Diff for /imach/src/imach.c between versions 1.3 and 1.86

version 1.3, 2001/05/02 17:21:42 version 1.86, 2003/06/17 20:04:08
Line 1 Line 1
      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.86  2003/06/17 20:04:08  brouard
   individuals from different ages are interviewed on their health status    (Module): Change position of html and gnuplot routines and added
   or degree of  disability. At least a second wave of interviews    routine fileappend.
   ("longitudinal") should  measure each new individual health status.  
   Health expectancies are computed from the transistions observed between    Revision 1.85  2003/06/17 13:12:43  brouard
   waves and are computed for each degree of severity of disability (number    * imach.c (Repository): Check when date of death was earlier that
   of life states). More degrees you consider, more time is necessary to    current date of interview. It may happen when the death was just
   reach the Maximum Likelihood of the parameters involved in the model.    prior to the death. In this case, dh was negative and likelihood
   The simplest model is the multinomial logistic model where pij is    was wrong (infinity). We still send an "Error" but patch by
   the probabibility to be observed in state j at the second wave conditional    assuming that the date of death was just one stepm after the
   to be observed in state i at the first wave. Therefore the model is:    interview.
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    (Repository): Because some people have very long ID (first column)
   is a covariate. If you want to have a more complex model than "constant and    we changed int to long in num[] and we added a new lvector for
   age", you should modify the program where the markup    memory allocation. But we also truncated to 8 characters (left
     *Covariates have to be included here again* invites you to do it.    truncation)
   More covariates you add, less is the speed of the convergence.    (Repository): No more line truncation errors.
   
   The advantage that this computer programme claims, comes from that if the    Revision 1.84  2003/06/13 21:44:43  brouard
   delay between waves is not identical for each individual, or if some    * imach.c (Repository): Replace "freqsummary" at a correct
   individual missed an interview, the information is not rounded or lost, but    place. It differs from routine "prevalence" which may be called
   taken into account using an interpolation or extrapolation.    many times. Probs is memory consuming and must be used with
   hPijx is the probability to be    parcimony.
   observed in state i at age x+h conditional to the observed state i at age    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   x. The delay 'h' can be split into an exact number (nh*stepm) of  
   unobserved intermediate  states. This elementary transition (by month or    Revision 1.83  2003/06/10 13:39:11  lievre
   quarter trimester, semester or year) is model as a multinomial logistic.    *** empty log message ***
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply hPijx.    Revision 1.82  2003/06/05 15:57:20  brouard
     Add log in  imach.c and  fullversion number is now printed.
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.  */
    /*
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).     Interpolated Markov Chain
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Short summary of the programme:
   from the European Union.    
   It is copyrighted identically to a GNU software product, ie programme and    This program computes Healthy Life Expectancies from
   software can be distributed freely for non commercial use. Latest version    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   can be accessed at http://euroreves.ined.fr/imach .    first survey ("cross") where individuals from different ages are
   **********************************************************************/    interviewed on their health status or degree of disability (in the
      case of a health survey which is our main interest) -2- at least a
 #include <math.h>    second wave of interviews ("longitudinal") which measure each change
 #include <stdio.h>    (if any) in individual health status.  Health expectancies are
 #include <stdlib.h>    computed from the time spent in each health state according to a
 #include <unistd.h>    model. More health states you consider, more time is necessary to reach the
     Maximum Likelihood of the parameters involved in the model.  The
 #define MAXLINE 256    simplest model is the multinomial logistic model where pij is the
 #define FILENAMELENGTH 80    probability to be observed in state j at the second wave
 /*#define DEBUG*/    conditional to be observed in state i at the first wave. Therefore
 #define windows    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
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    complex model than "constant and age", you should modify the program
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    where the markup *Covariates have to be included here again* invites
     you to do it.  More covariates you add, slower the
 #define NINTERVMAX 8    convergence.
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    The advantage of this computer programme, compared to a simple
 #define NCOVMAX 8 /* Maximum number of covariates */    multinomial logistic model, is clear when the delay between waves is not
 #define MAXN 20000    identical for each individual. Also, if a individual missed an
 #define YEARM 12. /* Number of months per year */    intermediate interview, the information is lost, but taken into
 #define AGESUP 130    account using an interpolation or extrapolation.  
 #define AGEBASE 40  
     hPijx is the probability to be observed in state i at age x+h
     conditional to the observed state i at age x. The delay 'h' can be
 int nvar;    split into an exact number (nh*stepm) of unobserved intermediate
 static int cptcov;    states. This elementary transition (by month, quarter,
 int cptcovn;    semester or year) is modelled as a multinomial logistic.  The hPx
 int npar=NPARMAX;    matrix is simply the matrix product of nh*stepm elementary matrices
 int nlstate=2; /* Number of live states */    and the contribution of each individual to the likelihood is simply
 int ndeath=1; /* Number of dead states */    hPijx.
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
     Also this programme outputs the covariance matrix of the parameters but also
 int *wav; /* Number of waves for this individuual 0 is possible */    of the life expectancies. It also computes the stable prevalence. 
 int maxwav; /* Maxim number of waves */    
 int mle, weightopt;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */             Institut national d'études démographiques, Paris.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    This software have been partly granted by Euro-REVES, a concerted action
 double **oldm, **newm, **savm; /* Working pointers to matrices */    from the European Union.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    It is copyrighted identically to a GNU software product, ie programme and
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    software can be distributed freely for non commercial use. Latest version
 FILE *ficgp, *fichtm;    can be accessed at http://euroreves.ined.fr/imach .
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
  FILE  *ficresvij;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   char fileresv[FILENAMELENGTH];    
  FILE  *ficresvpl;    **********************************************************************/
   char fileresvpl[FILENAMELENGTH];  /*
     main
     read parameterfile
     read datafile
     concatwav
 #define NR_END 1    freqsummary
 #define FREE_ARG char*    if (mle >= 1)
 #define FTOL 1.0e-10      mlikeli
     print results files
 #define NRANSI    if mle==1 
 #define ITMAX 200       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 #define TOL 2.0e-4        begin-prev-date,...
     open gnuplot file
 #define CGOLD 0.3819660    open html file
 #define ZEPS 1.0e-10    stable prevalence
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);     for age prevalim()
     h Pij x
 #define GOLD 1.618034    variance of p varprob
 #define GLIMIT 100.0    forecasting if prevfcast==1 prevforecast call prevalence()
 #define TINY 1.0e-20    health expectancies
     Variance-covariance of DFLE
 static double maxarg1,maxarg2;    prevalence()
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))     movingaverage()
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    varevsij() 
      if popbased==1 varevsij(,popbased)
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    total life expectancies
 #define rint(a) floor(a+0.5)    Variance of stable prevalence
    end
 static double sqrarg;  */
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
   
 int imx;   
 int stepm;  #include <math.h>
 /* Stepm, step in month: minimum step interpolation*/  #include <stdio.h>
   #include <stdlib.h>
 int m,nb;  #include <unistd.h>
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  #include <sys/time.h>
 double **pmmij;  #include <time.h>
   #include "timeval.h"
 double *weight;  
 int **s; /* Status */  #define MAXLINE 256
 double *agedc, **covar, idx;  #define GNUPLOTPROGRAM "gnuplot"
 int **nbcode, *Tcode, *Tvar, **codtab;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  /*#define DEBUG*/
 double ftolhess; /* Tolerance for computing hessian */  /*#define windows*/
   #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 /******************************************/  
   #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 void replace(char *s, char*t)  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 {  
   int i;  #define NINTERVMAX 8
   int lg=20;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   i=0;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   lg=strlen(t);  #define NCOVMAX 8 /* Maximum number of covariates */
   for(i=0; i<= lg; i++) {  #define MAXN 20000
     (s[i] = t[i]);  #define YEARM 12. /* Number of months per year */
     if (t[i]== '\\') s[i]='/';  #define AGESUP 130
   }  #define AGEBASE 40
 }  #ifdef unix
   #define DIRSEPARATOR '/'
 int nbocc(char *s, char occ)  #define ODIRSEPARATOR '\\'
 {  #else
   int i,j=0;  #define DIRSEPARATOR '\\'
   int lg=20;  #define ODIRSEPARATOR '/'
   i=0;  #endif
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {  /* $Id$ */
   if  (s[i] == occ ) j++;  /* $State$ */
   }  
   return j;  char version[]="Imach version 0.95a2, June 2003, INED-EUROREVES ";
 }  char fullversion[]="$Revision$ $Date$"; 
   int erreur; /* Error number */
 void cutv(char *u,char *v, char*t, char occ)  int nvar;
 {  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int i,lg,j,p;  int npar=NPARMAX;
   i=0;  int nlstate=2; /* Number of live states */
   for(j=0; j<=strlen(t)-1; j++) {  int ndeath=1; /* Number of dead states */
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   }  int popbased=0;
   
   lg=strlen(t);  int *wav; /* Number of waves for this individuual 0 is possible */
   for(j=0; j<p; j++) {  int maxwav; /* Maxim number of waves */
     (u[j] = t[j]);  int jmin, jmax; /* min, max spacing between 2 waves */
     u[p]='\0';  int mle, weightopt;
   }  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 */
    for(j=0; j<= lg; j++) {  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
     if (j>=(p+1))(v[j-p-1] = t[j]);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   }  double jmean; /* Mean space between 2 waves */
 }  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 /********************** nrerror ********************/  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   FILE *ficlog, *ficrespow;
 void nrerror(char error_text[])  int globpr; /* Global variable for printing or not */
 {  double fretone; /* Only one call to likelihood */
   fprintf(stderr,"ERREUR ...\n");  long ipmx; /* Number of contributions */
   fprintf(stderr,"%s\n",error_text);  double sw; /* Sum of weights */
   exit(1);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
 }  FILE *ficresilk;
 /*********************** vector *******************/  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 double *vector(int nl, int nh)  FILE *ficresprobmorprev;
 {  FILE *fichtm; /* Html File */
   double *v;  FILE *ficreseij;
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  char filerese[FILENAMELENGTH];
   if (!v) nrerror("allocation failure in vector");  FILE  *ficresvij;
   return v-nl+NR_END;  char fileresv[FILENAMELENGTH];
 }  FILE  *ficresvpl;
   char fileresvpl[FILENAMELENGTH];
 /************************ free vector ******************/  char title[MAXLINE];
 void free_vector(double*v, int nl, int nh)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 {  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   free((FREE_ARG)(v+nl-NR_END));  
 }  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   char filelog[FILENAMELENGTH]; /* Log file */
 /************************ivector *******************************/  char filerest[FILENAMELENGTH];
 int *ivector(long nl,long nh)  char fileregp[FILENAMELENGTH];
 {  char popfile[FILENAMELENGTH];
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
   if (!v) nrerror("allocation failure in ivector");  
   return v-nl+NR_END;  #define NR_END 1
 }  #define FREE_ARG char*
   #define FTOL 1.0e-10
 /******************free ivector **************************/  
 void free_ivector(int *v, long nl, long nh)  #define NRANSI 
 {  #define ITMAX 200 
   free((FREE_ARG)(v+nl-NR_END));  
 }  #define TOL 2.0e-4 
   
 /******************* imatrix *******************************/  #define CGOLD 0.3819660 
 int **imatrix(long nrl, long nrh, long ncl, long nch)  #define ZEPS 1.0e-10 
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  #define GOLD 1.618034 
   int **m;  #define GLIMIT 100.0 
    #define TINY 1.0e-20 
   /* allocate pointers to rows */  
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  static double maxarg1,maxarg2;
   if (!m) nrerror("allocation failure 1 in matrix()");  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   m += NR_END;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   m -= nrl;    
    #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
    #define rint(a) floor(a+0.5)
   /* allocate rows and set pointers to them */  
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  static double sqrarg;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   m[nrl] += NR_END;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   m[nrl] -= ncl;  
    int imx; 
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  int stepm;
    /* Stepm, step in month: minimum step interpolation*/
   /* return pointer to array of pointers to rows */  
   return m;  int estepm;
 }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
 /****************** free_imatrix *************************/  int m,nb;
 void free_imatrix(m,nrl,nrh,ncl,nch)  long *num;
       int **m;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
       long nch,ncl,nrh,nrl;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
      /* free an int matrix allocated by imatrix() */  double **pmmij, ***probs;
 {  double dateintmean=0;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));  double *weight;
 }  int **s; /* Status */
   double *agedc, **covar, idx;
 /******************* matrix *******************************/  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  double ftolhess; /* Tolerance for computing hessian */
   double **m;  
   /**************** split *************************/
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   if (!m) nrerror("allocation failure 1 in matrix()");  {
   m += NR_END;    char  *ss;                            /* pointer */
   m -= nrl;    int   l1, l2;                         /* length counters */
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    l1 = strlen(path );                   /* length of path */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   m[nrl] += NR_END;    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   m[nrl] -= ncl;    if ( ss == NULL ) {                   /* no directory, so use current */
       /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   return m;      /* get current working directory */
 }      /*    extern  char* getcwd ( char *buf , int len);*/
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 /*************************free matrix ************************/        return( GLOCK_ERROR_GETCWD );
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)      }
 {      strcpy( name, path );               /* we've got it */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    } else {                              /* strip direcotry from path */
   free((FREE_ARG)(m+nrl-NR_END));      ss++;                               /* after this, the filename */
 }      l2 = strlen( ss );                  /* length of filename */
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 /******************* ma3x *******************************/      strcpy( name, ss );         /* save file name */
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 {      dirc[l1-l2] = 0;                    /* add zero */
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    }
   double ***m;    l1 = strlen( dirc );                  /* length of directory */
     /*#ifdef windows
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   if (!m) nrerror("allocation failure 1 in matrix()");  #else
   m += NR_END;    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   m -= nrl;  #endif
     */
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    ss = strrchr( name, '.' );            /* find last / */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    ss++;
   m[nrl] += NR_END;    strcpy(ext,ss);                       /* save extension */
   m[nrl] -= ncl;    l1= strlen( name);
     l2= strlen(ss)+1;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    strncpy( finame, name, l1-l2);
     finame[l1-l2]= 0;
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    return( 0 );                          /* we're done */
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  }
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  
   for (j=ncl+1; j<=nch; j++)  /******************************************/
     m[nrl][j]=m[nrl][j-1]+nlay;  
    void replace(char *s, char*t)
   for (i=nrl+1; i<=nrh; i++) {  {
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    int i;
     for (j=ncl+1; j<=nch; j++)    int lg=20;
       m[i][j]=m[i][j-1]+nlay;    i=0;
   }    lg=strlen(t);
   return m;    for(i=0; i<= lg; i++) {
 }      (s[i] = t[i]);
       if (t[i]== '\\') s[i]='/';
 /*************************free ma3x ************************/    }
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  }
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  int nbocc(char *s, char occ)
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  {
   free((FREE_ARG)(m+nrl-NR_END));    int i,j=0;
 }    int lg=20;
     i=0;
 /***************** f1dim *************************/    lg=strlen(s);
 extern int ncom;    for(i=0; i<= lg; i++) {
 extern double *pcom,*xicom;    if  (s[i] == occ ) j++;
 extern double (*nrfunc)(double []);    }
      return j;
 double f1dim(double x)  }
 {  
   int j;  void cutv(char *u,char *v, char*t, char occ)
   double f;  {
   double *xt;    /* cuts string t into u and v where u is ended by char occ excluding it
         and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
   xt=vector(1,ncom);       gives u="abcedf" and v="ghi2j" */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    int i,lg,j,p=0;
   f=(*nrfunc)(xt);    i=0;
   free_vector(xt,1,ncom);    for(j=0; j<=strlen(t)-1; j++) {
   return f;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
 }    }
   
 /*****************brent *************************/    lg=strlen(t);
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    for(j=0; j<p; j++) {
 {      (u[j] = t[j]);
   int iter;    }
   double a,b,d,etemp;       u[p]='\0';
   double fu,fv,fw,fx;  
   double ftemp;     for(j=0; j<= lg; j++) {
   double p,q,r,tol1,tol2,u,v,w,x,xm;      if (j>=(p+1))(v[j-p-1] = t[j]);
   double e=0.0;    }
    }
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  /********************** nrerror ********************/
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);  void nrerror(char error_text[])
   for (iter=1;iter<=ITMAX;iter++) {  {
     xm=0.5*(a+b);    fprintf(stderr,"ERREUR ...\n");
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    fprintf(stderr,"%s\n",error_text);
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    exit(EXIT_FAILURE);
     printf(".");fflush(stdout);  }
 #ifdef DEBUG  /*********************** vector *******************/
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  double *vector(int nl, int nh)
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  {
 #endif    double *v;
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       *xmin=x;    if (!v) nrerror("allocation failure in vector");
       return fx;    return v-nl+NR_END;
     }  }
     ftemp=fu;  
     if (fabs(e) > tol1) {  /************************ free vector ******************/
       r=(x-w)*(fx-fv);  void free_vector(double*v, int nl, int nh)
       q=(x-v)*(fx-fw);  {
       p=(x-v)*q-(x-w)*r;    free((FREE_ARG)(v+nl-NR_END));
       q=2.0*(q-r);  }
       if (q > 0.0) p = -p;  
       q=fabs(q);  /************************ivector *******************************/
       etemp=e;  int *ivector(long nl,long nh)
       e=d;  {
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    int *v;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       else {    if (!v) nrerror("allocation failure in ivector");
         d=p/q;    return v-nl+NR_END;
         u=x+d;  }
         if (u-a < tol2 || b-u < tol2)  
           d=SIGN(tol1,xm-x);  /******************free ivector **************************/
       }  void free_ivector(int *v, long nl, long nh)
     } else {  {
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    free((FREE_ARG)(v+nl-NR_END));
     }  }
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  
     fu=(*f)(u);  /************************lvector *******************************/
     if (fu <= fx) {  long *lvector(long nl,long nh)
       if (u >= x) a=x; else b=x;  {
       SHFT(v,w,x,u)    long *v;
         SHFT(fv,fw,fx,fu)    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
         } else {    if (!v) nrerror("allocation failure in ivector");
           if (u < x) a=u; else b=u;    return v-nl+NR_END;
           if (fu <= fw || w == x) {  }
             v=w;  
             w=u;  /******************free lvector **************************/
             fv=fw;  void free_lvector(long *v, long nl, long nh)
             fw=fu;  {
           } else if (fu <= fv || v == x || v == w) {    free((FREE_ARG)(v+nl-NR_END));
             v=u;  }
             fv=fu;  
           }  /******************* imatrix *******************************/
         }  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   }       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   nrerror("Too many iterations in brent");  { 
   *xmin=x;    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   return fx;    int **m; 
 }    
     /* allocate pointers to rows */ 
 /****************** mnbrak ***********************/    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     if (!m) nrerror("allocation failure 1 in matrix()"); 
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    m += NR_END; 
             double (*func)(double))    m -= nrl; 
 {    
   double ulim,u,r,q, dum;    
   double fu;    /* allocate rows and set pointers to them */ 
      m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   *fa=(*func)(*ax);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   *fb=(*func)(*bx);    m[nrl] += NR_END; 
   if (*fb > *fa) {    m[nrl] -= ncl; 
     SHFT(dum,*ax,*bx,dum)    
       SHFT(dum,*fb,*fa,dum)    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
       }    
   *cx=(*bx)+GOLD*(*bx-*ax);    /* return pointer to array of pointers to rows */ 
   *fc=(*func)(*cx);    return m; 
   while (*fb > *fc) {  } 
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  /****************** free_imatrix *************************/
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  void free_imatrix(m,nrl,nrh,ncl,nch)
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));        int **m;
     ulim=(*bx)+GLIMIT*(*cx-*bx);        long nch,ncl,nrh,nrl; 
     if ((*bx-u)*(u-*cx) > 0.0) {       /* free an int matrix allocated by imatrix() */ 
       fu=(*func)(u);  { 
     } else if ((*cx-u)*(u-ulim) > 0.0) {    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       fu=(*func)(u);    free((FREE_ARG) (m+nrl-NR_END)); 
       if (fu < *fc) {  } 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))  /******************* matrix *******************************/
           }  double **matrix(long nrl, long nrh, long ncl, long nch)
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  {
       u=ulim;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       fu=(*func)(u);    double **m;
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       fu=(*func)(u);    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
     SHFT(*ax,*bx,*cx,u)    m -= nrl;
       SHFT(*fa,*fb,*fc,fu)  
       }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
 /*************** linmin ************************/    m[nrl] -= ncl;
   
 int ncom;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 double *pcom,*xicom;    return m;
 double (*nrfunc)(double []);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  }
 {  
   double brent(double ax, double bx, double cx,  /*************************free matrix ************************/
                double (*f)(double), double tol, double *xmin);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   double f1dim(double x);  {
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    free((FREE_ARG)(m[nrl]+ncl-NR_END));
               double *fc, double (*func)(double));    free((FREE_ARG)(m+nrl-NR_END));
   int j;  }
   double xx,xmin,bx,ax;  
   double fx,fb,fa;  /******************* ma3x *******************************/
    double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   ncom=n;  {
   pcom=vector(1,n);    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   xicom=vector(1,n);    double ***m;
   nrfunc=func;  
   for (j=1;j<=n;j++) {    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     pcom[j]=p[j];    if (!m) nrerror("allocation failure 1 in matrix()");
     xicom[j]=xi[j];    m += NR_END;
   }    m -= nrl;
   ax=0.0;  
   xx=1.0;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    m[nrl] += NR_END;
 #ifdef DEBUG    m[nrl] -= ncl;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
 #endif    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   for (j=1;j<=n;j++) {  
     xi[j] *= xmin;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     p[j] += xi[j];    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   }    m[nrl][ncl] += NR_END;
   free_vector(xicom,1,n);    m[nrl][ncl] -= nll;
   free_vector(pcom,1,n);    for (j=ncl+1; j<=nch; j++) 
 }      m[nrl][j]=m[nrl][j-1]+nlay;
     
 /*************** powell ************************/    for (i=nrl+1; i<=nrh; i++) {
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
             double (*func)(double []))      for (j=ncl+1; j<=nch; j++) 
 {        m[i][j]=m[i][j-1]+nlay;
   void linmin(double p[], double xi[], int n, double *fret,    }
               double (*func)(double []));    return m; 
   int i,ibig,j;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   double del,t,*pt,*ptt,*xit;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   double fp,fptt;    */
   double *xits;  }
   pt=vector(1,n);  
   ptt=vector(1,n);  /*************************free ma3x ************************/
   xit=vector(1,n);  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   xits=vector(1,n);  {
   *fret=(*func)(p);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   for (j=1;j<=n;j++) pt[j]=p[j];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   for (*iter=1;;++(*iter)) {    free((FREE_ARG)(m+nrl-NR_END));
     fp=(*fret);  }
     ibig=0;  
     del=0.0;  /***************** f1dim *************************/
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  extern int ncom; 
     for (i=1;i<=n;i++)  extern double *pcom,*xicom;
       printf(" %d %.12f",i, p[i]);  extern double (*nrfunc)(double []); 
     printf("\n");   
     for (i=1;i<=n;i++) {  double f1dim(double x) 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  { 
       fptt=(*fret);    int j; 
 #ifdef DEBUG    double f;
       printf("fret=%lf \n",*fret);    double *xt; 
 #endif   
       printf("%d",i);fflush(stdout);    xt=vector(1,ncom); 
       linmin(p,xit,n,fret,func);    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       if (fabs(fptt-(*fret)) > del) {    f=(*nrfunc)(xt); 
         del=fabs(fptt-(*fret));    free_vector(xt,1,ncom); 
         ibig=i;    return f; 
       }  } 
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  /*****************brent *************************/
       for (j=1;j<=n;j++) {  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  { 
         printf(" x(%d)=%.12e",j,xit[j]);    int iter; 
       }    double a,b,d,etemp;
       for(j=1;j<=n;j++)    double fu,fv,fw,fx;
         printf(" p=%.12e",p[j]);    double ftemp;
       printf("\n");    double p,q,r,tol1,tol2,u,v,w,x,xm; 
 #endif    double e=0.0; 
     }   
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    a=(ax < cx ? ax : cx); 
 #ifdef DEBUG    b=(ax > cx ? ax : cx); 
       int k[2],l;    x=w=v=bx; 
       k[0]=1;    fw=fv=fx=(*f)(x); 
       k[1]=-1;    for (iter=1;iter<=ITMAX;iter++) { 
       printf("Max: %.12e",(*func)(p));      xm=0.5*(a+b); 
       for (j=1;j<=n;j++)      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
         printf(" %.12e",p[j]);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       printf("\n");      printf(".");fflush(stdout);
       for(l=0;l<=1;l++) {      fprintf(ficlog,".");fflush(ficlog);
         for (j=1;j<=n;j++) {  #ifdef DEBUG
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      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);
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);      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)))) { */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  #endif
       }      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
 #endif        *xmin=x; 
         return fx; 
       } 
       free_vector(xit,1,n);      ftemp=fu;
       free_vector(xits,1,n);      if (fabs(e) > tol1) { 
       free_vector(ptt,1,n);        r=(x-w)*(fx-fv); 
       free_vector(pt,1,n);        q=(x-v)*(fx-fw); 
       return;        p=(x-v)*q-(x-w)*r; 
     }        q=2.0*(q-r); 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");        if (q > 0.0) p = -p; 
     for (j=1;j<=n;j++) {        q=fabs(q); 
       ptt[j]=2.0*p[j]-pt[j];        etemp=e; 
       xit[j]=p[j]-pt[j];        e=d; 
       pt[j]=p[j];        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)); 
     fptt=(*func)(ptt);        else { 
     if (fptt < fp) {          d=p/q; 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);          u=x+d; 
       if (t < 0.0) {          if (u-a < tol2 || b-u < tol2) 
         linmin(p,xit,n,fret,func);            d=SIGN(tol1,xm-x); 
         for (j=1;j<=n;j++) {        } 
           xi[j][ibig]=xi[j][n];      } else { 
           xi[j][n]=xit[j];        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         }      } 
 #ifdef DEBUG      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      fu=(*f)(u); 
         for(j=1;j<=n;j++)      if (fu <= fx) { 
           printf(" %.12e",xit[j]);        if (u >= x) a=x; else b=x; 
         printf("\n");        SHFT(v,w,x,u) 
 #endif          SHFT(fv,fw,fx,fu) 
       }          } else { 
     }            if (u < x) a=u; else b=u; 
   }            if (fu <= fw || w == x) { 
 }              v=w; 
               w=u; 
 /**** Prevalence limit ****************/              fv=fw; 
               fw=fu; 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)            } else if (fu <= fv || v == x || v == w) { 
 {              v=u; 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit              fv=fu; 
      matrix by transitions matrix until convergence is reached */            } 
           } 
   int i, ii,j,k;    } 
   double min, max, maxmin, maxmax,sumnew=0.;    nrerror("Too many iterations in brent"); 
   double **matprod2();    *xmin=x; 
   double **out, cov[NCOVMAX], **pmij();    return fx; 
   double **newm;  } 
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /****************** mnbrak ***********************/
   for (ii=1;ii<=nlstate+ndeath;ii++)  
     for (j=1;j<=nlstate+ndeath;j++){  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);              double (*func)(double)) 
     }  { 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    double ulim,u,r,q, dum;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    double fu; 
     newm=savm;   
     /* Covariates have to be included here again */    *fa=(*func)(*ax); 
     cov[1]=1.;    *fb=(*func)(*bx); 
     cov[2]=agefin;    if (*fb > *fa) { 
     if (cptcovn>0){      SHFT(dum,*ax,*bx,dum) 
       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]]);*/}        SHFT(dum,*fb,*fa,dum) 
     }        } 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    *cx=(*bx)+GOLD*(*bx-*ax); 
     *fc=(*func)(*cx); 
     savm=oldm;    while (*fb > *fc) { 
     oldm=newm;      r=(*bx-*ax)*(*fb-*fc); 
     maxmax=0.;      q=(*bx-*cx)*(*fb-*fa); 
     for(j=1;j<=nlstate;j++){      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       min=1.;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       max=0.;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       for(i=1; i<=nlstate; i++) {      if ((*bx-u)*(u-*cx) > 0.0) { 
         sumnew=0;        fu=(*func)(u); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         prlim[i][j]= newm[i][j]/(1-sumnew);        fu=(*func)(u); 
         max=FMAX(max,prlim[i][j]);        if (fu < *fc) { 
         min=FMIN(min,prlim[i][j]);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       }            SHFT(*fb,*fc,fu,(*func)(u)) 
       maxmin=max-min;            } 
       maxmax=FMAX(maxmax,maxmin);      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     }        u=ulim; 
     if(maxmax < ftolpl){        fu=(*func)(u); 
       return prlim;      } else { 
     }        u=(*cx)+GOLD*(*cx-*bx); 
   }        fu=(*func)(u); 
 }      } 
       SHFT(*ax,*bx,*cx,u) 
 /*************** transition probabilities **********/        SHFT(*fa,*fb,*fc,fu) 
         } 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  } 
 {  
   double s1, s2;  /*************** linmin ************************/
   /*double t34;*/  
   int i,j,j1, nc, ii, jj;  int ncom; 
   double *pcom,*xicom;
     for(i=1; i<= nlstate; i++){  double (*nrfunc)(double []); 
     for(j=1; j<i;j++){   
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
         /*s2 += param[i][j][nc]*cov[nc];*/  { 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    double brent(double ax, double bx, double cx, 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/                 double (*f)(double), double tol, double *xmin); 
       }    double f1dim(double x); 
       ps[i][j]=s2;    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/                double *fc, double (*func)(double)); 
     }    int j; 
     for(j=i+1; j<=nlstate+ndeath;j++){    double xx,xmin,bx,ax; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    double fx,fb,fa;
         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);*/    ncom=n; 
       }    pcom=vector(1,n); 
       ps[i][j]=s2;    xicom=vector(1,n); 
     }    nrfunc=func; 
   }    for (j=1;j<=n;j++) { 
   for(i=1; i<= nlstate; i++){      pcom[j]=p[j]; 
      s1=0;      xicom[j]=xi[j]; 
     for(j=1; j<i; j++)    } 
       s1+=exp(ps[i][j]);    ax=0.0; 
     for(j=i+1; j<=nlstate+ndeath; j++)    xx=1.0; 
       s1+=exp(ps[i][j]);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     ps[i][i]=1./(s1+1.);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     for(j=1; j<i; j++)  #ifdef DEBUG
       ps[i][j]= exp(ps[i][j])*ps[i][i];    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     for(j=i+1; j<=nlstate+ndeath; j++)    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       ps[i][j]= exp(ps[i][j])*ps[i][i];  #endif
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    for (j=1;j<=n;j++) { 
   } /* end i */      xi[j] *= xmin; 
       p[j] += xi[j]; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    } 
     for(jj=1; jj<= nlstate+ndeath; jj++){    free_vector(xicom,1,n); 
       ps[ii][jj]=0;    free_vector(pcom,1,n); 
       ps[ii][ii]=1;  } 
     }  
   }  /*************** powell ************************/
   void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){              double (*func)(double [])) 
     for(jj=1; jj<= nlstate+ndeath; jj++){  { 
      printf("%lf ",ps[ii][jj]);    void linmin(double p[], double xi[], int n, double *fret, 
    }                double (*func)(double [])); 
     printf("\n ");    int i,ibig,j; 
     }    double del,t,*pt,*ptt,*xit;
     printf("\n ");printf("%lf ",cov[2]);*/    double fp,fptt;
 /*    double *xits;
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    pt=vector(1,n); 
   goto end;*/    ptt=vector(1,n); 
     return ps;    xit=vector(1,n); 
 }    xits=vector(1,n); 
     *fret=(*func)(p); 
 /**************** Product of 2 matrices ******************/    for (j=1;j<=n;j++) pt[j]=p[j]; 
     for (*iter=1;;++(*iter)) { 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      fp=(*fret); 
 {      ibig=0; 
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times      del=0.0; 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
   /* in, b, out are matrice of pointers which should have been initialized      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
      before: only the contents of out is modified. The function returns      fprintf(ficrespow,"%d %.12f",*iter,*fret);
      a pointer to pointers identical to out */      for (i=1;i<=n;i++) {
   long i, j, k;        printf(" %d %.12f",i, p[i]);
   for(i=nrl; i<= nrh; i++)        fprintf(ficlog," %d %.12lf",i, p[i]);
     for(k=ncolol; k<=ncoloh; k++)        fprintf(ficrespow," %.12lf", p[i]);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)      }
         out[i][k] +=in[i][j]*b[j][k];      printf("\n");
       fprintf(ficlog,"\n");
   return out;      fprintf(ficrespow,"\n");
 }      for (i=1;i<=n;i++) { 
         for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         fptt=(*fret); 
 /************* Higher Matrix Product ***************/  #ifdef DEBUG
         printf("fret=%lf \n",*fret);
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )        fprintf(ficlog,"fret=%lf \n",*fret);
 {  #endif
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        printf("%d",i);fflush(stdout);
      duration (i.e. until        fprintf(ficlog,"%d",i);fflush(ficlog);
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.        linmin(p,xit,n,fret,func); 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        if (fabs(fptt-(*fret)) > del) { 
      (typically every 2 years instead of every month which is too big).          del=fabs(fptt-(*fret)); 
      Model is determined by parameters x and covariates have to be          ibig=i; 
      included manually here.        } 
   #ifdef DEBUG
      */        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
   int i, j, d, h, k;        for (j=1;j<=n;j++) {
   double **out, cov[NCOVMAX];          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   double **newm;          printf(" x(%d)=%.12e",j,xit[j]);
           fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   /* Hstepm could be zero and should return the unit matrix */        }
   for (i=1;i<=nlstate+ndeath;i++)        for(j=1;j<=n;j++) {
     for (j=1;j<=nlstate+ndeath;j++){          printf(" p=%.12e",p[j]);
       oldm[i][j]=(i==j ? 1.0 : 0.0);          fprintf(ficlog," p=%.12e",p[j]);
       po[i][j][0]=(i==j ? 1.0 : 0.0);        }
     }        printf("\n");
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        fprintf(ficlog,"\n");
   for(h=1; h <=nhstepm; h++){  #endif
     for(d=1; d <=hstepm; d++){      } 
       newm=savm;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       /* Covariates have to be included here again */  #ifdef DEBUG
       cov[1]=1.;        int k[2],l;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        k[0]=1;
       if (cptcovn>0){        k[1]=-1;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];        printf("Max: %.12e",(*func)(p));
     }        fprintf(ficlog,"Max: %.12e",(*func)(p));
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/        for (j=1;j<=n;j++) {
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/          printf(" %.12e",p[j]);
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,          fprintf(ficlog," %.12e",p[j]);
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        }
       savm=oldm;        printf("\n");
       oldm=newm;        fprintf(ficlog,"\n");
     }        for(l=0;l<=1;l++) {
     for(i=1; i<=nlstate+ndeath; i++)          for (j=1;j<=n;j++) {
       for(j=1;j<=nlstate+ndeath;j++) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
         po[i][j][h]=newm[i][j];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
          */          }
       }          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   } /* end h */          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   return po;        }
 }  #endif
   
   
 /*************** log-likelihood *************/        free_vector(xit,1,n); 
 double func( double *x)        free_vector(xits,1,n); 
 {        free_vector(ptt,1,n); 
   int i, ii, j, k, mi, d;        free_vector(pt,1,n); 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];        return; 
   double **out;      } 
   double sw; /* Sum of weights */      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   double lli; /* Individual log likelihood */      for (j=1;j<=n;j++) { 
   long ipmx;        ptt[j]=2.0*p[j]-pt[j]; 
   /*extern weight */        xit[j]=p[j]-pt[j]; 
   /* We are differentiating ll according to initial status */        pt[j]=p[j]; 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      } 
   /*for(i=1;i<imx;i++)      fptt=(*func)(ptt); 
 printf(" %d\n",s[4][i]);      if (fptt < fp) { 
   */        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         if (t < 0.0) { 
   for(k=1; k<=nlstate; k++) ll[k]=0.;          linmin(p,xit,n,fret,func); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){          for (j=1;j<=n;j++) { 
        for(mi=1; mi<= wav[i]-1; mi++){            xi[j][ibig]=xi[j][n]; 
       for (ii=1;ii<=nlstate+ndeath;ii++)            xi[j][n]=xit[j]; 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);          }
             for(d=0; d<dh[mi][i]; d++){  #ifdef DEBUG
         newm=savm;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           cov[1]=1.;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;          for(j=1;j<=n;j++){
           if (cptcovn>0){            printf(" %.12e",xit[j]);
             for (k=1; k<=cptcovn;k++) cov[2+k]=covar[1+k-1][i];            fprintf(ficlog," %.12e",xit[j]);
             }          }
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,          printf("\n");
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));          fprintf(ficlog,"\n");
           savm=oldm;  #endif
           oldm=newm;        }
       } 
     } 
       } /* end mult */  } 
      
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  /**** Prevalence limit (stable prevalence)  ****************/
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  
       ipmx +=1;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       sw += weight[i];  {
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     } /* end of wave */       matrix by transitions matrix until convergence is reached */
   } /* end of individual */  
     int i, ii,j,k;
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    double min, max, maxmin, maxmax,sumnew=0.;
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    double **matprod2();
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    double **out, cov[NCOVMAX], **pmij();
   return -l;    double **newm;
 }    double agefin, delaymax=50 ; /* Max number of years to converge */
   
     for (ii=1;ii<=nlstate+ndeath;ii++)
 /*********** Maximum Likelihood Estimation ***************/      for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      }
 {  
   int i,j, iter;     cov[1]=1.;
   double **xi,*delti;   
   double fret;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   xi=matrix(1,npar,1,npar);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   for (i=1;i<=npar;i++)      newm=savm;
     for (j=1;j<=npar;j++)      /* Covariates have to be included here again */
       xi[i][j]=(i==j ? 1.0 : 0.0);       cov[2]=agefin;
   printf("Powell\n");    
   powell(p,xi,npar,ftol,&iter,&fret,func);        for (k=1; k<=cptcovn;k++) {
           cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          /*      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]]);*/
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));        }
         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]]];
 /**** Computes Hessian and covariance matrix ***/  
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
 {        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   double  **a,**y,*x,pd;        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   double **hess;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   int i, j,jk;  
   int *indx;      savm=oldm;
       oldm=newm;
   double hessii(double p[], double delta, int theta, double delti[]);      maxmax=0.;
   double hessij(double p[], double delti[], int i, int j);      for(j=1;j<=nlstate;j++){
   void lubksb(double **a, int npar, int *indx, double b[]) ;        min=1.;
   void ludcmp(double **a, int npar, int *indx, double *d) ;        max=0.;
         for(i=1; i<=nlstate; i++) {
           sumnew=0;
   hess=matrix(1,npar,1,npar);          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
           prlim[i][j]= newm[i][j]/(1-sumnew);
   printf("\nCalculation of the hessian matrix. Wait...\n");          max=FMAX(max,prlim[i][j]);
   for (i=1;i<=npar;i++){          min=FMIN(min,prlim[i][j]);
     printf("%d",i);fflush(stdout);        }
     hess[i][i]=hessii(p,ftolhess,i,delti);        maxmin=max-min;
     /*printf(" %f ",p[i]);*/        maxmax=FMAX(maxmax,maxmin);
   }      }
       if(maxmax < ftolpl){
   for (i=1;i<=npar;i++) {        return prlim;
     for (j=1;j<=npar;j++)  {      }
       if (j>i) {    }
         printf(".%d%d",i,j);fflush(stdout);  }
         hess[i][j]=hessij(p,delti,i,j);  
         hess[j][i]=hess[i][j];  /*************** transition probabilities ***************/ 
       }  
     }  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   }  {
   printf("\n");    double s1, s2;
     /*double t34;*/
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    int i,j,j1, nc, ii, jj;
    
   a=matrix(1,npar,1,npar);      for(i=1; i<= nlstate; i++){
   y=matrix(1,npar,1,npar);      for(j=1; j<i;j++){
   x=vector(1,npar);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   indx=ivector(1,npar);          /*s2 += param[i][j][nc]*cov[nc];*/
   for (i=1;i<=npar;i++)          s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
   ludcmp(a,npar,indx,&pd);        }
         ps[i][j]=s2;
   for (j=1;j<=npar;j++) {        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
     for (i=1;i<=npar;i++) x[i]=0;      }
     x[j]=1;      for(j=i+1; j<=nlstate+ndeath;j++){
     lubksb(a,npar,indx,x);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     for (i=1;i<=npar;i++){          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
       matcov[i][j]=x[i];          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
     }        }
   }        ps[i][j]=s2;
       }
   printf("\n#Hessian matrix#\n");    }
   for (i=1;i<=npar;i++) {      /*ps[3][2]=1;*/
     for (j=1;j<=npar;j++) {  
       printf("%.3e ",hess[i][j]);    for(i=1; i<= nlstate; i++){
     }       s1=0;
     printf("\n");      for(j=1; j<i; j++)
   }        s1+=exp(ps[i][j]);
       for(j=i+1; j<=nlstate+ndeath; j++)
   /* Recompute Inverse */        s1+=exp(ps[i][j]);
   for (i=1;i<=npar;i++)      ps[i][i]=1./(s1+1.);
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      for(j=1; j<i; j++)
   ludcmp(a,npar,indx,&pd);        ps[i][j]= exp(ps[i][j])*ps[i][i];
       for(j=i+1; j<=nlstate+ndeath; j++)
   /*  printf("\n#Hessian matrix recomputed#\n");        ps[i][j]= exp(ps[i][j])*ps[i][i];
       /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   for (j=1;j<=npar;j++) {    } /* end i */
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     lubksb(a,npar,indx,x);      for(jj=1; jj<= nlstate+ndeath; jj++){
     for (i=1;i<=npar;i++){        ps[ii][jj]=0;
       y[i][j]=x[i];        ps[ii][ii]=1;
       printf("%.3e ",y[i][j]);      }
     }    }
     printf("\n");  
   }  
   */    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
       for(jj=1; jj<= nlstate+ndeath; jj++){
   free_matrix(a,1,npar,1,npar);       printf("%lf ",ps[ii][jj]);
   free_matrix(y,1,npar,1,npar);     }
   free_vector(x,1,npar);      printf("\n ");
   free_ivector(indx,1,npar);      }
   free_matrix(hess,1,npar,1,npar);      printf("\n ");printf("%lf ",cov[2]);*/
   /*
     for(i=1; i<= npar; i++) printf("%f ",x[i]);
 }    goto end;*/
       return ps;
 /*************** hessian matrix ****************/  }
 double hessii( double x[], double delta, int theta, double delti[])  
 {  /**************** Product of 2 matrices ******************/
   int i;  
   int l=1, lmax=20;  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   double k1,k2;  {
   double p2[NPARMAX+1];    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   double res;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    /* in, b, out are matrice of pointers which should have been initialized 
   double fx;       before: only the contents of out is modified. The function returns
   int k=0,kmax=10;       a pointer to pointers identical to out */
   double l1;    long i, j, k;
     for(i=nrl; i<= nrh; i++)
   fx=func(x);      for(k=ncolol; k<=ncoloh; k++)
   for (i=1;i<=npar;i++) p2[i]=x[i];        for(j=ncl,out[i][k]=0.; j<=nch; j++)
   for(l=0 ; l <=lmax; l++){          out[i][k] +=in[i][j]*b[j][k];
     l1=pow(10,l);  
     delts=delt;    return out;
     for(k=1 ; k <kmax; k=k+1){  }
       delt = delta*(l1*k);  
       p2[theta]=x[theta] +delt;  
       k1=func(p2)-fx;  /************* Higher Matrix Product ***************/
       p2[theta]=x[theta]-delt;  
       k2=func(p2)-fx;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
       /*res= (k1-2.0*fx+k2)/delt/delt; */  {
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    /* Computes the transition matrix starting at age 'age' over 
             'nhstepm*hstepm*stepm' months (i.e. until
 #ifdef DEBUG       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
       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);       nhstepm*hstepm matrices. 
 #endif       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */       (typically every 2 years instead of every month which is too big 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){       for the memory).
         k=kmax;       Model is determined by parameters x and covariates have to be 
       }       included manually here. 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  
         k=kmax; l=lmax*10.;       */
       }  
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    int i, j, d, h, k;
         delts=delt;    double **out, cov[NCOVMAX];
       }    double **newm;
     }  
   }    /* Hstepm could be zero and should return the unit matrix */
   delti[theta]=delts;    for (i=1;i<=nlstate+ndeath;i++)
   return res;      for (j=1;j<=nlstate+ndeath;j++){
          oldm[i][j]=(i==j ? 1.0 : 0.0);
 }        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }
 double hessij( double x[], double delti[], int thetai,int thetaj)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
 {    for(h=1; h <=nhstepm; h++){
   int i;      for(d=1; d <=hstepm; d++){
   int l=1, l1, lmax=20;        newm=savm;
   double k1,k2,k3,k4,res,fx;        /* Covariates have to be included here again */
   double p2[NPARMAX+1];        cov[1]=1.;
   int k;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   fx=func(x);        for (k=1; k<=cptcovage;k++)
   for (k=1; k<=2; k++) {          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     for (i=1;i<=npar;i++) p2[i]=x[i];        for (k=1; k<=cptcovprod;k++)
     p2[thetai]=x[thetai]+delti[thetai]/k;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k1=func(p2)-fx;  
          /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
     p2[thetai]=x[thetai]+delti[thetai]/k;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     k2=func(p2)-fx;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
          savm=oldm;
     p2[thetai]=x[thetai]-delti[thetai]/k;        oldm=newm;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      }
     k3=func(p2)-fx;      for(i=1; i<=nlstate+ndeath; i++)
          for(j=1;j<=nlstate+ndeath;j++) {
     p2[thetai]=x[thetai]-delti[thetai]/k;          po[i][j][h]=newm[i][j];
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
     k4=func(p2)-fx;           */
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        }
 #ifdef DEBUG    } /* end h */
     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);    return po;
 #endif  }
   }  
   return res;  
 }  /*************** log-likelihood *************/
   double func( double *x)
 /************** Inverse of matrix **************/  {
 void ludcmp(double **a, int n, int *indx, double *d)    int i, ii, j, k, mi, d, kk;
 {    double l, ll[NLSTATEMAX], cov[NCOVMAX];
   int i,imax,j,k;    double **out;
   double big,dum,sum,temp;    double sw; /* Sum of weights */
   double *vv;    double lli; /* Individual log likelihood */
      int s1, s2;
   vv=vector(1,n);    double bbh, survp;
   *d=1.0;    long ipmx;
   for (i=1;i<=n;i++) {    /*extern weight */
     big=0.0;    /* We are differentiating ll according to initial status */
     for (j=1;j<=n;j++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       if ((temp=fabs(a[i][j])) > big) big=temp;    /*for(i=1;i<imx;i++) 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");      printf(" %d\n",s[4][i]);
     vv[i]=1.0/big;    */
   }    cov[1]=1.;
   for (j=1;j<=n;j++) {  
     for (i=1;i<j;i++) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
       sum=a[i][j];  
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    if(mle==1){
       a[i][j]=sum;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     big=0.0;        for(mi=1; mi<= wav[i]-1; mi++){
     for (i=j;i<=n;i++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
       sum=a[i][j];            for (j=1;j<=nlstate+ndeath;j++){
       for (k=1;k<j;k++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         sum -= a[i][k]*a[k][j];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       a[i][j]=sum;            }
       if ( (dum=vv[i]*fabs(sum)) >= big) {          for(d=0; d<dh[mi][i]; d++){
         big=dum;            newm=savm;
         imax=i;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
     }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     if (j != imax) {            }
       for (k=1;k<=n;k++) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         dum=a[imax][k];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         a[imax][k]=a[j][k];            savm=oldm;
         a[j][k]=dum;            oldm=newm;
       }          } /* end mult */
       *d = -(*d);        
       vv[imax]=vv[j];          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     }          /* But now since version 0.9 we anticipate for bias and large stepm.
     indx[j]=imax;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     if (a[j][j] == 0.0) a[j][j]=TINY;           * (in months) between two waves is not a multiple of stepm, we rounded to 
     if (j != n) {           * the nearest (and in case of equal distance, to the lowest) interval but now
       dum=1.0/(a[j][j]);           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       for (i=j+1;i<=n;i++) a[i][j] *= dum;           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
     }           * probability in order to take into account the bias as a fraction of the way
   }           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
   free_vector(vv,1,n);  /* Doesn't work */           * -stepm/2 to stepm/2 .
 ;           * For stepm=1 the results are the same as for previous versions of Imach.
 }           * For stepm > 1 the results are less biased than in previous versions. 
            */
 void lubksb(double **a, int n, int *indx, double b[])          s1=s[mw[mi][i]][i];
 {          s2=s[mw[mi+1][i]][i];
   int i,ii=0,ip,j;          bbh=(double)bh[mi][i]/(double)stepm; 
   double sum;          /* bias is positive if real duration
             * is higher than the multiple of stepm and negative otherwise.
   for (i=1;i<=n;i++) {           */
     ip=indx[i];          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     sum=b[ip];          if( s2 > nlstate){ 
     b[ip]=b[i];            /* i.e. if s2 is a death state and if the date of death is known then the contribution
     if (ii)               to the likelihood is the probability to die between last step unit time and current 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];               step unit time, which is also the differences between probability to die before dh 
     else if (sum) ii=i;               and probability to die before dh-stepm . 
     b[i]=sum;               In version up to 0.92 likelihood was computed
   }          as if date of death was unknown. Death was treated as any other
   for (i=n;i>=1;i--) {          health state: the date of the interview describes the actual state
     sum=b[i];          and not the date of a change in health state. The former idea was
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          to consider that at each interview the state was recorded
     b[i]=sum/a[i][i];          (healthy, disable or death) and IMaCh was corrected; but when we
   }          introduced the exact date of death then we should have modified
 }          the contribution of an exact death to the likelihood. This new
           contribution is smaller and very dependent of the step unit
 /************ Frequencies ********************/          stepm. It is no more the probability to die between last interview
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)          and month of death but the probability to survive from last
 {  /* Some frequencies */          interview up to one month before death multiplied by the
            probability to die within a month. Thanks to Chris
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          Jackson for correcting this bug.  Former versions increased
   double ***freq; /* Frequencies */          mortality artificially. The bad side is that we add another loop
   double *pp;          which slows down the processing. The difference can be up to 10%
   double pos;          lower mortality.
   FILE *ficresp;            */
   char fileresp[FILENAMELENGTH];            lli=log(out[s1][s2] - savm[s1][s2]);
           }else{
   pp=vector(1,nlstate);            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
             /*  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 */
   strcpy(fileresp,"p");          } 
   strcat(fileresp,fileres);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   if((ficresp=fopen(fileresp,"w"))==NULL) {          /*if(lli ==000.0)*/
     printf("Problem with prevalence resultfile: %s\n", fileresp);          /*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); */
     exit(0);          ipmx +=1;
   }          sw += weight[i];
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   j1=0;        } /* end of wave */
       } /* end of individual */
   j=cptcovn;    }  else if(mle==2){
   if (cptcovn<1) {j=1;ncodemax[1]=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(k1=1; k1<=j;k1++){        for(mi=1; mi<= wav[i]-1; mi++){
    for(i1=1; i1<=ncodemax[k1];i1++){          for (ii=1;ii<=nlstate+ndeath;ii++)
        j1++;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for (i=-1; i<=nlstate+ndeath; i++)                savm[ii][j]=(ii==j ? 1.0 : 0.0);
          for (jk=-1; jk<=nlstate+ndeath; jk++)              }
            for(m=agemin; m <= agemax+3; m++)          for(d=0; d<=dh[mi][i]; d++){
              freq[i][jk][m]=0;            newm=savm;
                    cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
        for (i=1; i<=imx; i++) {            for (kk=1; kk<=cptcovage;kk++) {
          bool=1;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
          if  (cptcovn>0) {            }
            for (z1=1; z1<=cptcovn; z1++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
          }            savm=oldm;
           if (bool==1) {            oldm=newm;
            for(m=firstpass; m<=lastpass-1; m++){          } /* end mult */
              if(agev[m][i]==0) agev[m][i]=agemax+1;        
              if(agev[m][i]==1) agev[m][i]=agemax+2;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          /* But now since version 0.9 we anticipate for bias and large stepm.
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];           * 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 
          }           * the nearest (and in case of equal distance, to the lowest) interval but now
        }           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         if  (cptcovn>0) {           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
          fprintf(ficresp, "\n#Variable");           * probability in order to take into account the bias as a fraction of the way
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
        }           * -stepm/2 to stepm/2 .
        fprintf(ficresp, "\n#");           * For stepm=1 the results are the same as for previous versions of Imach.
        for(i=1; i<=nlstate;i++)           * For stepm > 1 the results are less biased than in previous versions. 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);           */
        fprintf(ficresp, "\n");          s1=s[mw[mi][i]][i];
                  s2=s[mw[mi+1][i]][i];
   for(i=(int)agemin; i <= (int)agemax+3; i++){          bbh=(double)bh[mi][i]/(double)stepm; 
     if(i==(int)agemax+3)          /* bias is positive if real duration
       printf("Total");           * is higher than the multiple of stepm and negative otherwise.
     else           */
       printf("Age %d", 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 */
     for(jk=1; jk <=nlstate ; jk++){          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          /*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 */
         pp[jk] += freq[jk][m][i];          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     }          /*if(lli ==000.0)*/
     for(jk=1; jk <=nlstate ; jk++){          /*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); */
       for(m=-1, pos=0; m <=0 ; m++)          ipmx +=1;
         pos += freq[jk][m][i];          sw += weight[i];
       if(pp[jk]>=1.e-10)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        } /* end of wave */
       else      } /* end of individual */
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);    }  else if(mle==3){  /* exponential inter-extrapolation */
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(jk=1; jk <=nlstate ; jk++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)        for(mi=1; mi<= wav[i]-1; mi++){
         pp[jk] += freq[jk][m][i];          for (ii=1;ii<=nlstate+ndeath;ii++)
     }            for (j=1;j<=nlstate+ndeath;j++){
     for(jk=1,pos=0; jk <=nlstate ; jk++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       pos += pp[jk];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(jk=1; jk <=nlstate ; jk++){            }
       if(pos>=1.e-5)          for(d=0; d<dh[mi][i]; d++){
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);            newm=savm;
       else            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);            for (kk=1; kk<=cptcovage;kk++) {
       if( i <= (int) agemax){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         if(pos>=1.e-5)            }
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       else                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);            savm=oldm;
       }            oldm=newm;
     }          } /* end mult */
     for(jk=-1; jk <=nlstate+ndeath; jk++)        
       for(m=-1; m <=nlstate+ndeath; m++)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          /* But now since version 0.9 we anticipate for bias and large stepm.
     if(i <= (int) agemax)           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       fprintf(ficresp,"\n");           * (in months) between two waves is not a multiple of stepm, we rounded to 
     printf("\n");           * the nearest (and in case of equal distance, to the lowest) interval but now
     }           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     }           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
  }           * probability in order to take into account the bias as a fraction of the way
             * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
   fclose(ficresp);           * -stepm/2 to stepm/2 .
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);           * For stepm=1 the results are the same as for previous versions of Imach.
   free_vector(pp,1,nlstate);           * For stepm > 1 the results are less biased than in previous versions. 
            */
 }  /* End of Freq */          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
 /************* Waves Concatenation ***************/          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias is positive if real duration
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)           * is higher than the multiple of stepm and negative otherwise.
 {           */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual 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 */
      Death is a valid wave (if date is known).          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 */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          /*if(lli ==000.0)*/
      and mw[mi+1][i]. dh depends on stepm.          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
      */          ipmx +=1;
           sw += weight[i];
   int i, mi, m;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        } /* end of wave */
 float sum=0.;      } /* end of individual */
     }else if (mle==4){  /* ml=4 no inter-extrapolation */
   for(i=1; i<=imx; i++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     mi=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     m=firstpass;        for(mi=1; mi<= wav[i]-1; mi++){
     while(s[m][i] <= nlstate){          for (ii=1;ii<=nlstate+ndeath;ii++)
       if(s[m][i]>=1)            for (j=1;j<=nlstate+ndeath;j++){
         mw[++mi][i]=m;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       if(m >=lastpass)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         break;            }
       else          for(d=0; d<dh[mi][i]; d++){
         m++;            newm=savm;
     }/* end while */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     if (s[m][i] > nlstate){            for (kk=1; kk<=cptcovage;kk++) {
       mi++;     /* Death is another wave */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       /* if(mi==0)  never been interviewed correctly before death */            }
          /* Only death is a correct wave */          
       mw[mi][i]=m;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
     wav[i]=mi;            oldm=newm;
     if(mi==0)          } /* end mult */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        
   }          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   for(i=1; i<=imx; i++){          if( s2 > nlstate){ 
     for(mi=1; mi<wav[i];mi++){            lli=log(out[s1][s2] - savm[s1][s2]);
       if (stepm <=0)          }else{
         dh[mi][i]=1;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       else{          }
         if (s[mw[mi+1][i]][i] > nlstate) {          ipmx +=1;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          sw += weight[i];
           if(j=0) j=1;  /* Survives at least one month after exam */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         else{        } /* end of wave */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));      } /* end of individual */
           k=k+1;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
           if (j >= jmax) jmax=j;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           else if (j <= jmin)jmin=j;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           sum=sum+j;        for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
         jk= j/stepm;            for (j=1;j<=nlstate+ndeath;j++){
         jl= j -jk*stepm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         ju= j -(jk+1)*stepm;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         if(jl <= -ju)            }
           dh[mi][i]=jk;          for(d=0; d<dh[mi][i]; d++){
         else            newm=savm;
           dh[mi][i]=jk+1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         if(dh[mi][i]==0)            for (kk=1; kk<=cptcovage;kk++) {
           dh[mi][i]=1; /* At least one step */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
     }          
   }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 }            savm=oldm;
 /*********** Tricode ****************************/            oldm=newm;
 void tricode(int *Tvar, int **nbcode, int imx)          } /* end mult */
 {        
   int Ndum[80],ij, k, j, i;          s1=s[mw[mi][i]][i];
   int cptcode=0;          s2=s[mw[mi+1][i]][i];
   for (k=0; k<79; k++) Ndum[k]=0;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   for (k=1; k<=7; k++) ncodemax[k]=0;          ipmx +=1;
            sw += weight[i];
   for (j=1; j<=cptcovn; j++) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for (i=1; i<=imx; i++) {          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
       ij=(int)(covar[Tvar[j]][i]);        } /* end of wave */
       Ndum[ij]++;      } /* end of individual */
       if (ij > cptcode) cptcode=ij;    } /* End of if */
     }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     for (i=0; i<=cptcode; i++) {    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       if(Ndum[i]!=0) ncodemax[j]++;    return -l;
     }  }
    
     ij=1;  /*************** log-likelihood *************/
     for (i=1; i<=ncodemax[j]; i++) {  double funcone( double *x)
       for (k=0; k<=79; k++) {  {
         if (Ndum[k] != 0) {    int i, ii, j, k, mi, d, kk;
           nbcode[Tvar[j]][ij]=k;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
           ij++;    double **out;
         }    double lli; /* Individual log likelihood */
         if (ij > ncodemax[j]) break;    int s1, s2;
       }      double bbh, survp;
     }    /*extern weight */
   }      /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   }    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
 /*********** Health Expectancies ****************/    */
     cov[1]=1.;
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)  
 {    for(k=1; k<=nlstate; k++) ll[k]=0.;
   /* Health expectancies */  
   int i, j, nhstepm, hstepm, h;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double age, agelim,hf;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double ***p3mat;      for(mi=1; mi<= wav[i]-1; mi++){
          for (ii=1;ii<=nlstate+ndeath;ii++)
   fprintf(ficreseij,"# Health expectancies\n");          for (j=1;j<=nlstate+ndeath;j++){
   fprintf(ficreseij,"# Age");            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(i=1; i<=nlstate;i++)            savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(j=1; j<=nlstate;j++)          }
       fprintf(ficreseij," %1d-%1d",i,j);        for(d=0; d<dh[mi][i]; d++){
   fprintf(ficreseij,"\n");          newm=savm;
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   hstepm=1*YEARM; /*  Every j years of age (in month) */          for (kk=1; kk<=cptcovage;kk++) {
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }
   agelim=AGESUP;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     /* nhstepm age range expressed in number of stepm */          savm=oldm;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          oldm=newm;
     /* Typically if 20 years = 20*12/6=40 stepm */        } /* end mult */
     if (stepm >= YEARM) hstepm=1;        
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */        s1=s[mw[mi][i]][i];
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        s2=s[mw[mi+1][i]][i];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        bbh=(double)bh[mi][i]/(double)stepm; 
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */        /* bias is positive if real duration
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);           * is higher than the multiple of stepm and negative otherwise.
          */
         if( s2 > nlstate && (mle <5) ){  /* Jackson */
     for(i=1; i<=nlstate;i++)          lli=log(out[s1][s2] - savm[s1][s2]);
       for(j=1; j<=nlstate;j++)        } else if (mle==1){
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           eij[i][j][(int)age] +=p3mat[i][j][h];        } else if(mle==2){
         }          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 */
            } else if(mle==3){  /* exponential inter-extrapolation */
     hf=1;          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
     if (stepm >= YEARM) hf=stepm/YEARM;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
     fprintf(ficreseij,"%.0f",age );          lli=log(out[s1][s2]); /* Original formula */
     for(i=1; i<=nlstate;i++)        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       for(j=1; j<=nlstate;j++){          lli=log(out[s1][s2]); /* Original formula */
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);        } /* End of if */
       }        ipmx +=1;
     fprintf(ficreseij,"\n");        sw += weight[i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   }  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
 }        if(globpr){
           fprintf(ficresilk,"%ld %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
 /************ Variance ******************/   %10.6f %10.6f %10.6f ", \
 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)                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
 {                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
   /* Variance of health expectancies */          for(k=1,l=0.; k<=nlstate; k++) 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            fprintf(ficresilk," %10.6f",ll[k]);
   double **newm;          fprintf(ficresilk,"\n");
   double **dnewm,**doldm;        }
   int i, j, nhstepm, hstepm, h;      } /* end of wave */
   int k, cptcode;    } /* end of individual */
    double *xp;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   double **gp, **gm;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double ***gradg, ***trgradg;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double ***p3mat;    return -l;
   double age,agelim;  }
   int theta;  
   
    fprintf(ficresvij,"# Covariances of life expectancies\n");  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpr, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   fprintf(ficresvij,"# Age");  {
   for(i=1; i<=nlstate;i++)    /* This routine should help understanding what is done with the selection of individuals/waves and
     for(j=1; j<=nlstate;j++)       to check the exact contribution to the likelihood.
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);       Plotting could be done.
   fprintf(ficresvij,"\n");     */
     int k;
   xp=vector(1,npar);    if(globpr !=0){ /* Just counts and sums no printings */
   dnewm=matrix(1,nlstate,1,npar);      strcpy(fileresilk,"ilk"); 
   doldm=matrix(1,nlstate,1,nlstate);      strcat(fileresilk,fileres);
        if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   hstepm=1*YEARM; /* Every year of age */        printf("Problem with resultfile: %s\n", fileresilk);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
   agelim = AGESUP;      }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      fprintf(ficresilk, "#individual(line's record) s1 s2 wave# effective_wave# number_of_product_matrix pij weight 2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state\n");
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight out sav ");
     if (stepm >= YEARM) hstepm=1;      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for(k=1; k<=nlstate; k++) 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficresilk," ll[%d]",k);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);      fprintf(ficresilk,"\n");
     gp=matrix(0,nhstepm,1,nlstate);    }
     gm=matrix(0,nhstepm,1,nlstate);  
     *fretone=(*funcone)(p);
     for(theta=1; theta <=npar; theta++){    if(globpr !=0){
       for(i=1; i<=npar; i++){ /* Computes gradient */      fclose(ficresilk);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       }        printf("Problem with html file: %s\n", optionfilehtm);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        exit(0);
       for(j=1; j<= nlstate; j++){      }
         for(h=0; h<=nhstepm; h++){      else{
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",fileresilk);
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        fclose(fichtm);
         }      }
       }    }
        return;
       for(i=1; i<=npar; i++) /* Computes gradient */  }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    /*********** Maximum Likelihood Estimation ***************/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(j=1; j<= nlstate; j++){  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
         for(h=0; h<=nhstepm; h++){  {
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    int i,j, iter;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    double **xi;
         }    double fret;
       }    double fretone; /* Only one call to likelihood */
       for(j=1; j<= nlstate; j++)    char filerespow[FILENAMELENGTH];
         for(h=0; h<=nhstepm; h++){    xi=matrix(1,npar,1,npar);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    for (i=1;i<=npar;i++)
         }      for (j=1;j<=npar;j++)
     } /* End theta */        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    strcpy(filerespow,"pow"); 
     strcat(filerespow,fileres);
     for(h=0; h<=nhstepm; h++)    if((ficrespow=fopen(filerespow,"w"))==NULL) {
       for(j=1; j<=nlstate;j++)      printf("Problem with resultfile: %s\n", filerespow);
         for(theta=1; theta <=npar; theta++)      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
           trgradg[h][j][theta]=gradg[h][theta][j];    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
     for(i=1;i<=nlstate;i++)    for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate;j++)      for(j=1;j<=nlstate+ndeath;j++)
         vareij[i][j][(int)age] =0.;        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for(h=0;h<=nhstepm;h++){    fprintf(ficrespow,"\n");
       for(k=0;k<=nhstepm;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    powell(p,xi,npar,ftol,&iter,&fret,func);
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  
         for(i=1;i<=nlstate;i++)    fclose(ficrespow);
           for(j=1;j<=nlstate;j++)    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
             vareij[i][j][(int)age] += doldm[i][j];    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       }    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     }  
     h=1;  }
     if (stepm >= YEARM) h=stepm/YEARM;  
     fprintf(ficresvij,"%.0f ",age );  /**** Computes Hessian and covariance matrix ***/
     for(i=1; i<=nlstate;i++)  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       for(j=1; j<=nlstate;j++){  {
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);    double  **a,**y,*x,pd;
       }    double **hess;
     fprintf(ficresvij,"\n");    int i, j,jk;
     free_matrix(gp,0,nhstepm,1,nlstate);    int *indx;
     free_matrix(gm,0,nhstepm,1,nlstate);  
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    double hessii(double p[], double delta, int theta, double delti[]);
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    double hessij(double p[], double delti[], int i, int j);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    void lubksb(double **a, int npar, int *indx, double b[]) ;
   } /* End age */    void ludcmp(double **a, int npar, int *indx, double *d) ;
    
   free_vector(xp,1,npar);    hess=matrix(1,npar,1,npar);
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    printf("\nCalculation of the hessian matrix. Wait...\n");
     fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
 }    for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
 /************ Variance of prevlim ******************/      fprintf(ficlog,"%d",i);fflush(ficlog);
 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)      hess[i][i]=hessii(p,ftolhess,i,delti);
 {      /*printf(" %f ",p[i]);*/
   /* Variance of prevalence limit */      /*printf(" %lf ",hess[i][i]);*/
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;    
   double **dnewm,**doldm;    for (i=1;i<=npar;i++) {
   int i, j, nhstepm, hstepm;      for (j=1;j<=npar;j++)  {
   int k, cptcode;        if (j>i) { 
   double *xp;          printf(".%d%d",i,j);fflush(stdout);
   double *gp, *gm;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double **gradg, **trgradg;          hess[i][j]=hessij(p,delti,i,j);
   double age,agelim;          hess[j][i]=hess[i][j];    
   int theta;          /*printf(" %lf ",hess[i][j]);*/
            }
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      }
   fprintf(ficresvpl,"# Age");    }
   for(i=1; i<=nlstate;i++)    printf("\n");
       fprintf(ficresvpl," %1d-%1d",i,i);    fprintf(ficlog,"\n");
   fprintf(ficresvpl,"\n");  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   xp=vector(1,npar);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   dnewm=matrix(1,nlstate,1,npar);    
   doldm=matrix(1,nlstate,1,nlstate);    a=matrix(1,npar,1,npar);
      y=matrix(1,npar,1,npar);
   hstepm=1*YEARM; /* Every year of age */    x=vector(1,npar);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    indx=ivector(1,npar);
   agelim = AGESUP;    for (i=1;i<=npar;i++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    ludcmp(a,npar,indx,&pd);
     if (stepm >= YEARM) hstepm=1;  
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    for (j=1;j<=npar;j++) {
     gradg=matrix(1,npar,1,nlstate);      for (i=1;i<=npar;i++) x[i]=0;
     gp=vector(1,nlstate);      x[j]=1;
     gm=vector(1,nlstate);      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
     for(theta=1; theta <=npar; theta++){        matcov[i][j]=x[i];
       for(i=1; i<=npar; i++){ /* Computes gradient */      }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    }
       }  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    printf("\n#Hessian matrix#\n");
       for(i=1;i<=nlstate;i++)    fprintf(ficlog,"\n#Hessian matrix#\n");
         gp[i] = prlim[i][i];    for (i=1;i<=npar;i++) { 
          for (j=1;j<=npar;j++) { 
       for(i=1; i<=npar; i++) /* Computes gradient */        printf("%.3e ",hess[i][j]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        fprintf(ficlog,"%.3e ",hess[i][j]);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      }
       for(i=1;i<=nlstate;i++)      printf("\n");
         gm[i] = prlim[i][i];      fprintf(ficlog,"\n");
     }
       for(i=1;i<=nlstate;i++)  
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    /* Recompute Inverse */
     } /* End theta */    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     trgradg =matrix(1,nlstate,1,npar);    ludcmp(a,npar,indx,&pd);
   
     for(j=1; j<=nlstate;j++)    /*  printf("\n#Hessian matrix recomputed#\n");
       for(theta=1; theta <=npar; theta++)  
         trgradg[j][theta]=gradg[theta][j];    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
     for(i=1;i<=nlstate;i++)      x[j]=1;
       varpl[i][(int)age] =0.;      lubksb(a,npar,indx,x);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      for (i=1;i<=npar;i++){ 
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);        y[i][j]=x[i];
     for(i=1;i<=nlstate;i++)        printf("%.3e ",y[i][j]);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */        fprintf(ficlog,"%.3e ",y[i][j]);
       }
     fprintf(ficresvpl,"%.0f ",age );      printf("\n");
     for(i=1; i<=nlstate;i++)      fprintf(ficlog,"\n");
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    }
     fprintf(ficresvpl,"\n");    */
     free_vector(gp,1,nlstate);  
     free_vector(gm,1,nlstate);    free_matrix(a,1,npar,1,npar);
     free_matrix(gradg,1,npar,1,nlstate);    free_matrix(y,1,npar,1,npar);
     free_matrix(trgradg,1,nlstate,1,npar);    free_vector(x,1,npar);
   } /* End age */    free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);  }
   
 }  /*************** hessian matrix ****************/
   double hessii( double x[], double delta, int theta, double delti[])
   {
     int i;
 /***********************************************/    int l=1, lmax=20;
 /**************** Main Program *****************/    double k1,k2;
 /***********************************************/    double p2[NPARMAX+1];
     double res;
 /*int main(int argc, char *argv[])*/    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
 int main()    double fx;
 {    int k=0,kmax=10;
     double l1;
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;  
   double agedeb, agefin,hf;    fx=func(x);
   double agemin=1.e20, agemax=-1.e20;    for (i=1;i<=npar;i++) p2[i]=x[i];
     for(l=0 ; l <=lmax; l++){
   double fret;      l1=pow(10,l);
   double **xi,tmp,delta;      delts=delt;
       for(k=1 ; k <kmax; k=k+1){
   double dum; /* Dummy variable */        delt = delta*(l1*k);
   double ***p3mat;        p2[theta]=x[theta] +delt;
   int *indx;        k1=func(p2)-fx;
   char line[MAXLINE], linepar[MAXLINE];        p2[theta]=x[theta]-delt;
   char title[MAXLINE];        k2=func(p2)-fx;
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];        /*res= (k1-2.0*fx+k2)/delt/delt; */
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   char filerest[FILENAMELENGTH];        
   char fileregp[FILENAMELENGTH];  #ifdef DEBUG
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        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);
   int firstobs=1, lastobs=10;        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);
   int sdeb, sfin; /* Status at beginning and end */  #endif
   int c,  h , cpt,l;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   int ju,jl, mi;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   int i1,j1, k1,jk,aa,bb, stepsize;          k=kmax;
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        }
          else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   int hstepm, nhstepm;          k=kmax; l=lmax*10.;
   double bage, fage, age, agelim, agebase;        }
   double ftolpl=FTOL;        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   double **prlim;          delts=delt;
   double *severity;        }
   double ***param; /* Matrix of parameters */      }
   double  *p;    }
   double **matcov; /* Matrix of covariance */    delti[theta]=delts;
   double ***delti3; /* Scale */    return res; 
   double *delti; /* Scale */    
   double ***eij, ***vareij;  }
   double **varpl; /* Variances of prevalence limits by age */  
   double *epj, vepp;  double hessij( double x[], double delti[], int thetai,int thetaj)
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";  {
   char *alph[]={"a","a","b","c","d","e"}, str[4];    int i;
   char z[1]="c", occ;    int l=1, l1, lmax=20;
 #include <sys/time.h>    double k1,k2,k3,k4,res,fx;
 #include <time.h>    double p2[NPARMAX+1];
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    int k;
   /* long total_usecs;  
   struct timeval start_time, end_time;    fx=func(x);
      for (k=1; k<=2; k++) {
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      for (i=1;i<=npar;i++) p2[i]=x[i];
       p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   printf("\nIMACH, Version 0.63");      k1=func(p2)-fx;
   printf("\nEnter the parameter file name: ");    
       p2[thetai]=x[thetai]+delti[thetai]/k;
 #ifdef windows      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   scanf("%s",pathtot);      k2=func(p2)-fx;
   getcwd(pathcd, size);    
   cutv(path,optionfile,pathtot,'\\');      p2[thetai]=x[thetai]-delti[thetai]/k;
   chdir(path);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   replace(pathc,path);      k3=func(p2)-fx;
 #endif    
 #ifdef unix      p2[thetai]=x[thetai]-delti[thetai]/k;
   scanf("%s",optionfile);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
 #endif      k4=func(p2)-fx;
       res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
 /*-------- arguments in the command line --------*/  #ifdef DEBUG
       printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   strcpy(fileres,"r");      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);
   strcat(fileres, optionfile);  #endif
     }
   /*---------arguments file --------*/    return res;
   }
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  
     printf("Problem with optionfile %s\n",optionfile);  /************** Inverse of matrix **************/
     goto end;  void ludcmp(double **a, int n, int *indx, double *d) 
   }  { 
     int i,imax,j,k; 
   strcpy(filereso,"o");    double big,dum,sum,temp; 
   strcat(filereso,fileres);    double *vv; 
   if((ficparo=fopen(filereso,"w"))==NULL) {   
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    vv=vector(1,n); 
   }    *d=1.0; 
     for (i=1;i<=n;i++) { 
   /* Reads comments: lines beginning with '#' */      big=0.0; 
   while((c=getc(ficpar))=='#' && c!= EOF){      for (j=1;j<=n;j++) 
     ungetc(c,ficpar);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     fgets(line, MAXLINE, ficpar);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     puts(line);      vv[i]=1.0/big; 
     fputs(line,ficparo);    } 
   }    for (j=1;j<=n;j++) { 
   ungetc(c,ficpar);      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
   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);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);        a[i][j]=sum; 
   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);      } 
       big=0.0; 
   covar=matrix(1,NCOVMAX,1,n);          for (i=j;i<=n;i++) { 
   if (strlen(model)<=1) cptcovn=0;        sum=a[i][j]; 
   else {        for (k=1;k<j;k++) 
     j=0;          sum -= a[i][k]*a[k][j]; 
     j=nbocc(model,'+');        a[i][j]=sum; 
     cptcovn=j+1;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   }          big=dum; 
           imax=i; 
   ncovmodel=2+cptcovn;        } 
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      } 
        if (j != imax) { 
   /* Read guess parameters */        for (k=1;k<=n;k++) { 
   /* Reads comments: lines beginning with '#' */          dum=a[imax][k]; 
   while((c=getc(ficpar))=='#' && c!= EOF){          a[imax][k]=a[j][k]; 
     ungetc(c,ficpar);          a[j][k]=dum; 
     fgets(line, MAXLINE, ficpar);        } 
     puts(line);        *d = -(*d); 
     fputs(line,ficparo);        vv[imax]=vv[j]; 
   }      } 
   ungetc(c,ficpar);      indx[j]=imax; 
        if (a[j][j] == 0.0) a[j][j]=TINY; 
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      if (j != n) { 
     for(i=1; i <=nlstate; i++)        dum=1.0/(a[j][j]); 
     for(j=1; j <=nlstate+ndeath-1; j++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);      } 
       fprintf(ficparo,"%1d%1d",i1,j1);    } 
       printf("%1d%1d",i,j);    free_vector(vv,1,n);  /* Doesn't work */
       for(k=1; k<=ncovmodel;k++){  ;
         fscanf(ficpar," %lf",&param[i][j][k]);  } 
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);  void lubksb(double **a, int n, int *indx, double b[]) 
       }  { 
       fscanf(ficpar,"\n");    int i,ii=0,ip,j; 
       printf("\n");    double sum; 
       fprintf(ficparo,"\n");   
     }    for (i=1;i<=n;i++) { 
        ip=indx[i]; 
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;      sum=b[ip]; 
   p=param[1][1];      b[ip]=b[i]; 
        if (ii) 
   /* Reads comments: lines beginning with '#' */        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   while((c=getc(ficpar))=='#' && c!= EOF){      else if (sum) ii=i; 
     ungetc(c,ficpar);      b[i]=sum; 
     fgets(line, MAXLINE, ficpar);    } 
     puts(line);    for (i=n;i>=1;i--) { 
     fputs(line,ficparo);      sum=b[i]; 
   }      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   ungetc(c,ficpar);      b[i]=sum/a[i][i]; 
     } 
   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++){  /************ Frequencies ********************/
     for(j=1; j <=nlstate+ndeath-1; j++){  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint)
       fscanf(ficpar,"%1d%1d",&i1,&j1);  {  /* Some frequencies */
       printf("%1d%1d",i,j);    
       fprintf(ficparo,"%1d%1d",i1,j1);    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
       for(k=1; k<=ncovmodel;k++){    int first;
         fscanf(ficpar,"%le",&delti3[i][j][k]);    double ***freq; /* Frequencies */
         printf(" %le",delti3[i][j][k]);    double *pp, **prop;
         fprintf(ficparo," %le",delti3[i][j][k]);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
       }    FILE *ficresp;
       fscanf(ficpar,"\n");    char fileresp[FILENAMELENGTH];
       printf("\n");    
       fprintf(ficparo,"\n");    pp=vector(1,nlstate);
     }    prop=matrix(1,nlstate,iagemin,iagemax+3);
   }    strcpy(fileresp,"p");
   delti=delti3[1][1];    strcat(fileresp,fileres);
      if((ficresp=fopen(fileresp,"w"))==NULL) {
   /* Reads comments: lines beginning with '#' */      printf("Problem with prevalence resultfile: %s\n", fileresp);
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     ungetc(c,ficpar);      exit(0);
     fgets(line, MAXLINE, ficpar);    }
     puts(line);    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
     fputs(line,ficparo);    j1=0;
   }    
   ungetc(c,ficpar);    j=cptcoveff;
      if (cptcovn<1) {j=1;ncodemax[1]=1;}
   matcov=matrix(1,npar,1,npar);  
   for(i=1; i <=npar; i++){    first=1;
     fscanf(ficpar,"%s",&str);  
     printf("%s",str);    for(k1=1; k1<=j;k1++){
     fprintf(ficparo,"%s",str);      for(i1=1; i1<=ncodemax[k1];i1++){
     for(j=1; j <=i; j++){        j1++;
       fscanf(ficpar," %le",&matcov[i][j]);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
       printf(" %.5le",matcov[i][j]);          scanf("%d", i);*/
       fprintf(ficparo," %.5le",matcov[i][j]);        for (i=-1; i<=nlstate+ndeath; i++)  
     }          for (jk=-1; jk<=nlstate+ndeath; jk++)  
     fscanf(ficpar,"\n");            for(m=iagemin; m <= iagemax+3; m++)
     printf("\n");              freq[i][jk][m]=0;
     fprintf(ficparo,"\n");  
   }      for (i=1; i<=nlstate; i++)  
   for(i=1; i <=npar; i++)        for(m=iagemin; m <= iagemax+3; m++)
     for(j=i+1;j<=npar;j++)          prop[i][m]=0;
       matcov[i][j]=matcov[j][i];        
            dateintsum=0;
   printf("\n");        k2cpt=0;
         for (i=1; i<=imx; i++) {
           bool=1;
    if(mle==1){          if  (cptcovn>0) {
     /*-------- data file ----------*/            for (z1=1; z1<=cptcoveff; z1++) 
     if((ficres =fopen(fileres,"w"))==NULL) {              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       printf("Problem with resultfile: %s\n", fileres);goto end;                bool=0;
     }          }
     fprintf(ficres,"#%s\n",version);          if (bool==1){
                for(m=firstpass; m<=lastpass; m++){
     if((fic=fopen(datafile,"r"))==NULL)    {              k2=anint[m][i]+(mint[m][i]/12.);
       printf("Problem with datafile: %s\n", datafile);goto end;              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
     n= lastobs;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     severity = vector(1,maxwav);                if (m<lastpass) {
     outcome=imatrix(1,maxwav+1,1,n);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     num=ivector(1,n);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     moisnais=vector(1,n);                }
     annais=vector(1,n);                
     moisdc=vector(1,n);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     andc=vector(1,n);                  dateintsum=dateintsum+k2;
     agedc=vector(1,n);                  k2cpt++;
     cod=ivector(1,n);                }
     weight=vector(1,n);                /*}*/
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */            }
     mint=matrix(1,maxwav,1,n);          }
     anint=matrix(1,maxwav,1,n);        }
     s=imatrix(1,maxwav+1,1,n);         
     adl=imatrix(1,maxwav+1,1,n);            /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
     tab=ivector(1,NCOVMAX);  
     ncodemax=ivector(1,8);        if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
     i=1;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     while (fgets(line, MAXLINE, fic) != NULL)    {          fprintf(ficresp, "**********\n#");
       if ((i >= firstobs) && (i <=lastobs)) {        }
                for(i=1; i<=nlstate;i++) 
         for (j=maxwav;j>=1;j--){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        fprintf(ficresp, "\n");
           strcpy(line,stra);        
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        for(i=iagemin; i <= iagemax+3; i++){
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          if(i==iagemax+3){
         }            fprintf(ficlog,"Total");
                  }else{
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            if(first==1){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);              first=0;
               printf("See log file for details...\n");
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);            }
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);            fprintf(ficlog,"Age %d", i);
           }
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);          for(jk=1; jk <=nlstate ; jk++){
         for (j=ncov;j>=1;j--){            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);              pp[jk] += freq[jk][m][i]; 
         }          }
         num[i]=atol(stra);          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pos=0; m <=0 ; m++)
         /*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]));*/              pos += freq[jk][m][i];
             if(pp[jk]>=1.e-10){
         i=i+1;              if(first==1){
       }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     }              }
               fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     /*scanf("%d",i);*/            }else{
   imx=i-1; /* Number of individuals */              if(first==1)
                 printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   /* Calculation of the number of parameter from char model*/              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   Tvar=ivector(1,8);                }
              }
   if (strlen(model) >1){  
     j=0;          for(jk=1; jk <=nlstate ; jk++){
     j=nbocc(model,'+');            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     cptcovn=j+1;              pp[jk] += freq[jk][m][i];
              }       
     strcpy(modelsav,model);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     if (j==0) {            pos += pp[jk];
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);            posprop += prop[jk][i];
     }          }
     else {          for(jk=1; jk <=nlstate ; jk++){
       for(i=j; i>=1;i--){            if(pos>=1.e-5){
         cutv(stra,strb,modelsav,'+');              if(first==1)
         if (strchr(strb,'*')) {                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           cutv(strd,strc,strb,'*');              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;            }else{
           cutv(strb,strc,strd,'V');              if(first==1)
           for (k=1; k<=lastobs;k++)                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
         }            }
         else {cutv(strd,strc,strb,'V');            if( i <= iagemax){
         Tvar[i+1]=atoi(strc);              if(pos>=1.e-5){
         }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         strcpy(modelsav,stra);                  /*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]);*/
       cutv(strd,strc,stra,'V');              }
       Tvar[1]=atoi(strc);              else
     }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   }            }
   /*printf("tvar=%d ",Tvar[1]);          }
   scanf("%d ",i);*/          
     fclose(fic);          for(jk=-1; jk <=nlstate+ndeath; jk++)
             for(m=-1; m <=nlstate+ndeath; m++)
     if (weightopt != 1) { /* Maximisation without weights*/              if(freq[jk][m][i] !=0 ) {
       for(i=1;i<=n;i++) weight[i]=1.0;              if(first==1)
     }                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     /*-calculation of age at interview from date of interview and age at death -*/                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     agev=matrix(1,maxwav,1,imx);              }
              if(i <= iagemax)
     for (i=1; i<=imx; i++)  {            fprintf(ficresp,"\n");
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          if(first==1)
       for(m=1; (m<= maxwav); m++){            printf("Others in log...\n");
         if(s[m][i] >0){          fprintf(ficlog,"\n");
           if (s[m][i] == nlstate+1) {        }
             if(agedc[i]>0)      }
               if(moisdc[i]!=99 && andc[i]!=9999)    }
               agev[m][i]=agedc[i];    dateintmean=dateintsum/k2cpt; 
             else{   
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    fclose(ficresp);
               agev[m][i]=-1;    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
             }    free_vector(pp,1,nlstate);
           }    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
           else if(s[m][i] !=9){ /* Should no more exist */    /* End of Freq */
             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;  /************ Prevalence ********************/
             else if(agev[m][i] <agemin){  void prevalence(double ***probs, double agemin, double 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)
               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);*/    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
             }       in each health status at the date of interview (if between dateprev1 and dateprev2).
             else if(agev[m][i] >agemax){       We still use firstpass and lastpass as another selection.
               agemax=agev[m][i];    */
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/   
             }    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
             /*agev[m][i]=anint[m][i]-annais[i];*/    double ***freq; /* Frequencies */
             /*   agev[m][i] = age[i]+2*m;*/    double *pp, **prop;
           }    double pos,posprop; 
           else { /* =9 */    double  y2; /* in fractional years */
             agev[m][i]=1;    int iagemin, iagemax;
             s[m][i]=-1;  
           }    iagemin= (int) agemin;
         }    iagemax= (int) agemax;
         else /*= 0 Unknown */    /*pp=vector(1,nlstate);*/
           agev[m][i]=1;    prop=matrix(1,nlstate,iagemin,iagemax+3); 
       }    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
        j1=0;
     }    
     for (i=1; i<=imx; i++)  {    j=cptcoveff;
       for(m=1; (m<= maxwav); m++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
         if (s[m][i] > (nlstate+ndeath)) {    
           printf("Error: Wrong value in nlstate or ndeath\n");      for(k1=1; k1<=j;k1++){
           goto end;      for(i1=1; i1<=ncodemax[k1];i1++){
         }        j1++;
       }        
     }        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);            prop[i][m]=0.0;
        
     free_vector(severity,1,maxwav);        for (i=1; i<=imx; i++) { /* Each individual */
     free_imatrix(outcome,1,maxwav+1,1,n);          bool=1;
     free_vector(moisnais,1,n);          if  (cptcovn>0) {
     free_vector(annais,1,n);            for (z1=1; z1<=cptcoveff; z1++) 
     free_matrix(mint,1,maxwav,1,n);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     free_matrix(anint,1,maxwav,1,n);                bool=0;
     free_vector(moisdc,1,n);          } 
     free_vector(andc,1,n);          if (bool==1) { 
             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 */
     wav=ivector(1,imx);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     dh=imatrix(1,lastpass-firstpass+1,1,imx);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                    if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
     /* Concatenates waves */                if (s[m][i]>0 && s[m][i]<=nlstate) { 
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
                   prop[s[m][i]][(int)agev[m][i]] += weight[i];
                   prop[s[m][i]][iagemax+3] += weight[i]; 
 Tcode=ivector(1,100);                } 
    nbcode=imatrix(1,nvar,1,8);                }
    ncodemax[1]=1;            } /* end selection of waves */
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);          }
          }
    codtab=imatrix(1,100,1,10);        for(i=iagemin; i <= iagemax+3; i++){  
    h=0;          
    m=pow(2,cptcovn);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
              posprop += prop[jk][i]; 
    for(k=1;k<=cptcovn; k++){          } 
      for(i=1; i <=(m/pow(2,k));i++){  
        for(j=1; j <= ncodemax[k]; j++){          for(jk=1; jk <=nlstate ; jk++){     
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){            if( i <=  iagemax){ 
            h++;              if(posprop>=1.e-5){ 
            if (h>m) h=1;codtab[h][k]=j;                probs[i][jk][j1]= prop[jk][i]/posprop;
          }              } 
        }            } 
      }          }/* end jk */ 
    }        }/* end i */ 
       } /* end i1 */
    /*for(i=1; i <=m ;i++){    } /* end k1 */
      for(k=1; k <=cptcovn; k++){    
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
      }    /*free_vector(pp,1,nlstate);*/
      printf("\n");    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
    }*/  }  /* End of prevalence */
    /*scanf("%d",i);*/  
      /************* Waves Concatenation ***************/
    /* Calculates basic frequencies. Computes observed prevalence at single age  
        and prints on file fileres'p'. */  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)
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        Death is a valid wave (if date is known).
   /*scanf("%d ",i);*/       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
        dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
        and mw[mi+1][i]. dh depends on stepm.
     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 */    int i, mi, m;
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */       double sum=0., jmean=0.;*/
        int first;
     /* For Powell, parameters are in a vector p[] starting at p[1]    int j, k=0,jk, ju, jl;
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    double sum=0.;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    first=0;
        jmin=1e+5;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    jmax=-1;
     jmean=0.;
        for(i=1; i<=imx; i++){
     /*--------- results files --------------*/      mi=0;
     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);      m=firstpass;
          while(s[m][i] <= nlstate){
    jk=1;        if(s[m][i]>=1)
    fprintf(ficres,"# Parameters\n");          mw[++mi][i]=m;
    printf("# Parameters\n");        if(m >=lastpass)
    for(i=1,jk=1; i <=nlstate; i++){          break;
      for(k=1; k <=(nlstate+ndeath); k++){        else
        if (k != i)          m++;
          {      }/* end while */
            printf("%d%d ",i,k);      if (s[m][i] > nlstate){
            fprintf(ficres,"%1d%1d ",i,k);        mi++;     /* Death is another wave */
            for(j=1; j <=ncovmodel; j++){        /* if(mi==0)  never been interviewed correctly before death */
              printf("%f ",p[jk]);           /* Only death is a correct wave */
              fprintf(ficres,"%f ",p[jk]);        mw[mi][i]=m;
              jk++;      }
            }  
            printf("\n");      wav[i]=mi;
            fprintf(ficres,"\n");      if(mi==0){
          }        if(first==0){
      }          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
    }          first=1;
         }
     /* Computing hessian and covariance matrix */        if(first==1){
     ftolhess=ftol; /* Usually correct */          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
     hesscov(matcov, p, npar, delti, ftolhess, func);        }
     fprintf(ficres,"# Scales\n");      } /* end mi==0 */
     printf("# Scales\n");    } /* End individuals */
      for(i=1,jk=1; i <=nlstate; i++){  
       for(j=1; j <=nlstate+ndeath; j++){    for(i=1; i<=imx; i++){
         if (j!=i) {      for(mi=1; mi<wav[i];mi++){
           fprintf(ficres,"%1d%1d",i,j);        if (stepm <=0)
           printf("%1d%1d",i,j);          dh[mi][i]=1;
           for(k=1; k<=ncovmodel;k++){        else{
             printf(" %.5e",delti[jk]);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
             fprintf(ficres," %.5e",delti[jk]);            if (agedc[i] < 2*AGESUP) {
             jk++;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
           }              if(j==0) j=1;  /* Survives at least one month after exam */
           printf("\n");              else if(j<0){
           fprintf(ficres,"\n");                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
         }                j=1; /* Careful Patch */
       }                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
       }                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                    fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
     k=1;              }
     fprintf(ficres,"# Covariance\n");              k=k+1;
     printf("# Covariance\n");              if (j >= jmax) jmax=j;
     for(i=1;i<=npar;i++){              if (j <= jmin) jmin=j;
       /*  if (k>nlstate) k=1;              sum=sum+j;
       i1=(i-1)/(ncovmodel*nlstate)+1;              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       printf("%s%d%d",alph[k],i1,tab[i]);*/            }
       fprintf(ficres,"%3d",i);          }
       printf("%3d",i);          else{
       for(j=1; j<=i;j++){            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
         fprintf(ficres," %.5e",matcov[i][j]);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
         printf(" %.5e",matcov[i][j]);            k=k+1;
       }            if (j >= jmax) jmax=j;
       fprintf(ficres,"\n");            else if (j <= jmin)jmin=j;
       printf("\n");            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       k++;            /*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]);*/
     }            if(j<0){
                  printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     while((c=getc(ficpar))=='#' && c!= EOF){              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       ungetc(c,ficpar);            }
       fgets(line, MAXLINE, ficpar);            sum=sum+j;
       puts(line);          }
       fputs(line,ficparo);          jk= j/stepm;
     }          jl= j -jk*stepm;
     ungetc(c,ficpar);          ju= j -(jk+1)*stepm;
            if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);            if(jl==0){
                  dh[mi][i]=jk;
     if (fage <= 2) {              bh[mi][i]=0;
       bage = agemin;            }else{ /* We want a negative bias in order to only have interpolation ie
       fage = agemax;                    * at the price of an extra matrix product in likelihood */
     }              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
     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\n",agemin,agemax,bage,fage);          }else{
 /*------------ gnuplot -------------*/            if(jl <= -ju){
 chdir(pathcd);              dh[mi][i]=jk;
   if((ficgp=fopen("graph.plt","w"))==NULL) {              bh[mi][i]=jl;       /* bias is positive if real duration
     printf("Problem with file graph.gp");goto end;                                   * is higher than the multiple of stepm and negative otherwise.
   }                                   */
 #ifdef windows            }
   fprintf(ficgp,"cd \"%s\" \n",pathc);            else{
 #endif              dh[mi][i]=jk+1;
 m=pow(2,cptcovn);              bh[mi][i]=ju;
              }
  /* 1eme*/            if(dh[mi][i]==0){
   for (cpt=1; cpt<= nlstate ; cpt ++) {              dh[mi][i]=1; /* At least one step */
    for (k1=1; k1<= m ; k1 ++) {              bh[mi][i]=ju; /* At least one step */
               /*  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);*/
 #ifdef windows            }
     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);          } /* end if mle */
 #endif        }
 #ifdef unix      } /* end wave */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);    }
 #endif    jmean=sum/k;
     printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
 for (i=1; i<= nlstate ; i ++) {    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");   }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }  /*********** Tricode ****************************/
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);  void tricode(int *Tvar, int **nbcode, int imx)
     for (i=1; i<= nlstate ; i ++) {  {
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    
   else fprintf(ficgp," \%%*lf (\%%*lf)");    int Ndum[20],ij=1, k, j, i, maxncov=19;
 }    int cptcode=0;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    cptcoveff=0; 
      for (i=1; i<= nlstate ; i ++) {   
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    for (k=0; k<maxncov; k++) Ndum[k]=0;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for (k=1; k<=7; k++) ncodemax[k]=0;
 }    
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
 #ifdef unix      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
 fprintf(ficgp,"\nset ter gif small size 400,300");                                 modality*/ 
 #endif        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        Ndum[ij]++; /*store the modality */
    }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
   }        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
   /*2 eme*/                                         Tvar[j]. If V=sex and male is 0 and 
                                          female is 1, then  cptcode=1.*/
   for (k1=1; k1<= m ; k1 ++) {      }
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);  
          for (i=0; i<=cptcode; i++) {
     for (i=1; i<= nlstate+1 ; 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 */
       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 ++) {      ij=1; 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      for (i=1; i<=ncodemax[j]; i++) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");        for (k=0; k<= maxncov; k++) {
 }            if (Ndum[k] != 0) {
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");            nbcode[Tvar[j]][ij]=k; 
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);            /* 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; */
     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 ++) {            ij++;
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          }
         else fprintf(ficgp," \%%*lf (\%%*lf)");          if (ij > ncodemax[j]) break; 
 }          }  
       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)");   for (k=0; k< maxncov; k++) Ndum[k]=0;
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }     for (i=1; i<=ncovmodel-2; i++) { 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
       else fprintf(ficgp,"\" t\"\" w l 0,");     ij=Tvar[i];
     }     Ndum[ij]++;
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);   }
   }  
     ij=1;
   /*3eme*/   for (i=1; i<= maxncov; i++) {
      if((Ndum[i]!=0) && (i<=ncovcol)){
    for (k1=1; k1<= m ; k1 ++) {       Tvaraff[ij]=i; /*For printing */
     for (cpt=1; cpt<= nlstate ; cpt ++) {       ij++;
       k=2+nlstate*(cpt-1);     }
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);   }
       for (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+i,cpt,i+1);   cptcoveff=ij-1; /*Number of simple covariates*/
       }  }
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  
     }  /*********** 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 )
   /* CV preval stat */  
     for (k1=1; k1<= m ; k1 ++) {  {
     for (cpt=1; cpt<nlstate ; cpt ++) {    /* Health expectancies */
       k=3;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);    double age, agelim, hf;
       for (i=1; i< nlstate ; i ++)    double ***p3mat,***varhe;
         fprintf(ficgp,"+$%d",k+i+1);    double **dnewm,**doldm;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    double *xp;
          double **gp, **gm;
       l=3+(nlstate+ndeath)*cpt;    double ***gradg, ***trgradg;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    int theta;
       for (i=1; i< nlstate ; i ++) {  
         l=3+(nlstate+ndeath)*cpt;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
         fprintf(ficgp,"+$%d",l+i+1);    xp=vector(1,npar);
       }    dnewm=matrix(1,nlstate*nlstate,1,npar);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    
     }    fprintf(ficreseij,"# Health expectancies\n");
   }    fprintf(ficreseij,"# Age");
      for(i=1; i<=nlstate;i++)
   /* proba elementaires */      for(j=1; j<=nlstate;j++)
   for(i=1,jk=1; i <=nlstate; i++){        fprintf(ficreseij," %1d-%1d (SE)",i,j);
     for(k=1; k <=(nlstate+ndeath); k++){    fprintf(ficreseij,"\n");
       if (k != i) {  
         /*  fprintf(ficgp,"%1d%1d ",i,k);*/    if(estepm < stepm){
         for(j=1; j <=ncovmodel; j++){      printf ("Problem %d lower than %d\n",estepm, stepm);
           fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);    }
           jk++;    else  hstepm=estepm;   
           fprintf(ficgp,"\n");    /* We compute the life expectancy from trapezoids spaced every estepm months
         }     * This is mainly to measure the difference between two models: for example
       }     * if stepm=24 months pijx are given only every 2 years and by summing them
     }     * we are calculating an estimate of the Life Expectancy assuming a linear 
   }     * progression in between and thus overestimating or underestimating according
   for(jk=1; jk <=m; jk++) {     * to the curvature of the survival function. If, for the same date, we 
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   for(i=1; i <=nlstate; i++) {     * to compare the new estimate of Life expectancy with the same linear 
     for(k=1; k <=(nlstate+ndeath); k++){     * hypothesis. A more precise result, taking into account a more precise
       if (k != i) {     * curvature will be obtained if estepm is as small as stepm. */
         fprintf(ficgp," exp(a%d%d+b%d%d*x",i,k,i,k);  
         for(j=3; j <=ncovmodel; j++)    /* For example we decided to compute the life expectancy with the smallest unit */
           fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         fprintf(ficgp,")/(1");       nhstepm is the number of hstepm from age to agelim 
         for(k1=1; k1 <=(nlstate+ndeath); k1++)       nstepm is the number of stepm from age to agelin. 
           if (k1 != i) {       Look at hpijx to understand the reason of that which relies in memory size
             fprintf(ficgp,"+exp(a%d%d+b%d%d*x",i,k1,i,k1);       and note for a fixed period like estepm months */
             for(j=3; j <=ncovmodel; j++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
               fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);       survival function given by stepm (the optimization length). Unfortunately it
             fprintf(ficgp,")");       means that if the survival funtion is printed only each two years of age and if
           }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
         fprintf(ficgp,") t \"p%d%d\" ", i,k);       results. So we changed our mind and took the option of the best precision.
       if ((i+k)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    */
       }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     }  
   }    agelim=AGESUP;
 fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      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); 
  fclose(ficgp);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
     chdir(path);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     free_matrix(agev,1,maxwav,1,imx);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ivector(wav,1,imx);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      gp=matrix(0,nhstepm,1,nlstate*nlstate);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      gm=matrix(0,nhstepm,1,nlstate*nlstate);
      
     free_imatrix(s,1,maxwav+1,1,n);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
             in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
          hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
     free_ivector(num,1,n);   
     free_vector(agedc,1,n);  
     free_vector(weight,1,n);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     /*free_matrix(covar,1,NCOVMAX,1,n);*/  
     fclose(ficparo);      /* Computing Variances of health expectancies */
     fclose(ficres);  
    }       for(theta=1; theta <=npar; theta++){
            for(i=1; i<=npar; i++){ 
    /*________fin mle=1_________*/          xp[i] = x[i] + (i==theta ?delti[theta]:0);
            }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
      
     /* No more information from the sample is required now */        cptj=0;
   /* Reads comments: lines beginning with '#' */        for(j=1; j<= nlstate; j++){
   while((c=getc(ficpar))=='#' && c!= EOF){          for(i=1; i<=nlstate; i++){
     ungetc(c,ficpar);            cptj=cptj+1;
     fgets(line, MAXLINE, ficpar);            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
     puts(line);              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
     fputs(line,ficparo);            }
   }          }
   ungetc(c,ficpar);        }
         
        
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        for(i=1; i<=npar; i++) 
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 /*--------- index.htm --------*/        
         cptj=0;
   if((fichtm=fopen("index.htm","w"))==NULL)    {        for(j=1; j<= nlstate; j++){
     printf("Problem with index.htm \n");goto end;          for(i=1;i<=nlstate;i++){
   }            cptj=cptj+1;
             for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
  fprintf(fichtm,"<body><ul> Imach, Version 0.63<hr> <li>Outputs files<br><br>\n  
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
 - 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>        }
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>        for(j=1; j<= nlstate*nlstate; j++)
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>          for(h=0; h<=nhstepm-1; h++){
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>          }
         - 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);       } 
      
  fprintf(fichtm," <li>Graphs</li>\n<p>");  /* End theta */
   
  m=cptcovn;       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  
        for(h=0; h<=nhstepm-1; h++)
  j1=0;        for(j=1; j<=nlstate*nlstate;j++)
  for(k1=1; k1<=m;k1++){          for(theta=1; theta <=npar; theta++)
    for(i1=1; i1<=ncodemax[k1];i1++){            trgradg[h][j][theta]=gradg[h][theta][j];
        j1++;       
        if (cptcovn > 0) {  
          fprintf(fichtm,"<hr>************ Results for covariates");       for(i=1;i<=nlstate*nlstate;i++)
          for (cpt=1; cpt<=cptcovn;cpt++)        for(j=1;j<=nlstate*nlstate;j++)
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);          varhe[i][j][(int)age] =0.;
          fprintf(fichtm," ************\n<hr>");  
        }       printf("%d|",(int)age);fflush(stdout);
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);           for(h=0;h<=nhstepm-1;h++){
        for(cpt=1; cpt<nlstate;cpt++){        for(k=0;k<=nhstepm-1;k++){
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
        }          for(i=1;i<=nlstate*nlstate;i++)
     for(cpt=1; cpt<=nlstate;cpt++) {            for(j=1;j<=nlstate*nlstate;j++)
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
 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);        }
      }      /* Computing expectancies */
      for(cpt=1; cpt<=nlstate;cpt++) {      for(i=1; i<=nlstate;i++)
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>        for(j=1; j<=nlstate;j++)
 <img src=\"ex%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
      }            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
      fprintf(fichtm,"\n<br>- Total life expectancy by age and            
 health expectancies in states (1) and (2): e%s%d.gif<br>  /* 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]);*/
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);  
 fprintf(fichtm,"\n</body>");          }
    }  
  }      fprintf(ficreseij,"%3.0f",age );
 fclose(fichtm);      cptj=0;
       for(i=1; i<=nlstate;i++)
   /*--------------- Prevalence limit --------------*/        for(j=1; j<=nlstate;j++){
            cptj++;
   strcpy(filerespl,"pl");          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
   strcat(filerespl,fileres);        }
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      fprintf(ficreseij,"\n");
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;     
   }      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   fprintf(ficrespl,"#Prevalence limit\n");      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   fprintf(ficrespl,"#Age ");      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficrespl,"\n");    }
      printf("\n");
   prlim=matrix(1,nlstate,1,nlstate);    fprintf(ficlog,"\n");
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    free_vector(xp,1,npar);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   k=0;  }
   agebase=agemin;  
   agelim=agemax;  /************ Variance ******************/
   ftolpl=1.e-10;  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)
   i1=cptcovn;  {
   if (cptcovn < 1){i1=1;}    /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   for(cptcov=1;cptcov<=i1;cptcov++){    /* double **newm;*/
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double **dnewm,**doldm;
         k=k+1;    double **dnewmp,**doldmp;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    int i, j, nhstepm, hstepm, h, nstepm ;
         fprintf(ficrespl,"\n#****** ");    int k, cptcode;
         for(j=1;j<=cptcovn;j++)    double *xp;
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    double **gp, **gm;  /* for var eij */
         fprintf(ficrespl,"******\n");    double ***gradg, ***trgradg; /*for var eij */
            double **gradgp, **trgradgp; /* for var p point j */
         for (age=agebase; age<=agelim; age++){    double *gpp, *gmp; /* for var p point j */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
           fprintf(ficrespl,"%.0f",age );    double ***p3mat;
           for(i=1; i<=nlstate;i++)    double age,agelim, hf;
           fprintf(ficrespl," %.5f", prlim[i][i]);    double ***mobaverage;
           fprintf(ficrespl,"\n");    int theta;
         }    char digit[4];
       }    char digitp[25];
     }  
   fclose(ficrespl);    char fileresprobmorprev[FILENAMELENGTH];
   /*------------- h Pij x at various ages ------------*/  
      if(popbased==1){
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      if(mobilav!=0)
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        strcpy(digitp,"-populbased-mobilav-");
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;      else strcpy(digitp,"-populbased-nomobil-");
   }    }
   printf("Computing pij: result on file '%s' \n", filerespij);    else 
        strcpy(digitp,"-stablbased-");
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=24) stepsize=2;    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   agelim=AGESUP;      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   hstepm=stepsize*YEARM; /* Every year of age */        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */        printf(" Error in movingaverage mobilav=%d\n",mobilav);
        }
   k=0;    }
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    strcpy(fileresprobmorprev,"prmorprev"); 
       k=k+1;    sprintf(digit,"%-d",ij);
         fprintf(ficrespij,"\n#****** ");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
         for(j=1;j<=cptcovn;j++)    strcat(fileresprobmorprev,digit); /* Tvar to be done */
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
         fprintf(ficrespij,"******\n");    strcat(fileresprobmorprev,fileres);
            if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      printf("Problem with resultfile: %s\n", fileresprobmorprev);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           oldm=oldms;savm=savms;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      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);
           fprintf(ficrespij,"# Age");    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           for(i=1; i<=nlstate;i++)    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
             for(j=1; j<=nlstate+ndeath;j++)      fprintf(ficresprobmorprev," p.%-d SE",j);
               fprintf(ficrespij," %1d-%1d",i,j);      for(i=1; i<=nlstate;i++)
           fprintf(ficrespij,"\n");        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           for (h=0; h<=nhstepm; h++){    }  
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    fprintf(ficresprobmorprev,"\n");
             for(i=1; i<=nlstate;i++)    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
               for(j=1; j<=nlstate+ndeath;j++)      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
             fprintf(ficrespij,"\n");      exit(0);
           }    }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    else{
           fprintf(ficrespij,"\n");      fprintf(ficgp,"\n# Routine varevsij");
         }    }
     }    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
   }      printf("Problem with html file: %s\n", optionfilehtm);
       fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
   fclose(ficrespij);      exit(0);
     }
   /*---------- Health expectancies and variances ------------*/    else{
       fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
   strcpy(filerest,"t");      fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   strcat(filerest,fileres);    }
   if((ficrest=fopen(filerest,"w"))==NULL) {    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  
   }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
   strcpy(filerese,"e");        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
   strcat(filerese,fileres);    fprintf(ficresvij,"\n");
   if((ficreseij=fopen(filerese,"w"))==NULL) {  
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    xp=vector(1,npar);
   }    dnewm=matrix(1,nlstate,1,npar);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
  strcpy(fileresv,"v");    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   strcat(fileresv,fileres);  
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    gpp=vector(nlstate+1,nlstate+ndeath);
   }    gmp=vector(nlstate+1,nlstate+ndeath);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
   k=0;    if(estepm < stepm){
   for(cptcov=1;cptcov<=i1;cptcov++){      printf ("Problem %d lower than %d\n",estepm, stepm);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    }
       k=k+1;    else  hstepm=estepm;   
       fprintf(ficrest,"\n#****** ");    /* For example we decided to compute the life expectancy with the smallest unit */
       for(j=1;j<=cptcovn;j++)    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);       nhstepm is the number of hstepm from age to agelim 
       fprintf(ficrest,"******\n");       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
       fprintf(ficreseij,"\n#****** ");       and note for a fixed period like k years */
       for(j=1;j<=cptcovn;j++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);       survival function given by stepm (the optimization length). Unfortunately it
       fprintf(ficreseij,"******\n");       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 
       fprintf(ficresvij,"\n#****** ");       results. So we changed our mind and took the option of the best precision.
       for(j=1;j<=cptcovn;j++)    */
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       fprintf(ficresvij,"******\n");    agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       oldm=oldms;savm=savms;      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       oldm=oldms;savm=savms;      gp=matrix(0,nhstepm,1,nlstate);
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      gm=matrix(0,nhstepm,1,nlstate);
        
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");  
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);      for(theta=1; theta <=npar; theta++){
       fprintf(ficrest,"\n");        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
                  xp[i] = x[i] + (i==theta ?delti[theta]:0);
       hf=1;        }
       if (stepm >= YEARM) hf=stepm/YEARM;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       epj=vector(1,nlstate+1);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       for(age=bage; age <=fage ;age++){  
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        if (popbased==1) {
         fprintf(ficrest," %.0f",age);          if(mobilav ==0){
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){            for(i=1; i<=nlstate;i++)
           for(i=1, epj[j]=0.;i <=nlstate;i++) {              prlim[i][i]=probs[(int)age][i][ij];
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];          }else{ /* mobilav */ 
           }            for(i=1; i<=nlstate;i++)
           epj[nlstate+1] +=epj[j];              prlim[i][i]=mobaverage[(int)age][i][ij];
         }          }
         for(i=1, vepp=0.;i <=nlstate;i++)        }
           for(j=1;j <=nlstate;j++)    
             vepp += vareij[i][j][(int)age];        for(j=1; j<= nlstate; j++){
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));          for(h=0; h<=nhstepm; h++){
         for(j=1;j <=nlstate;j++){            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
         }          }
         fprintf(ficrest,"\n");        }
       }        /* This for computing probability of death (h=1 means
     }           computed over hstepm matrices product = hstepm*stepm months) 
   }           as a weighted average of prlim.
                */
  fclose(ficreseij);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
  fclose(ficresvij);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
   fclose(ficrest);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   fclose(ficpar);        }    
   free_vector(epj,1,nlstate+1);        /* end probability of death */
   /*scanf("%d ",i); */  
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   /*------- Variance limit prevalence------*/            xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 strcpy(fileresvpl,"vpl");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   strcat(fileresvpl,fileres);   
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        if (popbased==1) {
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          if(mobilav ==0){
     exit(0);            for(i=1; i<=nlstate;i++)
   }              prlim[i][i]=probs[(int)age][i][ij];
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
  k=0;              prlim[i][i]=mobaverage[(int)age][i][ij];
  for(cptcov=1;cptcov<=i1;cptcov++){          }
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        }
      k=k+1;  
      fprintf(ficresvpl,"\n#****** ");        for(j=1; j<= nlstate; j++){
      for(j=1;j<=cptcovn;j++)          for(h=0; h<=nhstepm; h++){
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
      fprintf(ficresvpl,"******\n");              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
                }
      varpl=matrix(1,nlstate,(int) bage, (int) fage);        }
      oldm=oldms;savm=savms;        /* This for computing probability of death (h=1 means
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);           computed over hstepm matrices product = hstepm*stepm months) 
    }           as a weighted average of prlim.
  }        */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
   fclose(ficresvpl);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
   /*---------- End : free ----------------*/        }    
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        /* end probability of death */
    
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        for(j=1; j<= nlstate; j++) /* vareij */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);          for(h=0; h<=nhstepm; h++){
              gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
            }
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);        }
    
   free_matrix(matcov,1,npar,1,npar);      } /* End theta */
   free_vector(delti,1,npar);  
        trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  
       for(h=0; h<=nhstepm; h++) /* veij */
   printf("End of Imach\n");        for(j=1; j<=nlstate;j++)
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          for(theta=1; theta <=npar; theta++)
              trgradg[h][j][theta]=gradg[h][theta][j];
   /* 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);*/      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   /*------ End -----------*/        for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
  end:    
 #ifdef windows  
  chdir(pathcd);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 #endif      for(i=1;i<=nlstate;i++)
  system("wgnuplot graph.plt");        for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
 #ifdef windows  
   while (z[0] != 'q') {      for(h=0;h<=nhstepm;h++){
     chdir(pathcd);        for(k=0;k<=nhstepm;k++){
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
     scanf("%s",z);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
     if (z[0] == 'c') system("./imach");          for(i=1;i<=nlstate;i++)
     else if (z[0] == 'e') {            for(j=1;j<=nlstate;j++)
       chdir(path);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
       system("index.htm");        }
     }      }
     else if (z[0] == 'q') exit(0);    
   }      /* pptj */
 #endif      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
 }      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",fileresprobmorprev);
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",fileresprobmorprev);
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
     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);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
     fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fclose(ficgp);
     fclose(fichtm);
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
      
     fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     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 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       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);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     
     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");
     fprintf(ficresprobcov,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
       fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
       exit(0);
     }
     else{
       fprintf(ficgp,"\n# Routine varprob");
     }
     if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
       fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
       exit(0);
     }
     else{
       fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
       fprintf(fichtm,"\n");
   
       fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
       fprintf(fichtm,"\nWe have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
       fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");
   
     }
   
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)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]:(double)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])/(double)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 period 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 stable (period) */
     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, i1;
     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(probs, 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;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     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;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=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");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;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 +=stepsize) { 
           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*hstepm/YEARM*stepm ==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*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     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(probs, 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);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfile)
   {
     if((fichier=fopen(optionfile,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfile);
       fprintf(ficlog,"Problem with file: %s\n", optionfile);
       return (1);
     }
   
   }
   /***********************************************/
   /**************** 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=100,cptcode, cptcod;
     int jj;
     int numlinepar=0; /* Current linenumber of parameter file */
     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[132],pathc[132],pathcd[132],pathtot[132],model[132];
     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=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     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=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
   
     char *alph[]={"a","a","b","c","d","e"}, str[4];
   
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char *strt, *strtend;
     char *stratrunc;
     int lstra;
   
     long total_usecs;
     struct timeval start_time, end_time, curr_time;
     struct timezone tzp;
     extern int gettimeofday();
     struct tm tmg, tm, *gmtime(), *localtime();
     long time_value;
     extern long time();
    
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strt=asctime(&tm);
   
   /*  printf("Localtime (at start)=%s",strt); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strt);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strt=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strt); 
   */
   
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, 132)!= 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,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%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\n%s",version,fullversion);
     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);
   
     printf("Localtime (at start)=%s",strt);
     fprintf(ficlog,"Localtime (at start)=%s",strt);
     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);
       fflush(ficlog);
       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);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     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);
     numlinepar++;
     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);
     fprintf(ficlog,"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);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     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);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     for(i=1; i <=nlstate; i++){
       j=0;
       for(jj=1; jj <=nlstate+ndeath; jj++){
         if(jj==i) continue;
         j++;
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         if ((i1 != i) && (j1 != j)){
           printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
           exit(1);
         }
         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");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
     }  
     fflush(ficlog);
   
     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);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     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);
         if ((i1-i)*(j1-j)!=0){
           printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
           exit(1);
         }
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i1,j1);
         fprintf(ficlog,"%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]);
           fprintf(ficlog," %le",delti3[i][j][k]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
         fprintf(ficlog,"\n");
       }
     }
     fflush(ficlog);
   
     delti=delti3[1][1];
   
   
     /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     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]);
         fprintf(ficparo," %.5le",matcov[i][j]);
       }
       fscanf(ficpar,"\n");
       numlinepar++;
       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");
   
     fflush(ficlog);
   
     /*-------- 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=lvector(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);
         } 
         lstra=strlen(stra);
         if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
           stratrunc = &(stra[lstra-9]);
           num[i]=atol(stratrunc);
         }
         else
           num[i]=atol(stra);
           
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
           printf("%ld %.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("%ld %.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 (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     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((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld 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((int)mint[m][i]==99 || (int)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("%ld %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);*/
       
     /*------------ 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);
     /*--------- 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 <br> %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\
   <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>\n\
    - Date and time at start: %s</ul>\n",\
             version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt,\
             model,fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strt);
     fclose(fichtm);
   
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);
   
     if(fileappend(fichtm, optionfilehtm)){
       fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
           imx,agemin,agemax,jmin,jmax,jmean);
       fclose(fichtm);
     }
       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) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
     likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
     printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
     for (k=1; k<=npar;k++)
       printf(" %d %8.5f",k,p[k]);
     printf("\n");
     globpr=1; /* to print the contributions */
     likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
     printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
     for (k=1; k<=npar;k++)
       printf(" %d %8.5f",k,p[k]);
     printf("\n");
     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!=0){
       /* 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);*/
   
     printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);
   
     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_lvector(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, bage, fage,k,Tvar,nbcode, ncodemax);
   
     fclose(ficrespij);
   
     probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     /*---------- 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);
         /* (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);
   
     /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
     prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
   ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], 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_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
     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_ma3x(probs,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);
   
     /*  fclose(fichtm);*/
     /*  fclose(ficgp);*/ /* ALready done */
     
   
     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 */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strtend=asctime(&tm);
     printf("Localtime at start %s and at end=%s",strt, strtend); 
     fprintf(ficlog,"Localtime at start %s and at end=%s",strt, strtend); 
     /*  printf("Total time used %d Sec\n", asc_time(end_time.tv_sec -start_time.tv_sec);*/
   
     printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);
     fprintf(ficlog,"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);*/
     if(fileappend(fichtm,optionfilehtm)){
       fprintf(fichtm,"<br>Localtime at start %s and at end=%s<br>",strt, strtend);
       fclose(fichtm);
     }
     /*------ 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 graphs with: %s",plotcmd);fflush(stdout);
     system(plotcmd);
     printf(" Wait...");
   
    /*#ifdef windows*/
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");
       scanf("%s",z);
       if (z[0] == 'c') system("./imach");
       else if (z[0] == 'e') system(optionfilehtm);
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     /*#endif */
   }
   
   

Removed from v.1.3  
changed lines
  Added in v.1.86


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