(" %.12e",p[j]);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){          fprintf(ficlog," %.12e",p[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");
       }        for(l=0;l<=1;l++) {
       ps[i][j]=s2;          for (j=1;j<=n;j++) {
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/            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]);
     for(j=i+1; j<=nlstate+ndeath;j++){            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){          }
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       }        }
       ps[i][j]=s2;  #endif
     }  
   }  
   for(i=1; i<= nlstate; i++){        free_vector(xit,1,n); 
      s1=0;        free_vector(xits,1,n); 
     for(j=1; j<i; j++)        free_vector(ptt,1,n); 
       s1+=exp(ps[i][j]);        free_vector(pt,1,n); 
     for(j=i+1; j<=nlstate+ndeath; j++)        return; 
       s1+=exp(ps[i][j]);      } 
     ps[i][i]=1./(s1+1.);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     for(j=1; j<i; j++)      for (j=1;j<=n;j++) { 
       ps[i][j]= exp(ps[i][j])*ps[i][i];        ptt[j]=2.0*p[j]-pt[j]; 
     for(j=i+1; j<=nlstate+ndeath; j++)        xit[j]=p[j]-pt[j]; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];        pt[j]=p[j]; 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */      } 
   } /* end i */      fptt=(*func)(ptt); 
       if (fptt < fp) { 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     for(jj=1; jj<= nlstate+ndeath; jj++){        if (t < 0.0) { 
       ps[ii][jj]=0;          linmin(p,xit,n,fret,func); 
       ps[ii][ii]=1;          for (j=1;j<=n;j++) { 
     }            xi[j][ibig]=xi[j][n]; 
   }            xi[j][n]=xit[j]; 
           }
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  #ifdef DEBUG
     for(jj=1; jj<= nlstate+ndeath; jj++){          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
      printf("%lf ",ps[ii][jj]);          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
    }          for(j=1;j<=n;j++){
     printf("\n ");            printf(" %.12e",xit[j]);
     }            fprintf(ficlog," %.12e",xit[j]);
     printf("\n ");printf("%lf ",cov[2]);*/          }
 /*          printf("\n");
   for(i=1; i<= npar; i++) printf("%f ",x[i]);          fprintf(ficlog,"\n");
   goto end;*/  #endif
     return ps;        }
 }      } 
     } 
 /**************** Product of 2 matrices ******************/  } 
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  /**** Prevalence limit (stable prevalence)  ****************/
 {  
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  {
   /* in, b, out are matrice of pointers which should have been initialized    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
      before: only the contents of out is modified. The function returns       matrix by transitions matrix until convergence is reached */
      a pointer to pointers identical to out */  
   long i, j, k;    int i, ii,j,k;
   for(i=nrl; i<= nrh; i++)    double min, max, maxmin, maxmax,sumnew=0.;
     for(k=ncolol; k<=ncoloh; k++)    double **matprod2();
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    double **out, cov[NCOVMAX], **pmij();
         out[i][k] +=in[i][j]*b[j][k];    double **newm;
     double agefin, delaymax=50 ; /* Max number of years to converge */
   return out;  
 }    for (ii=1;ii<=nlstate+ndeath;ii++)
       for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /************* 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 )     cov[1]=1.;
 {   
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
      duration (i.e. until    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.      newm=savm;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step      /* Covariates have to be included here again */
      (typically every 2 years instead of every month which is too big).       cov[2]=agefin;
      Model is determined by parameters x and covariates have to be    
      included manually here.        for (k=1; k<=cptcovn;k++) {
           cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
      */          /*      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]]);*/
         }
   int i, j, d, h, k;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   double **out, cov[NCOVMAX];        for (k=1; k<=cptcovprod;k++)
   double **newm;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
   /* Hstepm could be zero and should return the unit matrix */        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   for (i=1;i<=nlstate+ndeath;i++)        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
     for (j=1;j<=nlstate+ndeath;j++){        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       oldm[i][j]=(i==j ? 1.0 : 0.0);      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }      savm=oldm;
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */      oldm=newm;
   for(h=1; h <=nhstepm; h++){      maxmax=0.;
     for(d=1; d <=hstepm; d++){      for(j=1;j<=nlstate;j++){
       newm=savm;        min=1.;
       /* Covariates have to be included here again */        max=0.;
       cov[1]=1.;        for(i=1; i<=nlstate; i++) {
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;          sumnew=0;
       if (cptcovn>0){          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];          prlim[i][j]= newm[i][j]/(1-sumnew);
     }          max=FMAX(max,prlim[i][j]);
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/          min=FMIN(min,prlim[i][j]);
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/        }
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,        maxmin=max-min;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        maxmax=FMAX(maxmax,maxmin);
       savm=oldm;      }
       oldm=newm;      if(maxmax < ftolpl){
     }        return prlim;
     for(i=1; i<=nlstate+ndeath; i++)      }
       for(j=1;j<=nlstate+ndeath;j++) {    }
         po[i][j][h]=newm[i][j];  }
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  
          */  /*************** transition probabilities ***************/ 
       }  
   } /* end h */  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   return po;  {
 }    double s1, s2;
     /*double t34;*/
     int i,j,j1, nc, ii, jj;
 /*************** log-likelihood *************/  
 double func( double *x)      for(i=1; i<= nlstate; i++){
 {      for(j=1; j<i;j++){
   int i, ii, j, k, mi, d;        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   double l, ll[NLSTATEMAX], cov[NCOVMAX];          /*s2 += param[i][j][nc]*cov[nc];*/
   double **out;          s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   double sw; /* Sum of weights */          /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
   double lli; /* Individual log likelihood */        }
   long ipmx;        ps[i][j]=s2;
   /*extern weight */        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
   /* We are differentiating ll according to initial status */      }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      for(j=i+1; j<=nlstate+ndeath;j++){
   /*for(i=1;i<imx;i++)        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
 printf(" %d\n",s[4][i]);          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   */          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
         }
   for(k=1; k<=nlstate; k++) ll[k]=0.;        ps[i][j]=s2;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      }
        for(mi=1; mi<= wav[i]-1; mi++){    }
       for (ii=1;ii<=nlstate+ndeath;ii++)      /*ps[3][2]=1;*/
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
             for(d=0; d<dh[mi][i]; d++){    for(i=1; i<= nlstate; i++){
         newm=savm;       s1=0;
           cov[1]=1.;      for(j=1; j<i; j++)
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;        s1+=exp(ps[i][j]);
           if (cptcovn>0){      for(j=i+1; j<=nlstate+ndeath; j++)
             for (k=1; k<=cptcovn;k++) cov[2+k]=covar[1+k-1][i];        s1+=exp(ps[i][j]);
             }      ps[i][i]=1./(s1+1.);
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      for(j=1; j<i; j++)
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        ps[i][j]= exp(ps[i][j])*ps[i][i];
           savm=oldm;      for(j=i+1; j<=nlstate+ndeath; j++)
           oldm=newm;        ps[i][j]= exp(ps[i][j])*ps[i][i];
       /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     } /* end i */
       } /* end mult */  
        for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      for(jj=1; jj<= nlstate+ndeath; jj++){
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        ps[ii][jj]=0;
       ipmx +=1;        ps[ii][ii]=1;
       sw += weight[i];      }
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    }
     } /* end of wave */  
   } /* end of individual */  
     /*   for(ii=1; ii<= nlstate+ndeath; ii++){
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      for(jj=1; jj<= nlstate+ndeath; jj++){
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */       printf("%lf ",ps[ii][jj]);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */     }
   return -l;      printf("\n ");
 }      }
       printf("\n ");printf("%lf ",cov[2]);*/
   /*
 /*********** Maximum Likelihood Estimation ***************/    for(i=1; i<= npar; i++) printf("%f ",x[i]);
     goto end;*/
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      return ps;
 {  }
   int i,j, iter;  
   double **xi,*delti;  /**************** Product of 2 matrices ******************/
   double fret;  
   xi=matrix(1,npar,1,npar);  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   for (i=1;i<=npar;i++)  {
     for (j=1;j<=npar;j++)    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       xi[i][j]=(i==j ? 1.0 : 0.0);       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   printf("Powell\n");    /* in, b, out are matrice of pointers which should have been initialized 
   powell(p,xi,npar,ftol,&iter,&fret,func);       before: only the contents of out is modified. The function returns
        a pointer to pointers identical to out */
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    long i, j, k;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    for(i=nrl; i<= nrh; i++)
       for(k=ncolol; k<=ncoloh; k++)
 }        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
 /**** Computes Hessian and covariance matrix ***/  
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    return out;
 {  }
   double  **a,**y,*x,pd;  
   double **hess;  
   int i, j,jk;  /************* Higher Matrix Product ***************/
   int *indx;  
   double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   double hessii(double p[], double delta, int theta, double delti[]);  {
   double hessij(double p[], double delti[], int i, int j);    /* Computes the transition matrix starting at age 'age' over 
   void lubksb(double **a, int npar, int *indx, double b[]) ;       'nhstepm*hstepm*stepm' months (i.e. until
   void ludcmp(double **a, int npar, int *indx, double *d) ;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
        Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   hess=matrix(1,npar,1,npar);       (typically every 2 years instead of every month which is too big 
        for the memory).
   printf("\nCalculation of the hessian matrix. Wait...\n");       Model is determined by parameters x and covariates have to be 
   for (i=1;i<=npar;i++){       included manually here. 
     printf("%d",i);fflush(stdout);  
     hess[i][i]=hessii(p,ftolhess,i,delti);       */
     /*printf(" %f ",p[i]);*/  
   }    int i, j, d, h, k;
     double **out, cov[NCOVMAX];
   for (i=1;i<=npar;i++) {    double **newm;
     for (j=1;j<=npar;j++)  {  
       if (j>i) {    /* Hstepm could be zero and should return the unit matrix */
         printf(".%d%d",i,j);fflush(stdout);    for (i=1;i<=nlstate+ndeath;i++)
         hess[i][j]=hessij(p,delti,i,j);      for (j=1;j<=nlstate+ndeath;j++){
         hess[j][i]=hess[i][j];        oldm[i][j]=(i==j ? 1.0 : 0.0);
       }        po[i][j][0]=(i==j ? 1.0 : 0.0);
     }      }
   }    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   printf("\n");    for(h=1; h <=nhstepm; h++){
       for(d=1; d <=hstepm; d++){
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        newm=savm;
          /* Covariates have to be included here again */
   a=matrix(1,npar,1,npar);        cov[1]=1.;
   y=matrix(1,npar,1,npar);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   x=vector(1,npar);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   indx=ivector(1,npar);        for (k=1; k<=cptcovage;k++)
   for (i=1;i<=npar;i++)          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];        for (k=1; k<=cptcovprod;k++)
   ludcmp(a,npar,indx,&pd);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
   for (j=1;j<=npar;j++) {  
     for (i=1;i<=npar;i++) x[i]=0;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
     x[j]=1;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
     lubksb(a,npar,indx,x);        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     for (i=1;i<=npar;i++){                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       matcov[i][j]=x[i];        savm=oldm;
     }        oldm=newm;
   }      }
       for(i=1; i<=nlstate+ndeath; i++)
   printf("\n#Hessian matrix#\n");        for(j=1;j<=nlstate+ndeath;j++) {
   for (i=1;i<=npar;i++) {          po[i][j][h]=newm[i][j];
     for (j=1;j<=npar;j++) {          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       printf("%.3e ",hess[i][j]);           */
     }        }
     printf("\n");    } /* end h */
   }    return po;
   }
   /* Recompute Inverse */  
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  /*************** log-likelihood *************/
   ludcmp(a,npar,indx,&pd);  double func( double *x)
   {
   /*  printf("\n#Hessian matrix recomputed#\n");    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX], cov[NCOVMAX];
   for (j=1;j<=npar;j++) {    double **out;
     for (i=1;i<=npar;i++) x[i]=0;    double sw; /* Sum of weights */
     x[j]=1;    double lli; /* Individual log likelihood */
     lubksb(a,npar,indx,x);    int s1, s2;
     for (i=1;i<=npar;i++){    double bbh, survp;
       y[i][j]=x[i];    long ipmx;
       printf("%.3e ",y[i][j]);    /*extern weight */
     }    /* We are differentiating ll according to initial status */
     printf("\n");    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   }    /*for(i=1;i<imx;i++) 
   */      printf(" %d\n",s[4][i]);
     */
   free_matrix(a,1,npar,1,npar);    cov[1]=1.;
   free_matrix(y,1,npar,1,npar);  
   free_vector(x,1,npar);    for(k=1; k<=nlstate; k++) ll[k]=0.;
   free_ivector(indx,1,npar);  
   free_matrix(hess,1,npar,1,npar);    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 }        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
 /*************** hessian matrix ****************/            for (j=1;j<=nlstate+ndeath;j++){
 double hessii( double x[], double delta, int theta, double delti[])              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i;            }
   int l=1, lmax=20;          for(d=0; d<dh[mi][i]; d++){
   double k1,k2;            newm=savm;
   double p2[NPARMAX+1];            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double res;            for (kk=1; kk<=cptcovage;kk++) {
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double fx;            }
   int k=0,kmax=10;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double l1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   fx=func(x);            oldm=newm;
   for (i=1;i<=npar;i++) p2[i]=x[i];          } /* end mult */
   for(l=0 ; l <=lmax; l++){        
     l1=pow(10,l);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     delts=delt;          /* But now since version 0.9 we anticipate for bias and large stepm.
     for(k=1 ; k <kmax; k=k+1){           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       delt = delta*(l1*k);           * (in months) between two waves is not a multiple of stepm, we rounded to 
       p2[theta]=x[theta] +delt;           * the nearest (and in case of equal distance, to the lowest) interval but now
       k1=func(p2)-fx;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       p2[theta]=x[theta]-delt;           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       k2=func(p2)-fx;           * probability in order to take into account the bias as a fraction of the way
       /*res= (k1-2.0*fx+k2)/delt/delt; */           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */           * -stepm/2 to stepm/2 .
                 * For stepm=1 the results are the same as for previous versions of Imach.
 #ifdef DEBUG           * For stepm > 1 the results are less biased than in previous versions. 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);           */
 #endif          s1=s[mw[mi][i]][i];
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          s2=s[mw[mi+1][i]][i];
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          bbh=(double)bh[mi][i]/(double)stepm; 
         k=kmax;          /* bias is positive if real duration
       }           * is higher than the multiple of stepm and negative otherwise.
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */           */
         k=kmax; l=lmax*10.;          /* 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 > nlstate){ 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){            /* i.e. if s2 is a death state and if the date of death is known then the contribution
         delts=delt;               to the likelihood is the probability to die between last step unit time and current 
       }               step unit time, which is also the differences between probability to die before dh 
     }               and probability to die before dh-stepm . 
   }               In version up to 0.92 likelihood was computed
   delti[theta]=delts;          as if date of death was unknown. Death was treated as any other
   return res;          health state: the date of the interview describes the actual state
            and not the date of a change in health state. The former idea was
 }          to consider that at each interview the state was recorded
           (healthy, disable or death) and IMaCh was corrected; but when we
 double hessij( double x[], double delti[], int thetai,int thetaj)          introduced the exact date of death then we should have modified
 {          the contribution of an exact death to the likelihood. This new
   int i;          contribution is smaller and very dependent of the step unit
   int l=1, l1, lmax=20;          stepm. It is no more the probability to die between last interview
   double k1,k2,k3,k4,res,fx;          and month of death but the probability to survive from last
   double p2[NPARMAX+1];          interview up to one month before death multiplied by the
   int k;          probability to die within a month. Thanks to Chris
           Jackson for correcting this bug.  Former versions increased
   fx=func(x);          mortality artificially. The bad side is that we add another loop
   for (k=1; k<=2; k++) {          which slows down the processing. The difference can be up to 10%
     for (i=1;i<=npar;i++) p2[i]=x[i];          lower mortality.
     p2[thetai]=x[thetai]+delti[thetai]/k;            */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;            lli=log(out[s1][s2] - savm[s1][s2]);
     k1=func(p2)-fx;          }else{
              lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     p2[thetai]=x[thetai]+delti[thetai]/k;            /*  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 */
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          } 
     k2=func(p2)-fx;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
            /*if(lli ==000.0)*/
     p2[thetai]=x[thetai]-delti[thetai]/k;          /*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); */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          ipmx +=1;
     k3=func(p2)-fx;          sw += weight[i];
            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     p2[thetai]=x[thetai]-delti[thetai]/k;        } /* end of wave */
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      } /* end of individual */
     k4=func(p2)-fx;    }  else if(mle==2){
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 #ifdef DEBUG        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);        for(mi=1; mi<= wav[i]-1; mi++){
 #endif          for (ii=1;ii<=nlstate+ndeath;ii++)
   }            for (j=1;j<=nlstate+ndeath;j++){
   return res;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
 /************** Inverse of matrix **************/          for(d=0; d<=dh[mi][i]; d++){
 void ludcmp(double **a, int n, int *indx, double *d)            newm=savm;
 {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   int i,imax,j,k;            for (kk=1; kk<=cptcovage;kk++) {
   double big,dum,sum,temp;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double *vv;            }
              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   vv=vector(1,n);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   *d=1.0;            savm=oldm;
   for (i=1;i<=n;i++) {            oldm=newm;
     big=0.0;          } /* end mult */
     for (j=1;j<=n;j++)        
       if ((temp=fabs(a[i][j])) > big) big=temp;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          /* But now since version 0.9 we anticipate for bias and large stepm.
     vv[i]=1.0/big;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   }           * (in months) between two waves is not a multiple of stepm, we rounded to 
   for (j=1;j<=n;j++) {           * the nearest (and in case of equal distance, to the lowest) interval but now
     for (i=1;i<j;i++) {           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       sum=a[i][j];           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];           * probability in order to take into account the bias as a fraction of the way
       a[i][j]=sum;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
     }           * -stepm/2 to stepm/2 .
     big=0.0;           * For stepm=1 the results are the same as for previous versions of Imach.
     for (i=j;i<=n;i++) {           * For stepm > 1 the results are less biased than in previous versions. 
       sum=a[i][j];           */
       for (k=1;k<j;k++)          s1=s[mw[mi][i]][i];
         sum -= a[i][k]*a[k][j];          s2=s[mw[mi+1][i]][i];
       a[i][j]=sum;          bbh=(double)bh[mi][i]/(double)stepm; 
       if ( (dum=vv[i]*fabs(sum)) >= big) {          /* bias is positive if real duration
         big=dum;           * is higher than the multiple of stepm and negative otherwise.
         imax=i;           */
       }          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= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     if (j != imax) {          /*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 */
       for (k=1;k<=n;k++) {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         dum=a[imax][k];          /*if(lli ==000.0)*/
         a[imax][k]=a[j][k];          /*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); */
         a[j][k]=dum;          ipmx +=1;
       }          sw += weight[i];
       *d = -(*d);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       vv[imax]=vv[j];        } /* end of wave */
     }      } /* end of individual */
     indx[j]=imax;    }  else if(mle==3){  /* exponential inter-extrapolation */
     if (a[j][j] == 0.0) a[j][j]=TINY;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     if (j != n) {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       dum=1.0/(a[j][j]);        for(mi=1; mi<= wav[i]-1; mi++){
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          for (ii=1;ii<=nlstate+ndeath;ii++)
     }            for (j=1;j<=nlstate+ndeath;j++){
   }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_vector(vv,1,n);  /* Doesn't work */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
 ;            }
 }          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
 void lubksb(double **a, int n, int *indx, double b[])            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 {            for (kk=1; kk<=cptcovage;kk++) {
   int i,ii=0,ip,j;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double sum;            }
              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for (i=1;i<=n;i++) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     ip=indx[i];            savm=oldm;
     sum=b[ip];            oldm=newm;
     b[ip]=b[i];          } /* end mult */
     if (ii)        
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     else if (sum) ii=i;          /* But now since version 0.9 we anticipate for bias and large stepm.
     b[i]=sum;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   }           * (in months) between two waves is not a multiple of stepm, we rounded to 
   for (i=n;i>=1;i--) {           * the nearest (and in case of equal distance, to the lowest) interval but now
     sum=b[i];           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
     b[i]=sum/a[i][i];           * probability in order to take into account the bias as a fraction of the way
   }           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
 }           * -stepm/2 to stepm/2 .
            * For stepm=1 the results are the same as for previous versions of Imach.
 /************ Frequencies ********************/           * For stepm > 1 the results are less biased than in previous versions. 
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)           */
 {  /* Some frequencies */          s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          bbh=(double)bh[mi][i]/(double)stepm; 
   double ***freq; /* Frequencies */          /* bias is positive if real duration
   double *pp;           * is higher than the multiple of stepm and negative otherwise.
   double pos;           */
   FILE *ficresp;          /* 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 */
   char fileresp[FILENAMELENGTH];          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 */
           /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   pp=vector(1,nlstate);          /*if(lli ==000.0)*/
           /*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); */
   strcpy(fileresp,"p");          ipmx +=1;
   strcat(fileresp,fileres);          sw += weight[i];
   if((ficresp=fopen(fileresp,"w"))==NULL) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     printf("Problem with prevalence resultfile: %s\n", fileresp);        } /* end of wave */
     exit(0);      } /* end of individual */
   }    }else{  /* ml=4 no inter-extrapolation */
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   j1=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
   j=cptcovn;          for (ii=1;ii<=nlstate+ndeath;ii++)
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(k1=1; k1<=j;k1++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    for(i1=1; i1<=ncodemax[k1];i1++){            }
        j1++;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
         for (i=-1; i<=nlstate+ndeath; i++)              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
          for (jk=-1; jk<=nlstate+ndeath; jk++)              for (kk=1; kk<=cptcovage;kk++) {
            for(m=agemin; m <= agemax+3; m++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              freq[i][jk][m]=0;            }
                  
        for (i=1; i<=imx; i++) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
          bool=1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
          if  (cptcovn>0) {            savm=oldm;
            for (z1=1; z1<=cptcovn; z1++)            oldm=newm;
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;          } /* end mult */
          }        
           if (bool==1) {          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
            for(m=firstpass; m<=lastpass-1; m++){          ipmx +=1;
              if(agev[m][i]==0) agev[m][i]=agemax+1;          sw += weight[i];
              if(agev[m][i]==1) agev[m][i]=agemax+2;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        } /* end of wave */
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      } /* end of individual */
            }    } /* End of if */
          }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
        }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         if  (cptcovn>0) {    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
          fprintf(ficresp, "\n#Variable");    return -l;
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);  }
        }  
        fprintf(ficresp, "\n#");  
        for(i=1; i<=nlstate;i++)  /*********** Maximum Likelihood Estimation ***************/
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  
        fprintf(ficresp, "\n");  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
          {
   for(i=(int)agemin; i <= (int)agemax+3; i++){    int i,j, iter;
     if(i==(int)agemax+3)    double **xi,*delti;
       printf("Total");    double fret;
     else    xi=matrix(1,npar,1,npar);
       printf("Age %d", i);    for (i=1;i<=npar;i++)
     for(jk=1; jk <=nlstate ; jk++){      for (j=1;j<=npar;j++)
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        xi[i][j]=(i==j ? 1.0 : 0.0);
         pp[jk] += freq[jk][m][i];    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     }    powell(p,xi,npar,ftol,&iter,&fret,func);
     for(jk=1; jk <=nlstate ; jk++){  
       for(m=-1, pos=0; m <=0 ; m++)     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         pos += freq[jk][m][i];    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       if(pp[jk]>=1.e-10)    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  
       else  }
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  
     }  /**** Computes Hessian and covariance matrix ***/
     for(jk=1; jk <=nlstate ; jk++){  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)  {
         pp[jk] += freq[jk][m][i];    double  **a,**y,*x,pd;
     }    double **hess;
     for(jk=1,pos=0; jk <=nlstate ; jk++)    int i, j,jk;
       pos += pp[jk];    int *indx;
     for(jk=1; jk <=nlstate ; jk++){  
       if(pos>=1.e-5)    double hessii(double p[], double delta, int theta, double delti[]);
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    double hessij(double p[], double delti[], int i, int j);
       else    void lubksb(double **a, int npar, int *indx, double b[]) ;
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    void ludcmp(double **a, int npar, int *indx, double *d) ;
       if( i <= (int) agemax){  
         if(pos>=1.e-5)    hess=matrix(1,npar,1,npar);
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  
       else    printf("\nCalculation of the hessian matrix. Wait...\n");
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
       }    for (i=1;i<=npar;i++){
     }      printf("%d",i);fflush(stdout);
     for(jk=-1; jk <=nlstate+ndeath; jk++)      fprintf(ficlog,"%d",i);fflush(ficlog);
       for(m=-1; m <=nlstate+ndeath; m++)      hess[i][i]=hessii(p,ftolhess,i,delti);
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      /*printf(" %f ",p[i]);*/
     if(i <= (int) agemax)      /*printf(" %lf ",hess[i][i]);*/
       fprintf(ficresp,"\n");    }
     printf("\n");    
     }    for (i=1;i<=npar;i++) {
     }      for (j=1;j<=npar;j++)  {
  }        if (j>i) { 
            printf(".%d%d",i,j);fflush(stdout);
   fclose(ficresp);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          hess[i][j]=hessij(p,delti,i,j);
   free_vector(pp,1,nlstate);          hess[j][i]=hess[i][j];    
           /*printf(" %lf ",hess[i][j]);*/
 }  /* End of Freq */        }
       }
 /************* Waves Concatenation ***************/    }
     printf("\n");
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    fprintf(ficlog,"\n");
 {  
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
      Death is a valid wave (if date is known).    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    a=matrix(1,npar,1,npar);
      and mw[mi+1][i]. dh depends on stepm.    y=matrix(1,npar,1,npar);
      */    x=vector(1,npar);
     indx=ivector(1,npar);
   int i, mi, m;    for (i=1;i<=npar;i++)
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
 float sum=0.;    ludcmp(a,npar,indx,&pd);
   
   for(i=1; i<=imx; i++){    for (j=1;j<=npar;j++) {
     mi=0;      for (i=1;i<=npar;i++) x[i]=0;
     m=firstpass;      x[j]=1;
     while(s[m][i] <= nlstate){      lubksb(a,npar,indx,x);
       if(s[m][i]>=1)      for (i=1;i<=npar;i++){ 
         mw[++mi][i]=m;        matcov[i][j]=x[i];
       if(m >=lastpass)      }
         break;    }
       else  
         m++;    printf("\n#Hessian matrix#\n");
     }/* end while */    fprintf(ficlog,"\n#Hessian matrix#\n");
     if (s[m][i] > nlstate){    for (i=1;i<=npar;i++) { 
       mi++;     /* Death is another wave */      for (j=1;j<=npar;j++) { 
       /* if(mi==0)  never been interviewed correctly before death */        printf("%.3e ",hess[i][j]);
          /* Only death is a correct wave */        fprintf(ficlog,"%.3e ",hess[i][j]);
       mw[mi][i]=m;      }
     }      printf("\n");
       fprintf(ficlog,"\n");
     wav[i]=mi;    }
     if(mi==0)  
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    /* Recompute Inverse */
   }    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   for(i=1; i<=imx; i++){    ludcmp(a,npar,indx,&pd);
     for(mi=1; mi<wav[i];mi++){  
       if (stepm <=0)    /*  printf("\n#Hessian matrix recomputed#\n");
         dh[mi][i]=1;  
       else{    for (j=1;j<=npar;j++) {
         if (s[mw[mi+1][i]][i] > nlstate) {      for (i=1;i<=npar;i++) x[i]=0;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);      x[j]=1;
           if(j=0) j=1;  /* Survives at least one month after exam */      lubksb(a,npar,indx,x);
         }      for (i=1;i<=npar;i++){ 
         else{        y[i][j]=x[i];
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        printf("%.3e ",y[i][j]);
           k=k+1;        fprintf(ficlog,"%.3e ",y[i][j]);
           if (j >= jmax) jmax=j;      }
           else if (j <= jmin)jmin=j;      printf("\n");
           sum=sum+j;      fprintf(ficlog,"\n");
         }    }
         jk= j/stepm;    */
         jl= j -jk*stepm;  
         ju= j -(jk+1)*stepm;    free_matrix(a,1,npar,1,npar);
         if(jl <= -ju)    free_matrix(y,1,npar,1,npar);
           dh[mi][i]=jk;    free_vector(x,1,npar);
         else    free_ivector(indx,1,npar);
           dh[mi][i]=jk+1;    free_matrix(hess,1,npar,1,npar);
         if(dh[mi][i]==0)  
           dh[mi][i]=1; /* At least one step */  
       }  }
     }  
   }  /*************** hessian matrix ****************/
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);  double hessii( double x[], double delta, int theta, double delti[])
 }  {
 /*********** Tricode ****************************/    int i;
 void tricode(int *Tvar, int **nbcode, int imx)    int l=1, lmax=20;
 {    double k1,k2;
   int Ndum[80],ij, k, j, i;    double p2[NPARMAX+1];
   int cptcode=0;    double res;
   for (k=0; k<79; k++) Ndum[k]=0;    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   for (k=1; k<=7; k++) ncodemax[k]=0;    double fx;
      int k=0,kmax=10;
   for (j=1; j<=cptcovn; j++) {    double l1;
     for (i=1; i<=imx; i++) {  
       ij=(int)(covar[Tvar[j]][i]);    fx=func(x);
       Ndum[ij]++;    for (i=1;i<=npar;i++) p2[i]=x[i];
       if (ij > cptcode) cptcode=ij;    for(l=0 ; l <=lmax; l++){
     }      l1=pow(10,l);
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/      delts=delt;
     for (i=0; i<=cptcode; i++) {      for(k=1 ; k <kmax; k=k+1){
       if(Ndum[i]!=0) ncodemax[j]++;        delt = delta*(l1*k);
     }        p2[theta]=x[theta] +delt;
          k1=func(p2)-fx;
     ij=1;        p2[theta]=x[theta]-delt;
     for (i=1; i<=ncodemax[j]; i++) {        k2=func(p2)-fx;
       for (k=0; k<=79; k++) {        /*res= (k1-2.0*fx+k2)/delt/delt; */
         if (Ndum[k] != 0) {        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
           nbcode[Tvar[j]][ij]=k;        
           ij++;  #ifdef DEBUG
         }        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         if (ij > ncodemax[j]) break;        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);
       }    #endif
     }        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   }          if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
   }        }
         else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
 /*********** Health Expectancies ****************/          k=kmax; l=lmax*10.;
         }
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
 {          delts=delt;
   /* Health expectancies */        }
   int i, j, nhstepm, hstepm, h;      }
   double age, agelim,hf;    }
   double ***p3mat;    delti[theta]=delts;
      return res; 
   fprintf(ficreseij,"# Health expectancies\n");    
   fprintf(ficreseij,"# Age");  }
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)  double hessij( double x[], double delti[], int thetai,int thetaj)
       fprintf(ficreseij," %1d-%1d",i,j);  {
   fprintf(ficreseij,"\n");    int i;
     int l=1, l1, lmax=20;
   hstepm=1*YEARM; /*  Every j years of age (in month) */    double k1,k2,k3,k4,res,fx;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    double p2[NPARMAX+1];
     int k;
   agelim=AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    fx=func(x);
     /* nhstepm age range expressed in number of stepm */    for (k=1; k<=2; k++) {
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);      for (i=1;i<=npar;i++) p2[i]=x[i];
     /* Typically if 20 years = 20*12/6=40 stepm */      p2[thetai]=x[thetai]+delti[thetai]/k;
     if (stepm >= YEARM) hstepm=1;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      k1=func(p2)-fx;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      p2[thetai]=x[thetai]+delti[thetai]/k;
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);        k2=func(p2)-fx;
     
       p2[thetai]=x[thetai]-delti[thetai]/k;
     for(i=1; i<=nlstate;i++)      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       for(j=1; j<=nlstate;j++)      k3=func(p2)-fx;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){    
           eij[i][j][(int)age] +=p3mat[i][j][h];      p2[thetai]=x[thetai]-delti[thetai]/k;
         }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
          k4=func(p2)-fx;
     hf=1;      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     if (stepm >= YEARM) hf=stepm/YEARM;  #ifdef DEBUG
     fprintf(ficreseij,"%.0f",age );      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(i=1; i<=nlstate;i++)      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(j=1; j<=nlstate;j++){  #endif
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);    }
       }    return res;
     fprintf(ficreseij,"\n");  }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   }  /************** Inverse of matrix **************/
 }  void ludcmp(double **a, int n, int *indx, double *d) 
   { 
 /************ Variance ******************/    int i,imax,j,k; 
 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)    double big,dum,sum,temp; 
 {    double *vv; 
   /* Variance of health expectancies */   
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    vv=vector(1,n); 
   double **newm;    *d=1.0; 
   double **dnewm,**doldm;    for (i=1;i<=n;i++) { 
   int i, j, nhstepm, hstepm, h;      big=0.0; 
   int k, cptcode;      for (j=1;j<=n;j++) 
    double *xp;        if ((temp=fabs(a[i][j])) > big) big=temp; 
   double **gp, **gm;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   double ***gradg, ***trgradg;      vv[i]=1.0/big; 
   double ***p3mat;    } 
   double age,agelim;    for (j=1;j<=n;j++) { 
   int theta;      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
    fprintf(ficresvij,"# Covariances of life expectancies\n");        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   fprintf(ficresvij,"# Age");        a[i][j]=sum; 
   for(i=1; i<=nlstate;i++)      } 
     for(j=1; j<=nlstate;j++)      big=0.0; 
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);      for (i=j;i<=n;i++) { 
   fprintf(ficresvij,"\n");        sum=a[i][j]; 
         for (k=1;k<j;k++) 
   xp=vector(1,npar);          sum -= a[i][k]*a[k][j]; 
   dnewm=matrix(1,nlstate,1,npar);        a[i][j]=sum; 
   doldm=matrix(1,nlstate,1,nlstate);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
            big=dum; 
   hstepm=1*YEARM; /* Every year of age */          imax=i; 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        } 
   agelim = AGESUP;      } 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      if (j != imax) { 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        for (k=1;k<=n;k++) { 
     if (stepm >= YEARM) hstepm=1;          dum=a[imax][k]; 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          a[imax][k]=a[j][k]; 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          a[j][k]=dum; 
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        } 
     gp=matrix(0,nhstepm,1,nlstate);        *d = -(*d); 
     gm=matrix(0,nhstepm,1,nlstate);        vv[imax]=vv[j]; 
       } 
     for(theta=1; theta <=npar; theta++){      indx[j]=imax; 
       for(i=1; i<=npar; i++){ /* Computes gradient */      if (a[j][j] == 0.0) a[j][j]=TINY; 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      if (j != n) { 
       }        dum=1.0/(a[j][j]); 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      } 
       for(j=1; j<= nlstate; j++){    } 
         for(h=0; h<=nhstepm; h++){    free_vector(vv,1,n);  /* Doesn't work */
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)  ;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];  } 
         }  
       }  void lubksb(double **a, int n, int *indx, double b[]) 
      { 
       for(i=1; i<=npar; i++) /* Computes gradient */    int i,ii=0,ip,j; 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double sum; 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);     
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for (i=1;i<=n;i++) { 
       for(j=1; j<= nlstate; j++){      ip=indx[i]; 
         for(h=0; h<=nhstepm; h++){      sum=b[ip]; 
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)      b[ip]=b[i]; 
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];      if (ii) 
         }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       }      else if (sum) ii=i; 
       for(j=1; j<= nlstate; j++)      b[i]=sum; 
         for(h=0; h<=nhstepm; h++){    } 
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    for (i=n;i>=1;i--) { 
         }      sum=b[i]; 
     } /* End theta */      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       b[i]=sum/a[i][i]; 
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    } 
   } 
     for(h=0; h<=nhstepm; h++)  
       for(j=1; j<=nlstate;j++)  /************ Frequencies ********************/
         for(theta=1; theta <=npar; theta++)  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)
           trgradg[h][j][theta]=gradg[h][theta][j];  {  /* Some frequencies */
     
     for(i=1;i<=nlstate;i++)    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
       for(j=1;j<=nlstate;j++)    int first;
         vareij[i][j][(int)age] =0.;    double ***freq; /* Frequencies */
     for(h=0;h<=nhstepm;h++){    double *pp;
       for(k=0;k<=nhstepm;k++){    double pos, k2, dateintsum=0,k2cpt=0;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    FILE *ficresp;
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    char fileresp[FILENAMELENGTH];
         for(i=1;i<=nlstate;i++)    
           for(j=1;j<=nlstate;j++)    pp=vector(1,nlstate);
             vareij[i][j][(int)age] += doldm[i][j];    probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       }    strcpy(fileresp,"p");
     }    strcat(fileresp,fileres);
     h=1;    if((ficresp=fopen(fileresp,"w"))==NULL) {
     if (stepm >= YEARM) h=stepm/YEARM;      printf("Problem with prevalence resultfile: %s\n", fileresp);
     fprintf(ficresvij,"%.0f ",age );      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     for(i=1; i<=nlstate;i++)      exit(0);
       for(j=1; j<=nlstate;j++){    }
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
       }    j1=0;
     fprintf(ficresvij,"\n");    
     free_matrix(gp,0,nhstepm,1,nlstate);    j=cptcoveff;
     free_matrix(gm,0,nhstepm,1,nlstate);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);  
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    first=1;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   } /* End age */    for(k1=1; k1<=j;k1++){
        for(i1=1; i1<=ncodemax[k1];i1++){
   free_vector(xp,1,npar);        j1++;
   free_matrix(doldm,1,nlstate,1,npar);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   free_matrix(dnewm,1,nlstate,1,nlstate);          scanf("%d", i);*/
         for (i=-1; i<=nlstate+ndeath; i++)  
 }          for (jk=-1; jk<=nlstate+ndeath; jk++)  
             for(m=agemin; m <= agemax+3; m++)
 /************ Variance of prevlim ******************/              freq[i][jk][m]=0;
 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)        
 {        dateintsum=0;
   /* Variance of prevalence limit */        k2cpt=0;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        for (i=1; i<=imx; i++) {
   double **newm;          bool=1;
   double **dnewm,**doldm;          if  (cptcovn>0) {
   int i, j, nhstepm, hstepm;            for (z1=1; z1<=cptcoveff; z1++) 
   int k, cptcode;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   double *xp;                bool=0;
   double *gp, *gm;          }
   double **gradg, **trgradg;          if (bool==1){
   double age,agelim;            for(m=firstpass; m<=lastpass; m++){
   int theta;              k2=anint[m][i]+(mint[m][i]/12.);
                  if ((k2>=dateprev1) && (k2<=dateprev2)) {
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");                if(agev[m][i]==0) agev[m][i]=agemax+1;
   fprintf(ficresvpl,"# Age");                if(agev[m][i]==1) agev[m][i]=agemax+2;
   for(i=1; i<=nlstate;i++)                if (m<lastpass) {
       fprintf(ficresvpl," %1d-%1d",i,i);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   fprintf(ficresvpl,"\n");                  freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];
                 }
   xp=vector(1,npar);                
   dnewm=matrix(1,nlstate,1,npar);                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {
   doldm=matrix(1,nlstate,1,nlstate);                  dateintsum=dateintsum+k2;
                    k2cpt++;
   hstepm=1*YEARM; /* Every year of age */                }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */              }
   agelim = AGESUP;            }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        }
     if (stepm >= YEARM) hstepm=1;         
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);
     gradg=matrix(1,npar,1,nlstate);  
     gp=vector(1,nlstate);        if  (cptcovn>0) {
     gm=vector(1,nlstate);          fprintf(ficresp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(theta=1; theta <=npar; theta++){          fprintf(ficresp, "**********\n#");
       for(i=1; i<=npar; i++){ /* Computes gradient */        }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        for(i=1; i<=nlstate;i++) 
       }          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        fprintf(ficresp, "\n");
       for(i=1;i<=nlstate;i++)        
         gp[i] = prlim[i][i];        for(i=(int)agemin; i <= (int)agemax+3; i++){
              if(i==(int)agemax+3){
       for(i=1; i<=npar; i++) /* Computes gradient */            fprintf(ficlog,"Total");
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          }else{
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            if(first==1){
       for(i=1;i<=nlstate;i++)              first=0;
         gm[i] = prlim[i][i];              printf("See log file for details...\n");
             }
       for(i=1;i<=nlstate;i++)            fprintf(ficlog,"Age %d", i);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          }
     } /* End theta */          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     trgradg =matrix(1,nlstate,1,npar);              pp[jk] += freq[jk][m][i]; 
           }
     for(j=1; j<=nlstate;j++)          for(jk=1; jk <=nlstate ; jk++){
       for(theta=1; theta <=npar; theta++)            for(m=-1, pos=0; m <=0 ; m++)
         trgradg[j][theta]=gradg[theta][j];              pos += freq[jk][m][i];
             if(pp[jk]>=1.e-10){
     for(i=1;i<=nlstate;i++)              if(first==1){
       varpl[i][(int)age] =0.;              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);              }
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     for(i=1;i<=nlstate;i++)            }else{
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */              if(first==1)
                 printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     fprintf(ficresvpl,"%.0f ",age );              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     for(i=1; i<=nlstate;i++)            }
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          }
     fprintf(ficresvpl,"\n");  
     free_vector(gp,1,nlstate);          for(jk=1; jk <=nlstate ; jk++){
     free_vector(gm,1,nlstate);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     free_matrix(gradg,1,npar,1,nlstate);              pp[jk] += freq[jk][m][i];
     free_matrix(trgradg,1,nlstate,1,npar);          }
   } /* End age */  
           for(jk=1,pos=0; jk <=nlstate ; jk++)
   free_vector(xp,1,npar);            pos += pp[jk];
   free_matrix(doldm,1,nlstate,1,npar);          for(jk=1; jk <=nlstate ; jk++){
   free_matrix(dnewm,1,nlstate,1,nlstate);            if(pos>=1.e-5){
               if(first==1)
 }                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
               fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
               if(first==1)
 /***********************************************/                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 /**************** Main Program *****************/              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 /***********************************************/            }
             if( i <= (int) agemax){
 /*int main(int argc, char *argv[])*/              if(pos>=1.e-5){
 int main()                fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);
 {                probs[i][jk][j1]= pp[jk]/pos;
                 /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;              }
   double agedeb, agefin,hf;              else
   double agemin=1.e20, agemax=-1.e20;                fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);
             }
   double fret;          }
   double **xi,tmp,delta;          
           for(jk=-1; jk <=nlstate+ndeath; jk++)
   double dum; /* Dummy variable */            for(m=-1; m <=nlstate+ndeath; m++)
   double ***p3mat;              if(freq[jk][m][i] !=0 ) {
   int *indx;              if(first==1)
   char line[MAXLINE], linepar[MAXLINE];                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   char title[MAXLINE];                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];              }
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];          if(i <= (int) agemax)
   char filerest[FILENAMELENGTH];            fprintf(ficresp,"\n");
   char fileregp[FILENAMELENGTH];          if(first==1)
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];            printf("Others in log...\n");
   int firstobs=1, lastobs=10;          fprintf(ficlog,"\n");
   int sdeb, sfin; /* Status at beginning and end */        }
   int c,  h , cpt,l;      }
   int ju,jl, mi;    }
   int i1,j1, k1,jk,aa,bb, stepsize;    dateintmean=dateintsum/k2cpt; 
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;   
      fclose(ficresp);
   int hstepm, nhstepm;    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
   double bage, fage, age, agelim, agebase;    free_vector(pp,1,nlstate);
   double ftolpl=FTOL;    
   double **prlim;    /* End of Freq */
   double *severity;  }
   double ***param; /* Matrix of parameters */  
   double  *p;  /************ Prevalence ********************/
   double **matcov; /* Matrix of covariance */  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, int firstpass, int lastpass)
   double ***delti3; /* Scale */  {  
   double *delti; /* Scale */    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   double ***eij, ***vareij;       in each health status at the date of interview (if between dateprev1 and dateprev2).
   double **varpl; /* Variances of prevalence limits by age */       We still use firstpass and lastpass as another selection.
   double *epj, vepp;    */
   char version[80]="Imach version 0.64, May 2000, INED-EUROREVES ";   
   char *alph[]={"a","a","b","c","d","e"}, str[4];    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
   char z[1]="c", occ;    double ***freq; /* Frequencies */
 #include <sys/time.h>    double *pp;
 #include <time.h>    double pos; 
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    double  y2; /* in fractional years */
   /* long total_usecs;  
   struct timeval start_time, end_time;    pp=vector(1,nlstate);
      
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
     j1=0;
     
   printf("\nIMACH, Version 0.64a");    j=cptcoveff;
   printf("\nEnter the parameter file name: ");    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     
 #ifdef windows    for(k1=1; k1<=j;k1++){
   scanf("%s",pathtot);      for(i1=1; i1<=ncodemax[k1];i1++){
   cygwin_split_path(pathtot,path,optionfile);        j1++;
      printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);        
      chdir(path);        for (i=-1; i<=nlstate+ndeath; i++)  
            for (jk=-1; jk<=nlstate+ndeath; jk++)  
   /*size=30;            for(m=agemin; m <= agemax+3; m++)
   getcwd(pathcd, size);                freq[i][jk][m]=0;
   printf("pathcd=%s, path=%s, optionfile=%s\n",pathcd,path,optionfile);       
   cutv(path,optionfile,pathtot,'\\');        for (i=1; i<=imx; i++) { /* Each individual */
   chdir(path);          bool=1;
   replace(pathc,path);          if  (cptcovn>0) {
   printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);            for (z1=1; z1<=cptcoveff; z1++) 
   */              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
 #endif                bool=0;
 #ifdef unix          } 
   scanf("%s",optionfile);          if (bool==1) { 
 #endif            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
               y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
 /*-------- arguments in the command line --------*/              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=agemax+1;
   strcpy(fileres,"r");                if(agev[m][i]==1) agev[m][i]=agemax+2;
   strcat(fileres, optionfile);                if (m<lastpass) {
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   /*---------arguments file --------*/                  freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i]; 
                 }
   if((ficpar=fopen(optionfile,"r"))==NULL)    {              }
     printf("Problem with optionfile %s\n",optionfile);            } /* end selection of waves */
     goto end;          }
   }        }
         for(i=(int)agemin; i <= (int)agemax+3; i++){ 
   strcpy(filereso,"o");          for(jk=1; jk <=nlstate ; jk++){
   strcat(filereso,fileres);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   if((ficparo=fopen(filereso,"w"))==NULL) {              pp[jk] += freq[jk][m][i]; 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;          }
   }          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pos=0; m <=0 ; m++)
   /* Reads comments: lines beginning with '#' */              pos += freq[jk][m][i];
   while((c=getc(ficpar))=='#' && c!= EOF){          }
     ungetc(c,ficpar);          
     fgets(line, MAXLINE, ficpar);          for(jk=1; jk <=nlstate ; jk++){
     puts(line);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     fputs(line,ficparo);              pp[jk] += freq[jk][m][i];
   }          }
   ungetc(c,ficpar);          
           for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];
   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);          for(jk=1; jk <=nlstate ; jk++){    
   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);            if( i <= (int) agemax){
               if(pos>=1.e-5){
   covar=matrix(1,NCOVMAX,1,n);                    probs[i][jk][j1]= pp[jk]/pos;
   if (strlen(model)<=1) cptcovn=0;              }
   else {            }
     j=0;          }/* end jk */
     j=nbocc(model,'+');        }/* end i */
     cptcovn=j+1;      } /* end i1 */
   }    } /* end k1 */
   
   ncovmodel=2+cptcovn;    
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
      free_vector(pp,1,nlstate);
   /* Read guess parameters */    
   /* Reads comments: lines beginning with '#' */  }  /* End of Freq */
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);  /************* Waves Concatenation ***************/
     fgets(line, MAXLINE, ficpar);  
     puts(line);  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)
     fputs(line,ficparo);  {
   }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   ungetc(c,ficpar);       Death is a valid wave (if date is known).
         mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     for(i=1; i <=nlstate; i++)       and mw[mi+1][i]. dh depends on stepm.
     for(j=1; j <=nlstate+ndeath-1; j++){       */
       fscanf(ficpar,"%1d%1d",&i1,&j1);  
       fprintf(ficparo,"%1d%1d",i1,j1);    int i, mi, m;
       printf("%1d%1d",i,j);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       for(k=1; k<=ncovmodel;k++){       double sum=0., jmean=0.;*/
         fscanf(ficpar," %lf",&param[i][j][k]);    int first;
         printf(" %lf",param[i][j][k]);    int j, k=0,jk, ju, jl;
         fprintf(ficparo," %lf",param[i][j][k]);    double sum=0.;
       }    first=0;
       fscanf(ficpar,"\n");    jmin=1e+5;
       printf("\n");    jmax=-1;
       fprintf(ficparo,"\n");    jmean=0.;
     }    for(i=1; i<=imx; i++){
        mi=0;
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;      m=firstpass;
   p=param[1][1];      while(s[m][i] <= nlstate){
          if(s[m][i]>=1)
   /* Reads comments: lines beginning with '#' */          mw[++mi][i]=m;
   while((c=getc(ficpar))=='#' && c!= EOF){        if(m >=lastpass)
     ungetc(c,ficpar);          break;
     fgets(line, MAXLINE, ficpar);        else
     puts(line);          m++;
     fputs(line,ficparo);      }/* end while */
   }      if (s[m][i] > nlstate){
   ungetc(c,ficpar);        mi++;     /* Death is another wave */
         /* if(mi==0)  never been interviewed correctly before death */
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);           /* Only death is a correct wave */
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        mw[mi][i]=m;
   for(i=1; i <=nlstate; i++){      }
     for(j=1; j <=nlstate+ndeath-1; j++){  
       fscanf(ficpar,"%1d%1d",&i1,&j1);      wav[i]=mi;
       printf("%1d%1d",i,j);      if(mi==0){
       fprintf(ficparo,"%1d%1d",i1,j1);        if(first==0){
       for(k=1; k<=ncovmodel;k++){          printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);
         fscanf(ficpar,"%le",&delti3[i][j][k]);          first=1;
         printf(" %le",delti3[i][j][k]);        }
         fprintf(ficparo," %le",delti3[i][j][k]);        if(first==1){
       }          fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);
       fscanf(ficpar,"\n");        }
       printf("\n");      } /* end mi==0 */
       fprintf(ficparo,"\n");    }
     }  
   }    for(i=1; i<=imx; i++){
   delti=delti3[1][1];      for(mi=1; mi<wav[i];mi++){
          if (stepm <=0)
   /* Reads comments: lines beginning with '#' */          dh[mi][i]=1;
   while((c=getc(ficpar))=='#' && c!= EOF){        else{
     ungetc(c,ficpar);          if (s[mw[mi+1][i]][i] > nlstate) {
     fgets(line, MAXLINE, ficpar);            if (agedc[i] < 2*AGESUP) {
     puts(line);            j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     fputs(line,ficparo);            if(j==0) j=1;  /* Survives at least one month after exam */
   }            k=k+1;
   ungetc(c,ficpar);            if (j >= jmax) jmax=j;
              if (j <= jmin) jmin=j;
   matcov=matrix(1,npar,1,npar);            sum=sum+j;
   for(i=1; i <=npar; i++){            /*if (j<0) printf("j=%d num=%d \n",j,i); */
     fscanf(ficpar,"%s",&str);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     printf("%s",str);            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
     fprintf(ficparo,"%s",str);            }
     for(j=1; j <=i; j++){          }
       fscanf(ficpar," %le",&matcov[i][j]);          else{
       printf(" %.5le",matcov[i][j]);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       fprintf(ficparo," %.5le",matcov[i][j]);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     }            k=k+1;
     fscanf(ficpar,"\n");            if (j >= jmax) jmax=j;
     printf("\n");            else if (j <= jmin)jmin=j;
     fprintf(ficparo,"\n");            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
   }            sum=sum+j;
   for(i=1; i <=npar; i++)          }
     for(j=i+1;j<=npar;j++)          jk= j/stepm;
       matcov[i][j]=matcov[j][i];          jl= j -jk*stepm;
              ju= j -(jk+1)*stepm;
   printf("\n");          if(mle <=1){ 
             if(jl==0){
               dh[mi][i]=jk;
    if(mle==1){              bh[mi][i]=0;
     /*-------- data file ----------*/            }else{ /* We want a negative bias in order to only have interpolation ie
     if((ficres =fopen(fileres,"w"))==NULL) {                    * at the price of an extra matrix product in likelihood */
       printf("Problem with resultfile: %s\n", fileres);goto end;              dh[mi][i]=jk+1;
     }              bh[mi][i]=ju;
     fprintf(ficres,"#%s\n",version);            }
              }else{
     if((fic=fopen(datafile,"r"))==NULL)    {            if(jl <= -ju){
       printf("Problem with datafile: %s\n", datafile);goto end;              dh[mi][i]=jk;
     }              bh[mi][i]=jl;       /* bias is positive if real duration
                                    * is higher than the multiple of stepm and negative otherwise.
     n= lastobs;                                   */
     severity = vector(1,maxwav);            }
     outcome=imatrix(1,maxwav+1,1,n);            else{
     num=ivector(1,n);              dh[mi][i]=jk+1;
     moisnais=vector(1,n);              bh[mi][i]=ju;
     annais=vector(1,n);            }
     moisdc=vector(1,n);            if(dh[mi][i]==0){
     andc=vector(1,n);              dh[mi][i]=1; /* At least one step */
     agedc=vector(1,n);              bh[mi][i]=ju; /* At least one step */
     cod=ivector(1,n);              /*  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);*/
     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);        } /* end if mle */
     anint=matrix(1,maxwav,1,n);      } /* end wave */
     s=imatrix(1,maxwav+1,1,n);    }
     adl=imatrix(1,maxwav+1,1,n);        jmean=sum/k;
     tab=ivector(1,NCOVMAX);    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
     ncodemax=ivector(1,8);    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
    }
     i=1;  
     while (fgets(line, MAXLINE, fic) != NULL)    {  /*********** Tricode ****************************/
       if ((i >= firstobs) && (i <=lastobs)) {  void tricode(int *Tvar, int **nbcode, int imx)
          {
         for (j=maxwav;j>=1;j--){    
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    int Ndum[20],ij=1, k, j, i, maxncov=19;
           strcpy(line,stra);    int cptcode=0;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    cptcoveff=0; 
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);   
         }    for (k=0; k<maxncov; k++) Ndum[k]=0;
            for (k=1; k<=7; k++) ncodemax[k]=0;
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);                                 modality*/ 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
         Ndum[ij]++; /*store the modality */
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         for (j=ncov;j>=1;j--){        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);                                         Tvar[j]. If V=sex and male is 0 and 
         }                                         female is 1, then  cptcode=1.*/
         num[i]=atol(stra);      }
   
         /*printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.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]),  (mint[5][i]), (anint[5][i]), (s[5][i]),  (mint[6][i]), (anint[6][i]), (s[6][i]));*/      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 */
         i=i+1;      }
       }  
     }      ij=1; 
       for (i=1; i<=ncodemax[j]; i++) {
     /*scanf("%d",i);*/        for (k=0; k<= maxncov; k++) {
   imx=i-1; /* Number of individuals */          if (Ndum[k] != 0) {
             nbcode[Tvar[j]][ij]=k; 
   /* Calculation of the number of parameter from char model*/            /* 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; */
   Tvar=ivector(1,8);                
                ij++;
   if (strlen(model) >1){          }
     j=0;          if (ij > ncodemax[j]) break; 
     j=nbocc(model,'+');        }  
     cptcovn=j+1;      } 
        }  
     strcpy(modelsav,model);  
     if (j==0) {   for (k=0; k< maxncov; k++) Ndum[k]=0;
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);  
     }   for (i=1; i<=ncovmodel-2; i++) { 
     else {     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
       for(i=j; i>=1;i--){     ij=Tvar[i];
         cutv(stra,strb,modelsav,'+');     Ndum[ij]++;
         if (strchr(strb,'*')) {   }
           cutv(strd,strc,strb,'*');  
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;   ij=1;
           cutv(strb,strc,strd,'V');   for (i=1; i<= maxncov; i++) {
           for (k=1; k<=lastobs;k++)     if((Ndum[i]!=0) && (i<=ncovcol)){
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];       Tvaraff[ij]=i; /*For printing */
         }       ij++;
         else {cutv(strd,strc,strb,'V');     }
         Tvar[i+1]=atoi(strc);   }
         }   
         strcpy(modelsav,stra);     cptcoveff=ij-1; /*Number of simple covariates*/
       }  }
       cutv(strd,strc,stra,'V');  
       Tvar[1]=atoi(strc);  /*********** Health Expectancies ****************/
     }  
   }  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )
   /*printf("tvar=%d ",Tvar[1]);  
   scanf("%d ",i);*/  {
     fclose(fic);    /* Health expectancies */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
     if (weightopt != 1) { /* Maximisation without weights*/    double age, agelim, hf;
       for(i=1;i<=n;i++) weight[i]=1.0;    double ***p3mat,***varhe;
     }    double **dnewm,**doldm;
     /*-calculation of age at interview from date of interview and age at death -*/    double *xp;
     agev=matrix(1,maxwav,1,imx);    double **gp, **gm;
        double ***gradg, ***trgradg;
     for (i=1; i<=imx; i++)  {    int theta;
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  
       for(m=1; (m<= maxwav); m++){    varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);
         if(s[m][i] >0){    xp=vector(1,npar);
           if (s[m][i] == nlstate+1) {    dnewm=matrix(1,nlstate*2,1,npar);
             if(agedc[i]>0)    doldm=matrix(1,nlstate*2,1,nlstate*2);
               if(moisdc[i]!=99 && andc[i]!=9999)    
               agev[m][i]=agedc[i];    fprintf(ficreseij,"# Health expectancies\n");
             else{    fprintf(ficreseij,"# Age");
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    for(i=1; i<=nlstate;i++)
               agev[m][i]=-1;      for(j=1; j<=nlstate;j++)
             }        fprintf(ficreseij," %1d-%1d (SE)",i,j);
           }    fprintf(ficreseij,"\n");
           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(estepm < stepm){
             if(mint[m][i]==99 || anint[m][i]==9999)      printf ("Problem %d lower than %d\n",estepm, stepm);
               agev[m][i]=1;    }
             else if(agev[m][i] <agemin){    else  hstepm=estepm;   
               agemin=agev[m][i];    /* We compute the life expectancy from trapezoids spaced every estepm months
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/     * 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
             else if(agev[m][i] >agemax){     * we are calculating an estimate of the Life Expectancy assuming a linear 
               agemax=agev[m][i];     * progression in between and thus overestimating or underestimating according
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/     * to the curvature of the survival function. If, for the same date, we 
             }     * estimate the model with stepm=1 month, we can keep estepm to 24 months
             /*agev[m][i]=anint[m][i]-annais[i];*/     * to compare the new estimate of Life expectancy with the same linear 
             /*   agev[m][i] = age[i]+2*m;*/     * hypothesis. A more precise result, taking into account a more precise
           }     * curvature will be obtained if estepm is as small as stepm. */
           else { /* =9 */  
             agev[m][i]=1;    /* For example we decided to compute the life expectancy with the smallest unit */
             s[m][i]=-1;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           }       nhstepm is the number of hstepm from age to agelim 
         }       nstepm is the number of stepm from age to agelin. 
         else /*= 0 Unknown */       Look at hpijx to understand the reason of that which relies in memory size
           agev[m][i]=1;       and note for a fixed period like estepm months */
       }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           survival function given by stepm (the optimization length). Unfortunately it
     }       means that if the survival funtion is printed only each two years of age and if
     for (i=1; i<=imx; i++)  {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       for(m=1; (m<= maxwav); m++){       results. So we changed our mind and took the option of the best precision.
         if (s[m][i] > (nlstate+ndeath)) {    */
           printf("Error: Wrong value in nlstate or ndeath\n");      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           goto end;  
         }    agelim=AGESUP;
       }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     }      /* nhstepm age range expressed in number of stepm */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); 
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
     free_vector(severity,1,maxwav);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     free_imatrix(outcome,1,maxwav+1,1,n);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_vector(moisnais,1,n);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);
     free_vector(annais,1,n);      gp=matrix(0,nhstepm,1,nlstate*2);
     free_matrix(mint,1,maxwav,1,n);      gm=matrix(0,nhstepm,1,nlstate*2);
     free_matrix(anint,1,maxwav,1,n);  
     free_vector(moisdc,1,n);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     free_vector(andc,1,n);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
       
     wav=ivector(1,imx);  
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);  
          /* Computing Variances of health expectancies */
     /* Concatenates waves */  
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
 Tcode=ivector(1,100);        }
    nbcode=imatrix(1,nvar,1,8);          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
    ncodemax[1]=1;    
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);        cptj=0;
          for(j=1; j<= nlstate; j++){
    codtab=imatrix(1,100,1,10);          for(i=1; i<=nlstate; i++){
    h=0;            cptj=cptj+1;
    m=pow(2,cptcovn);            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
                gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
    for(k=1;k<=cptcovn; k++){            }
      for(i=1; i <=(m/pow(2,k));i++){          }
        for(j=1; j <= ncodemax[k]; j++){        }
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){       
            h++;       
            if (h>m) h=1;codtab[h][k]=j;        for(i=1; i<=npar; i++) 
          }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
        }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
      }        
    }        cptj=0;
         for(j=1; j<= nlstate; j++){
    /*for(i=1; i <=m ;i++){          for(i=1;i<=nlstate;i++){
      for(k=1; k <=cptcovn; k++){            cptj=cptj+1;
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
      }              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
      printf("\n");            }
    }*/          }
    /*scanf("%d",i);*/        }
            for(j=1; j<= nlstate*2; j++)
    /* Calculates basic frequencies. Computes observed prevalence at single age          for(h=0; h<=nhstepm-1; h++){
        and prints on file fileres'p'. */            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);          }
        } 
      
   /*scanf("%d ",i);*/  /* End theta */
   
        trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       for(h=0; h<=nhstepm-1; h++)
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(j=1; j<=nlstate*2;j++)
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(theta=1; theta <=npar; theta++)
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            trgradg[h][j][theta]=gradg[h][theta][j];
           
     /* 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] */       for(i=1;i<=nlstate*2;i++)
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */        for(j=1;j<=nlstate*2;j++)
              varhe[i][j][(int)age] =0.;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);  
        printf("%d|",(int)age);fflush(stdout);
           fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     /*--------- results files --------------*/       for(h=0;h<=nhstepm-1;h++){
     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);        for(k=0;k<=nhstepm-1;k++){
              matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);
    jk=1;          matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);
    fprintf(ficres,"# Parameters\n");          for(i=1;i<=nlstate*2;i++)
    printf("# Parameters\n");            for(j=1;j<=nlstate*2;j++)
    for(i=1,jk=1; i <=nlstate; i++){              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
      for(k=1; k <=(nlstate+ndeath); k++){        }
        if (k != i)      }
          {      /* Computing expectancies */
            printf("%d%d ",i,k);      for(i=1; i<=nlstate;i++)
            fprintf(ficres,"%1d%1d ",i,k);        for(j=1; j<=nlstate;j++)
            for(j=1; j <=ncovmodel; j++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
              printf("%f ",p[jk]);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
              fprintf(ficres,"%f ",p[jk]);            
              jk++;  /* 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]);*/
            }  
            printf("\n");          }
            fprintf(ficres,"\n");  
          }      fprintf(ficreseij,"%3.0f",age );
      }      cptj=0;
    }      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
     /* Computing hessian and covariance matrix */          cptj++;
     ftolhess=ftol; /* Usually correct */          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
     hesscov(matcov, p, npar, delti, ftolhess, func);        }
     fprintf(ficres,"# Scales\n");      fprintf(ficreseij,"\n");
     printf("# Scales\n");     
      for(i=1,jk=1; i <=nlstate; i++){      free_matrix(gm,0,nhstepm,1,nlstate*2);
       for(j=1; j <=nlstate+ndeath; j++){      free_matrix(gp,0,nhstepm,1,nlstate*2);
         if (j!=i) {      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);
           fprintf(ficres,"%1d%1d",i,j);      free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);
           printf("%1d%1d",i,j);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           for(k=1; k<=ncovmodel;k++){    }
             printf(" %.5e",delti[jk]);    printf("\n");
             fprintf(ficres," %.5e",delti[jk]);    fprintf(ficlog,"\n");
             jk++;  
           }    free_vector(xp,1,npar);
           printf("\n");    free_matrix(dnewm,1,nlstate*2,1,npar);
           fprintf(ficres,"\n");    free_matrix(doldm,1,nlstate*2,1,nlstate*2);
         }    free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);
       }  }
       }  
      /************ Variance ******************/
     k=1;  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)
     fprintf(ficres,"# Covariance\n");  {
     printf("# Covariance\n");    /* Variance of health expectancies */
     for(i=1;i<=npar;i++){    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
       /*  if (k>nlstate) k=1;    /* double **newm;*/
       i1=(i-1)/(ncovmodel*nlstate)+1;    double **dnewm,**doldm;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    double **dnewmp,**doldmp;
       printf("%s%d%d",alph[k],i1,tab[i]);*/    int i, j, nhstepm, hstepm, h, nstepm ;
       fprintf(ficres,"%3d",i);    int k, cptcode;
       printf("%3d",i);    double *xp;
       for(j=1; j<=i;j++){    double **gp, **gm;  /* for var eij */
         fprintf(ficres," %.5e",matcov[i][j]);    double ***gradg, ***trgradg; /*for var eij */
         printf(" %.5e",matcov[i][j]);    double **gradgp, **trgradgp; /* for var p point j */
       }    double *gpp, *gmp; /* for var p point j */
       fprintf(ficres,"\n");    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       printf("\n");    double ***p3mat;
       k++;    double age,agelim, hf;
     }    double ***mobaverage;
        int theta;
     while((c=getc(ficpar))=='#' && c!= EOF){    char digit[4];
       ungetc(c,ficpar);    char digitp[25];
       fgets(line, MAXLINE, ficpar);  
       puts(line);    char fileresprobmorprev[FILENAMELENGTH];
       fputs(line,ficparo);  
     }    if(popbased==1){
     ungetc(c,ficpar);      if(mobilav!=0)
          strcpy(digitp,"-populbased-mobilav-");
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      else strcpy(digitp,"-populbased-nomobil-");
        }
     if (fage <= 2) {    else 
       bage = agemin;      strcpy(digitp,"-stablbased-");
       fage = agemax;  
     }    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
 /*------------ gnuplot -------------*/        printf(" Error in movingaverage mobilav=%d\n",mobilav);
 chdir(pathcd);      }
   if((ficgp=fopen("graph.plt","w"))==NULL) {    }
     printf("Problem with file graph.plt");goto end;  
   }    strcpy(fileresprobmorprev,"prmorprev"); 
 #ifdef windows    sprintf(digit,"%-d",ij);
   fprintf(ficgp,"cd \"%s\" \n",pathc);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
 #endif    strcat(fileresprobmorprev,digit); /* Tvar to be done */
 m=pow(2,cptcovn);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
      strcat(fileresprobmorprev,fileres);
  /* 1eme*/    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   for (cpt=1; cpt<= nlstate ; cpt ++) {      printf("Problem with resultfile: %s\n", fileresprobmorprev);
    for (k1=1; k1<= m ; k1 ++) {      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
 #ifdef windows    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     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);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
 #endif    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);
 #ifdef unix    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
 #endif      fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
 for (i=1; i<= nlstate ; i ++) {        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    }  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    fprintf(ficresprobmorprev,"\n");
 }    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
     for (i=1; i<= nlstate ; i ++) {      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      exit(0);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    }
 }    else{
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);      fprintf(ficgp,"\n# Routine varevsij");
      for (i=1; i<= nlstate ; i ++) {    }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");      printf("Problem with html file: %s\n", optionfilehtm);
 }        fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));      exit(0);
 #ifdef unix    }
 fprintf(ficgp,"\nset ter gif small size 400,300");    else{
 #endif      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");
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
    }    }
   }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   /*2 eme*/  
     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");
   for (k1=1; k1<= m ; k1 ++) {    fprintf(ficresvij,"# Age");
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++)
     for (i=1; i<= nlstate+1 ; i ++) {        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
       k=2*i;    fprintf(ficresvij,"\n");
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {    xp=vector(1,npar);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    dnewm=matrix(1,nlstate,1,npar);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    doldm=matrix(1,nlstate,1,nlstate);
 }      dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       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);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       for (j=1; j<= nlstate+1 ; j ++) {    gpp=vector(nlstate+1,nlstate+ndeath);
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    gmp=vector(nlstate+1,nlstate+ndeath);
         else fprintf(ficgp," \%%*lf (\%%*lf)");    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
 }      
       fprintf(ficgp,"\" t\"\" w l 0,");    if(estepm < stepm){
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);      printf ("Problem %d lower than %d\n",estepm, stepm);
       for (j=1; j<= nlstate+1 ; j ++) {    }
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    else  hstepm=estepm;   
   else fprintf(ficgp," \%%*lf (\%%*lf)");    /* For example we decided to compute the life expectancy with the smallest unit */
 }      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");       nhstepm is the number of hstepm from age to agelim 
       else fprintf(ficgp,"\" t\"\" w l 0,");       nstepm is the number of stepm from age to agelin. 
     }       Look at hpijx to understand the reason of that which relies in memory size
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);       and note for a fixed period like k years */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         survival function given by stepm (the optimization length). Unfortunately it
   /*3eme*/       means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
    for (k1=1; k1<= m ; k1 ++) {       results. So we changed our mind and took the option of the best precision.
     for (cpt=1; cpt<= nlstate ; cpt ++) {    */
       k=2+nlstate*(cpt-1);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       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);    agelim = AGESUP;
       for (i=1; i< nlstate ; i ++) {    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         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);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
    }      gp=matrix(0,nhstepm,1,nlstate);
        gm=matrix(0,nhstepm,1,nlstate);
   /* CV preval stat */  
     for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {      for(theta=1; theta <=npar; theta++){
       k=3;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       for (i=1; i< nlstate ; i ++)        }
         fprintf(ficgp,"+$%d",k+i+1);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
        
       l=3+(nlstate+ndeath)*cpt;        if (popbased==1) {
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);          if(mobilav ==0){
       for (i=1; i< nlstate ; i ++) {            for(i=1; i<=nlstate;i++)
         l=3+(nlstate+ndeath)*cpt;              prlim[i][i]=probs[(int)age][i][ij];
         fprintf(ficgp,"+$%d",l+i+1);          }else{ /* mobilav */ 
       }            for(i=1; i<=nlstate;i++)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                prlim[i][i]=mobaverage[(int)age][i][ij];
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          }
     }        }
   }    
          for(j=1; j<= nlstate; j++){
   /* proba elementaires */          for(h=0; h<=nhstepm; h++){
   for(i=1,jk=1; i <=nlstate; i++){            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     for(k=1; k <=(nlstate+ndeath); k++){              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       if (k != i) {          }
         /*  fprintf(ficgp,"%1d%1d ",i,k);*/        }
         for(j=1; j <=ncovmodel; j++){        /* This for computing probability of death (h=1 means
           fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);           computed over hstepm 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,gpp[j]=0.; i<= nlstate; i++)
     }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   }        }    
   for(jk=1; jk <=m; jk++) {        /* end probability of death */
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);  
   for(i=1; i <=nlstate; i++) {        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
     for(k=1; k <=(nlstate+ndeath); k++){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       if (k != i) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         fprintf(ficgp," exp(a%d%d+b%d%d*x",i,k,i,k);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(j=3; j <=ncovmodel; j++)   
           fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        if (popbased==1) {
         fprintf(ficgp,")/(1");          if(mobilav ==0){
         for(k1=1; k1 <=(nlstate+ndeath); k1++)            for(i=1; i<=nlstate;i++)
           if (k1 != i) {              prlim[i][i]=probs[(int)age][i][ij];
             fprintf(ficgp,"+exp(a%d%d+b%d%d*x",i,k1,i,k1);          }else{ /* mobilav */ 
             for(j=3; j <=ncovmodel; j++)            for(i=1; i<=nlstate;i++)
               fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);              prlim[i][i]=mobaverage[(int)age][i][ij];
             fprintf(ficgp,")");          }
           }        }
         fprintf(ficgp,") t \"p%d%d\" ", i,k);  
       if ((i+k)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        for(j=1; j<= nlstate; j++){
       }          for(h=0; h<=nhstepm; h++){
     }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   }              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
 fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);            }
   }        }
          /* This for computing probability of death (h=1 means
  fclose(ficgp);           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
     chdir(path);        */
     free_matrix(agev,1,maxwav,1,imx);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     free_ivector(wav,1,imx);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);        }    
            /* end probability of death */
     free_imatrix(s,1,maxwav+1,1,n);  
            for(j=1; j<= nlstate; j++) /* vareij */
              for(h=0; h<=nhstepm; h++){
     free_ivector(num,1,n);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     free_vector(agedc,1,n);          }
     free_vector(weight,1,n);  
     /*free_matrix(covar,1,NCOVMAX,1,n);*/        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     fclose(ficparo);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     fclose(ficres);        }
    }  
          } /* End theta */
    /*________fin mle=1_________*/  
          trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
        for(h=0; h<=nhstepm; h++) /* veij */
     /* No more information from the sample is required now */        for(j=1; j<=nlstate;j++)
   /* Reads comments: lines beginning with '#' */          for(theta=1; theta <=npar; theta++)
   while((c=getc(ficpar))=='#' && c!= EOF){            trgradg[h][j][theta]=gradg[h][theta][j];
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     puts(line);        for(theta=1; theta <=npar; theta++)
     fputs(line,ficparo);          trgradgp[j][theta]=gradgp[theta][j];
   }    
   ungetc(c,ficpar);  
        hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        for(j=1;j<=nlstate;j++)
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);          vareij[i][j][(int)age] =0.;
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  
 /*--------- index.htm --------*/      for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
   if((fichtm=fopen("index.htm","w"))==NULL)    {          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
     printf("Problem with index.htm \n");goto end;          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   }          for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
  fprintf(fichtm,"<body><ul> Imach, Version 0.63<hr> <li>Outputs files<br><br>\n              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        }
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>      }
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>    
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      /* pptj */
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>      for(j=nlstate+1;j<=nlstate+ndeath;j++)
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>        for(i=nlstate+1;i<=nlstate+ndeath;i++)
         - 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);          varppt[j][i]=doldmp[j][i];
       /* end ppptj */
  fprintf(fichtm," <li>Graphs</li>\n<p>");      /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
  m=cptcovn;      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}   
       if (popbased==1) {
  j1=0;        if(mobilav ==0){
  for(k1=1; k1<=m;k1++){          for(i=1; i<=nlstate;i++)
    for(i1=1; i1<=ncodemax[k1];i1++){            prlim[i][i]=probs[(int)age][i][ij];
        j1++;        }else{ /* mobilav */ 
        if (cptcovn > 0) {          for(i=1; i<=nlstate;i++)
          fprintf(fichtm,"<hr>************ Results for covariates");            prlim[i][i]=mobaverage[(int)age][i][ij];
          for (cpt=1; cpt<=cptcovn;cpt++)        }
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);      }
          fprintf(fichtm," ************\n<hr>");               
        }      /* This for computing probability of death (h=1 means
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);             as a weighted average of prlim.
        for(cpt=1; cpt<nlstate;cpt++){      */
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>      for(j=nlstate+1;j<=nlstate+ndeath;j++){
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
        }          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     for(cpt=1; cpt<=nlstate;cpt++) {      }    
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      /* end probability of death */
 interval) in state (%d): v%s%d%d.gif <br>  
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
      }      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
      for(cpt=1; cpt<=nlstate;cpt++) {        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>        for(i=1; i<=nlstate;i++){
 <img src=\"ex%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
      }        }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      } 
 health expectancies in states (1) and (2): e%s%d.gif<br>      fprintf(ficresprobmorprev,"\n");
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);  
 fprintf(fichtm,"\n</body>");      fprintf(ficresvij,"%.0f ",age );
    }      for(i=1; i<=nlstate;i++)
  }        for(j=1; j<=nlstate;j++){
 fclose(fichtm);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
   /*--------------- Prevalence limit --------------*/      fprintf(ficresvij,"\n");
        free_matrix(gp,0,nhstepm,1,nlstate);
   strcpy(filerespl,"pl");      free_matrix(gm,0,nhstepm,1,nlstate);
   strcat(filerespl,fileres);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }    } /* End age */
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    free_vector(gpp,nlstate+1,nlstate+ndeath);
   fprintf(ficrespl,"#Prevalence limit\n");    free_vector(gmp,nlstate+1,nlstate+ndeath);
   fprintf(ficrespl,"#Age ");    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   fprintf(ficrespl,"\n");    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 */
   prlim=matrix(1,nlstate,1,nlstate);    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",fileresprobmorprev);
   k=0;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",fileresprobmorprev);
   agebase=agemin;    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
   agelim=agemax;    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s%s.png\"> <br>\n", estepm,digitp,optionfilefiname,digit);
   ftolpl=1.e-10;    /*  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);
   i1=cptcovn;  */
   if (cptcovn < 1){i1=1;}    fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit);
   
   for(cptcov=1;cptcov<=i1;cptcov++){    free_vector(xp,1,npar);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    free_matrix(doldm,1,nlstate,1,nlstate);
         k=k+1;    free_matrix(dnewm,1,nlstate,1,npar);
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         fprintf(ficrespl,"\n#****** ");    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
         for(j=1;j<=cptcovn;j++)    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         fprintf(ficrespl,"******\n");    fclose(ficresprobmorprev);
            fclose(ficgp);
         for (age=agebase; age<=agelim; age++){    fclose(fichtm);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  }  
           fprintf(ficrespl,"%.0f",age );  
           for(i=1; i<=nlstate;i++)  /************ Variance of prevlim ******************/
           fprintf(ficrespl," %.5f", prlim[i][i]);  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(ficrespl,"\n");  {
         }    /* Variance of prevalence limit */
       }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     }    double **newm;
   fclose(ficrespl);    double **dnewm,**doldm;
   /*------------- h Pij x at various ages ------------*/    int i, j, nhstepm, hstepm;
      int k, cptcode;
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    double *xp;
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    double *gp, *gm;
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    double **gradg, **trgradg;
   }    double age,agelim;
   printf("Computing pij: result on file '%s' \n", filerespij);    int theta;
       
   stepsize=(int) (stepm+YEARM-1)/YEARM;    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
   if (stepm<=24) stepsize=2;    fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
   agelim=AGESUP;        fprintf(ficresvpl," %1d-%1d",i,i);
   hstepm=stepsize*YEARM; /* Every year of age */    fprintf(ficresvpl,"\n");
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
      xp=vector(1,npar);
   k=0;    dnewm=matrix(1,nlstate,1,npar);
   for(cptcov=1;cptcov<=i1;cptcov++){    doldm=matrix(1,nlstate,1,nlstate);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    
       k=k+1;    hstepm=1*YEARM; /* Every year of age */
         fprintf(ficrespij,"\n#****** ");    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
         for(j=1;j<=cptcovn;j++)    agelim = AGESUP;
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         fprintf(ficrespij,"******\n");      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
              if (stepm >= YEARM) hstepm=1;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      gradg=matrix(1,npar,1,nlstate);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      gp=vector(1,nlstate);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      gm=vector(1,nlstate);
           oldm=oldms;savm=savms;  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        for(theta=1; theta <=npar; theta++){
           fprintf(ficrespij,"# Age");        for(i=1; i<=npar; i++){ /* Computes gradient */
           for(i=1; i<=nlstate;i++)          xp[i] = x[i] + (i==theta ?delti[theta]:0);
             for(j=1; j<=nlstate+ndeath;j++)        }
               fprintf(ficrespij," %1d-%1d",i,j);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           fprintf(ficrespij,"\n");        for(i=1;i<=nlstate;i++)
           for (h=0; h<=nhstepm; h++){          gp[i] = prlim[i][i];
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      
             for(i=1; i<=nlstate;i++)        for(i=1; i<=npar; i++) /* Computes gradient */
               for(j=1; j<=nlstate+ndeath;j++)          xp[i] = x[i] - (i==theta ?delti[theta]:0);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
             fprintf(ficrespij,"\n");        for(i=1;i<=nlstate;i++)
           }          gm[i] = prlim[i][i];
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           fprintf(ficrespij,"\n");        for(i=1;i<=nlstate;i++)
         }          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
     }      } /* End theta */
   }  
       trgradg =matrix(1,nlstate,1,npar);
   fclose(ficrespij);  
       for(j=1; j<=nlstate;j++)
   /*---------- Health expectancies and variances ------------*/        for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   strcpy(filerest,"t");  
   strcat(filerest,fileres);      for(i=1;i<=nlstate;i++)
   if((ficrest=fopen(filerest,"w"))==NULL) {        varpl[i][(int)age] =0.;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
   }      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
   strcpy(filerese,"e");      fprintf(ficresvpl,"%.0f ",age );
   strcat(filerese,fileres);      for(i=1; i<=nlstate;i++)
   if((ficreseij=fopen(filerese,"w"))==NULL) {        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);      fprintf(ficresvpl,"\n");
   }      free_vector(gp,1,nlstate);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
  strcpy(fileresv,"v");      free_matrix(trgradg,1,nlstate,1,npar);
   strcat(fileresv,fileres);    } /* End age */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {  
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    free_vector(xp,1,npar);
   }    free_matrix(doldm,1,nlstate,1,npar);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    free_matrix(dnewm,1,nlstate,1,nlstate);
   
   k=0;  }
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  /************ Variance of one-step probabilities  ******************/
       k=k+1;  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
       fprintf(ficrest,"\n#****** ");  {
       for(j=1;j<=cptcovn;j++)    int i, j=0,  i1, k1, l1, t, tj;
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    int k2, l2, j1,  z1;
       fprintf(ficrest,"******\n");    int k=0,l, cptcode;
     int first=1, first1;
       fprintf(ficreseij,"\n#****** ");    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
       for(j=1;j<=cptcovn;j++)    double **dnewm,**doldm;
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    double *xp;
       fprintf(ficreseij,"******\n");    double *gp, *gm;
     double **gradg, **trgradg;
       fprintf(ficresvij,"\n#****** ");    double **mu;
       for(j=1;j<=cptcovn;j++)    double age,agelim, cov[NCOVMAX];
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
       fprintf(ficresvij,"******\n");    int theta;
     char fileresprob[FILENAMELENGTH];
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    char fileresprobcov[FILENAMELENGTH];
       oldm=oldms;savm=savms;    char fileresprobcor[FILENAMELENGTH];
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);    
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    double ***varpij;
       oldm=oldms;savm=savms;  
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    strcpy(fileresprob,"prob"); 
          strcat(fileresprob,fileres);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);      printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficrest,"\n");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
            }
       hf=1;    strcpy(fileresprobcov,"probcov"); 
       if (stepm >= YEARM) hf=stepm/YEARM;    strcat(fileresprobcov,fileres);
       epj=vector(1,nlstate+1);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       for(age=bage; age <=fage ;age++){      printf("Problem with resultfile: %s\n", fileresprobcov);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
         fprintf(ficrest," %.0f",age);    }
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    strcpy(fileresprobcor,"probcor"); 
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    strcat(fileresprobcor,fileres);
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
           }      printf("Problem with resultfile: %s\n", fileresprobcor);
           epj[nlstate+1] +=epj[j];      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
         }    }
         for(i=1, vepp=0.;i <=nlstate;i++)    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           for(j=1;j <=nlstate;j++)    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
             vepp += vareij[i][j][(int)age];    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
         for(j=1;j <=nlstate;j++){    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
         }    
         fprintf(ficrest,"\n");    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
       }    fprintf(ficresprob,"# Age");
     }    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   }    fprintf(ficresprobcov,"# Age");
            fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
  fclose(ficreseij);    fprintf(ficresprobcov,"# Age");
  fclose(ficresvij);  
   fclose(ficrest);  
   fclose(ficpar);    for(i=1; i<=nlstate;i++)
   free_vector(epj,1,nlstate+1);      for(j=1; j<=(nlstate+ndeath);j++){
   /*scanf("%d ",i); */        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
   /*------- Variance limit prevalence------*/          fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
 strcpy(fileresvpl,"vpl");   /* fprintf(ficresprob,"\n");
   strcat(fileresvpl,fileres);    fprintf(ficresprobcov,"\n");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    fprintf(ficresprobcor,"\n");
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);   */
     exit(0);   xp=vector(1,npar);
   }    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
  k=0;    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
  for(cptcov=1;cptcov<=i1;cptcov++){    first=1;
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
      k=k+1;      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
      fprintf(ficresvpl,"\n#****** ");      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
      for(j=1;j<=cptcovn;j++)      exit(0);
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    }
      fprintf(ficresvpl,"******\n");    else{
            fprintf(ficgp,"\n# Routine varprob");
      varpl=matrix(1,nlstate,(int) bage, (int) fage);    }
      oldm=oldms;savm=savms;    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      printf("Problem with html file: %s\n", optionfilehtm);
    }      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
  }      exit(0);
     }
   fclose(ficresvpl);    else{
       fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   /*---------- End : free ----------------*/      fprintf(fichtm,"\n");
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);  
        fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      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");
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");
    
      }
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);    cov[1]=1;
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    tj=cptcoveff;
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
      j1=0;
   free_matrix(matcov,1,npar,1,npar);    for(t=1; t<=tj;t++){
   free_vector(delti,1,npar);      for(i1=1; i1<=ncodemax[t];i1++){ 
          j1++;
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
   printf("End of Imach\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          fprintf(ficresprob, "**********\n#\n");
            fprintf(ficresprobcov, "\n#********** Variable "); 
   /* 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);*/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   /*printf("Total time was %d uSec.\n", total_usecs);*/          fprintf(ficresprobcov, "**********\n#\n");
   /*------ End -----------*/          
           fprintf(ficgp, "\n#********** Variable "); 
  end:          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 #ifdef windows          fprintf(ficgp, "**********\n#\n");
  chdir(pathcd);          
 #endif          
  system("wgnuplot graph.plt");          fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 #ifdef windows          fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   while (z[0] != 'q') {          
     chdir(pathcd);          fprintf(ficresprobcor, "\n#********** Variable ");    
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     scanf("%s",z);          fprintf(ficresprobcor, "**********\n#");    
     if (z[0] == 'c') system("./imach");        }
     else if (z[0] == 'e') {        
       chdir(path);        for (age=bage; age<=fage; age ++){ 
       system("index.htm");          cov[2]=age;
     }          for (k=1; k<=cptcovn;k++) {
     else if (z[0] == 'q') exit(0);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   }          }
 #endif          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 }          for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(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+1.96*$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:($2-1.96*$3) \"\%%lf",fileres,k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%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 bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     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;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     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,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
     for(cptcov=1, k=0;cptcov<=cptcoveff;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, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp++) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (YEARM*yearp)) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h==(int)(YEARM*yearp))
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                 }
                 if (h==(int)(YEARM*yearp)){
                   fprintf(ficresf," %.3f", ppij);
                 }
               }
             }
             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 *****not tested NB*************/
   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 calagedatem, 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;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     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,k=0;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)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %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) (calagedatem+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)(calagedatem+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+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+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)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %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) (calagedatem+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)(calagedatem+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 mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1;
   
     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]));}*/
     
    for (i=1; i<=imx; i++)
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* 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=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if(moisdc[i]!=99 && andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if (andc[i]!=9999){
                   printf("Warning negative age at death: %d line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a
                                    month */
             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=firstpass; (m<=lastpass); 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;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%d %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
     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);
     printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
     fprintf(ficlog,"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+(mprev1-1)/12.+(jprev1-1)/365.;
     dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/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,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
     fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
     printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
     fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
     fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
     /* day and month of proj2 are not used but only year 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(j=1;j<=cptcoveff;j++)
             fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           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*/
   
     fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
     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,"# Cov Agex agex+h hpijx with i,j=");
           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 %3.f %3.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)){*/
     if(prevfcast==1){
       if(stepm ==1){
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         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);
   
     prevalence(ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
   
     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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  Added in v.1.72


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