Diff for /imach/src/imach.c between versions 1.5 and 1.85

version 1.5, 2001/05/02 17:42:45 version 1.85, 2003/06/17 13:12:43
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 1.85  2003/06/17 13:12:43  brouard
   individuals from different ages are interviewed on their health status    * imach.c (Repository): Check when date of death was earlier that
   or degree of  disability. At least a second wave of interviews    current date of interview. It may happen when the death was just
   ("longitudinal") should  measure each new individual health status.    prior to the death. In this case, dh was negative and likelihood
   Health expectancies are computed from the transistions observed between    was wrong (infinity). We still send an "Error" but patch by
   waves and are computed for each degree of severity of disability (number    assuming that the date of death was just one stepm after the
   of life states). More degrees you consider, more time is necessary to    interview.
   reach the Maximum Likelihood of the parameters involved in the model.    (Repository): Because some people have very long ID (first column)
   The simplest model is the multinomial logistic model where pij is    we changed int to long in num[] and we added a new lvector for
   the probabibility to be observed in state j at the second wave conditional    memory allocation. But we also truncated to 8 characters (left
   to be observed in state i at the first wave. Therefore the model is:    truncation)
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    (Repository): No more line truncation errors.
   is a covariate. If you want to have a more complex model than "constant and  
   age", you should modify the program where the markup    Revision 1.84  2003/06/13 21:44:43  brouard
     *Covariates have to be included here again* invites you to do it.    * imach.c (Repository): Replace "freqsummary" at a correct
   More covariates you add, less is the speed of the convergence.    place. It differs from routine "prevalence" which may be called
     many times. Probs is memory consuming and must be used with
   The advantage that this computer programme claims, comes from that if the    parcimony.
   delay between waves is not identical for each individual, or if some    Version 0.95a2 (should output exactly the same maximization than 0.8a2)
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    Revision 1.83  2003/06/10 13:39:11  lievre
   hPijx is the probability to be    *** empty log message ***
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Revision 1.82  2003/06/05 15:57:20  brouard
   unobserved intermediate  states. This elementary transition (by month or    Add log in  imach.c and  fullversion number is now printed.
   quarter trimester, semester or year) is model as a multinomial logistic.  
   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.  /*
      Interpolated Markov Chain
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Short summary of the programme:
      
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    This program computes Healthy Life Expectancies from
            Institut national d'études démographiques, Paris.    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   This software have been partly granted by Euro-REVES, a concerted action    first survey ("cross") where individuals from different ages are
   from the European Union.    interviewed on their health status or degree of disability (in the
   It is copyrighted identically to a GNU software product, ie programme and    case of a health survey which is our main interest) -2- at least a
   software can be distributed freely for non commercial use. Latest version    second wave of interviews ("longitudinal") which measure each change
   can be accessed at http://euroreves.ined.fr/imach .    (if any) in individual health status.  Health expectancies are
   **********************************************************************/    computed from the time spent in each health state according to a
      model. More health states you consider, more time is necessary to reach the
 #include <math.h>    Maximum Likelihood of the parameters involved in the model.  The
 #include <stdio.h>    simplest model is the multinomial logistic model where pij is the
 #include <stdlib.h>    probability to be observed in state j at the second wave
 #include <unistd.h>    conditional to be observed in state i at the first wave. Therefore
     the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 #define MAXLINE 256    'age' is age and 'sex' is a covariate. If you want to have a more
 #define FILENAMELENGTH 80    complex model than "constant and age", you should modify the program
 /*#define DEBUG*/    where the markup *Covariates have to be included here again* invites
 #define windows    you to do it.  More covariates you add, slower the
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    convergence.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     The advantage of this computer programme, compared to a simple
     multinomial logistic model, is clear when the delay between waves is not
     identical for each individual. Also, if a individual missed an
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    intermediate interview, the information is lost, but taken into
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    account using an interpolation or extrapolation.  
   
 #define NINTERVMAX 8    hPijx is the probability to be observed in state i at age x+h
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    conditional to the observed state i at age x. The delay 'h' can be
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    split into an exact number (nh*stepm) of unobserved intermediate
 #define NCOVMAX 8 /* Maximum number of covariates */    states. This elementary transition (by month, quarter,
 #define MAXN 20000    semester or year) is modelled as a multinomial logistic.  The hPx
 #define YEARM 12. /* Number of months per year */    matrix is simply the matrix product of nh*stepm elementary matrices
 #define AGESUP 130    and the contribution of each individual to the likelihood is simply
 #define AGEBASE 40    hPijx.
   
     Also this programme outputs the covariance matrix of the parameters but also
 int nvar;    of the life expectancies. It also computes the stable prevalence. 
 static int cptcov;    
 int cptcovn;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 int npar=NPARMAX;             Institut national d'études démographiques, Paris.
 int nlstate=2; /* Number of live states */    This software have been partly granted by Euro-REVES, a concerted action
 int ndeath=1; /* Number of dead states */    from the European Union.
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
 int *wav; /* Number of waves for this individuual 0 is possible */    can be accessed at http://euroreves.ined.fr/imach .
 int maxwav; /* Maxim number of waves */  
 int mle, weightopt;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    
 double **oldm, **newm, **savm; /* Working pointers to matrices */    **********************************************************************/
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  /*
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    main
 FILE *ficgp, *fichtm;    read parameterfile
 FILE *ficreseij;    read datafile
   char filerese[FILENAMELENGTH];    concatwav
  FILE  *ficresvij;    freqsummary
   char fileresv[FILENAMELENGTH];    if (mle >= 1)
  FILE  *ficresvpl;      mlikeli
   char fileresvpl[FILENAMELENGTH];    print results files
     if mle==1 
        computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
         begin-prev-date,...
 #define NR_END 1    open gnuplot file
 #define FREE_ARG char*    open html file
 #define FTOL 1.0e-10    stable prevalence
      for age prevalim()
 #define NRANSI    h Pij x
 #define ITMAX 200    variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
 #define TOL 2.0e-4    health expectancies
     Variance-covariance of DFLE
 #define CGOLD 0.3819660    prevalence()
 #define ZEPS 1.0e-10     movingaverage()
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    varevsij() 
     if popbased==1 varevsij(,popbased)
 #define GOLD 1.618034    total life expectancies
 #define GLIMIT 100.0    Variance of stable prevalence
 #define TINY 1.0e-20   end
   */
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
     
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  #include <math.h>
 #define rint(a) floor(a+0.5)  #include <stdio.h>
   #include <stdlib.h>
 static double sqrarg;  #include <unistd.h>
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  #define MAXLINE 256
   #define GNUPLOTPROGRAM "gnuplot"
 int imx;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 int stepm;  #define FILENAMELENGTH 132
 /* Stepm, step in month: minimum step interpolation*/  /*#define DEBUG*/
   /*#define windows*/
 int m,nb;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 double *weight;  
 int **s; /* Status */  #define NINTERVMAX 8
 double *agedc, **covar, idx;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 int **nbcode, *Tcode, *Tvar, **codtab;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   #define NCOVMAX 8 /* Maximum number of covariates */
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  #define MAXN 20000
 double ftolhess; /* Tolerance for computing hessian */  #define YEARM 12. /* Number of months per year */
   #define AGESUP 130
   #define AGEBASE 40
 static  int split( char *path, char *dirc, char *name )  #ifdef unix
 {  #define DIRSEPARATOR '/'
    char *s;                             /* pointer */  #define ODIRSEPARATOR '\\'
    int  l1, l2;                         /* length counters */  #else
   #define DIRSEPARATOR '\\'
    l1 = strlen( path );                 /* length of path */  #define ODIRSEPARATOR '/'
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  #endif
    s = strrchr( path, '\\' );           /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */  /* $Id$ */
 #if     defined(__bsd__)                /* get current working directory */  /* $State$ */
       extern char       *getwd( );  
   char version[]="Imach version 0.95a2, June 2003, INED-EUROREVES ";
       if ( getwd( dirc ) == NULL ) {  char fullversion[]="$Revision$ $Date$"; 
 #else  int erreur; /* Error number */
       extern char       *getcwd( );  int nvar;
   int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  int npar=NPARMAX;
 #endif  int nlstate=2; /* Number of live states */
          return( GLOCK_ERROR_GETCWD );  int ndeath=1; /* Number of dead states */
       }  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       strcpy( name, path );             /* we've got it */  int popbased=0;
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */  int *wav; /* Number of waves for this individuual 0 is possible */
       l2 = strlen( s );                 /* length of filename */  int maxwav; /* Maxim number of waves */
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );  int jmin, jmax; /* min, max spacing between 2 waves */
       strcpy( name, s );                /* save file name */  int mle, weightopt;
       strncpy( dirc, path, l1 - l2 );   /* now the directory */  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       dirc[l1-l2] = 0;                  /* add zero */  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
    }  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
    l1 = strlen( dirc );                 /* length of directory */             * wave mi and wave mi+1 is not an exact multiple of stepm. */
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  double jmean; /* Mean space between 2 waves */
    return( 0 );                         /* we're done */  double **oldm, **newm, **savm; /* Working pointers to matrices */
 }  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   FILE *ficlog, *ficrespow;
 /******************************************/  int globpr; /* Global variable for printing or not */
   double fretone; /* Only one call to likelihood */
 void replace(char *s, char*t)  long ipmx; /* Number of contributions */
 {  double sw; /* Sum of weights */
   int i;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   int lg=20;  FILE *ficresilk;
   i=0;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   lg=strlen(t);  FILE *ficresprobmorprev;
   for(i=0; i<= lg; i++) {  FILE *fichtm; /* Html File */
     (s[i] = t[i]);  FILE *ficreseij;
     if (t[i]== '\\') s[i]='/';  char filerese[FILENAMELENGTH];
   }  FILE  *ficresvij;
 }  char fileresv[FILENAMELENGTH];
   FILE  *ficresvpl;
 int nbocc(char *s, char occ)  char fileresvpl[FILENAMELENGTH];
 {  char title[MAXLINE];
   int i,j=0;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   int lg=20;  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   i=0;  
   lg=strlen(s);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   for(i=0; i<= lg; i++) {  char filelog[FILENAMELENGTH]; /* Log file */
   if  (s[i] == occ ) j++;  char filerest[FILENAMELENGTH];
   }  char fileregp[FILENAMELENGTH];
   return j;  char popfile[FILENAMELENGTH];
 }  
   char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
 void cutv(char *u,char *v, char*t, char occ)  
 {  #define NR_END 1
   int i,lg,j,p;  #define FREE_ARG char*
   i=0;  #define FTOL 1.0e-10
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  #define NRANSI 
   }  #define ITMAX 200 
   
   lg=strlen(t);  #define TOL 2.0e-4 
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);  #define CGOLD 0.3819660 
     u[p]='\0';  #define ZEPS 1.0e-10 
   }  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   
    for(j=0; j<= lg; j++) {  #define GOLD 1.618034 
     if (j>=(p+1))(v[j-p-1] = t[j]);  #define GLIMIT 100.0 
   }  #define TINY 1.0e-20 
 }  
   static double maxarg1,maxarg2;
 /********************** nrerror ********************/  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 void nrerror(char error_text[])    
 {  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   fprintf(stderr,"ERREUR ...\n");  #define rint(a) floor(a+0.5)
   fprintf(stderr,"%s\n",error_text);  
   exit(1);  static double sqrarg;
 }  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 /*********************** vector *******************/  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 double *vector(int nl, int nh)  
 {  int imx; 
   double *v;  int stepm;
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  /* Stepm, step in month: minimum step interpolation*/
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;  int estepm;
 }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
 /************************ free vector ******************/  int m,nb;
 void free_vector(double*v, int nl, int nh)  long *num;
 {  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
   free((FREE_ARG)(v+nl-NR_END));  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
 }  double **pmmij, ***probs;
   double dateintmean=0;
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)  double *weight;
 {  int **s; /* Status */
   int *v;  double *agedc, **covar, idx;
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   if (!v) nrerror("allocation failure in ivector");  
   return v-nl+NR_END;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 }  double ftolhess; /* Tolerance for computing hessian */
   
 /******************free ivector **************************/  /**************** split *************************/
 void free_ivector(int *v, long nl, long nh)  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 {  {
   free((FREE_ARG)(v+nl-NR_END));    char  *ss;                            /* pointer */
 }    int   l1, l2;                         /* length counters */
   
 /******************* imatrix *******************************/    l1 = strlen(path );                   /* length of path */
 int **imatrix(long nrl, long nrh, long ncl, long nch)    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 {    if ( ss == NULL ) {                   /* no directory, so use current */
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   int **m;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
        /* get current working directory */
   /* allocate pointers to rows */      /*    extern  char* getcwd ( char *buf , int len);*/
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   if (!m) nrerror("allocation failure 1 in matrix()");        return( GLOCK_ERROR_GETCWD );
   m += NR_END;      }
   m -= nrl;      strcpy( name, path );               /* we've got it */
      } else {                              /* strip direcotry from path */
        ss++;                               /* after this, the filename */
   /* allocate rows and set pointers to them */      l2 = strlen( ss );                  /* length of filename */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");      strcpy( name, ss );         /* save file name */
   m[nrl] += NR_END;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   m[nrl] -= ncl;      dirc[l1-l2] = 0;                    /* add zero */
      }
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    l1 = strlen( dirc );                  /* length of directory */
      /*#ifdef windows
   /* return pointer to array of pointers to rows */    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   return m;  #else
 }    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   #endif
 /****************** free_imatrix *************************/    */
 void free_imatrix(m,nrl,nrh,ncl,nch)    ss = strrchr( name, '.' );            /* find last / */
       int **m;    ss++;
       long nch,ncl,nrh,nrl;    strcpy(ext,ss);                       /* save extension */
      /* free an int matrix allocated by imatrix() */    l1= strlen( name);
 {    l2= strlen(ss)+1;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    strncpy( finame, name, l1-l2);
   free((FREE_ARG) (m+nrl-NR_END));    finame[l1-l2]= 0;
 }    return( 0 );                          /* we're done */
   }
 /******************* matrix *******************************/  
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {  /******************************************/
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  
   double **m;  void replace(char *s, char*t)
   {
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    int i;
   if (!m) nrerror("allocation failure 1 in matrix()");    int lg=20;
   m += NR_END;    i=0;
   m -= nrl;    lg=strlen(t);
     for(i=0; i<= lg; i++) {
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));      (s[i] = t[i]);
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");      if (t[i]== '\\') s[i]='/';
   m[nrl] += NR_END;    }
   m[nrl] -= ncl;  }
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  int nbocc(char *s, char occ)
   return m;  {
 }    int i,j=0;
     int lg=20;
 /*************************free matrix ************************/    i=0;
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    lg=strlen(s);
 {    for(i=0; i<= lg; i++) {
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    if  (s[i] == occ ) j++;
   free((FREE_ARG)(m+nrl-NR_END));    }
 }    return j;
   }
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  void cutv(char *u,char *v, char*t, char occ)
 {  {
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    /* cuts string t into u and v where u is ended by char occ excluding it
   double ***m;       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
        gives u="abcedf" and v="ghi2j" */
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    int i,lg,j,p=0;
   if (!m) nrerror("allocation failure 1 in matrix()");    i=0;
   m += NR_END;    for(j=0; j<=strlen(t)-1; j++) {
   m -= nrl;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     }
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    lg=strlen(t);
   m[nrl] += NR_END;    for(j=0; j<p; j++) {
   m[nrl] -= ncl;      (u[j] = t[j]);
     }
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;       u[p]='\0';
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));     for(j=0; j<= lg; j++) {
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");      if (j>=(p+1))(v[j-p-1] = t[j]);
   m[nrl][ncl] += NR_END;    }
   m[nrl][ncl] -= nll;  }
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  /********************** nrerror ********************/
    
   for (i=nrl+1; i<=nrh; i++) {  void nrerror(char error_text[])
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  {
     for (j=ncl+1; j<=nch; j++)    fprintf(stderr,"ERREUR ...\n");
       m[i][j]=m[i][j-1]+nlay;    fprintf(stderr,"%s\n",error_text);
   }    exit(EXIT_FAILURE);
   return m;  }
 }  /*********************** vector *******************/
   double *vector(int nl, int nh)
 /*************************free ma3x ************************/  {
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    double *v;
 {    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    if (!v) nrerror("allocation failure in vector");
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    return v-nl+NR_END;
   free((FREE_ARG)(m+nrl-NR_END));  }
 }  
   /************************ free vector ******************/
 /***************** f1dim *************************/  void free_vector(double*v, int nl, int nh)
 extern int ncom;  {
 extern double *pcom,*xicom;    free((FREE_ARG)(v+nl-NR_END));
 extern double (*nrfunc)(double []);  }
    
 double f1dim(double x)  /************************ivector *******************************/
 {  int *ivector(long nl,long nh)
   int j;  {
   double f;    int *v;
   double *xt;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
      if (!v) nrerror("allocation failure in ivector");
   xt=vector(1,ncom);    return v-nl+NR_END;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  }
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  /******************free ivector **************************/
   return f;  void free_ivector(int *v, long nl, long nh)
 }  {
     free((FREE_ARG)(v+nl-NR_END));
 /*****************brent *************************/  }
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {  /************************lvector *******************************/
   int iter;  long *lvector(long nl,long nh)
   double a,b,d,etemp;  {
   double fu,fv,fw,fx;    long *v;
   double ftemp;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   double p,q,r,tol1,tol2,u,v,w,x,xm;    if (!v) nrerror("allocation failure in ivector");
   double e=0.0;    return v-nl+NR_END;
    }
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  /******************free lvector **************************/
   x=w=v=bx;  void free_lvector(long *v, long nl, long nh)
   fw=fv=fx=(*f)(x);  {
   for (iter=1;iter<=ITMAX;iter++) {    free((FREE_ARG)(v+nl-NR_END));
     xm=0.5*(a+b);  }
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  /******************* imatrix *******************************/
     printf(".");fflush(stdout);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
 #ifdef DEBUG       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  { 
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
 #endif    int **m; 
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    
       *xmin=x;    /* allocate pointers to rows */ 
       return fx;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     ftemp=fu;    m += NR_END; 
     if (fabs(e) > tol1) {    m -= nrl; 
       r=(x-w)*(fx-fv);    
       q=(x-v)*(fx-fw);    
       p=(x-v)*q-(x-w)*r;    /* allocate rows and set pointers to them */ 
       q=2.0*(q-r);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       if (q > 0.0) p = -p;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       q=fabs(q);    m[nrl] += NR_END; 
       etemp=e;    m[nrl] -= ncl; 
       e=d;    
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    
       else {    /* return pointer to array of pointers to rows */ 
         d=p/q;    return m; 
         u=x+d;  } 
         if (u-a < tol2 || b-u < tol2)  
           d=SIGN(tol1,xm-x);  /****************** free_imatrix *************************/
       }  void free_imatrix(m,nrl,nrh,ncl,nch)
     } else {        int **m;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));        long nch,ncl,nrh,nrl; 
     }       /* free an int matrix allocated by imatrix() */ 
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  { 
     fu=(*f)(u);    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     if (fu <= fx) {    free((FREE_ARG) (m+nrl-NR_END)); 
       if (u >= x) a=x; else b=x;  } 
       SHFT(v,w,x,u)  
         SHFT(fv,fw,fx,fu)  /******************* matrix *******************************/
         } else {  double **matrix(long nrl, long nrh, long ncl, long nch)
           if (u < x) a=u; else b=u;  {
           if (fu <= fw || w == x) {    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
             v=w;    double **m;
             w=u;  
             fv=fw;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
             fw=fu;    if (!m) nrerror("allocation failure 1 in matrix()");
           } else if (fu <= fv || v == x || v == w) {    m += NR_END;
             v=u;    m -= nrl;
             fv=fu;  
           }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   }    m[nrl] += NR_END;
   nrerror("Too many iterations in brent");    m[nrl] -= ncl;
   *xmin=x;  
   return fx;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 }    return m;
     /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
 /****************** mnbrak ***********************/     */
   }
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  /*************************free matrix ************************/
 {  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   double ulim,u,r,q, dum;  {
   double fu;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
      free((FREE_ARG)(m+nrl-NR_END));
   *fa=(*func)(*ax);  }
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  /******************* ma3x *******************************/
     SHFT(dum,*ax,*bx,dum)  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       SHFT(dum,*fb,*fa,dum)  {
       }    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   *cx=(*bx)+GOLD*(*bx-*ax);    double ***m;
   *fc=(*func)(*cx);  
   while (*fb > *fc) {    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     r=(*bx-*ax)*(*fb-*fc);    if (!m) nrerror("allocation failure 1 in matrix()");
     q=(*bx-*cx)*(*fb-*fa);    m += NR_END;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    m -= nrl;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if ((*bx-u)*(u-*cx) > 0.0) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       fu=(*func)(u);    m[nrl] += NR_END;
     } else if ((*cx-u)*(u-ulim) > 0.0) {    m[nrl] -= ncl;
       fu=(*func)(u);  
       if (fu < *fc) {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
           }    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    m[nrl][ncl] += NR_END;
       u=ulim;    m[nrl][ncl] -= nll;
       fu=(*func)(u);    for (j=ncl+1; j<=nch; j++) 
     } else {      m[nrl][j]=m[nrl][j-1]+nlay;
       u=(*cx)+GOLD*(*cx-*bx);    
       fu=(*func)(u);    for (i=nrl+1; i<=nrh; i++) {
     }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     SHFT(*ax,*bx,*cx,u)      for (j=ncl+1; j<=nch; j++) 
       SHFT(*fa,*fb,*fc,fu)        m[i][j]=m[i][j-1]+nlay;
       }    }
 }    return m; 
     /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 /*************** linmin ************************/             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     */
 int ncom;  }
 double *pcom,*xicom;  
 double (*nrfunc)(double []);  /*************************free ma3x ************************/
    void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  {
 {    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   double brent(double ax, double bx, double cx,    free((FREE_ARG)(m[nrl]+ncl-NR_END));
                double (*f)(double), double tol, double *xmin);    free((FREE_ARG)(m+nrl-NR_END));
   double f1dim(double x);  }
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  
               double *fc, double (*func)(double));  /***************** f1dim *************************/
   int j;  extern int ncom; 
   double xx,xmin,bx,ax;  extern double *pcom,*xicom;
   double fx,fb,fa;  extern double (*nrfunc)(double []); 
     
   ncom=n;  double f1dim(double x) 
   pcom=vector(1,n);  { 
   xicom=vector(1,n);    int j; 
   nrfunc=func;    double f;
   for (j=1;j<=n;j++) {    double *xt; 
     pcom[j]=p[j];   
     xicom[j]=xi[j];    xt=vector(1,ncom); 
   }    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   ax=0.0;    f=(*nrfunc)(xt); 
   xx=1.0;    free_vector(xt,1,ncom); 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    return f; 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  } 
 #ifdef DEBUG  
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  /*****************brent *************************/
 #endif  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   for (j=1;j<=n;j++) {  { 
     xi[j] *= xmin;    int iter; 
     p[j] += xi[j];    double a,b,d,etemp;
   }    double fu,fv,fw,fx;
   free_vector(xicom,1,n);    double ftemp;
   free_vector(pcom,1,n);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
 }    double e=0.0; 
    
 /*************** powell ************************/    a=(ax < cx ? ax : cx); 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    b=(ax > cx ? ax : cx); 
             double (*func)(double []))    x=w=v=bx; 
 {    fw=fv=fx=(*f)(x); 
   void linmin(double p[], double xi[], int n, double *fret,    for (iter=1;iter<=ITMAX;iter++) { 
               double (*func)(double []));      xm=0.5*(a+b); 
   int i,ibig,j;      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   double del,t,*pt,*ptt,*xit;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   double fp,fptt;      printf(".");fflush(stdout);
   double *xits;      fprintf(ficlog,".");fflush(ficlog);
   pt=vector(1,n);  #ifdef DEBUG
   ptt=vector(1,n);      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   xit=vector(1,n);      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   xits=vector(1,n);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   *fret=(*func)(p);  #endif
   for (j=1;j<=n;j++) pt[j]=p[j];      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for (*iter=1;;++(*iter)) {        *xmin=x; 
     fp=(*fret);        return fx; 
     ibig=0;      } 
     del=0.0;      ftemp=fu;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      if (fabs(e) > tol1) { 
     for (i=1;i<=n;i++)        r=(x-w)*(fx-fv); 
       printf(" %d %.12f",i, p[i]);        q=(x-v)*(fx-fw); 
     printf("\n");        p=(x-v)*q-(x-w)*r; 
     for (i=1;i<=n;i++) {        q=2.0*(q-r); 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];        if (q > 0.0) p = -p; 
       fptt=(*fret);        q=fabs(q); 
 #ifdef DEBUG        etemp=e; 
       printf("fret=%lf \n",*fret);        e=d; 
 #endif        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
       printf("%d",i);fflush(stdout);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       linmin(p,xit,n,fret,func);        else { 
       if (fabs(fptt-(*fret)) > del) {          d=p/q; 
         del=fabs(fptt-(*fret));          u=x+d; 
         ibig=i;          if (u-a < tol2 || b-u < tol2) 
       }            d=SIGN(tol1,xm-x); 
 #ifdef DEBUG        } 
       printf("%d %.12e",i,(*fret));      } else { 
       for (j=1;j<=n;j++) {        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      } 
         printf(" x(%d)=%.12e",j,xit[j]);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       }      fu=(*f)(u); 
       for(j=1;j<=n;j++)      if (fu <= fx) { 
         printf(" p=%.12e",p[j]);        if (u >= x) a=x; else b=x; 
       printf("\n");        SHFT(v,w,x,u) 
 #endif          SHFT(fv,fw,fx,fu) 
     }          } else { 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {            if (u < x) a=u; else b=u; 
 #ifdef DEBUG            if (fu <= fw || w == x) { 
       int k[2],l;              v=w; 
       k[0]=1;              w=u; 
       k[1]=-1;              fv=fw; 
       printf("Max: %.12e",(*func)(p));              fw=fu; 
       for (j=1;j<=n;j++)            } else if (fu <= fv || v == x || v == w) { 
         printf(" %.12e",p[j]);              v=u; 
       printf("\n");              fv=fu; 
       for(l=0;l<=1;l++) {            } 
         for (j=1;j<=n;j++) {          } 
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    } 
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    nrerror("Too many iterations in brent"); 
         }    *xmin=x; 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    return fx; 
       }  } 
 #endif  
   /****************** mnbrak ***********************/
   
       free_vector(xit,1,n);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       free_vector(xits,1,n);              double (*func)(double)) 
       free_vector(ptt,1,n);  { 
       free_vector(pt,1,n);    double ulim,u,r,q, dum;
       return;    double fu; 
     }   
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    *fa=(*func)(*ax); 
     for (j=1;j<=n;j++) {    *fb=(*func)(*bx); 
       ptt[j]=2.0*p[j]-pt[j];    if (*fb > *fa) { 
       xit[j]=p[j]-pt[j];      SHFT(dum,*ax,*bx,dum) 
       pt[j]=p[j];        SHFT(dum,*fb,*fa,dum) 
     }        } 
     fptt=(*func)(ptt);    *cx=(*bx)+GOLD*(*bx-*ax); 
     if (fptt < fp) {    *fc=(*func)(*cx); 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    while (*fb > *fc) { 
       if (t < 0.0) {      r=(*bx-*ax)*(*fb-*fc); 
         linmin(p,xit,n,fret,func);      q=(*bx-*cx)*(*fb-*fa); 
         for (j=1;j<=n;j++) {      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
           xi[j][ibig]=xi[j][n];        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
           xi[j][n]=xit[j];      ulim=(*bx)+GLIMIT*(*cx-*bx); 
         }      if ((*bx-u)*(u-*cx) > 0.0) { 
 #ifdef DEBUG        fu=(*func)(u); 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         for(j=1;j<=n;j++)        fu=(*func)(u); 
           printf(" %.12e",xit[j]);        if (fu < *fc) { 
         printf("\n");          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
 #endif            SHFT(*fb,*fc,fu,(*func)(u)) 
       }            } 
     }      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   }        u=ulim; 
 }        fu=(*func)(u); 
       } else { 
 /**** Prevalence limit ****************/        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      } 
 {      SHFT(*ax,*bx,*cx,u) 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit        SHFT(*fa,*fb,*fc,fu) 
      matrix by transitions matrix until convergence is reached */        } 
   } 
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  /*************** linmin ************************/
   double **matprod2();  
   double **out, cov[NCOVMAX], **pmij();  int ncom; 
   double **newm;  double *pcom,*xicom;
   double agefin, delaymax=50 ; /* Max number of years to converge */  double (*nrfunc)(double []); 
    
   for (ii=1;ii<=nlstate+ndeath;ii++)  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
     for (j=1;j<=nlstate+ndeath;j++){  { 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    double brent(double ax, double bx, double cx, 
     }                 double (*f)(double), double tol, double *xmin); 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    double f1dim(double x); 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     newm=savm;                double *fc, double (*func)(double)); 
     /* Covariates have to be included here again */    int j; 
     cov[1]=1.;    double xx,xmin,bx,ax; 
     cov[2]=agefin;    double fx,fb,fa;
     if (cptcovn>0){   
       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]]);*/}    ncom=n; 
     }    pcom=vector(1,n); 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    xicom=vector(1,n); 
     nrfunc=func; 
     savm=oldm;    for (j=1;j<=n;j++) { 
     oldm=newm;      pcom[j]=p[j]; 
     maxmax=0.;      xicom[j]=xi[j]; 
     for(j=1;j<=nlstate;j++){    } 
       min=1.;    ax=0.0; 
       max=0.;    xx=1.0; 
       for(i=1; i<=nlstate; i++) {    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
         sumnew=0;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  #ifdef DEBUG
         prlim[i][j]= newm[i][j]/(1-sumnew);    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         max=FMAX(max,prlim[i][j]);    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         min=FMIN(min,prlim[i][j]);  #endif
       }    for (j=1;j<=n;j++) { 
       maxmin=max-min;      xi[j] *= xmin; 
       maxmax=FMAX(maxmax,maxmin);      p[j] += xi[j]; 
     }    } 
     if(maxmax < ftolpl){    free_vector(xicom,1,n); 
       return prlim;    free_vector(pcom,1,n); 
     }  } 
   }  
 }  /*************** powell ************************/
   void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
 /*************** transition probabilities **********/              double (*func)(double [])) 
   { 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    void linmin(double p[], double xi[], int n, double *fret, 
 {                double (*func)(double [])); 
   double s1, s2;    int i,ibig,j; 
   /*double t34;*/    double del,t,*pt,*ptt,*xit;
   int i,j,j1, nc, ii, jj;    double fp,fptt;
     double *xits;
     for(i=1; i<= nlstate; i++){    pt=vector(1,n); 
     for(j=1; j<i;j++){    ptt=vector(1,n); 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    xit=vector(1,n); 
         /*s2 += param[i][j][nc]*cov[nc];*/    xits=vector(1,n); 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    *fret=(*func)(p); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    for (j=1;j<=n;j++) pt[j]=p[j]; 
       }    for (*iter=1;;++(*iter)) { 
       ps[i][j]=s2;      fp=(*fret); 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/      ibig=0; 
     }      del=0.0; 
     for(j=i+1; j<=nlstate+ndeath;j++){      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      fprintf(ficrespow,"%d %.12f",*iter,*fret);
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/      for (i=1;i<=n;i++) {
       }        printf(" %d %.12f",i, p[i]);
       ps[i][j]=s2;        fprintf(ficlog," %d %.12lf",i, p[i]);
     }        fprintf(ficrespow," %.12lf", p[i]);
   }      }
   for(i=1; i<= nlstate; i++){      printf("\n");
      s1=0;      fprintf(ficlog,"\n");
     for(j=1; j<i; j++)      fprintf(ficrespow,"\n");
       s1+=exp(ps[i][j]);      for (i=1;i<=n;i++) { 
     for(j=i+1; j<=nlstate+ndeath; j++)        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
       s1+=exp(ps[i][j]);        fptt=(*fret); 
     ps[i][i]=1./(s1+1.);  #ifdef DEBUG
     for(j=1; j<i; j++)        printf("fret=%lf \n",*fret);
       ps[i][j]= exp(ps[i][j])*ps[i][i];        fprintf(ficlog,"fret=%lf \n",*fret);
     for(j=i+1; j<=nlstate+ndeath; j++)  #endif
       ps[i][j]= exp(ps[i][j])*ps[i][i];        printf("%d",i);fflush(stdout);
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */        fprintf(ficlog,"%d",i);fflush(ficlog);
   } /* end i */        linmin(p,xit,n,fret,func); 
         if (fabs(fptt-(*fret)) > del) { 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){          del=fabs(fptt-(*fret)); 
     for(jj=1; jj<= nlstate+ndeath; jj++){          ibig=i; 
       ps[ii][jj]=0;        } 
       ps[ii][ii]=1;  #ifdef DEBUG
     }        printf("%d %.12e",i,(*fret));
   }        fprintf(ficlog,"%d %.12e",i,(*fret));
         for (j=1;j<=n;j++) {
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     for(jj=1; jj<= nlstate+ndeath; jj++){          printf(" x(%d)=%.12e",j,xit[j]);
      printf("%lf ",ps[ii][jj]);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
    }        }
     printf("\n ");        for(j=1;j<=n;j++) {
     }          printf(" p=%.12e",p[j]);
     printf("\n ");printf("%lf ",cov[2]);*/          fprintf(ficlog," p=%.12e",p[j]);
 /*        }
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        printf("\n");
   goto end;*/        fprintf(ficlog,"\n");
     return ps;  #endif
 }      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
 /**************** Product of 2 matrices ******************/  #ifdef DEBUG
         int k[2],l;
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)        k[0]=1;
 {        k[1]=-1;
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        printf("Max: %.12e",(*func)(p));
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */        fprintf(ficlog,"Max: %.12e",(*func)(p));
   /* in, b, out are matrice of pointers which should have been initialized        for (j=1;j<=n;j++) {
      before: only the contents of out is modified. The function returns          printf(" %.12e",p[j]);
      a pointer to pointers identical to out */          fprintf(ficlog," %.12e",p[j]);
   long i, j, k;        }
   for(i=nrl; i<= nrh; i++)        printf("\n");
     for(k=ncolol; k<=ncoloh; k++)        fprintf(ficlog,"\n");
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        for(l=0;l<=1;l++) {
         out[i][k] +=in[i][j]*b[j][k];          for (j=1;j<=n;j++) {
             ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   return out;            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,"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)));
 /************* Higher Matrix Product ***************/          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         }
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  #endif
 {  
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until        free_vector(xit,1,n); 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.        free_vector(xits,1,n); 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        free_vector(ptt,1,n); 
      (typically every 2 years instead of every month which is too big).        free_vector(pt,1,n); 
      Model is determined by parameters x and covariates have to be        return; 
      included manually here.      } 
       if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
      */      for (j=1;j<=n;j++) { 
         ptt[j]=2.0*p[j]-pt[j]; 
   int i, j, d, h, k;        xit[j]=p[j]-pt[j]; 
   double **out, cov[NCOVMAX];        pt[j]=p[j]; 
   double **newm;      } 
       fptt=(*func)(ptt); 
   /* Hstepm could be zero and should return the unit matrix */      if (fptt < fp) { 
   for (i=1;i<=nlstate+ndeath;i++)        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     for (j=1;j<=nlstate+ndeath;j++){        if (t < 0.0) { 
       oldm[i][j]=(i==j ? 1.0 : 0.0);          linmin(p,xit,n,fret,func); 
       po[i][j][0]=(i==j ? 1.0 : 0.0);          for (j=1;j<=n;j++) { 
     }            xi[j][ibig]=xi[j][n]; 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */            xi[j][n]=xit[j]; 
   for(h=1; h <=nhstepm; h++){          }
     for(d=1; d <=hstepm; d++){  #ifdef DEBUG
       newm=savm;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       /* Covariates have to be included here again */          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       cov[1]=1.;          for(j=1;j<=n;j++){
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;            printf(" %.12e",xit[j]);
       if (cptcovn>0){            fprintf(ficlog," %.12e",xit[j]);
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];          }
     }          printf("\n");
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/          fprintf(ficlog,"\n");
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  #endif
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,        }
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      } 
       savm=oldm;    } 
       oldm=newm;  } 
     }  
     for(i=1; i<=nlstate+ndeath; i++)  /**** Prevalence limit (stable prevalence)  ****************/
       for(j=1;j<=nlstate+ndeath;j++) {  
         po[i][j][h]=newm[i][j];  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  {
          */    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       }       matrix by transitions matrix until convergence is reached */
   } /* end h */  
   return po;    int i, ii,j,k;
 }    double min, max, maxmin, maxmax,sumnew=0.;
     double **matprod2();
     double **out, cov[NCOVMAX], **pmij();
 /*************** log-likelihood *************/    double **newm;
 double func( double *x)    double agefin, delaymax=50 ; /* Max number of years to converge */
 {  
   int i, ii, j, k, mi, d;    for (ii=1;ii<=nlstate+ndeath;ii++)
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      for (j=1;j<=nlstate+ndeath;j++){
   double **out;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double sw; /* Sum of weights */      }
   double lli; /* Individual log likelihood */  
   long ipmx;     cov[1]=1.;
   /*extern weight */   
   /* We are differentiating ll according to initial status */   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   /*for(i=1;i<imx;i++)      newm=savm;
 printf(" %d\n",s[4][i]);      /* Covariates have to be included here again */
   */       cov[2]=agefin;
     
   for(k=1; k<=nlstate; k++) ll[k]=0.;        for (k=1; k<=cptcovn;k++) {
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
        for(mi=1; mi<= wav[i]-1; mi++){          /*      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]]);*/
       for (ii=1;ii<=nlstate+ndeath;ii++)        }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
             for(d=0; d<dh[mi][i]; d++){        for (k=1; k<=cptcovprod;k++)
         newm=savm;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           cov[1]=1.;  
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
           if (cptcovn>0){        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
             for (k=1; k<=cptcovn;k++) cov[2+k]=covar[1+k-1][i];        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
             }      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));      savm=oldm;
           savm=oldm;      oldm=newm;
           oldm=newm;      maxmax=0.;
       for(j=1;j<=nlstate;j++){
         min=1.;
       } /* end mult */        max=0.;
            for(i=1; i<=nlstate; i++) {
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);          sumnew=0;
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
       ipmx +=1;          prlim[i][j]= newm[i][j]/(1-sumnew);
       sw += weight[i];          max=FMAX(max,prlim[i][j]);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;          min=FMIN(min,prlim[i][j]);
     } /* end of wave */        }
   } /* end of individual */        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      }
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      if(maxmax < ftolpl){
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */        return prlim;
   return -l;      }
 }    }
   }
   
 /*********** Maximum Likelihood Estimation ***************/  /*************** transition probabilities ***************/ 
   
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
 {  {
   int i,j, iter;    double s1, s2;
   double **xi,*delti;    /*double t34;*/
   double fret;    int i,j,j1, nc, ii, jj;
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)      for(i=1; i<= nlstate; i++){
     for (j=1;j<=npar;j++)      for(j=1; j<i;j++){
       xi[i][j]=(i==j ? 1.0 : 0.0);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   printf("Powell\n");          /*s2 += param[i][j][nc]*cov[nc];*/
   powell(p,xi,npar,ftol,&iter,&fret,func);          s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
           /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));        }
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));        ps[i][j]=s2;
         /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
 }      }
       for(j=i+1; j<=nlstate+ndeath;j++){
 /**** Computes Hessian and covariance matrix ***/        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))          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);*/
   double  **a,**y,*x,pd;        }
   double **hess;        ps[i][j]=s2;
   int i, j,jk;      }
   int *indx;    }
       /*ps[3][2]=1;*/
   double hessii(double p[], double delta, int theta, double delti[]);  
   double hessij(double p[], double delti[], int i, int j);    for(i=1; i<= nlstate; i++){
   void lubksb(double **a, int npar, int *indx, double b[]) ;       s1=0;
   void ludcmp(double **a, int npar, int *indx, double *d) ;      for(j=1; j<i; j++)
         s1+=exp(ps[i][j]);
       for(j=i+1; j<=nlstate+ndeath; j++)
   hess=matrix(1,npar,1,npar);        s1+=exp(ps[i][j]);
       ps[i][i]=1./(s1+1.);
   printf("\nCalculation of the hessian matrix. Wait...\n");      for(j=1; j<i; j++)
   for (i=1;i<=npar;i++){        ps[i][j]= exp(ps[i][j])*ps[i][i];
     printf("%d",i);fflush(stdout);      for(j=i+1; j<=nlstate+ndeath; j++)
     hess[i][i]=hessii(p,ftolhess,i,delti);        ps[i][j]= exp(ps[i][j])*ps[i][i];
     /*printf(" %f ",p[i]);*/      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   }    } /* end i */
   
   for (i=1;i<=npar;i++) {    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     for (j=1;j<=npar;j++)  {      for(jj=1; jj<= nlstate+ndeath; jj++){
       if (j>i) {        ps[ii][jj]=0;
         printf(".%d%d",i,j);fflush(stdout);        ps[ii][ii]=1;
         hess[i][j]=hessij(p,delti,i,j);      }
         hess[j][i]=hess[i][j];    }
       }  
     }  
   }    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
   printf("\n");      for(jj=1; jj<= nlstate+ndeath; jj++){
        printf("%lf ",ps[ii][jj]);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");     }
        printf("\n ");
   a=matrix(1,npar,1,npar);      }
   y=matrix(1,npar,1,npar);      printf("\n ");printf("%lf ",cov[2]);*/
   x=vector(1,npar);  /*
   indx=ivector(1,npar);    for(i=1; i<= npar; i++) printf("%f ",x[i]);
   for (i=1;i<=npar;i++)    goto end;*/
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      return ps;
   ludcmp(a,npar,indx,&pd);  }
   
   for (j=1;j<=npar;j++) {  /**************** Product of 2 matrices ******************/
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
     lubksb(a,npar,indx,x);  {
     for (i=1;i<=npar;i++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       matcov[i][j]=x[i];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     }    /* in, b, out are matrice of pointers which should have been initialized 
   }       before: only the contents of out is modified. The function returns
        a pointer to pointers identical to out */
   printf("\n#Hessian matrix#\n");    long i, j, k;
   for (i=1;i<=npar;i++) {    for(i=nrl; i<= nrh; i++)
     for (j=1;j<=npar;j++) {      for(k=ncolol; k<=ncoloh; k++)
       printf("%.3e ",hess[i][j]);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     }          out[i][k] +=in[i][j]*b[j][k];
     printf("\n");  
   }    return out;
   }
   /* Recompute Inverse */  
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  /************* Higher Matrix Product ***************/
   ludcmp(a,npar,indx,&pd);  
   double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   /*  printf("\n#Hessian matrix recomputed#\n");  {
     /* Computes the transition matrix starting at age 'age' over 
   for (j=1;j<=npar;j++) {       'nhstepm*hstepm*stepm' months (i.e. until
     for (i=1;i<=npar;i++) x[i]=0;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     x[j]=1;       nhstepm*hstepm matrices. 
     lubksb(a,npar,indx,x);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     for (i=1;i<=npar;i++){       (typically every 2 years instead of every month which is too big 
       y[i][j]=x[i];       for the memory).
       printf("%.3e ",y[i][j]);       Model is determined by parameters x and covariates have to be 
     }       included manually here. 
     printf("\n");  
   }       */
   */  
     int i, j, d, h, k;
   free_matrix(a,1,npar,1,npar);    double **out, cov[NCOVMAX];
   free_matrix(y,1,npar,1,npar);    double **newm;
   free_vector(x,1,npar);  
   free_ivector(indx,1,npar);    /* Hstepm could be zero and should return the unit matrix */
   free_matrix(hess,1,npar,1,npar);    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
 }        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }
 /*************** hessian matrix ****************/    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
 double hessii( double x[], double delta, int theta, double delti[])    for(h=1; h <=nhstepm; h++){
 {      for(d=1; d <=hstepm; d++){
   int i;        newm=savm;
   int l=1, lmax=20;        /* Covariates have to be included here again */
   double k1,k2;        cov[1]=1.;
   double p2[NPARMAX+1];        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   double res;        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        for (k=1; k<=cptcovage;k++)
   double fx;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   int k=0,kmax=10;        for (k=1; k<=cptcovprod;k++)
   double l1;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
   fx=func(x);  
   for (i=1;i<=npar;i++) p2[i]=x[i];        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   for(l=0 ; l <=lmax; l++){        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
     l1=pow(10,l);        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     delts=delt;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(k=1 ; k <kmax; k=k+1){        savm=oldm;
       delt = delta*(l1*k);        oldm=newm;
       p2[theta]=x[theta] +delt;      }
       k1=func(p2)-fx;      for(i=1; i<=nlstate+ndeath; i++)
       p2[theta]=x[theta]-delt;        for(j=1;j<=nlstate+ndeath;j++) {
       k2=func(p2)-fx;          po[i][j][h]=newm[i][j];
       /*res= (k1-2.0*fx+k2)/delt/delt; */          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */           */
              }
 #ifdef DEBUG    } /* end h */
       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);    return po;
 #endif  }
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  
         k=kmax;  /*************** log-likelihood *************/
       }  double func( double *x)
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  {
         k=kmax; l=lmax*10.;    int i, ii, j, k, mi, d, kk;
       }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    double **out;
         delts=delt;    double sw; /* Sum of weights */
       }    double lli; /* Individual log likelihood */
     }    int s1, s2;
   }    double bbh, survp;
   delti[theta]=delts;    long ipmx;
   return res;    /*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++) 
 double hessij( double x[], double delti[], int thetai,int thetaj)      printf(" %d\n",s[4][i]);
 {    */
   int i;    cov[1]=1.;
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   double p2[NPARMAX+1];  
   int k;    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   fx=func(x);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   for (k=1; k<=2; k++) {        for(mi=1; mi<= wav[i]-1; mi++){
     for (i=1;i<=npar;i++) p2[i]=x[i];          for (ii=1;ii<=nlstate+ndeath;ii++)
     p2[thetai]=x[thetai]+delti[thetai]/k;            for (j=1;j<=nlstate+ndeath;j++){
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     k1=func(p2)-fx;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
     p2[thetai]=x[thetai]+delti[thetai]/k;          for(d=0; d<dh[mi][i]; d++){
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            newm=savm;
     k2=func(p2)-fx;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
     p2[thetai]=x[thetai]-delti[thetai]/k;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;            }
     k3=func(p2)-fx;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     p2[thetai]=x[thetai]-delti[thetai]/k;            savm=oldm;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            oldm=newm;
     k4=func(p2)-fx;          } /* end mult */
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        
 #ifdef DEBUG          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     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);          /* But now since version 0.9 we anticipate for bias and large stepm.
 #endif           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   }           * (in months) between two waves is not a multiple of stepm, we rounded to 
   return res;           * 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
 /************** Inverse of matrix **************/           * probability in order to take into account the bias as a fraction of the way
 void ludcmp(double **a, int n, int *indx, double *d)           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
 {           * -stepm/2 to stepm/2 .
   int i,imax,j,k;           * For stepm=1 the results are the same as for previous versions of Imach.
   double big,dum,sum,temp;           * For stepm > 1 the results are less biased than in previous versions. 
   double *vv;           */
            s1=s[mw[mi][i]][i];
   vv=vector(1,n);          s2=s[mw[mi+1][i]][i];
   *d=1.0;          bbh=(double)bh[mi][i]/(double)stepm; 
   for (i=1;i<=n;i++) {          /* bias is positive if real duration
     big=0.0;           * is higher than the multiple of stepm and negative otherwise.
     for (j=1;j<=n;j++)           */
       if ((temp=fabs(a[i][j])) > big) big=temp;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          if( s2 > nlstate){ 
     vv[i]=1.0/big;            /* i.e. if s2 is a death state and if the date of death is known then the contribution
   }               to the likelihood is the probability to die between last step unit time and current 
   for (j=1;j<=n;j++) {               step unit time, which is also the differences between probability to die before dh 
     for (i=1;i<j;i++) {               and probability to die before dh-stepm . 
       sum=a[i][j];               In version up to 0.92 likelihood was computed
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          as if date of death was unknown. Death was treated as any other
       a[i][j]=sum;          health state: the date of the interview describes the actual state
     }          and not the date of a change in health state. The former idea was
     big=0.0;          to consider that at each interview the state was recorded
     for (i=j;i<=n;i++) {          (healthy, disable or death) and IMaCh was corrected; but when we
       sum=a[i][j];          introduced the exact date of death then we should have modified
       for (k=1;k<j;k++)          the contribution of an exact death to the likelihood. This new
         sum -= a[i][k]*a[k][j];          contribution is smaller and very dependent of the step unit
       a[i][j]=sum;          stepm. It is no more the probability to die between last interview
       if ( (dum=vv[i]*fabs(sum)) >= big) {          and month of death but the probability to survive from last
         big=dum;          interview up to one month before death multiplied by the
         imax=i;          probability to die within a month. Thanks to Chris
       }          Jackson for correcting this bug.  Former versions increased
     }          mortality artificially. The bad side is that we add another loop
     if (j != imax) {          which slows down the processing. The difference can be up to 10%
       for (k=1;k<=n;k++) {          lower mortality.
         dum=a[imax][k];            */
         a[imax][k]=a[j][k];            lli=log(out[s1][s2] - savm[s1][s2]);
         a[j][k]=dum;          }else{
       }            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       *d = -(*d);            /*  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 */
       vv[imax]=vv[j];          } 
     }          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     indx[j]=imax;          /*if(lli ==000.0)*/
     if (a[j][j] == 0.0) a[j][j]=TINY;          /*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); */
     if (j != n) {          ipmx +=1;
       dum=1.0/(a[j][j]);          sw += weight[i];
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        } /* end of wave */
   }      } /* end of individual */
   free_vector(vv,1,n);  /* Doesn't work */    }  else if(mle==2){
 ;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
 void lubksb(double **a, int n, int *indx, double b[])          for (ii=1;ii<=nlstate+ndeath;ii++)
 {            for (j=1;j<=nlstate+ndeath;j++){
   int i,ii=0,ip,j;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double sum;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
   for (i=1;i<=n;i++) {          for(d=0; d<=dh[mi][i]; d++){
     ip=indx[i];            newm=savm;
     sum=b[ip];            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     b[ip]=b[i];            for (kk=1; kk<=cptcovage;kk++) {
     if (ii)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];            }
     else if (sum) ii=i;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     b[i]=sum;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   }            savm=oldm;
   for (i=n;i>=1;i--) {            oldm=newm;
     sum=b[i];          } /* end mult */
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        
     b[i]=sum/a[i][i];          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   }          /* But now since version 0.9 we anticipate for bias and large stepm.
 }           * If stepm is larger than one month (smallest stepm) and if the exact delay 
            * (in months) between two waves is not a multiple of stepm, we rounded to 
 /************ Frequencies ********************/           * the nearest (and in case of equal distance, to the lowest) interval but now
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
 {  /* Some frequencies */           * (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
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
   double ***freq; /* Frequencies */           * -stepm/2 to stepm/2 .
   double *pp;           * For stepm=1 the results are the same as for previous versions of Imach.
   double pos;           * For stepm > 1 the results are less biased than in previous versions. 
   FILE *ficresp;           */
   char fileresp[FILENAMELENGTH];          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   pp=vector(1,nlstate);          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias is positive if real duration
   strcpy(fileresp,"p");           * is higher than the multiple of stepm and negative otherwise.
   strcat(fileresp,fileres);           */
   if((ficresp=fopen(fileresp,"w"))==NULL) {          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 */
     printf("Problem with prevalence resultfile: %s\n", fileresp);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     exit(0);          /*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 */
   }          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          /*if(lli ==000.0)*/
   j1=0;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
           ipmx +=1;
   j=cptcovn;          sw += weight[i];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
   for(k1=1; k1<=j;k1++){      } /* end of individual */
    for(i1=1; i1<=ncodemax[k1];i1++){    }  else if(mle==3){  /* exponential inter-extrapolation */
        j1++;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for (i=-1; i<=nlstate+ndeath; i++)          for(mi=1; mi<= wav[i]-1; mi++){
          for (jk=-1; jk<=nlstate+ndeath; jk++)            for (ii=1;ii<=nlstate+ndeath;ii++)
            for(m=agemin; m <= agemax+3; m++)            for (j=1;j<=nlstate+ndeath;j++){
              freq[i][jk][m]=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                      savm[ii][j]=(ii==j ? 1.0 : 0.0);
        for (i=1; i<=imx; i++) {            }
          bool=1;          for(d=0; d<dh[mi][i]; d++){
          if  (cptcovn>0) {            newm=savm;
            for (z1=1; z1<=cptcovn; z1++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;            for (kk=1; kk<=cptcovage;kk++) {
          }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           if (bool==1) {            }
            for(m=firstpass; m<=lastpass-1; m++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
              if(agev[m][i]==0) agev[m][i]=agemax+1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
              if(agev[m][i]==1) agev[m][i]=agemax+2;            savm=oldm;
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];            oldm=newm;
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          } /* end mult */
            }        
          }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
        }          /* But now since version 0.9 we anticipate for bias and large stepm.
         if  (cptcovn>0) {           * If stepm is larger than one month (smallest stepm) and if the exact delay 
          fprintf(ficresp, "\n#Variable");           * (in months) between two waves is not a multiple of stepm, we rounded to 
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);           * 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
        fprintf(ficresp, "\n#");           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
        for(i=1; i<=nlstate;i++)           * probability in order to take into account the bias as a fraction of the way
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
        fprintf(ficresp, "\n");           * -stepm/2 to stepm/2 .
                   * For stepm=1 the results are the same as for previous versions of Imach.
   for(i=(int)agemin; i <= (int)agemax+3; i++){           * For stepm > 1 the results are less biased than in previous versions. 
     if(i==(int)agemax+3)           */
       printf("Total");          s1=s[mw[mi][i]][i];
     else          s2=s[mw[mi+1][i]][i];
       printf("Age %d", i);          bbh=(double)bh[mi][i]/(double)stepm; 
     for(jk=1; jk <=nlstate ; jk++){          /* bias is positive if real duration
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)           * is higher than the multiple of stepm and negative otherwise.
         pp[jk] += freq[jk][m][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])); /* exponential inter-extrapolation */
       for(m=-1, pos=0; m <=0 ; m++)          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         pos += freq[jk][m][i];          /*if(lli ==000.0)*/
       if(pp[jk]>=1.e-10)          /*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); */
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          ipmx +=1;
       else          sw += weight[i];
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        } /* end of wave */
     for(jk=1; jk <=nlstate ; jk++){      } /* end of individual */
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)    }else if (mle==4){  /* ml=4 no inter-extrapolation */
         pp[jk] += freq[jk][m][i];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     for(jk=1,pos=0; jk <=nlstate ; jk++)        for(mi=1; mi<= wav[i]-1; mi++){
       pos += pp[jk];          for (ii=1;ii<=nlstate+ndeath;ii++)
     for(jk=1; jk <=nlstate ; jk++){            for (j=1;j<=nlstate+ndeath;j++){
       if(pos>=1.e-5)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       else            }
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          for(d=0; d<dh[mi][i]; d++){
       if( i <= (int) agemax){            newm=savm;
         if(pos>=1.e-5)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);            for (kk=1; kk<=cptcovage;kk++) {
       else              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);            }
       }          
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(jk=-1; jk <=nlstate+ndeath; jk++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(m=-1; m <=nlstate+ndeath; m++)            savm=oldm;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);            oldm=newm;
     if(i <= (int) agemax)          } /* end mult */
       fprintf(ficresp,"\n");        
     printf("\n");          s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
     }          if( s2 > nlstate){ 
  }            lli=log(out[s1][s2] - savm[s1][s2]);
            }else{
   fclose(ficresp);            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          }
   free_vector(pp,1,nlstate);          ipmx +=1;
           sw += weight[i];
 }  /* End of Freq */          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]); */
 /************* Waves Concatenation ***************/        } /* end of wave */
       } /* end of individual */
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
 {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      Death is a valid wave (if date is known).        for(mi=1; mi<= wav[i]-1; mi++){
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          for (ii=1;ii<=nlstate+ndeath;ii++)
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]            for (j=1;j<=nlstate+ndeath;j++){
      and mw[mi+1][i]. dh depends on stepm.              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
   int i, mi, m;          for(d=0; d<dh[mi][i]; d++){
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;            newm=savm;
 float sum=0.;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
   for(i=1; i<=imx; i++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     mi=0;            }
     m=firstpass;          
     while(s[m][i] <= nlstate){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       if(s[m][i]>=1)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         mw[++mi][i]=m;            savm=oldm;
       if(m >=lastpass)            oldm=newm;
         break;          } /* end mult */
       else        
         m++;          s1=s[mw[mi][i]][i];
     }/* end while */          s2=s[mw[mi+1][i]][i];
     if (s[m][i] > nlstate){          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       mi++;     /* Death is another wave */          ipmx +=1;
       /* if(mi==0)  never been interviewed correctly before death */          sw += weight[i];
          /* Only death is a correct wave */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       mw[mi][i]=m;          /*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]);*/
     }        } /* end of wave */
       } /* end of individual */
     wav[i]=mi;    } /* End of if */
     if(mi==0)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     return -l;
   for(i=1; i<=imx; i++){  }
     for(mi=1; mi<wav[i];mi++){  
       if (stepm <=0)  /*************** log-likelihood *************/
         dh[mi][i]=1;  double funcone( double *x)
       else{  {
         if (s[mw[mi+1][i]][i] > nlstate) {    int i, ii, j, k, mi, d, kk;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
           if(j=0) j=1;  /* Survives at least one month after exam */    double **out;
         }    double lli; /* Individual log likelihood */
         else{    int s1, s2;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    double bbh, survp;
           k=k+1;    /*extern weight */
           if (j >= jmax) jmax=j;    /* We are differentiating ll according to initial status */
           else if (j <= jmin)jmin=j;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
           sum=sum+j;    /*for(i=1;i<imx;i++) 
         }      printf(" %d\n",s[4][i]);
         jk= j/stepm;    */
         jl= j -jk*stepm;    cov[1]=1.;
         ju= j -(jk+1)*stepm;  
         if(jl <= -ju)    for(k=1; k<=nlstate; k++) ll[k]=0.;
           dh[mi][i]=jk;  
         else    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           dh[mi][i]=jk+1;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         if(dh[mi][i]==0)      for(mi=1; mi<= wav[i]-1; mi++){
           dh[mi][i]=1; /* At least one step */        for (ii=1;ii<=nlstate+ndeath;ii++)
       }          for (j=1;j<=nlstate+ndeath;j++){
     }            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   }            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);          }
 }        for(d=0; d<dh[mi][i]; d++){
 /*********** Tricode ****************************/          newm=savm;
 void tricode(int *Tvar, int **nbcode, int imx)          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 {          for (kk=1; kk<=cptcovage;kk++) {
   int Ndum[80],ij, k, j, i;            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int cptcode=0;          }
   for (k=0; k<79; k++) Ndum[k]=0;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for (k=1; k<=7; k++) ncodemax[k]=0;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
            savm=oldm;
   for (j=1; j<=cptcovn; j++) {          oldm=newm;
     for (i=1; i<=imx; i++) {        } /* end mult */
       ij=(int)(covar[Tvar[j]][i]);        
       Ndum[ij]++;        s1=s[mw[mi][i]][i];
       if (ij > cptcode) cptcode=ij;        s2=s[mw[mi+1][i]][i];
     }        bbh=(double)bh[mi][i]/(double)stepm; 
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/        /* bias is positive if real duration
     for (i=0; i<=cptcode; i++) {         * is higher than the multiple of stepm and negative otherwise.
       if(Ndum[i]!=0) ncodemax[j]++;         */
     }        if( s2 > nlstate && (mle <5) ){  /* Jackson */
            lli=log(out[s1][s2] - savm[s1][s2]);
     ij=1;        } else if (mle==1){
     for (i=1; i<=ncodemax[j]; i++) {          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for (k=0; k<=79; k++) {        } else if(mle==2){
         if (Ndum[k] != 0) {          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 */
           nbcode[Tvar[j]][ij]=k;        } else if(mle==3){  /* exponential inter-extrapolation */
           ij++;          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 */
         }        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         if (ij > ncodemax[j]) break;          lli=log(out[s1][s2]); /* Original formula */
       }          } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
     }          lli=log(out[s1][s2]); /* Original formula */
   }          } /* End of if */
         ipmx +=1;
   }        sw += weight[i];
         ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 /*********** Health Expectancies ****************/  /*       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){
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          fprintf(ficresilk,"%6d %1d %1d %1d %1d %3d %10.6f %6.4f %10.6f %10.6f %10.6f ", \
 {                  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
   /* Health expectancies */          for(k=1,l=0.; k<=nlstate; k++) 
   int i, j, nhstepm, hstepm, h;            fprintf(ficresilk," %10.6f",ll[k]);
   double age, agelim,hf;          fprintf(ficresilk,"\n");
   double ***p3mat;        }
        } /* end of wave */
   fprintf(ficreseij,"# Health expectancies\n");    } /* end of individual */
   fprintf(ficreseij,"# Age");    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   for(i=1; i<=nlstate;i++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     for(j=1; j<=nlstate;j++)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       fprintf(ficreseij," %1d-%1d",i,j);    return -l;
   fprintf(ficreseij,"\n");  }
   
   hstepm=1*YEARM; /*  Every j years of age (in month) */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpr, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
   agelim=AGESUP;    /* This routine should help understanding what is done with the selection of individuals/waves and
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */       to check the exact contribution to the likelihood.
     /* nhstepm age range expressed in number of stepm */       Plotting could be done.
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);     */
     /* Typically if 20 years = 20*12/6=40 stepm */    int k;
     if (stepm >= YEARM) hstepm=1;    if(globpr !=0){ /* Just counts and sums no printings */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      strcpy(fileresilk,"ilk"); 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      strcat(fileresilk,fileres);
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */        printf("Problem with resultfile: %s\n", fileresilk);
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);          fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
       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");
     for(i=1; i<=nlstate;i++)      fprintf(ficresilk, "# i s1 s2 mi mw dh likeli weight out sav ");
       for(j=1; j<=nlstate;j++)      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){      for(k=1; k<=nlstate; k++) 
           eij[i][j][(int)age] +=p3mat[i][j][h];        fprintf(ficresilk," ll[%d]",k);
         }      fprintf(ficresilk,"\n");
        }
     hf=1;  
     if (stepm >= YEARM) hf=stepm/YEARM;    *fretone=(*funcone)(p);
     fprintf(ficreseij,"%.0f",age );    if(globpr !=0)
     for(i=1; i<=nlstate;i++)      fclose(ficresilk);
       for(j=1; j<=nlstate;j++){    return;
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);  }
       }  
     fprintf(ficreseij,"\n");  /*********** Maximum Likelihood Estimation ***************/
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   }  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
 }  {
     int i,j, iter;
 /************ Variance ******************/    double **xi;
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)    double fret;
 {    double fretone; /* Only one call to likelihood */
   /* Variance of health expectancies */    char filerespow[FILENAMELENGTH];
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    xi=matrix(1,npar,1,npar);
   double **newm;    for (i=1;i<=npar;i++)
   double **dnewm,**doldm;      for (j=1;j<=npar;j++)
   int i, j, nhstepm, hstepm, h;        xi[i][j]=(i==j ? 1.0 : 0.0);
   int k, cptcode;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
    double *xp;    strcpy(filerespow,"pow"); 
   double **gp, **gm;    strcat(filerespow,fileres);
   double ***gradg, ***trgradg;    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   double ***p3mat;      printf("Problem with resultfile: %s\n", filerespow);
   double age,agelim;      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   int theta;    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
    fprintf(ficresvij,"# Covariances of life expectancies\n");    for (i=1;i<=nlstate;i++)
   fprintf(ficresvij,"# Age");      for(j=1;j<=nlstate+ndeath;j++)
   for(i=1; i<=nlstate;i++)        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for(j=1; j<=nlstate;j++)    fprintf(ficrespow,"\n");
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);  
   fprintf(ficresvij,"\n");    powell(p,xi,npar,ftol,&iter,&fret,func);
   
   xp=vector(1,npar);    fclose(ficrespow);
   dnewm=matrix(1,nlstate,1,npar);    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
   doldm=matrix(1,nlstate,1,nlstate);    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));
   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 */  /**** Computes Hessian and covariance matrix ***/
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     if (stepm >= YEARM) hstepm=1;  {
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    double  **a,**y,*x,pd;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double **hess;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    int i, j,jk;
     gp=matrix(0,nhstepm,1,nlstate);    int *indx;
     gm=matrix(0,nhstepm,1,nlstate);  
     double hessii(double p[], double delta, int theta, double delti[]);
     for(theta=1; theta <=npar; theta++){    double hessij(double p[], double delti[], int i, int j);
       for(i=1; i<=npar; i++){ /* Computes gradient */    void lubksb(double **a, int npar, int *indx, double b[]) ;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    void ludcmp(double **a, int npar, int *indx, double *d) ;
       }  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      hess=matrix(1,npar,1,npar);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(j=1; j<= nlstate; j++){    printf("\nCalculation of the hessian matrix. Wait...\n");
         for(h=0; h<=nhstepm; h++){    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    for (i=1;i<=npar;i++){
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      printf("%d",i);fflush(stdout);
         }      fprintf(ficlog,"%d",i);fflush(ficlog);
       }      hess[i][i]=hessii(p,ftolhess,i,delti);
          /*printf(" %f ",p[i]);*/
       for(i=1; i<=npar; i++) /* Computes gradient */      /*printf(" %lf ",hess[i][i]);*/
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for (i=1;i<=npar;i++) {
       for(j=1; j<= nlstate; j++){      for (j=1;j<=npar;j++)  {
         for(h=0; h<=nhstepm; h++){        if (j>i) { 
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          printf(".%d%d",i,j);fflush(stdout);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
         }          hess[i][j]=hessij(p,delti,i,j);
       }          hess[j][i]=hess[i][j];    
       for(j=1; j<= nlstate; j++)          /*printf(" %lf ",hess[i][j]);*/
         for(h=0; h<=nhstepm; h++){        }
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      }
         }    }
     } /* End theta */    printf("\n");
     fprintf(ficlog,"\n");
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     for(h=0; h<=nhstepm; h++)    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
       for(j=1; j<=nlstate;j++)    
         for(theta=1; theta <=npar; theta++)    a=matrix(1,npar,1,npar);
           trgradg[h][j][theta]=gradg[h][theta][j];    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
     for(i=1;i<=nlstate;i++)    indx=ivector(1,npar);
       for(j=1;j<=nlstate;j++)    for (i=1;i<=npar;i++)
         vareij[i][j][(int)age] =0.;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     for(h=0;h<=nhstepm;h++){    ludcmp(a,npar,indx,&pd);
       for(k=0;k<=nhstepm;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    for (j=1;j<=npar;j++) {
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      for (i=1;i<=npar;i++) x[i]=0;
         for(i=1;i<=nlstate;i++)      x[j]=1;
           for(j=1;j<=nlstate;j++)      lubksb(a,npar,indx,x);
             vareij[i][j][(int)age] += doldm[i][j];      for (i=1;i<=npar;i++){ 
       }        matcov[i][j]=x[i];
     }      }
     h=1;    }
     if (stepm >= YEARM) h=stepm/YEARM;  
     fprintf(ficresvij,"%.0f ",age );    printf("\n#Hessian matrix#\n");
     for(i=1; i<=nlstate;i++)    fprintf(ficlog,"\n#Hessian matrix#\n");
       for(j=1; j<=nlstate;j++){    for (i=1;i<=npar;i++) { 
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);      for (j=1;j<=npar;j++) { 
       }        printf("%.3e ",hess[i][j]);
     fprintf(ficresvij,"\n");        fprintf(ficlog,"%.3e ",hess[i][j]);
     free_matrix(gp,0,nhstepm,1,nlstate);      }
     free_matrix(gm,0,nhstepm,1,nlstate);      printf("\n");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      fprintf(ficlog,"\n");
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   } /* End age */    /* Recompute Inverse */
      for (i=1;i<=npar;i++)
   free_vector(xp,1,npar);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   free_matrix(doldm,1,nlstate,1,npar);    ludcmp(a,npar,indx,&pd);
   free_matrix(dnewm,1,nlstate,1,nlstate);  
     /*  printf("\n#Hessian matrix recomputed#\n");
 }  
     for (j=1;j<=npar;j++) {
 /************ Variance of prevlim ******************/      for (i=1;i<=npar;i++) x[i]=0;
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      x[j]=1;
 {      lubksb(a,npar,indx,x);
   /* Variance of prevalence limit */      for (i=1;i<=npar;i++){ 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        y[i][j]=x[i];
   double **newm;        printf("%.3e ",y[i][j]);
   double **dnewm,**doldm;        fprintf(ficlog,"%.3e ",y[i][j]);
   int i, j, nhstepm, hstepm;      }
   int k, cptcode;      printf("\n");
   double *xp;      fprintf(ficlog,"\n");
   double *gp, *gm;    }
   double **gradg, **trgradg;    */
   double age,agelim;  
   int theta;    free_matrix(a,1,npar,1,npar);
        free_matrix(y,1,npar,1,npar);
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");    free_vector(x,1,npar);
   fprintf(ficresvpl,"# Age");    free_ivector(indx,1,npar);
   for(i=1; i<=nlstate;i++)    free_matrix(hess,1,npar,1,npar);
       fprintf(ficresvpl," %1d-%1d",i,i);  
   fprintf(ficresvpl,"\n");  
   }
   xp=vector(1,npar);  
   dnewm=matrix(1,nlstate,1,npar);  /*************** hessian matrix ****************/
   doldm=matrix(1,nlstate,1,nlstate);  double hessii( double x[], double delta, int theta, double delti[])
    {
   hstepm=1*YEARM; /* Every year of age */    int i;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    int l=1, lmax=20;
   agelim = AGESUP;    double k1,k2;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    double p2[NPARMAX+1];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    double res;
     if (stepm >= YEARM) hstepm=1;    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    double fx;
     gradg=matrix(1,npar,1,nlstate);    int k=0,kmax=10;
     gp=vector(1,nlstate);    double l1;
     gm=vector(1,nlstate);  
     fx=func(x);
     for(theta=1; theta <=npar; theta++){    for (i=1;i<=npar;i++) p2[i]=x[i];
       for(i=1; i<=npar; i++){ /* Computes gradient */    for(l=0 ; l <=lmax; l++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      l1=pow(10,l);
       }      delts=delt;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for(k=1 ; k <kmax; k=k+1){
       for(i=1;i<=nlstate;i++)        delt = delta*(l1*k);
         gp[i] = prlim[i][i];        p2[theta]=x[theta] +delt;
            k1=func(p2)-fx;
       for(i=1; i<=npar; i++) /* Computes gradient */        p2[theta]=x[theta]-delt;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        k2=func(p2)-fx;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        /*res= (k1-2.0*fx+k2)/delt/delt; */
       for(i=1;i<=nlstate;i++)        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         gm[i] = prlim[i][i];        
   #ifdef DEBUG
       for(i=1;i<=nlstate;i++)        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);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        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);
     } /* End theta */  #endif
         /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     trgradg =matrix(1,nlstate,1,npar);        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
     for(j=1; j<=nlstate;j++)        }
       for(theta=1; theta <=npar; theta++)        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
         trgradg[j][theta]=gradg[theta][j];          k=kmax; l=lmax*10.;
         }
     for(i=1;i<=nlstate;i++)        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       varpl[i][(int)age] =0.;          delts=delt;
     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 */    delti[theta]=delts;
     return res; 
     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");  double hessij( double x[], double delti[], int thetai,int thetaj)
     free_vector(gp,1,nlstate);  {
     free_vector(gm,1,nlstate);    int i;
     free_matrix(gradg,1,npar,1,nlstate);    int l=1, l1, lmax=20;
     free_matrix(trgradg,1,nlstate,1,npar);    double k1,k2,k3,k4,res,fx;
   } /* End age */    double p2[NPARMAX+1];
     int k;
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    fx=func(x);
   free_matrix(dnewm,1,nlstate,1,nlstate);    for (k=1; k<=2; k++) {
       for (i=1;i<=npar;i++) p2[i]=x[i];
 }      p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k1=func(p2)-fx;
     
 /***********************************************/      p2[thetai]=x[thetai]+delti[thetai]/k;
 /**************** Main Program *****************/      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
 /***********************************************/      k2=func(p2)-fx;
     
 /*int main(int argc, char *argv[])*/      p2[thetai]=x[thetai]-delti[thetai]/k;
 int main()      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
 {      k3=func(p2)-fx;
     
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;      p2[thetai]=x[thetai]-delti[thetai]/k;
   double agedeb, agefin,hf;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   double agemin=1.e20, agemax=-1.e20;      k4=func(p2)-fx;
       res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   double fret;  #ifdef DEBUG
   double **xi,tmp,delta;      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);
       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);
   double dum; /* Dummy variable */  #endif
   double ***p3mat;    }
   int *indx;    return res;
   char line[MAXLINE], linepar[MAXLINE];  }
   char title[MAXLINE];  
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];  /************** Inverse of matrix **************/
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];  void ludcmp(double **a, int n, int *indx, double *d) 
   char filerest[FILENAMELENGTH];  { 
   char fileregp[FILENAMELENGTH];    int i,imax,j,k; 
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    double big,dum,sum,temp; 
   int firstobs=1, lastobs=10;    double *vv; 
   int sdeb, sfin; /* Status at beginning and end */   
   int c,  h , cpt,l;    vv=vector(1,n); 
   int ju,jl, mi;    *d=1.0; 
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize;    for (i=1;i<=n;i++) { 
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      big=0.0; 
        for (j=1;j<=n;j++) 
   int hstepm, nhstepm;        if ((temp=fabs(a[i][j])) > big) big=temp; 
   double bage, fage, age, agelim, agebase;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   double ftolpl=FTOL;      vv[i]=1.0/big; 
   double **prlim;    } 
   double *severity;    for (j=1;j<=n;j++) { 
   double ***param; /* Matrix of parameters */      for (i=1;i<j;i++) { 
   double  *p;        sum=a[i][j]; 
   double **matcov; /* Matrix of covariance */        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   double ***delti3; /* Scale */        a[i][j]=sum; 
   double *delti; /* Scale */      } 
   double ***eij, ***vareij;      big=0.0; 
   double **varpl; /* Variances of prevalence limits by age */      for (i=j;i<=n;i++) { 
   double *epj, vepp;        sum=a[i][j]; 
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";        for (k=1;k<j;k++) 
   char *alph[]={"a","a","b","c","d","e"}, str[4];          sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
   char z[1]="c", occ;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
 #include <sys/time.h>          big=dum; 
 #include <time.h>          imax=i; 
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];        } 
   /* long total_usecs;      } 
   struct timeval start_time, end_time;      if (j != imax) { 
          for (k=1;k<=n;k++) { 
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */          dum=a[imax][k]; 
           a[imax][k]=a[j][k]; 
           a[j][k]=dum; 
   printf("\nIMACH, Version 0.64a");        } 
   printf("\nEnter the parameter file name: ");        *d = -(*d); 
         vv[imax]=vv[j]; 
 #ifdef windows      } 
   scanf("%s",pathtot);      indx[j]=imax; 
   getcwd(pathcd, size);      if (a[j][j] == 0.0) a[j][j]=TINY; 
   /*cygwin_split_path(pathtot,path,optionfile);      if (j != n) { 
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/        dum=1.0/(a[j][j]); 
   /* cutv(path,optionfile,pathtot,'\\');*/        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       } 
 split(pathtot, path,optionfile);    } 
   chdir(path);    free_vector(vv,1,n);  /* Doesn't work */
   replace(pathc,path);  ;
 #endif  } 
 #ifdef unix  
   scanf("%s",optionfile);  void lubksb(double **a, int n, int *indx, double b[]) 
 #endif  { 
     int i,ii=0,ip,j; 
 /*-------- arguments in the command line --------*/    double sum; 
    
   strcpy(fileres,"r");    for (i=1;i<=n;i++) { 
   strcat(fileres, optionfile);      ip=indx[i]; 
       sum=b[ip]; 
   /*---------arguments file --------*/      b[ip]=b[i]; 
       if (ii) 
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     printf("Problem with optionfile %s\n",optionfile);      else if (sum) ii=i; 
     goto end;      b[i]=sum; 
   }    } 
     for (i=n;i>=1;i--) { 
   strcpy(filereso,"o");      sum=b[i]; 
   strcat(filereso,fileres);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   if((ficparo=fopen(filereso,"w"))==NULL) {      b[i]=sum/a[i][i]; 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    } 
   }  } 
   
   /* Reads comments: lines beginning with '#' */  /************ Frequencies ********************/
   while((c=getc(ficpar))=='#' && c!= EOF){  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)
     ungetc(c,ficpar);  {  /* Some frequencies */
     fgets(line, MAXLINE, ficpar);    
     puts(line);    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     fputs(line,ficparo);    int first;
   }    double ***freq; /* Frequencies */
   ungetc(c,ficpar);    double *pp, **prop;
     double pos,posprop, k2, dateintsum=0,k2cpt=0;
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    FILE *ficresp;
   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);    char fileresp[FILENAMELENGTH];
   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);    
     pp=vector(1,nlstate);
   covar=matrix(1,NCOVMAX,1,n);        prop=matrix(1,nlstate,iagemin,iagemax+3);
   if (strlen(model)<=1) cptcovn=0;    strcpy(fileresp,"p");
   else {    strcat(fileresp,fileres);
     j=0;    if((ficresp=fopen(fileresp,"w"))==NULL) {
     j=nbocc(model,'+');      printf("Problem with prevalence resultfile: %s\n", fileresp);
     cptcovn=j+1;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   }      exit(0);
     }
   ncovmodel=2+cptcovn;    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    j1=0;
      
   /* Read guess parameters */    j=cptcoveff;
   /* Reads comments: lines beginning with '#' */    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    first=1;
     fgets(line, MAXLINE, ficpar);  
     puts(line);    for(k1=1; k1<=j;k1++){
     fputs(line,ficparo);      for(i1=1; i1<=ncodemax[k1];i1++){
   }        j1++;
   ungetc(c,ficpar);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
            scanf("%d", i);*/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        for (i=-1; i<=nlstate+ndeath; i++)  
     for(i=1; i <=nlstate; i++)          for (jk=-1; jk<=nlstate+ndeath; jk++)  
     for(j=1; j <=nlstate+ndeath-1; j++){            for(m=iagemin; m <= iagemax+3; m++)
       fscanf(ficpar,"%1d%1d",&i1,&j1);              freq[i][jk][m]=0;
       fprintf(ficparo,"%1d%1d",i1,j1);  
       printf("%1d%1d",i,j);      for (i=1; i<=nlstate; i++)  
       for(k=1; k<=ncovmodel;k++){        for(m=iagemin; m <= iagemax+3; m++)
         fscanf(ficpar," %lf",&param[i][j][k]);          prop[i][m]=0;
         printf(" %lf",param[i][j][k]);        
         fprintf(ficparo," %lf",param[i][j][k]);        dateintsum=0;
       }        k2cpt=0;
       fscanf(ficpar,"\n");        for (i=1; i<=imx; i++) {
       printf("\n");          bool=1;
       fprintf(ficparo,"\n");          if  (cptcovn>0) {
     }            for (z1=1; z1<=cptcoveff; z1++) 
                if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;                bool=0;
   p=param[1][1];          }
            if (bool==1){
   /* Reads comments: lines beginning with '#' */            for(m=firstpass; m<=lastpass; m++){
   while((c=getc(ficpar))=='#' && c!= EOF){              k2=anint[m][i]+(mint[m][i]/12.);
     ungetc(c,ficpar);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     fgets(line, MAXLINE, ficpar);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     puts(line);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     fputs(line,ficparo);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   }                if (m<lastpass) {
   ungetc(c,ficpar);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[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++){                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     for(j=1; j <=nlstate+ndeath-1; j++){                  dateintsum=dateintsum+k2;
       fscanf(ficpar,"%1d%1d",&i1,&j1);                  k2cpt++;
       printf("%1d%1d",i,j);                }
       fprintf(ficparo,"%1d%1d",i1,j1);                /*}*/
       for(k=1; k<=ncovmodel;k++){            }
         fscanf(ficpar,"%le",&delti3[i][j][k]);          }
         printf(" %le",delti3[i][j][k]);        }
         fprintf(ficparo," %le",delti3[i][j][k]);         
       }        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       fscanf(ficpar,"\n");  
       printf("\n");        if  (cptcovn>0) {
       fprintf(ficparo,"\n");          fprintf(ficresp, "\n#********** Variable "); 
     }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   }          fprintf(ficresp, "**********\n#");
   delti=delti3[1][1];        }
          for(i=1; i<=nlstate;i++) 
   /* Reads comments: lines beginning with '#' */          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   while((c=getc(ficpar))=='#' && c!= EOF){        fprintf(ficresp, "\n");
     ungetc(c,ficpar);        
     fgets(line, MAXLINE, ficpar);        for(i=iagemin; i <= iagemax+3; i++){
     puts(line);          if(i==iagemax+3){
     fputs(line,ficparo);            fprintf(ficlog,"Total");
   }          }else{
   ungetc(c,ficpar);            if(first==1){
                first=0;
   matcov=matrix(1,npar,1,npar);              printf("See log file for details...\n");
   for(i=1; i <=npar; i++){            }
     fscanf(ficpar,"%s",&str);            fprintf(ficlog,"Age %d", i);
     printf("%s",str);          }
     fprintf(ficparo,"%s",str);          for(jk=1; jk <=nlstate ; jk++){
     for(j=1; j <=i; j++){            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
       fscanf(ficpar," %le",&matcov[i][j]);              pp[jk] += freq[jk][m][i]; 
       printf(" %.5le",matcov[i][j]);          }
       fprintf(ficparo," %.5le",matcov[i][j]);          for(jk=1; jk <=nlstate ; jk++){
     }            for(m=-1, pos=0; m <=0 ; m++)
     fscanf(ficpar,"\n");              pos += freq[jk][m][i];
     printf("\n");            if(pp[jk]>=1.e-10){
     fprintf(ficparo,"\n");              if(first==1){
   }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   for(i=1; i <=npar; i++)              }
     for(j=i+1;j<=npar;j++)              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       matcov[i][j]=matcov[j][i];            }else{
                  if(first==1)
   printf("\n");                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             }
    if(mle==1){          }
     /*-------- data file ----------*/  
     if((ficres =fopen(fileres,"w"))==NULL) {          for(jk=1; jk <=nlstate ; jk++){
       printf("Problem with resultfile: %s\n", fileres);goto end;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     }              pp[jk] += freq[jk][m][i];
     fprintf(ficres,"#%s\n",version);          }       
              for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     if((fic=fopen(datafile,"r"))==NULL)    {            pos += pp[jk];
       printf("Problem with datafile: %s\n", datafile);goto end;            posprop += prop[jk][i];
     }          }
           for(jk=1; jk <=nlstate ; jk++){
     n= lastobs;            if(pos>=1.e-5){
     severity = vector(1,maxwav);              if(first==1)
     outcome=imatrix(1,maxwav+1,1,n);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     num=ivector(1,n);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     moisnais=vector(1,n);            }else{
     annais=vector(1,n);              if(first==1)
     moisdc=vector(1,n);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     andc=vector(1,n);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     agedc=vector(1,n);            }
     cod=ivector(1,n);            if( i <= iagemax){
     weight=vector(1,n);              if(pos>=1.e-5){
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     mint=matrix(1,maxwav,1,n);                /*probs[i][jk][j1]= pp[jk]/pos;*/
     anint=matrix(1,maxwav,1,n);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     s=imatrix(1,maxwav+1,1,n);              }
     adl=imatrix(1,maxwav+1,1,n);                  else
     tab=ivector(1,NCOVMAX);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     ncodemax=ivector(1,8);            }
           }
     i=1;          
     while (fgets(line, MAXLINE, fic) != NULL)    {          for(jk=-1; jk <=nlstate+ndeath; jk++)
       if ((i >= firstobs) && (i <=lastobs)) {            for(m=-1; m <=nlstate+ndeath; m++)
                      if(freq[jk][m][i] !=0 ) {
         for (j=maxwav;j>=1;j--){              if(first==1)
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
           strcpy(line,stra);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
           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);          if(i <= iagemax)
         }            fprintf(ficresp,"\n");
                  if(first==1)
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            printf("Others in log...\n");
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          fprintf(ficlog,"\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);    }
     dateintmean=dateintsum/k2cpt; 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);   
         for (j=ncov;j>=1;j--){    fclose(ficresp);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
         }    free_vector(pp,1,nlstate);
         num[i]=atol(stra);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     /* End of Freq */
         /*printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/  }
   
         i=i+1;  /************ Prevalence ********************/
       }  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)
     }  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
     /*scanf("%d",i);*/       in each health status at the date of interview (if between dateprev1 and dateprev2).
   imx=i-1; /* Number of individuals */       We still use firstpass and lastpass as another selection.
     */
   /* Calculation of the number of parameter from char model*/   
   Tvar=ivector(1,8);        int i, m, jk, k1, i1, j1, bool, z1,z2,j;
        double ***freq; /* Frequencies */
   if (strlen(model) >1){    double *pp, **prop;
     j=0;    double pos,posprop; 
     j=nbocc(model,'+');    double  y2; /* in fractional years */
     cptcovn=j+1;    int iagemin, iagemax;
      
     strcpy(modelsav,model);    iagemin= (int) agemin;
     if (j==0) {    iagemax= (int) agemax;
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);    /*pp=vector(1,nlstate);*/
     }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     else {    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
       for(i=j; i>=1;i--){    j1=0;
         cutv(stra,strb,modelsav,'+');    
         if (strchr(strb,'*')) {    j=cptcoveff;
           cutv(strd,strc,strb,'*');    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;    
           cutv(strb,strc,strd,'V');    for(k1=1; k1<=j;k1++){
           for (k=1; k<=lastobs;k++)      for(i1=1; i1<=ncodemax[k1];i1++){
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        j1++;
         }        
         else {cutv(strd,strc,strb,'V');        for (i=1; i<=nlstate; i++)  
         Tvar[i+1]=atoi(strc);          for(m=iagemin; m <= iagemax+3; m++)
         }            prop[i][m]=0.0;
         strcpy(modelsav,stra);         
       }        for (i=1; i<=imx; i++) { /* Each individual */
       cutv(strd,strc,stra,'V');          bool=1;
       Tvar[1]=atoi(strc);          if  (cptcovn>0) {
     }            for (z1=1; z1<=cptcoveff; z1++) 
   }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   /*printf("tvar=%d ",Tvar[1]);                bool=0;
   scanf("%d ",i);*/          } 
     fclose(fic);          if (bool==1) { 
             for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     if (weightopt != 1) { /* Maximisation without weights*/              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       for(i=1;i<=n;i++) weight[i]=1.0;              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     /*-calculation of age at interview from date of interview and age at death -*/                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     agev=matrix(1,maxwav,1,imx);                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); 
                    if (s[m][i]>0 && s[m][i]<=nlstate) { 
     for (i=1; i<=imx; i++)  {                  /*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]]);*/
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
       for(m=1; (m<= maxwav); m++){                  prop[s[m][i]][iagemax+3] += weight[i]; 
         if(s[m][i] >0){                } 
           if (s[m][i] == nlstate+1) {              }
             if(agedc[i]>0)            } /* end selection of waves */
               if(moisdc[i]!=99 && andc[i]!=9999)          }
               agev[m][i]=agedc[i];        }
             else{        for(i=iagemin; i <= iagemax+3; i++){  
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          
               agev[m][i]=-1;          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             }            posprop += prop[jk][i]; 
           }          } 
           else if(s[m][i] !=9){ /* Should no more exist */  
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          for(jk=1; jk <=nlstate ; jk++){     
             if(mint[m][i]==99 || anint[m][i]==9999)            if( i <=  iagemax){ 
               agev[m][i]=1;              if(posprop>=1.e-5){ 
             else if(agev[m][i] <agemin){                probs[i][jk][j1]= prop[jk][i]/posprop;
               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);*/            } 
             }          }/* end jk */ 
             else if(agev[m][i] >agemax){        }/* end i */ 
               agemax=agev[m][i];      } /* end i1 */
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    } /* end k1 */
             }    
             /*agev[m][i]=anint[m][i]-annais[i];*/    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
             /*   agev[m][i] = age[i]+2*m;*/    /*free_vector(pp,1,nlstate);*/
           }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
           else { /* =9 */  }  /* End of prevalence */
             agev[m][i]=1;  
             s[m][i]=-1;  /************* Waves Concatenation ***************/
           }  
         }  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)
         else /*= 0 Unknown */  {
           agev[m][i]=1;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       }       Death is a valid wave (if date is known).
           mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     for (i=1; i<=imx; i++)  {       and mw[mi+1][i]. dh depends on stepm.
       for(m=1; (m<= maxwav); m++){       */
         if (s[m][i] > (nlstate+ndeath)) {  
           printf("Error: Wrong value in nlstate or ndeath\n");      int i, mi, m;
           goto end;    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
         }       double sum=0., jmean=0.;*/
       }    int first;
     }    int j, k=0,jk, ju, jl;
     double sum=0.;
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    first=0;
     jmin=1e+5;
     free_vector(severity,1,maxwav);    jmax=-1;
     free_imatrix(outcome,1,maxwav+1,1,n);    jmean=0.;
     free_vector(moisnais,1,n);    for(i=1; i<=imx; i++){
     free_vector(annais,1,n);      mi=0;
     free_matrix(mint,1,maxwav,1,n);      m=firstpass;
     free_matrix(anint,1,maxwav,1,n);      while(s[m][i] <= nlstate){
     free_vector(moisdc,1,n);        if(s[m][i]>=1)
     free_vector(andc,1,n);          mw[++mi][i]=m;
         if(m >=lastpass)
              break;
     wav=ivector(1,imx);        else
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          m++;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);      }/* end while */
          if (s[m][i] > nlstate){
     /* Concatenates waves */        mi++;     /* Death is another wave */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);        /* if(mi==0)  never been interviewed correctly before death */
            /* Only death is a correct wave */
         mw[mi][i]=m;
 Tcode=ivector(1,100);      }
    nbcode=imatrix(1,nvar,1,8);    
    ncodemax[1]=1;      wav[i]=mi;
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);      if(mi==0){
          if(first==0){
    codtab=imatrix(1,100,1,10);          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
    h=0;          first=1;
    m=pow(2,cptcovn);        }
          if(first==1){
    for(k=1;k<=cptcovn; k++){          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
      for(i=1; i <=(m/pow(2,k));i++){        }
        for(j=1; j <= ncodemax[k]; j++){      } /* end mi==0 */
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){    } /* End individuals */
            h++;  
            if (h>m) h=1;codtab[h][k]=j;    for(i=1; i<=imx; i++){
          }      for(mi=1; mi<wav[i];mi++){
        }        if (stepm <=0)
      }          dh[mi][i]=1;
    }        else{
           if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
    /*for(i=1; i <=m ;i++){            if (agedc[i] < 2*AGESUP) {
      for(k=1; k <=cptcovn; k++){              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);              if(j==0) j=1;  /* Survives at least one month after exam */
      }              else if(j<0){
      printf("\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 */
    /*scanf("%d",i);*/                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 fixe 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]);
    /* Calculates basic frequencies. Computes observed prevalence at single age                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);
        and prints on file fileres'p'. */              }
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);              k=k+1;
               if (j >= jmax) jmax=j;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              if (j <= jmin) jmin=j;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              sum=sum+j;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            }
              }
     /* For Powell, parameters are in a vector p[] starting at p[1]          else{
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
                k=k+1;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);            if (j >= jmax) jmax=j;
             else if (j <= jmin)jmin=j;
                /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     /*--------- results files --------------*/            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
     fprintf(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);            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]);
    jk=1;              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]);
    fprintf(ficres,"# Parameters\n");            }
    printf("# Parameters\n");            sum=sum+j;
    for(i=1,jk=1; i <=nlstate; i++){          }
      for(k=1; k <=(nlstate+ndeath); k++){          jk= j/stepm;
        if (k != i)          jl= j -jk*stepm;
          {          ju= j -(jk+1)*stepm;
            printf("%d%d ",i,k);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
            fprintf(ficres,"%1d%1d ",i,k);            if(jl==0){
            for(j=1; j <=ncovmodel; j++){              dh[mi][i]=jk;
              printf("%f ",p[jk]);              bh[mi][i]=0;
              fprintf(ficres,"%f ",p[jk]);            }else{ /* We want a negative bias in order to only have interpolation ie
              jk++;                    * at the price of an extra matrix product in likelihood */
            }              dh[mi][i]=jk+1;
            printf("\n");              bh[mi][i]=ju;
            fprintf(ficres,"\n");            }
          }          }else{
      }            if(jl <= -ju){
    }              dh[mi][i]=jk;
               bh[mi][i]=jl;       /* bias is positive if real duration
     /* Computing hessian and covariance matrix */                                   * is higher than the multiple of stepm and negative otherwise.
     ftolhess=ftol; /* Usually correct */                                   */
     hesscov(matcov, p, npar, delti, ftolhess, func);            }
     fprintf(ficres,"# Scales\n");            else{
     printf("# Scales\n");              dh[mi][i]=jk+1;
      for(i=1,jk=1; i <=nlstate; i++){              bh[mi][i]=ju;
       for(j=1; j <=nlstate+ndeath; j++){            }
         if (j!=i) {            if(dh[mi][i]==0){
           fprintf(ficres,"%1d%1d",i,j);              dh[mi][i]=1; /* At least one step */
           printf("%1d%1d",i,j);              bh[mi][i]=ju; /* At least one step */
           for(k=1; k<=ncovmodel;k++){              /*  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);*/
             printf(" %.5e",delti[jk]);            }
             fprintf(ficres," %.5e",delti[jk]);          } /* end if mle */
             jk++;        }
           }      } /* end wave */
           printf("\n");    }
           fprintf(ficres,"\n");    jmean=sum/k;
         }    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       }    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       }   }
      
     k=1;  /*********** Tricode ****************************/
     fprintf(ficres,"# Covariance\n");  void tricode(int *Tvar, int **nbcode, int imx)
     printf("# Covariance\n");  {
     for(i=1;i<=npar;i++){    
       /*  if (k>nlstate) k=1;    int Ndum[20],ij=1, k, j, i, maxncov=19;
       i1=(i-1)/(ncovmodel*nlstate)+1;    int cptcode=0;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    cptcoveff=0; 
       printf("%s%d%d",alph[k],i1,tab[i]);*/   
       fprintf(ficres,"%3d",i);    for (k=0; k<maxncov; k++) Ndum[k]=0;
       printf("%3d",i);    for (k=1; k<=7; k++) ncodemax[k]=0;
       for(j=1; j<=i;j++){  
         fprintf(ficres," %.5e",matcov[i][j]);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
         printf(" %.5e",matcov[i][j]);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
       }                                 modality*/ 
       fprintf(ficres,"\n");        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
       printf("\n");        Ndum[ij]++; /*store the modality */
       k++;        /*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 
                                             Tvar[j]. If V=sex and male is 0 and 
     while((c=getc(ficpar))=='#' && c!= EOF){                                         female is 1, then  cptcode=1.*/
       ungetc(c,ficpar);      }
       fgets(line, MAXLINE, ficpar);  
       puts(line);      for (i=0; i<=cptcode; i++) {
       fputs(line,ficparo);        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 */
     }      }
     ungetc(c,ficpar);  
        ij=1; 
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      for (i=1; i<=ncodemax[j]; i++) {
            for (k=0; k<= maxncov; k++) {
     if (fage <= 2) {          if (Ndum[k] != 0) {
       bage = agemin;            nbcode[Tvar[j]][ij]=k; 
       fage = agemax;            /* 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; */
     }            
             ij++;
     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);          if (ij > ncodemax[j]) break; 
 /*------------ gnuplot -------------*/        }  
 chdir(pathcd);      } 
   if((ficgp=fopen("graph.plt","w"))==NULL) {    }  
     printf("Problem with file graph.gp");goto end;  
   }   for (k=0; k< maxncov; k++) Ndum[k]=0;
 #ifdef windows  
   fprintf(ficgp,"cd \"%s\" \n",pathc);   for (i=1; i<=ncovmodel-2; i++) { 
 #endif     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
 m=pow(2,cptcovn);     ij=Tvar[i];
       Ndum[ij]++;
  /* 1eme*/   }
   for (cpt=1; cpt<= nlstate ; cpt ++) {  
    for (k1=1; k1<= m ; k1 ++) {   ij=1;
    for (i=1; i<= maxncov; i++) {
 #ifdef windows     if((Ndum[i]!=0) && (i<=ncovcol)){
     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);       Tvaraff[ij]=i; /*For printing */
 #endif       ij++;
 #ifdef unix     }
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);   }
 #endif   
    cptcoveff=ij-1; /*Number of simple covariates*/
 for (i=1; i<= nlstate ; i ++) {  }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");  /*********** Health Expectancies ****************/
 }  
     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 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 )
     for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  {
   else fprintf(ficgp," \%%*lf (\%%*lf)");    /* Health expectancies */
 }    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    double age, agelim, hf;
      for (i=1; i<= nlstate ; i ++) {    double ***p3mat,***varhe;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double **dnewm,**doldm;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double *xp;
 }      double **gp, **gm;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    double ***gradg, ***trgradg;
 #ifdef unix    int theta;
 fprintf(ficgp,"\nset ter gif small size 400,300");  
 #endif    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    xp=vector(1,npar);
    }    dnewm=matrix(1,nlstate*nlstate,1,npar);
   }    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   /*2 eme*/    
     fprintf(ficreseij,"# Health expectancies\n");
   for (k1=1; k1<= m ; k1 ++) {    fprintf(ficreseij,"# Age");
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++)
     for (i=1; i<= nlstate+1 ; i ++) {        fprintf(ficreseij," %1d-%1d (SE)",i,j);
       k=2*i;    fprintf(ficreseij,"\n");
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {    if(estepm < stepm){
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      printf ("Problem %d lower than %d\n",estepm, stepm);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    }
 }      else  hstepm=estepm;   
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    /* We compute the life expectancy from trapezoids spaced every estepm months
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);     * This is mainly to measure the difference between two models: for example
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);     * if stepm=24 months pijx are given only every 2 years and by summing them
       for (j=1; j<= nlstate+1 ; j ++) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");     * progression in between and thus overestimating or underestimating according
         else fprintf(ficgp," \%%*lf (\%%*lf)");     * to the curvature of the survival function. If, for the same date, we 
 }       * estimate the model with stepm=1 month, we can keep estepm to 24 months
       fprintf(ficgp,"\" t\"\" w l 0,");     * to compare the new estimate of Life expectancy with the same linear 
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);     * hypothesis. A more precise result, taking into account a more precise
       for (j=1; j<= nlstate+1 ; j ++) {     * curvature will be obtained if estepm is as small as stepm. */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    /* For example we decided to compute the life expectancy with the smallest unit */
 }      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");       nhstepm is the number of hstepm from age to agelim 
       else fprintf(ficgp,"\" t\"\" w l 0,");       nstepm is the number of stepm from age to agelin. 
     }       Look at hpijx to understand the reason of that which relies in memory size
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);       and note for a fixed period like estepm months */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         survival function given by stepm (the optimization length). Unfortunately it
   /*3eme*/       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 
   for (k1=1; k1<= m ; k1 ++) {       results. So we changed our mind and took the option of the best precision.
     for (cpt=1; cpt<= nlstate ; cpt ++) {    */
       k=2+nlstate*(cpt-1);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);  
       for (i=1; i< nlstate ; i ++) {    agelim=AGESUP;
         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);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       }      /* nhstepm age range expressed in number of stepm */
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
     }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   }      /* if (stepm >= YEARM) hstepm=1;*/
        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   /* CV preval stat */      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   for (k1=1; k1<= m ; k1 ++) {      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     for (cpt=1; cpt<nlstate ; cpt ++) {      gp=matrix(0,nhstepm,1,nlstate*nlstate);
       k=3;      gm=matrix(0,nhstepm,1,nlstate*nlstate);
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);  
       for (i=1; i< nlstate ; i ++)      /* Computed by stepm unit matrices, product of hstepm matrices, stored
         fprintf(ficgp,"+$%d",k+i+1);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
         
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for (i=1; i< nlstate ; i ++) {  
         l=3+(nlstate+ndeath)*cpt;      /* Computing Variances of health expectancies */
         fprintf(ficgp,"+$%d",l+i+1);  
       }       for(theta=1; theta <=npar; theta++){
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);          for(i=1; i<=npar; i++){ 
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     }        }
   }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     
   /* proba elementaires */        cptj=0;
    for(i=1,jk=1; i <=nlstate; i++){        for(j=1; j<= nlstate; j++){
     for(k=1; k <=(nlstate+ndeath); k++){          for(i=1; i<=nlstate; i++){
       if (k != i) {            cptj=cptj+1;
         for(j=1; j <=ncovmodel; j++){            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
           /*fprintf(ficgp,"%s",alph[1]);*/            }
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);          }
           jk++;        }
           fprintf(ficgp,"\n");       
         }       
       }        for(i=1; i<=npar; i++) 
     }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         
   for(jk=1; jk <=m; jk++) {        cptj=0;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);        for(j=1; j<= nlstate; j++){
    i=1;          for(i=1;i<=nlstate;i++){
    for(k2=1; k2<=nlstate; k2++) {            cptj=cptj+1;
      k3=i;            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
      for(k=1; k<=(nlstate+ndeath); k++) {  
        if (k != k2){              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);            }
           }
         for(j=3; j <=ncovmodel; j++)        }
           fprintf(ficgp,"+p%d*%d",k2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        for(j=1; j<= nlstate*nlstate; j++)
         fprintf(ficgp,")/(1");          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
         for(k1=1; k1 <=nlstate+1; k1=k1+2){            }
             fprintf(ficgp,"+exp(p%d+p%d*x",k1+k3-1,k1+k3);       } 
      
             for(j=3; j <=ncovmodel; j++)  /* End theta */
               fprintf(ficgp,"+p%d*%d",k2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  
             fprintf(ficgp,")");       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
         }  
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);       for(h=0; h<=nhstepm-1; h++)
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        for(j=1; j<=nlstate*nlstate;j++)
     i=i+ncovmodel;          for(theta=1; theta <=npar; theta++)
        }            trgradg[h][j][theta]=gradg[h][theta][j];
      }       
    }  
   fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);       for(i=1;i<=nlstate*nlstate;i++)
    }        for(j=1;j<=nlstate*nlstate;j++)
              varhe[i][j][(int)age] =0.;
   fclose(ficgp);  
           printf("%d|",(int)age);fflush(stdout);
 chdir(path);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     free_matrix(agev,1,maxwav,1,imx);       for(h=0;h<=nhstepm-1;h++){
     free_ivector(wav,1,imx);        for(k=0;k<=nhstepm-1;k++){
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
              for(i=1;i<=nlstate*nlstate;i++)
     free_imatrix(s,1,maxwav+1,1,n);            for(j=1;j<=nlstate*nlstate;j++)
                  varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
            }
     free_ivector(num,1,n);      }
     free_vector(agedc,1,n);      /* Computing expectancies */
     free_vector(weight,1,n);      for(i=1; i<=nlstate;i++)
     /*free_matrix(covar,1,NCOVMAX,1,n);*/        for(j=1; j<=nlstate;j++)
     fclose(ficparo);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     fclose(ficres);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
    }            
      /* 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]);*/
    /*________fin mle=1_________*/  
              }
   
        fprintf(ficreseij,"%3.0f",age );
     /* No more information from the sample is required now */      cptj=0;
   /* Reads comments: lines beginning with '#' */      for(i=1; i<=nlstate;i++)
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate;j++){
     ungetc(c,ficpar);          cptj++;
     fgets(line, MAXLINE, ficpar);          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
     puts(line);        }
     fputs(line,ficparo);      fprintf(ficreseij,"\n");
   }     
   ungetc(c,ficpar);      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
        free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 /*--------- index.htm --------*/    }
     printf("\n");
   if((fichtm=fopen("index.htm","w"))==NULL)    {    fprintf(ficlog,"\n");
     printf("Problem with index.htm \n");goto end;  
   }    free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
  fprintf(fichtm,"<body><ul> Imach, Version 0.64a<hr> <li>Outputs files<br><br>\n    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
 - 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>  /************ Variance ******************/
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  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)
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>  {
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    /* Variance of health expectancies */
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
         - 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);    /* double **newm;*/
     double **dnewm,**doldm;
  fprintf(fichtm," <li>Graphs</li>\n<p>");    double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
  m=cptcovn;    int k, cptcode;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    double *xp;
     double **gp, **gm;  /* for var eij */
  j1=0;    double ***gradg, ***trgradg; /*for var eij */
  for(k1=1; k1<=m;k1++){    double **gradgp, **trgradgp; /* for var p point j */
    for(i1=1; i1<=ncodemax[k1];i1++){    double *gpp, *gmp; /* for var p point j */
        j1++;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
        if (cptcovn > 0) {    double ***p3mat;
          fprintf(fichtm,"<hr>************ Results for covariates");    double age,agelim, hf;
          for (cpt=1; cpt<=cptcovn;cpt++)    double ***mobaverage;
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);    int theta;
          fprintf(fichtm," ************\n<hr>");    char digit[4];
        }    char digitp[25];
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>  
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);        char fileresprobmorprev[FILENAMELENGTH];
        for(cpt=1; cpt<nlstate;cpt++){  
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    if(popbased==1){
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      if(mobilav!=0)
        }        strcpy(digitp,"-populbased-mobilav-");
     for(cpt=1; cpt<=nlstate;cpt++) {      else strcpy(digitp,"-populbased-nomobil-");
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    }
 interval) in state (%d): v%s%d%d.gif <br>    else 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        strcpy(digitp,"-stablbased-");
      }  
      for(cpt=1; cpt<=nlstate;cpt++) {    if (mobilav!=0) {
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
      }        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
      fprintf(fichtm,"\n<br>- Total life expectancy by age and        printf(" Error in movingaverage mobilav=%d\n",mobilav);
 health expectancies in states (1) and (2): e%s%d.gif<br>      }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);    }
 fprintf(fichtm,"\n</body>");  
    }    strcpy(fileresprobmorprev,"prmorprev"); 
  }    sprintf(digit,"%-d",ij);
 fclose(fichtm);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
   /*--------------- Prevalence limit --------------*/    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
      strcat(fileresprobmorprev,fileres);
   strcpy(filerespl,"pl");    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   strcat(filerespl,fileres);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    }
   }    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   fprintf(ficrespl,"#Prevalence limit\n");    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(ficrespl,"#Age ");    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   fprintf(ficrespl,"\n");      fprintf(ficresprobmorprev," p.%-d SE",j);
        for(i=1; i<=nlstate;i++)
   prlim=matrix(1,nlstate,1,nlstate);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    }  
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprobmorprev,"\n");
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
   k=0;      exit(0);
   agebase=agemin;    }
   agelim=agemax;    else{
   ftolpl=1.e-10;      fprintf(ficgp,"\n# Routine varevsij");
   i1=cptcovn;    }
   if (cptcovn < 1){i1=1;}    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
   for(cptcov=1;cptcov<=i1;cptcov++){      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      exit(0);
         k=k+1;    }
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    else{
         fprintf(ficrespl,"\n#****** ");      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");
         for(j=1;j<=cptcovn;j++)      fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    }
         fprintf(ficrespl,"******\n");    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
          
         for (age=agebase; age<=agelim; age++){    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");
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    fprintf(ficresvij,"# Age");
           fprintf(ficrespl,"%.0f",age );    for(i=1; i<=nlstate;i++)
           for(i=1; i<=nlstate;i++)      for(j=1; j<=nlstate;j++)
           fprintf(ficrespl," %.5f", prlim[i][i]);        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
           fprintf(ficrespl,"\n");    fprintf(ficresvij,"\n");
         }  
       }    xp=vector(1,npar);
     }    dnewm=matrix(1,nlstate,1,npar);
   fclose(ficrespl);    doldm=matrix(1,nlstate,1,nlstate);
   /*------------- h Pij x at various ages ------------*/    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
      doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    gpp=vector(nlstate+1,nlstate+ndeath);
   }    gmp=vector(nlstate+1,nlstate+ndeath);
   printf("Computing pij: result on file '%s' \n", filerespij);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
      
   stepsize=(int) (stepm+YEARM-1)/YEARM;    if(estepm < stepm){
   if (stepm<=24) stepsize=2;      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
   agelim=AGESUP;    else  hstepm=estepm;   
   hstepm=stepsize*YEARM; /* Every year of age */    /* For example we decided to compute the life expectancy with the smallest unit */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         nhstepm is the number of hstepm from age to agelim 
   k=0;       nstepm is the number of stepm from age to agelin. 
   for(cptcov=1;cptcov<=i1;cptcov++){       Look at hpijx to understand the reason of that which relies in memory size
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       and note for a fixed period like k years */
       k=k+1;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         fprintf(ficrespij,"\n#****** ");       survival function given by stepm (the optimization length). Unfortunately it
         for(j=1;j<=cptcovn;j++)       means that if the survival funtion is printed every two years of age and if
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
         fprintf(ficrespij,"******\n");       results. So we changed our mind and took the option of the best precision.
            */
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    agelim = AGESUP;
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      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 */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"# Age");      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
           for(i=1; i<=nlstate;i++)      gp=matrix(0,nhstepm,1,nlstate);
             for(j=1; j<=nlstate+ndeath;j++)      gm=matrix(0,nhstepm,1,nlstate);
               fprintf(ficrespij," %1d-%1d",i,j);  
           fprintf(ficrespij,"\n");  
           for (h=0; h<=nhstepm; h++){      for(theta=1; theta <=npar; theta++){
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
             for(i=1; i<=nlstate;i++)          xp[i] = x[i] + (i==theta ?delti[theta]:0);
               for(j=1; j<=nlstate+ndeath;j++)        }
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             fprintf(ficrespij,"\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           }  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        if (popbased==1) {
           fprintf(ficrespij,"\n");          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++)
   fclose(ficrespij);              prlim[i][i]=mobaverage[(int)age][i][ij];
           }
   /*---------- Health expectancies and variances ------------*/        }
     
   strcpy(filerest,"t");        for(j=1; j<= nlstate; j++){
   strcat(filerest,fileres);          for(h=0; h<=nhstepm; h++){
   if((ficrest=fopen(filerest,"w"))==NULL) {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
   }          }
   printf("Computing Total LEs with variances: file '%s' \n", filerest);        }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
   strcpy(filerese,"e");           as a weighted average of prlim.
   strcat(filerese,fileres);        */
   if((ficreseij=fopen(filerese,"w"))==NULL) {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
   }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);        }    
         /* end probability of death */
  strcpy(fileresv,"v");  
   strcat(fileresv,fileres);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);   
         if (popbased==1) {
   k=0;          if(mobilav ==0){
   for(cptcov=1;cptcov<=i1;cptcov++){            for(i=1; i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              prlim[i][i]=probs[(int)age][i][ij];
       k=k+1;          }else{ /* mobilav */ 
       fprintf(ficrest,"\n#****** ");            for(i=1; i<=nlstate;i++)
       for(j=1;j<=cptcovn;j++)              prlim[i][i]=mobaverage[(int)age][i][ij];
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);          }
       fprintf(ficrest,"******\n");        }
   
       fprintf(ficreseij,"\n#****** ");        for(j=1; j<= nlstate; j++){
       for(j=1;j<=cptcovn;j++)          for(h=0; h<=nhstepm; h++){
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
       fprintf(ficreseij,"******\n");              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
       fprintf(ficresvij,"\n#****** ");        }
       for(j=1;j<=cptcovn;j++)        /* This for computing probability of death (h=1 means
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);           computed over hstepm matrices product = hstepm*stepm months) 
       fprintf(ficresvij,"******\n");           as a weighted average of prlim.
         */
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       oldm=oldms;savm=savms;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);             gmp[j] += prlim[i][i]*p3mat[i][j][1];
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        }    
       oldm=oldms;savm=savms;        /* end probability of death */
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  
              for(j=1; j<= nlstate; j++) /* vareij */
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          for(h=0; h<=nhstepm; h++){
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       fprintf(ficrest,"\n");          }
          
       hf=1;        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
       if (stepm >= YEARM) hf=stepm/YEARM;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
       epj=vector(1,nlstate+1);        }
       for(age=bage; age <=fage ;age++){  
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      } /* End theta */
         fprintf(ficrest," %.0f",age);  
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
           for(i=1, epj[j]=0.;i <=nlstate;i++) {  
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];      for(h=0; h<=nhstepm; h++) /* veij */
           }        for(j=1; j<=nlstate;j++)
           epj[nlstate+1] +=epj[j];          for(theta=1; theta <=npar; theta++)
         }            trgradg[h][j][theta]=gradg[h][theta][j];
         for(i=1, vepp=0.;i <=nlstate;i++)  
           for(j=1;j <=nlstate;j++)      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
             vepp += vareij[i][j][(int)age];        for(theta=1; theta <=npar; theta++)
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));          trgradgp[j][theta]=gradgp[theta][j];
         for(j=1;j <=nlstate;j++){    
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));  
         }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         fprintf(ficrest,"\n");      for(i=1;i<=nlstate;i++)
       }        for(j=1;j<=nlstate;j++)
     }          vareij[i][j][(int)age] =0.;
   }  
              for(h=0;h<=nhstepm;h++){
  fclose(ficreseij);        for(k=0;k<=nhstepm;k++){
  fclose(ficresvij);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
   fclose(ficrest);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   fclose(ficpar);          for(i=1;i<=nlstate;i++)
   free_vector(epj,1,nlstate+1);            for(j=1;j<=nlstate;j++)
   /*  scanf("%d ",i); */              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
   /*------- Variance limit prevalence------*/        }
     
 strcpy(fileresvpl,"vpl");      /* pptj */
   strcat(fileresvpl,fileres);      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);      for(j=nlstate+1;j<=nlstate+ndeath;j++)
     exit(0);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
   }          varppt[j][i]=doldmp[j][i];
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);      /* end ppptj */
       /*  x centered again */
  k=0;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
  for(cptcov=1;cptcov<=i1;cptcov++){      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   
      k=k+1;      if (popbased==1) {
      fprintf(ficresvpl,"\n#****** ");        if(mobilav ==0){
      for(j=1;j<=cptcovn;j++)          for(i=1; i<=nlstate;i++)
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);            prlim[i][i]=probs[(int)age][i][ij];
      fprintf(ficresvpl,"******\n");        }else{ /* mobilav */ 
                for(i=1; i<=nlstate;i++)
      varpl=matrix(1,nlstate,(int) bage, (int) fage);            prlim[i][i]=mobaverage[(int)age][i][ij];
      oldm=oldms;savm=savms;        }
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      }
    }               
  }      /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
   fclose(ficresvpl);         as a weighted average of prlim.
       */
   /*---------- End : free ----------------*/      for(j=nlstate+1;j<=nlstate+ndeath;j++){
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
            gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      }    
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      /* end probability of death */
    
        fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(i=1; i<=nlstate;i++){
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
          }
   free_matrix(matcov,1,npar,1,npar);      } 
   free_vector(delti,1,npar);      fprintf(ficresprobmorprev,"\n");
    
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);      fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
   printf("End of Imach\n");        for(j=1; j<=nlstate;j++){
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
          }
   /* 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(ficresvij,"\n");
   /*printf("Total time was %d uSec.\n", total_usecs);*/      free_matrix(gp,0,nhstepm,1,nlstate);
   /*------ End -----------*/      free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
  end:      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
 #ifdef windows      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  chdir(pathcd);    } /* End age */
 #endif    free_vector(gpp,nlstate+1,nlstate+ndeath);
  system("wgnuplot graph.plt");    free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
 #ifdef windows    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   while (z[0] != 'q') {    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     chdir(pathcd);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     printf("\nType e to edit output files, c to start again, and q for exiting: ");    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
     scanf("%s",z);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
     if (z[0] == 'c') system("./imach");  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
     else if (z[0] == 'e') {  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
       chdir(path);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
       system("index.htm");    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);
     else if (z[0] == 'q') exit(0);    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);
 #endif    /*  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 */
   
   /***********************************************/
   /**************** 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;
   #include <sys/time.h>
   #include <time.h>
     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);*/
       
     /* 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);
   
       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 ipmx number of contributions and 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);*/
   
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     strcat(optionfilegnuplot,".gp");
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     fclose(ficgp);
     printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfile);
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   Total number of observations=%d <br>\n\
   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\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",\
             version,title,datafile,firstpass,lastpass,stepm, weightopt,\
             model,imx,agemin,agemax,jmin,jmax,jmean,fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot);
     fclose(fichtm);
   
     printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                  model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                  jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
    
     /*------------ free_vector  -------------*/
     chdir(path);
    
     free_ivector(wav,1,imx);
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
     free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
     free_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);*/
     /*------ 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.1.5  
changed lines
  Added in v.1.85


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