Diff for /imach/src/imach.c between versions 1.41.2.2 and 1.85

version 1.41.2.2, 2003/06/13 07:45:28 version 1.85, 2003/06/17 13:12:43
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.85  2003/06/17 13:12:43  brouard
      * imach.c (Repository): Check when date of death was earlier that
   This program computes Healthy Life Expectancies from    current date of interview. It may happen when the death was just
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    prior to the death. In this case, dh was negative and likelihood
   first survey ("cross") where individuals from different ages are    was wrong (infinity). We still send an "Error" but patch by
   interviewed on their health status or degree of disability (in the    assuming that the date of death was just one stepm after the
   case of a health survey which is our main interest) -2- at least a    interview.
   second wave of interviews ("longitudinal") which measure each change    (Repository): Because some people have very long ID (first column)
   (if any) in individual health status.  Health expectancies are    we changed int to long in num[] and we added a new lvector for
   computed from the time spent in each health state according to a    memory allocation. But we also truncated to 8 characters (left
   model. More health states you consider, more time is necessary to reach the    truncation)
   Maximum Likelihood of the parameters involved in the model.  The    (Repository): No more line truncation errors.
   simplest model is the multinomial logistic model where pij is the  
   probability to be observed in state j at the second wave    Revision 1.84  2003/06/13 21:44:43  brouard
   conditional to be observed in state i at the first wave. Therefore    * imach.c (Repository): Replace "freqsummary" at a correct
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    place. It differs from routine "prevalence" which may be called
   'age' is age and 'sex' is a covariate. If you want to have a more    many times. Probs is memory consuming and must be used with
   complex model than "constant and age", you should modify the program    parcimony.
   where the markup *Covariates have to be included here again* invites    Version 0.95a2 (should output exactly the same maximization than 0.8a2)
   you to do it.  More covariates you add, slower the  
   convergence.    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.82  2003/06/05 15:57:20  brouard
   identical for each individual. Also, if a individual missed an    Add log in  imach.c and  fullversion number is now printed.
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.    */
   /*
   hPijx is the probability to be observed in state i at age x+h     Interpolated Markov Chain
   conditional to the observed state i at age x. The delay 'h' can be  
   split into an exact number (nh*stepm) of unobserved intermediate    Short summary of the programme:
   states. This elementary transition (by month or quarter trimester,    
   semester or year) is model as a multinomial logistic.  The hPx    This program computes Healthy Life Expectancies from
   matrix is simply the matrix product of nh*stepm elementary matrices    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   and the contribution of each individual to the likelihood is simply    first survey ("cross") where individuals from different ages are
   hPijx.    interviewed on their health status or degree of disability (in the
     case of a health survey which is our main interest) -2- at least a
   Also this programme outputs the covariance matrix of the parameters but also    second wave of interviews ("longitudinal") which measure each change
   of the life expectancies. It also computes the prevalence limits.    (if any) in individual health status.  Health expectancies are
      computed from the time spent in each health state according to a
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    model. More health states you consider, more time is necessary to reach the
            Institut national d'études démographiques, Paris.    Maximum Likelihood of the parameters involved in the model.  The
   This software have been partly granted by Euro-REVES, a concerted action    simplest model is the multinomial logistic model where pij is the
   from the European Union.    probability to be observed in state j at the second wave
   It is copyrighted identically to a GNU software product, ie programme and    conditional to be observed in state i at the first wave. Therefore
   software can be distributed freely for non commercial use. Latest version    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   can be accessed at http://euroreves.ined.fr/imach .    'age' is age and 'sex' is a covariate. If you want to have a more
   **********************************************************************/    complex model than "constant and age", you should modify the program
      where the markup *Covariates have to be included here again* invites
 #include <math.h>    you to do it.  More covariates you add, slower the
 #include <stdio.h>    convergence.
 #include <stdlib.h>  
 #include <unistd.h>    The advantage of this computer programme, compared to a simple
     multinomial logistic model, is clear when the delay between waves is not
 #define MAXLINE 256    identical for each individual. Also, if a individual missed an
 #define GNUPLOTPROGRAM "wgnuplot"    intermediate interview, the information is lost, but taken into
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    account using an interpolation or extrapolation.  
 #define FILENAMELENGTH 80  
 /*#define DEBUG*/    hPijx is the probability to be observed in state i at age x+h
     conditional to the observed state i at age x. The delay 'h' can be
 /*#define windows*/    split into an exact number (nh*stepm) of unobserved intermediate
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    states. This elementary transition (by month, quarter,
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    semester or year) is modelled as a multinomial logistic.  The hPx
     matrix is simply the matrix product of nh*stepm elementary matrices
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    and the contribution of each individual to the likelihood is simply
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    hPijx.
   
 #define NINTERVMAX 8    Also this programme outputs the covariance matrix of the parameters but also
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    of the life expectancies. It also computes the stable prevalence. 
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    
 #define NCOVMAX 8 /* Maximum number of covariates */    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 #define MAXN 20000             Institut national d'études démographiques, Paris.
 #define YEARM 12. /* Number of months per year */    This software have been partly granted by Euro-REVES, a concerted action
 #define AGESUP 130    from the European Union.
 #define AGEBASE 40    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
     can be accessed at http://euroreves.ined.fr/imach .
 int erreur; /* Error number */  
 int nvar;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 int npar=NPARMAX;    
 int nlstate=2; /* Number of live states */    **********************************************************************/
 int ndeath=1; /* Number of dead states */  /*
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    main
 int popbased=0;    read parameterfile
     read datafile
 int *wav; /* Number of waves for this individuual 0 is possible */    concatwav
 int maxwav; /* Maxim number of waves */    freqsummary
 int jmin, jmax; /* min, max spacing between 2 waves */    if (mle >= 1)
 int mle, weightopt;      mlikeli
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    print results files
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    if mle==1 
 double jmean; /* Mean space between 2 waves */       computes hessian
 double **oldm, **newm, **savm; /* Working pointers to matrices */    read end of parameter file: agemin, agemax, bage, fage, estepm
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */        begin-prev-date,...
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    open gnuplot file
 FILE *ficgp,*ficresprob,*ficpop;    open html file
 FILE *ficreseij;    stable prevalence
   char filerese[FILENAMELENGTH];     for age prevalim()
  FILE  *ficresvij;    h Pij x
   char fileresv[FILENAMELENGTH];    variance of p varprob
  FILE  *ficresvpl;    forecasting if prevfcast==1 prevforecast call prevalence()
   char fileresvpl[FILENAMELENGTH];    health expectancies
     Variance-covariance of DFLE
 #define NR_END 1    prevalence()
 #define FREE_ARG char*     movingaverage()
 #define FTOL 1.0e-10    varevsij() 
     if popbased==1 varevsij(,popbased)
 #define NRANSI    total life expectancies
 #define ITMAX 200    Variance of stable prevalence
    end
 #define TOL 2.0e-4  */
   
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);   
   #include <math.h>
 #define GOLD 1.618034  #include <stdio.h>
 #define GLIMIT 100.0  #include <stdlib.h>
 #define TINY 1.0e-20  #include <unistd.h>
   
 static double maxarg1,maxarg2;  #define MAXLINE 256
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  #define GNUPLOTPROGRAM "gnuplot"
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
    #define FILENAMELENGTH 132
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  /*#define DEBUG*/
 #define rint(a) floor(a+0.5)  /*#define windows*/
   #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 static double sqrarg;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 int imx;  
 int stepm;  #define NINTERVMAX 8
 /* Stepm, step in month: minimum step interpolation*/  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 int estepm;  #define NCOVMAX 8 /* Maximum number of covariates */
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  #define MAXN 20000
   #define YEARM 12. /* Number of months per year */
 int m,nb;  #define AGESUP 130
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  #define AGEBASE 40
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  #ifdef unix
 double **pmmij, ***probs, ***mobaverage;  #define DIRSEPARATOR '/'
 double dateintmean=0;  #define ODIRSEPARATOR '\\'
   #else
 double *weight;  #define DIRSEPARATOR '\\'
 int **s; /* Status */  #define ODIRSEPARATOR '/'
 double *agedc, **covar, idx;  #endif
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
   /* $Id$ */
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  /* $State$ */
 double ftolhess; /* Tolerance for computing hessian */  
   char version[]="Imach version 0.95a2, June 2003, INED-EUROREVES ";
 /**************** split *************************/  char fullversion[]="$Revision$ $Date$"; 
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  int erreur; /* Error number */
 {  int nvar;
    char *s;                             /* pointer */  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
    int  l1, l2;                         /* length counters */  int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
    l1 = strlen( path );                 /* length of path */  int ndeath=1; /* Number of dead states */
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #ifdef windows  int popbased=0;
    s = strrchr( path, '\\' );           /* find last / */  
 #else  int *wav; /* Number of waves for this individuual 0 is possible */
    s = strrchr( path, '/' );            /* find last / */  int maxwav; /* Maxim number of waves */
 #endif  int jmin, jmax; /* min, max spacing between 2 waves */
    if ( s == NULL ) {                   /* no directory, so use current */  int mle, weightopt;
 #if     defined(__bsd__)                /* get current working directory */  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       extern char       *getwd( );  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
       if ( getwd( dirc ) == NULL ) {             * wave mi and wave mi+1 is not an exact multiple of stepm. */
 #else  double jmean; /* Mean space between 2 waves */
       extern char       *getcwd( );  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 #endif  FILE *ficlog, *ficrespow;
          return( GLOCK_ERROR_GETCWD );  int globpr; /* Global variable for printing or not */
       }  double fretone; /* Only one call to likelihood */
       strcpy( name, path );             /* we've got it */  long ipmx; /* Number of contributions */
    } else {                             /* strip direcotry from path */  double sw; /* Sum of weights */
       s++;                              /* after this, the filename */  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       l2 = strlen( s );                 /* length of filename */  FILE *ficresilk;
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       strcpy( name, s );                /* save file name */  FILE *ficresprobmorprev;
       strncpy( dirc, path, l1 - l2 );   /* now the directory */  FILE *fichtm; /* Html File */
       dirc[l1-l2] = 0;                  /* add zero */  FILE *ficreseij;
    }  char filerese[FILENAMELENGTH];
    l1 = strlen( dirc );                 /* length of directory */  FILE  *ficresvij;
 #ifdef windows  char fileresv[FILENAMELENGTH];
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  FILE  *ficresvpl;
 #else  char fileresvpl[FILENAMELENGTH];
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }  char title[MAXLINE];
 #endif  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
    s = strrchr( name, '.' );            /* find last / */  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
    s++;  
    strcpy(ext,s);                       /* save extension */  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
    l1= strlen( name);  char filelog[FILENAMELENGTH]; /* Log file */
    l2= strlen( s)+1;  char filerest[FILENAMELENGTH];
    strncpy( finame, name, l1-l2);  char fileregp[FILENAMELENGTH];
    finame[l1-l2]= 0;  char popfile[FILENAMELENGTH];
    return( 0 );                         /* we're done */  
 }  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
   
   #define NR_END 1
 /******************************************/  #define FREE_ARG char*
   #define FTOL 1.0e-10
 void replace(char *s, char*t)  
 {  #define NRANSI 
   int i;  #define ITMAX 200 
   int lg=20;  
   i=0;  #define TOL 2.0e-4 
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {  #define CGOLD 0.3819660 
     (s[i] = t[i]);  #define ZEPS 1.0e-10 
     if (t[i]== '\\') s[i]='/';  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   }  
 }  #define GOLD 1.618034 
   #define GLIMIT 100.0 
 int nbocc(char *s, char occ)  #define TINY 1.0e-20 
 {  
   int i,j=0;  static double maxarg1,maxarg2;
   int lg=20;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   i=0;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   lg=strlen(s);    
   for(i=0; i<= lg; i++) {  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   if  (s[i] == occ ) j++;  #define rint(a) floor(a+0.5)
   }  
   return j;  static double sqrarg;
 }  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 void cutv(char *u,char *v, char*t, char occ)  
 {  int imx; 
   int i,lg,j,p=0;  int stepm;
   i=0;  /* Stepm, step in month: minimum step interpolation*/
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  int estepm;
   }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
   lg=strlen(t);  int m,nb;
   for(j=0; j<p; j++) {  long *num;
     (u[j] = t[j]);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
   }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
      u[p]='\0';  double **pmmij, ***probs;
   double dateintmean=0;
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);  double *weight;
   }  int **s; /* Status */
 }  double *agedc, **covar, idx;
   int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 /********************** nrerror ********************/  
   double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 void nrerror(char error_text[])  double ftolhess; /* Tolerance for computing hessian */
 {  
   fprintf(stderr,"ERREUR ...\n");  /**************** split *************************/
   fprintf(stderr,"%s\n",error_text);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   exit(1);  {
 }    char  *ss;                            /* pointer */
 /*********************** vector *******************/    int   l1, l2;                         /* length counters */
 double *vector(int nl, int nh)  
 {    l1 = strlen(path );                   /* length of path */
   double *v;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   if (!v) nrerror("allocation failure in vector");    if ( ss == NULL ) {                   /* no directory, so use current */
   return v-nl+NR_END;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
 }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       /* get current working directory */
 /************************ free vector ******************/      /*    extern  char* getcwd ( char *buf , int len);*/
 void free_vector(double*v, int nl, int nh)      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 {        return( GLOCK_ERROR_GETCWD );
   free((FREE_ARG)(v+nl-NR_END));      }
 }      strcpy( name, path );               /* we've got it */
     } else {                              /* strip direcotry from path */
 /************************ivector *******************************/      ss++;                               /* after this, the filename */
 int *ivector(long nl,long nh)      l2 = strlen( ss );                  /* length of filename */
 {      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   int *v;      strcpy( name, ss );         /* save file name */
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   if (!v) nrerror("allocation failure in ivector");      dirc[l1-l2] = 0;                    /* add zero */
   return v-nl+NR_END;    }
 }    l1 = strlen( dirc );                  /* length of directory */
     /*#ifdef windows
 /******************free ivector **************************/    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
 void free_ivector(int *v, long nl, long nh)  #else
 {    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   free((FREE_ARG)(v+nl-NR_END));  #endif
 }    */
     ss = strrchr( name, '.' );            /* find last / */
 /******************* imatrix *******************************/    ss++;
 int **imatrix(long nrl, long nrh, long ncl, long nch)    strcpy(ext,ss);                       /* save extension */
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    l1= strlen( name);
 {    l2= strlen(ss)+1;
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    strncpy( finame, name, l1-l2);
   int **m;    finame[l1-l2]= 0;
      return( 0 );                          /* we're done */
   /* allocate pointers to rows */  }
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  /******************************************/
   m -= nrl;  
    void replace(char *s, char*t)
    {
   /* allocate rows and set pointers to them */    int i;
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    int lg=20;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    i=0;
   m[nrl] += NR_END;    lg=strlen(t);
   m[nrl] -= ncl;    for(i=0; i<= lg; i++) {
        (s[i] = t[i]);
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;      if (t[i]== '\\') s[i]='/';
      }
   /* return pointer to array of pointers to rows */  }
   return m;  
 }  int nbocc(char *s, char occ)
   {
 /****************** free_imatrix *************************/    int i,j=0;
 void free_imatrix(m,nrl,nrh,ncl,nch)    int lg=20;
       int **m;    i=0;
       long nch,ncl,nrh,nrl;    lg=strlen(s);
      /* free an int matrix allocated by imatrix() */    for(i=0; i<= lg; i++) {
 {    if  (s[i] == occ ) j++;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    }
   free((FREE_ARG) (m+nrl-NR_END));    return j;
 }  }
   
 /******************* matrix *******************************/  void cutv(char *u,char *v, char*t, char occ)
 double **matrix(long nrl, long nrh, long ncl, long nch)  {
 {    /* cuts string t into u and v where u is ended by char occ excluding it
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
   double **m;       gives u="abcedf" and v="ghi2j" */
     int i,lg,j,p=0;
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    i=0;
   if (!m) nrerror("allocation failure 1 in matrix()");    for(j=0; j<=strlen(t)-1; j++) {
   m += NR_END;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   m -= nrl;    }
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    lg=strlen(t);
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    for(j=0; j<p; j++) {
   m[nrl] += NR_END;      (u[j] = t[j]);
   m[nrl] -= ncl;    }
        u[p]='\0';
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   return m;     for(j=0; j<= lg; j++) {
 }      if (j>=(p+1))(v[j-p-1] = t[j]);
     }
 /*************************free matrix ************************/  }
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  
 {  /********************** nrerror ********************/
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  void nrerror(char error_text[])
 }  {
     fprintf(stderr,"ERREUR ...\n");
 /******************* ma3x *******************************/    fprintf(stderr,"%s\n",error_text);
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    exit(EXIT_FAILURE);
 {  }
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  /*********************** vector *******************/
   double ***m;  double *vector(int nl, int nh)
   {
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    double *v;
   if (!m) nrerror("allocation failure 1 in matrix()");    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   m += NR_END;    if (!v) nrerror("allocation failure in vector");
   m -= nrl;    return v-nl+NR_END;
   }
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /************************ free vector ******************/
   m[nrl] += NR_END;  void free_vector(double*v, int nl, int nh)
   m[nrl] -= ncl;  {
     free((FREE_ARG)(v+nl-NR_END));
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  }
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  /************************ivector *******************************/
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  int *ivector(long nl,long nh)
   m[nrl][ncl] += NR_END;  {
   m[nrl][ncl] -= nll;    int *v;
   for (j=ncl+1; j<=nch; j++)    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     m[nrl][j]=m[nrl][j-1]+nlay;    if (!v) nrerror("allocation failure in ivector");
      return v-nl+NR_END;
   for (i=nrl+1; i<=nrh; i++) {  }
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  /******************free ivector **************************/
       m[i][j]=m[i][j-1]+nlay;  void free_ivector(int *v, long nl, long nh)
   }  {
   return m;    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************************free ma3x ************************/  /************************lvector *******************************/
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  long *lvector(long nl,long nh)
 {  {
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    long *v;
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   free((FREE_ARG)(m+nrl-NR_END));    if (!v) nrerror("allocation failure in ivector");
 }    return v-nl+NR_END;
   }
 /***************** f1dim *************************/  
 extern int ncom;  /******************free lvector **************************/
 extern double *pcom,*xicom;  void free_lvector(long *v, long nl, long nh)
 extern double (*nrfunc)(double []);  {
      free((FREE_ARG)(v+nl-NR_END));
 double f1dim(double x)  }
 {  
   int j;  /******************* imatrix *******************************/
   double f;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   double *xt;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
    { 
   xt=vector(1,ncom);    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    int **m; 
   f=(*nrfunc)(xt);    
   free_vector(xt,1,ncom);    /* allocate pointers to rows */ 
   return f;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
 }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
 /*****************brent *************************/    m -= nrl; 
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    
 {    
   int iter;    /* allocate rows and set pointers to them */ 
   double a,b,d,etemp;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   double fu,fv,fw,fx;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   double ftemp;    m[nrl] += NR_END; 
   double p,q,r,tol1,tol2,u,v,w,x,xm;    m[nrl] -= ncl; 
   double e=0.0;    
      for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   a=(ax < cx ? ax : cx);    
   b=(ax > cx ? ax : cx);    /* return pointer to array of pointers to rows */ 
   x=w=v=bx;    return m; 
   fw=fv=fx=(*f)(x);  } 
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);  /****************** free_imatrix *************************/
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  void free_imatrix(m,nrl,nrh,ncl,nch)
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/        int **m;
     printf(".");fflush(stdout);        long nch,ncl,nrh,nrl; 
 #ifdef DEBUG       /* free an int matrix allocated by imatrix() */ 
     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)))) { */    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 #endif    free((FREE_ARG) (m+nrl-NR_END)); 
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  } 
       *xmin=x;  
       return fx;  /******************* matrix *******************************/
     }  double **matrix(long nrl, long nrh, long ncl, long nch)
     ftemp=fu;  {
     if (fabs(e) > tol1) {    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       r=(x-w)*(fx-fv);    double **m;
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       q=2.0*(q-r);    if (!m) nrerror("allocation failure 1 in matrix()");
       if (q > 0.0) p = -p;    m += NR_END;
       q=fabs(q);    m -= nrl;
       etemp=e;  
       e=d;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    m[nrl] += NR_END;
       else {    m[nrl] -= ncl;
         d=p/q;  
         u=x+d;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         if (u-a < tol2 || b-u < tol2)    return m;
           d=SIGN(tol1,xm-x);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       }     */
     } else {  }
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  
     }  /*************************free matrix ************************/
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     fu=(*f)(u);  {
     if (fu <= fx) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       if (u >= x) a=x; else b=x;    free((FREE_ARG)(m+nrl-NR_END));
       SHFT(v,w,x,u)  }
         SHFT(fv,fw,fx,fu)  
         } else {  /******************* ma3x *******************************/
           if (u < x) a=u; else b=u;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
           if (fu <= fw || w == x) {  {
             v=w;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
             w=u;    double ***m;
             fv=fw;  
             fw=fu;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
           } else if (fu <= fv || v == x || v == w) {    if (!m) nrerror("allocation failure 1 in matrix()");
             v=u;    m += NR_END;
             fv=fu;    m -= nrl;
           }  
         }    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   nrerror("Too many iterations in brent");    m[nrl] += NR_END;
   *xmin=x;    m[nrl] -= ncl;
   return fx;  
 }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   
 /****************** mnbrak ***********************/    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    m[nrl][ncl] += NR_END;
             double (*func)(double))    m[nrl][ncl] -= nll;
 {    for (j=ncl+1; j<=nch; j++) 
   double ulim,u,r,q, dum;      m[nrl][j]=m[nrl][j-1]+nlay;
   double fu;    
      for (i=nrl+1; i<=nrh; i++) {
   *fa=(*func)(*ax);      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   *fb=(*func)(*bx);      for (j=ncl+1; j<=nch; j++) 
   if (*fb > *fa) {        m[i][j]=m[i][j-1]+nlay;
     SHFT(dum,*ax,*bx,dum)    }
       SHFT(dum,*fb,*fa,dum)    return m; 
       }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   *cx=(*bx)+GOLD*(*bx-*ax);             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   *fc=(*func)(*cx);    */
   while (*fb > *fc) {  }
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  /*************************free ma3x ************************/
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  {
     ulim=(*bx)+GLIMIT*(*cx-*bx);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     if ((*bx-u)*(u-*cx) > 0.0) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       fu=(*func)(u);    free((FREE_ARG)(m+nrl-NR_END));
     } else if ((*cx-u)*(u-ulim) > 0.0) {  }
       fu=(*func)(u);  
       if (fu < *fc) {  /***************** f1dim *************************/
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  extern int ncom; 
           SHFT(*fb,*fc,fu,(*func)(u))  extern double *pcom,*xicom;
           }  extern double (*nrfunc)(double []); 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {   
       u=ulim;  double f1dim(double x) 
       fu=(*func)(u);  { 
     } else {    int j; 
       u=(*cx)+GOLD*(*cx-*bx);    double f;
       fu=(*func)(u);    double *xt; 
     }   
     SHFT(*ax,*bx,*cx,u)    xt=vector(1,ncom); 
       SHFT(*fa,*fb,*fc,fu)    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       }    f=(*nrfunc)(xt); 
 }    free_vector(xt,1,ncom); 
     return f; 
 /*************** linmin ************************/  } 
   
 int ncom;  /*****************brent *************************/
 double *pcom,*xicom;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
 double (*nrfunc)(double []);  { 
      int iter; 
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    double a,b,d,etemp;
 {    double fu,fv,fw,fx;
   double brent(double ax, double bx, double cx,    double ftemp;
                double (*f)(double), double tol, double *xmin);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   double f1dim(double x);    double e=0.0; 
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,   
               double *fc, double (*func)(double));    a=(ax < cx ? ax : cx); 
   int j;    b=(ax > cx ? ax : cx); 
   double xx,xmin,bx,ax;    x=w=v=bx; 
   double fx,fb,fa;    fw=fv=fx=(*f)(x); 
      for (iter=1;iter<=ITMAX;iter++) { 
   ncom=n;      xm=0.5*(a+b); 
   pcom=vector(1,n);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   xicom=vector(1,n);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   nrfunc=func;      printf(".");fflush(stdout);
   for (j=1;j<=n;j++) {      fprintf(ficlog,".");fflush(ficlog);
     pcom[j]=p[j];  #ifdef DEBUG
     xicom[j]=xi[j];      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   }      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);
   ax=0.0;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   xx=1.0;  #endif
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);        *xmin=x; 
 #ifdef DEBUG        return fx; 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);      } 
 #endif      ftemp=fu;
   for (j=1;j<=n;j++) {      if (fabs(e) > tol1) { 
     xi[j] *= xmin;        r=(x-w)*(fx-fv); 
     p[j] += xi[j];        q=(x-v)*(fx-fw); 
   }        p=(x-v)*q-(x-w)*r; 
   free_vector(xicom,1,n);        q=2.0*(q-r); 
   free_vector(pcom,1,n);        if (q > 0.0) p = -p; 
 }        q=fabs(q); 
         etemp=e; 
 /*************** powell ************************/        e=d; 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
             double (*func)(double []))          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
 {        else { 
   void linmin(double p[], double xi[], int n, double *fret,          d=p/q; 
               double (*func)(double []));          u=x+d; 
   int i,ibig,j;          if (u-a < tol2 || b-u < tol2) 
   double del,t,*pt,*ptt,*xit;            d=SIGN(tol1,xm-x); 
   double fp,fptt;        } 
   double *xits;      } else { 
   pt=vector(1,n);        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   ptt=vector(1,n);      } 
   xit=vector(1,n);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   xits=vector(1,n);      fu=(*f)(u); 
   *fret=(*func)(p);      if (fu <= fx) { 
   for (j=1;j<=n;j++) pt[j]=p[j];        if (u >= x) a=x; else b=x; 
   for (*iter=1;;++(*iter)) {        SHFT(v,w,x,u) 
     fp=(*fret);          SHFT(fv,fw,fx,fu) 
     ibig=0;          } else { 
     del=0.0;            if (u < x) a=u; else b=u; 
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);            if (fu <= fw || w == x) { 
     for (i=1;i<=n;i++)              v=w; 
       printf(" %d %.12f",i, p[i]);              w=u; 
     printf("\n");              fv=fw; 
     for (i=1;i<=n;i++) {              fw=fu; 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];            } else if (fu <= fv || v == x || v == w) { 
       fptt=(*fret);              v=u; 
 #ifdef DEBUG              fv=fu; 
       printf("fret=%lf \n",*fret);            } 
 #endif          } 
       printf("%d",i);fflush(stdout);    } 
       linmin(p,xit,n,fret,func);    nrerror("Too many iterations in brent"); 
       if (fabs(fptt-(*fret)) > del) {    *xmin=x; 
         del=fabs(fptt-(*fret));    return fx; 
         ibig=i;  } 
       }  
 #ifdef DEBUG  /****************** mnbrak ***********************/
       printf("%d %.12e",i,(*fret));  
       for (j=1;j<=n;j++) {  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);              double (*func)(double)) 
         printf(" x(%d)=%.12e",j,xit[j]);  { 
       }    double ulim,u,r,q, dum;
       for(j=1;j<=n;j++)    double fu; 
         printf(" p=%.12e",p[j]);   
       printf("\n");    *fa=(*func)(*ax); 
 #endif    *fb=(*func)(*bx); 
     }    if (*fb > *fa) { 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      SHFT(dum,*ax,*bx,dum) 
 #ifdef DEBUG        SHFT(dum,*fb,*fa,dum) 
       int k[2],l;        } 
       k[0]=1;    *cx=(*bx)+GOLD*(*bx-*ax); 
       k[1]=-1;    *fc=(*func)(*cx); 
       printf("Max: %.12e",(*func)(p));    while (*fb > *fc) { 
       for (j=1;j<=n;j++)      r=(*bx-*ax)*(*fb-*fc); 
         printf(" %.12e",p[j]);      q=(*bx-*cx)*(*fb-*fa); 
       printf("\n");      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       for(l=0;l<=1;l++) {        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
         for (j=1;j<=n;j++) {      ulim=(*bx)+GLIMIT*(*cx-*bx); 
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      if ((*bx-u)*(u-*cx) > 0.0) { 
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);        fu=(*func)(u); 
         }      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));        fu=(*func)(u); 
       }        if (fu < *fc) { 
 #endif          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
             } 
       free_vector(xit,1,n);      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       free_vector(xits,1,n);        u=ulim; 
       free_vector(ptt,1,n);        fu=(*func)(u); 
       free_vector(pt,1,n);      } else { 
       return;        u=(*cx)+GOLD*(*cx-*bx); 
     }        fu=(*func)(u); 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");      } 
     for (j=1;j<=n;j++) {      SHFT(*ax,*bx,*cx,u) 
       ptt[j]=2.0*p[j]-pt[j];        SHFT(*fa,*fb,*fc,fu) 
       xit[j]=p[j]-pt[j];        } 
       pt[j]=p[j];  } 
     }  
     fptt=(*func)(ptt);  /*************** linmin ************************/
     if (fptt < fp) {  
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  int ncom; 
       if (t < 0.0) {  double *pcom,*xicom;
         linmin(p,xit,n,fret,func);  double (*nrfunc)(double []); 
         for (j=1;j<=n;j++) {   
           xi[j][ibig]=xi[j][n];  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
           xi[j][n]=xit[j];  { 
         }    double brent(double ax, double bx, double cx, 
 #ifdef DEBUG                 double (*f)(double), double tol, double *xmin); 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    double f1dim(double x); 
         for(j=1;j<=n;j++)    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
           printf(" %.12e",xit[j]);                double *fc, double (*func)(double)); 
         printf("\n");    int j; 
 #endif    double xx,xmin,bx,ax; 
       }    double fx,fb,fa;
     }   
   }    ncom=n; 
 }    pcom=vector(1,n); 
     xicom=vector(1,n); 
 /**** Prevalence limit ****************/    nrfunc=func; 
     for (j=1;j<=n;j++) { 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      pcom[j]=p[j]; 
 {      xicom[j]=xi[j]; 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    } 
      matrix by transitions matrix until convergence is reached */    ax=0.0; 
     xx=1.0; 
   int i, ii,j,k;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   double min, max, maxmin, maxmax,sumnew=0.;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   double **matprod2();  #ifdef DEBUG
   double **out, cov[NCOVMAX], **pmij();    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   double **newm;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   double agefin, delaymax=50 ; /* Max number of years to converge */  #endif
     for (j=1;j<=n;j++) { 
   for (ii=1;ii<=nlstate+ndeath;ii++)      xi[j] *= xmin; 
     for (j=1;j<=nlstate+ndeath;j++){      p[j] += xi[j]; 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    } 
     }    free_vector(xicom,1,n); 
     free_vector(pcom,1,n); 
    cov[1]=1.;  } 
    
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /*************** powell ************************/
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     newm=savm;              double (*func)(double [])) 
     /* Covariates have to be included here again */  { 
      cov[2]=agefin;    void linmin(double p[], double xi[], int n, double *fret, 
                  double (*func)(double [])); 
       for (k=1; k<=cptcovn;k++) {    int i,ibig,j; 
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    double del,t,*pt,*ptt,*xit;
         /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/    double fp,fptt;
       }    double *xits;
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    pt=vector(1,n); 
       for (k=1; k<=cptcovprod;k++)    ptt=vector(1,n); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    xit=vector(1,n); 
     xits=vector(1,n); 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    *fret=(*func)(p); 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    for (j=1;j<=n;j++) pt[j]=p[j]; 
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    for (*iter=1;;++(*iter)) { 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);      fp=(*fret); 
       ibig=0; 
     savm=oldm;      del=0.0; 
     oldm=newm;      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
     maxmax=0.;      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
     for(j=1;j<=nlstate;j++){      fprintf(ficrespow,"%d %.12f",*iter,*fret);
       min=1.;      for (i=1;i<=n;i++) {
       max=0.;        printf(" %d %.12f",i, p[i]);
       for(i=1; i<=nlstate; i++) {        fprintf(ficlog," %d %.12lf",i, p[i]);
         sumnew=0;        fprintf(ficrespow," %.12lf", p[i]);
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];      }
         prlim[i][j]= newm[i][j]/(1-sumnew);      printf("\n");
         max=FMAX(max,prlim[i][j]);      fprintf(ficlog,"\n");
         min=FMIN(min,prlim[i][j]);      fprintf(ficrespow,"\n");
       }      for (i=1;i<=n;i++) { 
       maxmin=max-min;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
       maxmax=FMAX(maxmax,maxmin);        fptt=(*fret); 
     }  #ifdef DEBUG
     if(maxmax < ftolpl){        printf("fret=%lf \n",*fret);
       return prlim;        fprintf(ficlog,"fret=%lf \n",*fret);
     }  #endif
   }        printf("%d",i);fflush(stdout);
 }        fprintf(ficlog,"%d",i);fflush(ficlog);
         linmin(p,xit,n,fret,func); 
 /*************** transition probabilities ***************/        if (fabs(fptt-(*fret)) > del) { 
           del=fabs(fptt-(*fret)); 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )          ibig=i; 
 {        } 
   double s1, s2;  #ifdef DEBUG
   /*double t34;*/        printf("%d %.12e",i,(*fret));
   int i,j,j1, nc, ii, jj;        fprintf(ficlog,"%d %.12e",i,(*fret));
         for (j=1;j<=n;j++) {
     for(i=1; i<= nlstate; i++){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     for(j=1; j<i;j++){          printf(" x(%d)=%.12e",j,xit[j]);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         /*s2 += param[i][j][nc]*cov[nc];*/        }
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];        for(j=1;j<=n;j++) {
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/          printf(" p=%.12e",p[j]);
       }          fprintf(ficlog," p=%.12e",p[j]);
       ps[i][j]=s2;        }
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/        printf("\n");
     }        fprintf(ficlog,"\n");
     for(j=i+1; j<=nlstate+ndeath;j++){  #endif
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      } 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  #ifdef DEBUG
       }        int k[2],l;
       ps[i][j]=s2;        k[0]=1;
     }        k[1]=-1;
   }        printf("Max: %.12e",(*func)(p));
     /*ps[3][2]=1;*/        fprintf(ficlog,"Max: %.12e",(*func)(p));
         for (j=1;j<=n;j++) {
   for(i=1; i<= nlstate; i++){          printf(" %.12e",p[j]);
      s1=0;          fprintf(ficlog," %.12e",p[j]);
     for(j=1; j<i; j++)        }
       s1+=exp(ps[i][j]);        printf("\n");
     for(j=i+1; j<=nlstate+ndeath; j++)        fprintf(ficlog,"\n");
       s1+=exp(ps[i][j]);        for(l=0;l<=1;l++) {
     ps[i][i]=1./(s1+1.);          for (j=1;j<=n;j++) {
     for(j=1; j<i; j++)            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
       ps[i][j]= exp(ps[i][j])*ps[i][i];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     for(j=i+1; j<=nlstate+ndeath; j++)            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       ps[i][j]= exp(ps[i][j])*ps[i][i];          }
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   } /* end i */          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         }
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  #endif
     for(jj=1; jj<= nlstate+ndeath; jj++){  
       ps[ii][jj]=0;  
       ps[ii][ii]=1;        free_vector(xit,1,n); 
     }        free_vector(xits,1,n); 
   }        free_vector(ptt,1,n); 
         free_vector(pt,1,n); 
         return; 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      } 
     for(jj=1; jj<= nlstate+ndeath; jj++){      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
      printf("%lf ",ps[ii][jj]);      for (j=1;j<=n;j++) { 
    }        ptt[j]=2.0*p[j]-pt[j]; 
     printf("\n ");        xit[j]=p[j]-pt[j]; 
     }        pt[j]=p[j]; 
     printf("\n ");printf("%lf ",cov[2]);*/      } 
 /*      fptt=(*func)(ptt); 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);      if (fptt < fp) { 
   goto end;*/        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     return ps;        if (t < 0.0) { 
 }          linmin(p,xit,n,fret,func); 
           for (j=1;j<=n;j++) { 
 /**************** Product of 2 matrices ******************/            xi[j][ibig]=xi[j][n]; 
             xi[j][n]=xit[j]; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)          }
 {  #ifdef DEBUG
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   /* 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",xit[j]);
      a pointer to pointers identical to out */            fprintf(ficlog," %.12e",xit[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++)  #endif
         out[i][k] +=in[i][j]*b[j][k];        }
       } 
   return out;    } 
 }  } 
   
   /**** Prevalence limit (stable prevalence)  ****************/
 /************* Higher Matrix Product ***************/  
   double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  {
 {    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month       matrix by transitions matrix until convergence is reached */
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    int i, ii,j,k;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    double min, max, maxmin, maxmax,sumnew=0.;
      (typically every 2 years instead of every month which is too big).    double **matprod2();
      Model is determined by parameters x and covariates have to be    double **out, cov[NCOVMAX], **pmij();
      included manually here.    double **newm;
     double agefin, delaymax=50 ; /* Max number of years to converge */
      */  
     for (ii=1;ii<=nlstate+ndeath;ii++)
   int i, j, d, h, k;      for (j=1;j<=nlstate+ndeath;j++){
   double **out, cov[NCOVMAX];        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **newm;      }
   
   /* Hstepm could be zero and should return the unit matrix */     cov[1]=1.;
   for (i=1;i<=nlstate+ndeath;i++)   
     for (j=1;j<=nlstate+ndeath;j++){   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       oldm[i][j]=(i==j ? 1.0 : 0.0);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       po[i][j][0]=(i==j ? 1.0 : 0.0);      newm=savm;
     }      /* Covariates have to be included here again */
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */       cov[2]=agefin;
   for(h=1; h <=nhstepm; h++){    
     for(d=1; d <=hstepm; d++){        for (k=1; k<=cptcovn;k++) {
       newm=savm;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       /* Covariates have to be included here again */          /*      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]]);*/
       cov[1]=1.;        }
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];        for (k=1; k<=cptcovprod;k++)
       for (k=1; k<=cptcovage;k++)          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  
       for (k=1; k<=cptcovprod;k++)        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         /*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);
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/      savm=oldm;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,      oldm=newm;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      maxmax=0.;
       savm=oldm;      for(j=1;j<=nlstate;j++){
       oldm=newm;        min=1.;
     }        max=0.;
     for(i=1; i<=nlstate+ndeath; i++)        for(i=1; i<=nlstate; i++) {
       for(j=1;j<=nlstate+ndeath;j++) {          sumnew=0;
         po[i][j][h]=newm[i][j];          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);          prlim[i][j]= newm[i][j]/(1-sumnew);
          */          max=FMAX(max,prlim[i][j]);
       }          min=FMIN(min,prlim[i][j]);
   } /* end h */        }
   return po;        maxmin=max-min;
 }        maxmax=FMAX(maxmax,maxmin);
       }
       if(maxmax < ftolpl){
 /*************** log-likelihood *************/        return prlim;
 double func( double *x)      }
 {    }
   int i, ii, j, k, mi, d, kk;  }
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;  /*************** transition probabilities ***************/ 
   double sw; /* Sum of weights */  
   double lli; /* Individual log likelihood */  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   int s1, s2;  {
   long ipmx;    double s1, s2;
   /*extern weight */    /*double t34;*/
   /* We are differentiating ll according to initial status */    int i,j,j1, nc, ii, jj;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  
   /*for(i=1;i<imx;i++)      for(i=1; i<= nlstate; i++){
     printf(" %d\n",s[4][i]);      for(j=1; j<i;j++){
   */        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   cov[1]=1.;          /*s2 += param[i][j][nc]*cov[nc];*/
           s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   for(k=1; k<=nlstate; k++) ll[k]=0.;          /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){        }
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];        ps[i][j]=s2;
     for(mi=1; mi<= wav[i]-1; mi++){        /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
       for (ii=1;ii<=nlstate+ndeath;ii++)      }
         for (j=1;j<=nlstate+ndeath;j++){      for(j=i+1; j<=nlstate+ndeath;j++){
           oldm[ii][j]=(ii==j ? 1.0 : 0.0);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
           savm[ii][j]=(ii==j ? 1.0 : 0.0);          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
         }          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
       for(d=0; d<dh[mi][i]; d++){        }
         newm=savm;        ps[i][j]=s2;
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      }
         for (kk=1; kk<=cptcovage;kk++) {    }
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      /*ps[3][2]=1;*/
         }  
            for(i=1; i<= nlstate; i++){
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,       s1=0;
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));      for(j=1; j<i; j++)
         savm=oldm;        s1+=exp(ps[i][j]);
         oldm=newm;      for(j=i+1; j<=nlstate+ndeath; j++)
                s1+=exp(ps[i][j]);
              ps[i][i]=1./(s1+1.);
       } /* end mult */      for(j=1; j<i; j++)
              ps[i][j]= exp(ps[i][j])*ps[i][i];
       s1=s[mw[mi][i]][i];      for(j=i+1; j<=nlstate+ndeath; j++)
       s2=s[mw[mi+1][i]][i];        ps[i][j]= exp(ps[i][j])*ps[i][i];
       if( s2 > nlstate){      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         /* i.e. if s2 is a death state and if the date of death is known then the contribution    } /* end i */
            to the likelihood is the probability to die between last step unit time and current  
            step unit time, which is also the differences between probability to die before dh    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
            and probability to die before dh-stepm .      for(jj=1; jj<= nlstate+ndeath; jj++){
            In version up to 0.92 likelihood was computed        ps[ii][jj]=0;
            as if date of death was unknown. Death was treated as any other        ps[ii][ii]=1;
            health state: the date of the interview describes the actual state      }
            and not the date of a change in health state. The former idea was    }
            to consider that at each interview the state was recorded  
            (healthy, disable or death) and IMaCh was corrected; but when we  
            introduced the exact date of death then we should have modified    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
            the contribution of an exact death to the likelihood. This new      for(jj=1; jj<= nlstate+ndeath; jj++){
            contribution is smaller and very dependent of the step unit       printf("%lf ",ps[ii][jj]);
            stepm. It is no more the probability to die between last interview     }
            and month of death but the probability to survive from last      printf("\n ");
            interview up to one month before death multiplied by the      }
            probability to die within a month. Thanks to Chris      printf("\n ");printf("%lf ",cov[2]);*/
            Jackson for correcting this bug.  Former versions increased  /*
            mortality artificially. The bad side is that we add another loop    for(i=1; i<= npar; i++) printf("%f ",x[i]);
            which slows down the processing. The difference can be up to 10%    goto end;*/
            lower mortality.      return ps;
         */  }
         lli=log(out[s1][s2] - savm[s1][s2]);  
       }else{  /**************** Product of 2 matrices ******************/
         lli=log(out[s1][s2]); /* or     lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); */  
         /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       }  {
       ipmx +=1;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       sw += weight[i];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    /* in, b, out are matrice of pointers which should have been initialized 
       /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d lli=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],lli,weight[i],out[s1][s2],savm[s1][s2]);*/       before: only the contents of out is modified. The function returns
     } /* end of wave */       a pointer to pointers identical to out */
   } /* end of individual */    long i, j, k;
     for(i=nrl; i<= nrh; i++)
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      for(k=ncolol; k<=ncoloh; k++)
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */        for(j=ncl,out[i][k]=0.; j<=nch; j++)
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */          out[i][k] +=in[i][j]*b[j][k];
   /*exit(0);*/  
   return -l;    return out;
 }  }
   
   
 /*********** Maximum Likelihood Estimation ***************/  /************* Higher Matrix Product ***************/
   
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
 {  {
   int i,j, iter;    /* Computes the transition matrix starting at age 'age' over 
   double **xi,*delti;       'nhstepm*hstepm*stepm' months (i.e. until
   double fret;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   xi=matrix(1,npar,1,npar);       nhstepm*hstepm matrices. 
   for (i=1;i<=npar;i++)       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     for (j=1;j<=npar;j++)       (typically every 2 years instead of every month which is too big 
       xi[i][j]=(i==j ? 1.0 : 0.0);       for the memory).
   printf("Powell\n");       Model is determined by parameters x and covariates have to be 
   powell(p,xi,npar,ftol,&iter,&fret,func);       included manually here. 
   
    printf("\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));  
     int i, j, d, h, k;
 }    double **out, cov[NCOVMAX];
     double **newm;
 /**** Computes Hessian and covariance matrix ***/  
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    /* Hstepm could be zero and should return the unit matrix */
 {    for (i=1;i<=nlstate+ndeath;i++)
   double  **a,**y,*x,pd;      for (j=1;j<=nlstate+ndeath;j++){
   double **hess;        oldm[i][j]=(i==j ? 1.0 : 0.0);
   int i, j,jk;        po[i][j][0]=(i==j ? 1.0 : 0.0);
   int *indx;      }
     /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   double hessii(double p[], double delta, int theta, double delti[]);    for(h=1; h <=nhstepm; h++){
   double hessij(double p[], double delti[], int i, int j);      for(d=1; d <=hstepm; d++){
   void lubksb(double **a, int npar, int *indx, double b[]) ;        newm=savm;
   void ludcmp(double **a, int npar, int *indx, double *d) ;        /* Covariates have to be included here again */
         cov[1]=1.;
   hess=matrix(1,npar,1,npar);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   printf("\nCalculation of the hessian matrix. Wait...\n");        for (k=1; k<=cptcovage;k++)
   for (i=1;i<=npar;i++){          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     printf("%d",i);fflush(stdout);        for (k=1; k<=cptcovprod;k++)
     hess[i][i]=hessii(p,ftolhess,i,delti);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     /*printf(" %f ",p[i]);*/  
     /*printf(" %lf ",hess[i][i]);*/  
   }        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   for (i=1;i<=npar;i++) {        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     for (j=1;j<=npar;j++)  {                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       if (j>i) {        savm=oldm;
         printf(".%d%d",i,j);fflush(stdout);        oldm=newm;
         hess[i][j]=hessij(p,delti,i,j);      }
         hess[j][i]=hess[i][j];          for(i=1; i<=nlstate+ndeath; i++)
         /*printf(" %lf ",hess[i][j]);*/        for(j=1;j<=nlstate+ndeath;j++) {
       }          po[i][j][h]=newm[i][j];
     }          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
   }           */
   printf("\n");        }
     } /* end h */
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    return po;
    }
   a=matrix(1,npar,1,npar);  
   y=matrix(1,npar,1,npar);  
   x=vector(1,npar);  /*************** log-likelihood *************/
   indx=ivector(1,npar);  double func( double *x)
   for (i=1;i<=npar;i++)  {
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    int i, ii, j, k, mi, d, kk;
   ludcmp(a,npar,indx,&pd);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     double **out;
   for (j=1;j<=npar;j++) {    double sw; /* Sum of weights */
     for (i=1;i<=npar;i++) x[i]=0;    double lli; /* Individual log likelihood */
     x[j]=1;    int s1, s2;
     lubksb(a,npar,indx,x);    double bbh, survp;
     for (i=1;i<=npar;i++){    long ipmx;
       matcov[i][j]=x[i];    /*extern weight */
     }    /* We are differentiating ll according to initial status */
   }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     /*for(i=1;i<imx;i++) 
   printf("\n#Hessian matrix#\n");      printf(" %d\n",s[4][i]);
   for (i=1;i<=npar;i++) {    */
     for (j=1;j<=npar;j++) {    cov[1]=1.;
       printf("%.3e ",hess[i][j]);  
     }    for(k=1; k<=nlstate; k++) ll[k]=0.;
     printf("\n");  
   }    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /* Recompute Inverse */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   for (i=1;i<=npar;i++)        for(mi=1; mi<= wav[i]-1; mi++){
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];          for (ii=1;ii<=nlstate+ndeath;ii++)
   ludcmp(a,npar,indx,&pd);            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /*  printf("\n#Hessian matrix recomputed#\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
   for (j=1;j<=npar;j++) {          for(d=0; d<dh[mi][i]; d++){
     for (i=1;i<=npar;i++) x[i]=0;            newm=savm;
     x[j]=1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     lubksb(a,npar,indx,x);            for (kk=1; kk<=cptcovage;kk++) {
     for (i=1;i<=npar;i++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       y[i][j]=x[i];            }
       printf("%.3e ",y[i][j]);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     printf("\n");            savm=oldm;
   }            oldm=newm;
   */          } /* end mult */
         
   free_matrix(a,1,npar,1,npar);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   free_matrix(y,1,npar,1,npar);          /* But now since version 0.9 we anticipate for bias and large stepm.
   free_vector(x,1,npar);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   free_ivector(indx,1,npar);           * (in months) between two waves is not a multiple of stepm, we rounded to 
   free_matrix(hess,1,npar,1,npar);           * the nearest (and in case of equal distance, to the lowest) interval but now
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
            * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
 }           * probability in order to take into account the bias as a fraction of the way
            * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
 /*************** hessian matrix ****************/           * -stepm/2 to stepm/2 .
 double hessii( double x[], double delta, int theta, double delti[])           * For stepm=1 the results are the same as for previous versions of Imach.
 {           * For stepm > 1 the results are less biased than in previous versions. 
   int i;           */
   int l=1, lmax=20;          s1=s[mw[mi][i]][i];
   double k1,k2;          s2=s[mw[mi+1][i]][i];
   double p2[NPARMAX+1];          bbh=(double)bh[mi][i]/(double)stepm; 
   double res;          /* bias is positive if real duration
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;           * is higher than the multiple of stepm and negative otherwise.
   double fx;           */
   int k=0,kmax=10;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   double l1;          if( s2 > nlstate){ 
             /* i.e. if s2 is a death state and if the date of death is known then the contribution
   fx=func(x);               to the likelihood is the probability to die between last step unit time and current 
   for (i=1;i<=npar;i++) p2[i]=x[i];               step unit time, which is also the differences between probability to die before dh 
   for(l=0 ; l <=lmax; l++){               and probability to die before dh-stepm . 
     l1=pow(10,l);               In version up to 0.92 likelihood was computed
     delts=delt;          as if date of death was unknown. Death was treated as any other
     for(k=1 ; k <kmax; k=k+1){          health state: the date of the interview describes the actual state
       delt = delta*(l1*k);          and not the date of a change in health state. The former idea was
       p2[theta]=x[theta] +delt;          to consider that at each interview the state was recorded
       k1=func(p2)-fx;          (healthy, disable or death) and IMaCh was corrected; but when we
       p2[theta]=x[theta]-delt;          introduced the exact date of death then we should have modified
       k2=func(p2)-fx;          the contribution of an exact death to the likelihood. This new
       /*res= (k1-2.0*fx+k2)/delt/delt; */          contribution is smaller and very dependent of the step unit
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */          stepm. It is no more the probability to die between last interview
                and month of death but the probability to survive from last
 #ifdef DEBUG          interview up to one month before death multiplied by the
       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);          probability to die within a month. Thanks to Chris
 #endif          Jackson for correcting this bug.  Former versions increased
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          mortality artificially. The bad side is that we add another loop
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          which slows down the processing. The difference can be up to 10%
         k=kmax;          lower mortality.
       }            */
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */            lli=log(out[s1][s2] - savm[s1][s2]);
         k=kmax; l=lmax*10.;          }else{
       }            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){            /*  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 */
         delts=delt;          } 
       }          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     }          /*if(lli ==000.0)*/
   }          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
   delti[theta]=delts;          ipmx +=1;
   return res;          sw += weight[i];
            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 }        } /* end of wave */
       } /* end of individual */
 double hessij( double x[], double delti[], int thetai,int thetaj)    }  else if(mle==2){
 {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   int i;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int l=1, l1, lmax=20;        for(mi=1; mi<= wav[i]-1; mi++){
   double k1,k2,k3,k4,res,fx;          for (ii=1;ii<=nlstate+ndeath;ii++)
   double p2[NPARMAX+1];            for (j=1;j<=nlstate+ndeath;j++){
   int k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fx=func(x);            }
   for (k=1; k<=2; k++) {          for(d=0; d<=dh[mi][i]; d++){
     for (i=1;i<=npar;i++) p2[i]=x[i];            newm=savm;
     p2[thetai]=x[thetai]+delti[thetai]/k;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;            for (kk=1; kk<=cptcovage;kk++) {
     k1=func(p2)-fx;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              }
     p2[thetai]=x[thetai]+delti[thetai]/k;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     k2=func(p2)-fx;            savm=oldm;
              oldm=newm;
     p2[thetai]=x[thetai]-delti[thetai]/k;          } /* end mult */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        
     k3=func(p2)-fx;          /*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.
     p2[thetai]=x[thetai]-delti[thetai]/k;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;           * (in months) between two waves is not a multiple of stepm, we rounded to 
     k4=func(p2)-fx;           * the nearest (and in case of equal distance, to the lowest) interval but now
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */           * we keep into memory the bias bh[mi][i] and also the previous matrix product
 #ifdef DEBUG           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
     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);           * probability in order to take into account the bias as a fraction of the way
 #endif           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
   }           * -stepm/2 to stepm/2 .
   return res;           * For stepm=1 the results are the same as for previous versions of Imach.
 }           * For stepm > 1 the results are less biased than in previous versions. 
            */
 /************** Inverse of matrix **************/          s1=s[mw[mi][i]][i];
 void ludcmp(double **a, int n, int *indx, double *d)          s2=s[mw[mi+1][i]][i];
 {          bbh=(double)bh[mi][i]/(double)stepm; 
   int i,imax,j,k;          /* bias is positive if real duration
   double big,dum,sum,temp;           * is higher than the multiple of stepm and negative otherwise.
   double *vv;           */
            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=vector(1,n);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   *d=1.0;          /*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 */
   for (i=1;i<=n;i++) {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     big=0.0;          /*if(lli ==000.0)*/
     for (j=1;j<=n;j++)          /*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 ((temp=fabs(a[i][j])) > big) big=temp;          ipmx +=1;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          sw += weight[i];
     vv[i]=1.0/big;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   }        } /* end of wave */
   for (j=1;j<=n;j++) {      } /* end of individual */
     for (i=1;i<j;i++) {    }  else if(mle==3){  /* exponential inter-extrapolation */
       sum=a[i][j];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       a[i][j]=sum;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
     big=0.0;            for (j=1;j<=nlstate+ndeath;j++){
     for (i=j;i<=n;i++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       sum=a[i][j];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for (k=1;k<j;k++)            }
         sum -= a[i][k]*a[k][j];          for(d=0; d<dh[mi][i]; d++){
       a[i][j]=sum;            newm=savm;
       if ( (dum=vv[i]*fabs(sum)) >= big) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         big=dum;            for (kk=1; kk<=cptcovage;kk++) {
         imax=i;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     if (j != imax) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for (k=1;k<=n;k++) {            savm=oldm;
         dum=a[imax][k];            oldm=newm;
         a[imax][k]=a[j][k];          } /* end mult */
         a[j][k]=dum;        
       }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       *d = -(*d);          /* But now since version 0.9 we anticipate for bias and large stepm.
       vv[imax]=vv[j];           * 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 
     indx[j]=imax;           * the nearest (and in case of equal distance, to the lowest) interval but now
     if (a[j][j] == 0.0) a[j][j]=TINY;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     if (j != n) {           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       dum=1.0/(a[j][j]);           * probability in order to take into account the bias as a fraction of the way
       for (i=j+1;i<=n;i++) a[i][j] *= dum;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
     }           * -stepm/2 to stepm/2 .
   }           * For stepm=1 the results are the same as for previous versions of Imach.
   free_vector(vv,1,n);  /* Doesn't work */           * For stepm > 1 the results are less biased than in previous versions. 
 ;           */
 }          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
 void lubksb(double **a, int n, int *indx, double b[])          bbh=(double)bh[mi][i]/(double)stepm; 
 {          /* bias is positive if real duration
   int i,ii=0,ip,j;           * is higher than the multiple of stepm and negative otherwise.
   double sum;           */
            /* lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); */ /* linear interpolation */
   for (i=1;i<=n;i++) {          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
     ip=indx[i];          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     sum=b[ip];          /*if(lli ==000.0)*/
     b[ip]=b[i];          /*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 (ii)          ipmx +=1;
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          sw += weight[i];
     else if (sum) ii=i;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     b[i]=sum;        } /* end of wave */
   }      } /* end of individual */
   for (i=n;i>=1;i--) {    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     sum=b[i];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     b[i]=sum/a[i][i];        for(mi=1; mi<= wav[i]-1; mi++){
   }          for (ii=1;ii<=nlstate+ndeath;ii++)
 }            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /************ Frequencies ********************/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)            }
 {  /* Some frequencies */          for(d=0; d<dh[mi][i]; d++){
              newm=savm;
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double ***freq; /* Frequencies */            for (kk=1; kk<=cptcovage;kk++) {
   double *pp;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double pos, k2, dateintsum=0,k2cpt=0;            }
   FILE *ficresp;          
   char fileresp[FILENAMELENGTH];            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   pp=vector(1,nlstate);            savm=oldm;
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);            oldm=newm;
   strcpy(fileresp,"p");          } /* end mult */
   strcat(fileresp,fileres);        
   if((ficresp=fopen(fileresp,"w"))==NULL) {          s1=s[mw[mi][i]][i];
     printf("Problem with prevalence resultfile: %s\n", fileresp);          s2=s[mw[mi+1][i]][i];
     exit(0);          if( s2 > nlstate){ 
   }            lli=log(out[s1][s2] - savm[s1][s2]);
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          }else{
   j1=0;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
            }
   j=cptcoveff;          ipmx +=1;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          sw += weight[i];
            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   for(k1=1; k1<=j;k1++){  /*      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]); */
     for(i1=1; i1<=ncodemax[k1];i1++){        } /* end of wave */
       j1++;      } /* end of individual */
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
         scanf("%d", i);*/      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for (i=-1; i<=nlstate+ndeath; i++)          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for (jk=-1; jk<=nlstate+ndeath; jk++)          for(mi=1; mi<= wav[i]-1; mi++){
           for(m=agemin; m <= agemax+3; m++)          for (ii=1;ii<=nlstate+ndeath;ii++)
             freq[i][jk][m]=0;            for (j=1;j<=nlstate+ndeath;j++){
                    oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       dateintsum=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       k2cpt=0;            }
       for (i=1; i<=imx; i++) {          for(d=0; d<dh[mi][i]; d++){
         bool=1;            newm=savm;
         if  (cptcovn>0) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           for (z1=1; z1<=cptcoveff; z1++)            for (kk=1; kk<=cptcovage;kk++) {
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
               bool=0;            }
         }          
         if (bool==1) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           for(m=firstpass; m<=lastpass; m++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             k2=anint[m][i]+(mint[m][i]/12.);            savm=oldm;
             if ((k2>=dateprev1) && (k2<=dateprev2)) {            oldm=newm;
               if(agev[m][i]==0) agev[m][i]=agemax+1;          } /* end mult */
               if(agev[m][i]==1) agev[m][i]=agemax+2;        
               if (m<lastpass) {          s1=s[mw[mi][i]][i];
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          s2=s[mw[mi+1][i]][i];
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
               }          ipmx +=1;
                        sw += weight[i];
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
                 dateintsum=dateintsum+k2;          /*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]);*/
                 k2cpt++;        } /* end of wave */
               }      } /* end of individual */
             }    } /* End of if */
           }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
            return -l;
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  }
   
       if  (cptcovn>0) {  /*************** log-likelihood *************/
         fprintf(ficresp, "\n#********** Variable ");  double funcone( double *x)
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  {
         fprintf(ficresp, "**********\n#");    int i, ii, j, k, mi, d, kk;
       }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
       for(i=1; i<=nlstate;i++)    double **out;
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    double lli; /* Individual log likelihood */
       fprintf(ficresp, "\n");    int s1, s2;
          double bbh, survp;
       for(i=(int)agemin; i <= (int)agemax+3; i++){    /*extern weight */
         if(i==(int)agemax+3)    /* We are differentiating ll according to initial status */
           printf("Total");    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         else    /*for(i=1;i<imx;i++) 
           printf("Age %d", i);      printf(" %d\n",s[4][i]);
         for(jk=1; jk <=nlstate ; jk++){    */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    cov[1]=1.;
             pp[jk] += freq[jk][m][i];  
         }    for(k=1; k<=nlstate; k++) ll[k]=0.;
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pos=0; m <=0 ; m++)    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
             pos += freq[jk][m][i];      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           if(pp[jk]>=1.e-10)      for(mi=1; mi<= wav[i]-1; mi++){
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        for (ii=1;ii<=nlstate+ndeath;ii++)
           else          for (j=1;j<=nlstate+ndeath;j++){
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }
         for(jk=1; jk <=nlstate ; jk++){        for(d=0; d<dh[mi][i]; d++){
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          newm=savm;
             pp[jk] += freq[jk][m][i];          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         }          for (kk=1; kk<=cptcovage;kk++) {
             cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for(jk=1,pos=0; jk <=nlstate ; jk++)          }
           pos += pp[jk];          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(jk=1; jk <=nlstate ; jk++){                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           if(pos>=1.e-5)          savm=oldm;
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          oldm=newm;
           else        } /* end mult */
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        
           if( i <= (int) agemax){        s1=s[mw[mi][i]][i];
             if(pos>=1.e-5){        s2=s[mw[mi+1][i]][i];
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        bbh=(double)bh[mi][i]/(double)stepm; 
               probs[i][jk][j1]= pp[jk]/pos;        /* bias is positive if real duration
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/         * is higher than the multiple of stepm and negative otherwise.
             }         */
             else        if( s2 > nlstate && (mle <5) ){  /* Jackson */
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);          lli=log(out[s1][s2] - savm[s1][s2]);
           }        } else if (mle==1){
         }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
                } else if(mle==2){
         for(jk=-1; jk <=nlstate+ndeath; jk++)          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(m=-1; m <=nlstate+ndeath; m++)        } else if(mle==3){  /* exponential inter-extrapolation */
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
         if(i <= (int) agemax)        } else if (mle==4){  /* mle=4 no inter-extrapolation */
           fprintf(ficresp,"\n");          lli=log(out[s1][s2]); /* Original formula */
         printf("\n");        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       }          lli=log(out[s1][s2]); /* Original formula */
     }        } /* End of if */
   }        ipmx +=1;
   dateintmean=dateintsum/k2cpt;        sw += weight[i];
          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fclose(ficresp);  /*       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]); */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        if(globpr){
   free_vector(pp,1,nlstate);          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]);
   /* End of Freq */          for(k=1,l=0.; k<=nlstate; k++) 
 }            fprintf(ficresilk," %10.6f",ll[k]);
           fprintf(ficresilk,"\n");
 /************ Prevalence ********************/        }
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)      } /* end of wave */
 {  /* Some frequencies */    } /* end of individual */
      for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double ***freq; /* Frequencies */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double *pp;    return -l;
   double pos, k2;  }
   
   pp=vector(1,nlstate);  
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpr, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
    {
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    /* This routine should help understanding what is done with the selection of individuals/waves and
   j1=0;       to check the exact contribution to the likelihood.
         Plotting could be done.
   j=cptcoveff;     */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    int k;
      if(globpr !=0){ /* Just counts and sums no printings */
  for(k1=1; k1<=j;k1++){      strcpy(fileresilk,"ilk"); 
     for(i1=1; i1<=ncodemax[k1];i1++){      strcat(fileresilk,fileres);
       j1++;      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
          printf("Problem with resultfile: %s\n", fileresilk);
       for (i=-1; i<=nlstate+ndeath; i++)          fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
         for (jk=-1; jk<=nlstate+ndeath; jk++)        }
           for(m=agemin; m <= agemax+3; m++)      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");
             freq[i][jk][m]=0;      fprintf(ficresilk, "# i s1 s2 mi mw dh likeli weight out sav ");
            /*  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 (i=1; i<=imx; i++) {      for(k=1; k<=nlstate; k++) 
         bool=1;        fprintf(ficresilk," ll[%d]",k);
         if  (cptcovn>0) {      fprintf(ficresilk,"\n");
           for (z1=1; z1<=cptcoveff; z1++)    }
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  
               bool=0;    *fretone=(*funcone)(p);
         }    if(globpr !=0)
         if (bool==1) {      fclose(ficresilk);
           for(m=firstpass; m<=lastpass; m++){    return;
             k2=anint[m][i]+(mint[m][i]/12.);  }
             if ((k2>=dateprev1) && (k2<=dateprev2)) {  
               if(agev[m][i]==0) agev[m][i]=agemax+1;  /*********** Maximum Likelihood Estimation ***************/
               if(agev[m][i]==1) agev[m][i]=agemax+2;  
               if (m<lastpass)  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
                 if (calagedate>0) freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];  {
               else    int i,j, iter;
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    double **xi;
                freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];    double fret;
             }    double fretone; /* Only one call to likelihood */
           }    char filerespow[FILENAMELENGTH];
         }    xi=matrix(1,npar,1,npar);
       }    for (i=1;i<=npar;i++)
         for(i=(int)agemin; i <= (int)agemax+3; i++){      for (j=1;j<=npar;j++)
           for(jk=1; jk <=nlstate ; jk++){        xi[i][j]=(i==j ? 1.0 : 0.0);
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    printf("Powell\n");  fprintf(ficlog,"Powell\n");
               pp[jk] += freq[jk][m][i];    strcpy(filerespow,"pow"); 
           }    strcat(filerespow,fileres);
           for(jk=1; jk <=nlstate ; jk++){    if((ficrespow=fopen(filerespow,"w"))==NULL) {
             for(m=-1, pos=0; m <=0 ; m++)      printf("Problem with resultfile: %s\n", filerespow);
             pos += freq[jk][m][i];      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
         }    }
            fprintf(ficrespow,"# Powell\n# iter -2*LL");
          for(jk=1; jk <=nlstate ; jk++){    for (i=1;i<=nlstate;i++)
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      for(j=1;j<=nlstate+ndeath;j++)
              pp[jk] += freq[jk][m][i];        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
          }    fprintf(ficrespow,"\n");
            
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];    powell(p,xi,npar,ftol,&iter,&fret,func);
   
          for(jk=1; jk <=nlstate ; jk++){              fclose(ficrespow);
            if( i <= (int) agemax){    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
              if(pos>=1.e-5){    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
                probs[i][jk][j1]= pp[jk]/pos;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
              }  
            }  }
          }  
            /**** Computes Hessian and covariance matrix ***/
         }  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     }  {
   }    double  **a,**y,*x,pd;
     double **hess;
      int i, j,jk;
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    int *indx;
   free_vector(pp,1,nlstate);  
      double hessii(double p[], double delta, int theta, double delti[]);
 }  /* End of Freq */    double hessij(double p[], double delti[], int i, int j);
     void lubksb(double **a, int npar, int *indx, double b[]) ;
 /************* Waves Concatenation ***************/    void ludcmp(double **a, int npar, int *indx, double *d) ;
   
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    hess=matrix(1,npar,1,npar);
 {  
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    printf("\nCalculation of the hessian matrix. Wait...\n");
      Death is a valid wave (if date is known).    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    for (i=1;i<=npar;i++){
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]      printf("%d",i);fflush(stdout);
      and mw[mi+1][i]. dh depends on stepm.      fprintf(ficlog,"%d",i);fflush(ficlog);
      */      hess[i][i]=hessii(p,ftolhess,i,delti);
       /*printf(" %f ",p[i]);*/
   int i, mi, m;      /*printf(" %lf ",hess[i][i]);*/
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    }
      double sum=0., jmean=0.;*/    
     for (i=1;i<=npar;i++) {
   int j, k=0,jk, ju, jl;      for (j=1;j<=npar;j++)  {
   double sum=0.;        if (j>i) { 
   jmin=1e+5;          printf(".%d%d",i,j);fflush(stdout);
   jmax=-1;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   jmean=0.;          hess[i][j]=hessij(p,delti,i,j);
   for(i=1; i<=imx; i++){          hess[j][i]=hess[i][j];    
     mi=0;          /*printf(" %lf ",hess[i][j]);*/
     m=firstpass;        }
     while(s[m][i] <= nlstate){      }
       if(s[m][i]>=1)    }
         mw[++mi][i]=m;    printf("\n");
       if(m >=lastpass)    fprintf(ficlog,"\n");
         break;  
       else    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
         m++;    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     }/* end while */    
     if (s[m][i] > nlstate){    a=matrix(1,npar,1,npar);
       mi++;     /* Death is another wave */    y=matrix(1,npar,1,npar);
       /* if(mi==0)  never been interviewed correctly before death */    x=vector(1,npar);
          /* Only death is a correct wave */    indx=ivector(1,npar);
       mw[mi][i]=m;    for (i=1;i<=npar;i++)
     }      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     ludcmp(a,npar,indx,&pd);
     wav[i]=mi;  
     if(mi==0)    for (j=1;j<=npar;j++) {
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);      for (i=1;i<=npar;i++) x[i]=0;
   }      x[j]=1;
       lubksb(a,npar,indx,x);
   for(i=1; i<=imx; i++){      for (i=1;i<=npar;i++){ 
     for(mi=1; mi<wav[i];mi++){        matcov[i][j]=x[i];
       if (stepm <=0)      }
         dh[mi][i]=1;    }
       else{  
         if (s[mw[mi+1][i]][i] > nlstate) {    printf("\n#Hessian matrix#\n");
           if (agedc[i] < 2*AGESUP) {    fprintf(ficlog,"\n#Hessian matrix#\n");
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);    for (i=1;i<=npar;i++) { 
           if(j==0) j=1;  /* Survives at least one month after exam */      for (j=1;j<=npar;j++) { 
           k=k+1;        printf("%.3e ",hess[i][j]);
           if (j >= jmax) jmax=j;        fprintf(ficlog,"%.3e ",hess[i][j]);
           if (j <= jmin) jmin=j;      }
           sum=sum+j;      printf("\n");
           /*if (j<0) printf("j=%d num=%d \n",j,i); */      fprintf(ficlog,"\n");
           }    }
         }  
         else{    /* Recompute Inverse */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    for (i=1;i<=npar;i++)
           k=k+1;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
           if (j >= jmax) jmax=j;    ludcmp(a,npar,indx,&pd);
           else if (j <= jmin)jmin=j;  
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    /*  printf("\n#Hessian matrix recomputed#\n");
           sum=sum+j;  
         }    for (j=1;j<=npar;j++) {
         jk= j/stepm;      for (i=1;i<=npar;i++) x[i]=0;
         jl= j -jk*stepm;      x[j]=1;
         ju= j -(jk+1)*stepm;      lubksb(a,npar,indx,x);
         if(jl <= -ju)      for (i=1;i<=npar;i++){ 
           dh[mi][i]=jk;        y[i][j]=x[i];
         else        printf("%.3e ",y[i][j]);
           dh[mi][i]=jk+1;        fprintf(ficlog,"%.3e ",y[i][j]);
         if(dh[mi][i]==0)      }
           dh[mi][i]=1; /* At least one step */      printf("\n");
       }      fprintf(ficlog,"\n");
     }    }
   }    */
   jmean=sum/k;  
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);    free_matrix(a,1,npar,1,npar);
  }    free_matrix(y,1,npar,1,npar);
 /*********** Tricode ****************************/    free_vector(x,1,npar);
 void tricode(int *Tvar, int **nbcode, int imx)    free_ivector(indx,1,npar);
 {    free_matrix(hess,1,npar,1,npar);
   int Ndum[20],ij=1, k, j, i;  
   int cptcode=0;  
   cptcoveff=0;  }
    
   for (k=0; k<19; k++) Ndum[k]=0;  /*************** hessian matrix ****************/
   for (k=1; k<=7; k++) ncodemax[k]=0;  double hessii( double x[], double delta, int theta, double delti[])
   {
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {    int i;
     for (i=1; i<=imx; i++) {    int l=1, lmax=20;
       ij=(int)(covar[Tvar[j]][i]);    double k1,k2;
       Ndum[ij]++;    double p2[NPARMAX+1];
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    double res;
       if (ij > cptcode) cptcode=ij;    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     }    double fx;
     int k=0,kmax=10;
     for (i=0; i<=cptcode; i++) {    double l1;
       if(Ndum[i]!=0) ncodemax[j]++;  
     }    fx=func(x);
     ij=1;    for (i=1;i<=npar;i++) p2[i]=x[i];
     for(l=0 ; l <=lmax; l++){
       l1=pow(10,l);
     for (i=1; i<=ncodemax[j]; i++) {      delts=delt;
       for (k=0; k<=19; k++) {      for(k=1 ; k <kmax; k=k+1){
         if (Ndum[k] != 0) {        delt = delta*(l1*k);
           nbcode[Tvar[j]][ij]=k;        p2[theta]=x[theta] +delt;
                  k1=func(p2)-fx;
           ij++;        p2[theta]=x[theta]-delt;
         }        k2=func(p2)-fx;
         if (ij > ncodemax[j]) break;        /*res= (k1-2.0*fx+k2)/delt/delt; */
       }          res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     }        
   }    #ifdef DEBUG
         printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
  for (k=0; k<19; k++) Ndum[k]=0;        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   #endif
  for (i=1; i<=ncovmodel-2; i++) {        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       ij=Tvar[i];        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       Ndum[ij]++;          k=kmax;
     }        }
         else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
  ij=1;          k=kmax; l=lmax*10.;
  for (i=1; i<=10; i++) {        }
    if((Ndum[i]!=0) && (i<=ncovcol)){        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
      Tvaraff[ij]=i;          delts=delt;
      ij++;        }
    }      }
  }    }
      delti[theta]=delts;
     cptcoveff=ij-1;    return res; 
 }    
   }
 /*********** Health Expectancies ****************/  
   double hessij( double x[], double delti[], int thetai,int thetaj)
 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 )  {
     int i;
 {    int l=1, l1, lmax=20;
   /* Health expectancies */    double k1,k2,k3,k4,res,fx;
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;    double p2[NPARMAX+1];
   double age, agelim, hf;    int k;
   double ***p3mat,***varhe;  
   double **dnewm,**doldm;    fx=func(x);
   double *xp;    for (k=1; k<=2; k++) {
   double **gp, **gm;      for (i=1;i<=npar;i++) p2[i]=x[i];
   double ***gradg, ***trgradg;      p2[thetai]=x[thetai]+delti[thetai]/k;
   int theta;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k1=func(p2)-fx;
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);    
   xp=vector(1,npar);      p2[thetai]=x[thetai]+delti[thetai]/k;
   dnewm=matrix(1,nlstate*2,1,npar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   doldm=matrix(1,nlstate*2,1,nlstate*2);      k2=func(p2)-fx;
      
   fprintf(ficreseij,"# Health expectancies\n");      p2[thetai]=x[thetai]-delti[thetai]/k;
   fprintf(ficreseij,"# Age");      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   for(i=1; i<=nlstate;i++)      k3=func(p2)-fx;
     for(j=1; j<=nlstate;j++)    
       fprintf(ficreseij," %1d-%1d (SE)",i,j);      p2[thetai]=x[thetai]-delti[thetai]/k;
   fprintf(ficreseij,"\n");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k4=func(p2)-fx;
   if(estepm < stepm){      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     printf ("Problem %d lower than %d\n",estepm, stepm);  #ifdef DEBUG
   }      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   else  hstepm=estepm;        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);
   /* We compute the life expectancy from trapezoids spaced every estepm months  #endif
    * This is mainly to measure the difference between two models: for example    }
    * if stepm=24 months pijx are given only every 2 years and by summing them    return res;
    * we are calculating an estimate of the Life Expectancy assuming a linear  }
    * progression inbetween and thus overestimating or underestimating according  
    * to the curvature of the survival function. If, for the same date, we  /************** Inverse of matrix **************/
    * estimate the model with stepm=1 month, we can keep estepm to 24 months  void ludcmp(double **a, int n, int *indx, double *d) 
    * to compare the new estimate of Life expectancy with the same linear  { 
    * hypothesis. A more precise result, taking into account a more precise    int i,imax,j,k; 
    * curvature will be obtained if estepm is as small as stepm. */    double big,dum,sum,temp; 
     double *vv; 
   /* 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.    vv=vector(1,n); 
      nhstepm is the number of hstepm from age to agelim    *d=1.0; 
      nstepm is the number of stepm from age to agelin.    for (i=1;i<=n;i++) { 
      Look at hpijx to understand the reason of that which relies in memory size      big=0.0; 
      and note for a fixed period like estepm months */      for (j=1;j<=n;j++) 
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        if ((temp=fabs(a[i][j])) > big) big=temp; 
      survival function given by stepm (the optimization length). Unfortunately it      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
      means that if the survival funtion is printed only each two years of age and if      vv[i]=1.0/big; 
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    } 
      results. So we changed our mind and took the option of the best precision.    for (j=1;j<=n;j++) { 
   */      for (i=1;i<j;i++) { 
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        sum=a[i][j]; 
         for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   agelim=AGESUP;        a[i][j]=sum; 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      } 
     /* nhstepm age range expressed in number of stepm */      big=0.0; 
     nstepm=(int) rint((agelim-age)*YEARM/stepm);      for (i=j;i<=n;i++) { 
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */        sum=a[i][j]; 
     /* if (stepm >= YEARM) hstepm=1;*/        for (k=1;k<j;k++) 
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          sum -= a[i][k]*a[k][j]; 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        a[i][j]=sum; 
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
     gp=matrix(0,nhstepm,1,nlstate*2);          big=dum; 
     gm=matrix(0,nhstepm,1,nlstate*2);          imax=i; 
         } 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      } 
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      if (j != imax) { 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);          for (k=1;k<=n;k++) { 
            dum=a[imax][k]; 
           a[imax][k]=a[j][k]; 
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          a[j][k]=dum; 
         } 
     /* Computing Variances of health expectancies */        *d = -(*d); 
         vv[imax]=vv[j]; 
      for(theta=1; theta <=npar; theta++){      } 
       for(i=1; i<=npar; i++){      indx[j]=imax; 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      if (a[j][j] == 0.0) a[j][j]=TINY; 
       }      if (j != n) { 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          dum=1.0/(a[j][j]); 
          for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       cptj=0;      } 
       for(j=1; j<= nlstate; j++){    } 
         for(i=1; i<=nlstate; i++){    free_vector(vv,1,n);  /* Doesn't work */
           cptj=cptj+1;  ;
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){  } 
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;  
           }  void lubksb(double **a, int n, int *indx, double b[]) 
         }  { 
       }    int i,ii=0,ip,j; 
          double sum; 
         
       for(i=1; i<=npar; i++)    for (i=1;i<=n;i++) { 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      ip=indx[i]; 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        sum=b[ip]; 
            b[ip]=b[i]; 
       cptj=0;      if (ii) 
       for(j=1; j<= nlstate; j++){        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
         for(i=1;i<=nlstate;i++){      else if (sum) ii=i; 
           cptj=cptj+1;      b[i]=sum; 
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){    } 
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;    for (i=n;i>=1;i--) { 
           }      sum=b[i]; 
         }      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       }      b[i]=sum/a[i][i]; 
          } 
      } 
   
       for(j=1; j<= nlstate*2; j++)  /************ Frequencies ********************/
         for(h=0; h<=nhstepm-1; h++){  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)
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  {  /* Some frequencies */
         }    
     int i, m, jk, k1,i1, j1, bool, z1,z2,j;
      }    int first;
        double ***freq; /* Frequencies */
 /* End theta */    double *pp, **prop;
     double pos,posprop, k2, dateintsum=0,k2cpt=0;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);    FILE *ficresp;
     char fileresp[FILENAMELENGTH];
      for(h=0; h<=nhstepm-1; h++)    
       for(j=1; j<=nlstate*2;j++)    pp=vector(1,nlstate);
         for(theta=1; theta <=npar; theta++)    prop=matrix(1,nlstate,iagemin,iagemax+3);
         trgradg[h][j][theta]=gradg[h][theta][j];    strcpy(fileresp,"p");
     strcat(fileresp,fileres);
     if((ficresp=fopen(fileresp,"w"))==NULL) {
      for(i=1;i<=nlstate*2;i++)      printf("Problem with prevalence resultfile: %s\n", fileresp);
       for(j=1;j<=nlstate*2;j++)      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
         varhe[i][j][(int)age] =0.;      exit(0);
     }
     for(h=0;h<=nhstepm-1;h++){    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
       for(k=0;k<=nhstepm-1;k++){    j1=0;
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);    
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);    j=cptcoveff;
         for(i=1;i<=nlstate*2;i++)    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           for(j=1;j<=nlstate*2;j++)  
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;    first=1;
       }  
     }    for(k1=1; k1<=j;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
              j1++;
     /* Computing expectancies */        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
     for(i=1; i<=nlstate;i++)          scanf("%d", i);*/
       for(j=1; j<=nlstate;j++)        for (i=-1; i<=nlstate+ndeath; i++)  
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){          for (jk=-1; jk<=nlstate+ndeath; jk++)  
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;            for(m=iagemin; m <= iagemax+3; m++)
                        freq[i][jk][m]=0;
 /* 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]);*/  
       for (i=1; i<=nlstate; i++)  
         }        for(m=iagemin; m <= iagemax+3; m++)
           prop[i][m]=0;
     fprintf(ficreseij,"%3.0f",age );        
     cptj=0;        dateintsum=0;
     for(i=1; i<=nlstate;i++)        k2cpt=0;
       for(j=1; j<=nlstate;j++){        for (i=1; i<=imx; i++) {
         cptj++;          bool=1;
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          if  (cptcovn>0) {
       }            for (z1=1; z1<=cptcoveff; z1++) 
     fprintf(ficreseij,"\n");              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                    bool=0;
     free_matrix(gm,0,nhstepm,1,nlstate*2);          }
     free_matrix(gp,0,nhstepm,1,nlstate*2);          if (bool==1){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);            for(m=firstpass; m<=lastpass; m++){
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);              k2=anint[m][i]+(mint[m][i]/12.);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   free_vector(xp,1,npar);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   free_matrix(dnewm,1,nlstate*2,1,npar);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);                if (m<lastpass) {
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);                  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];
                 }
 /************ Variance ******************/                
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
 {                  dateintsum=dateintsum+k2;
   /* Variance of health expectancies */                  k2cpt++;
   /*  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, h, nstepm ;          }
   int k, cptcode;        }
   double *xp;         
   double **gp, **gm;        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
   double ***gradg, ***trgradg;  
   double ***p3mat;        if  (cptcovn>0) {
   double age,agelim, hf;          fprintf(ficresp, "\n#********** Variable "); 
   int theta;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresp, "**********\n#");
    fprintf(ficresvij,"# Covariances of life expectancies\n");        }
   fprintf(ficresvij,"# Age");        for(i=1; i<=nlstate;i++) 
   for(i=1; i<=nlstate;i++)          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
     for(j=1; j<=nlstate;j++)        fprintf(ficresp, "\n");
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        
   fprintf(ficresvij,"\n");        for(i=iagemin; i <= iagemax+3; i++){
           if(i==iagemax+3){
   xp=vector(1,npar);            fprintf(ficlog,"Total");
   dnewm=matrix(1,nlstate,1,npar);          }else{
   doldm=matrix(1,nlstate,1,nlstate);            if(first==1){
                first=0;
   if(estepm < stepm){              printf("See log file for details...\n");
     printf ("Problem %d lower than %d\n",estepm, stepm);            }
   }            fprintf(ficlog,"Age %d", i);
   else  hstepm=estepm;            }
   /* For example we decided to compute the life expectancy with the smallest unit */          for(jk=1; jk <=nlstate ; jk++){
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
      nhstepm is the number of hstepm from age to agelim              pp[jk] += freq[jk][m][i]; 
      nstepm is the number of stepm from age to agelin.          }
      Look at hpijx to understand the reason of that which relies in memory size          for(jk=1; jk <=nlstate ; jk++){
      and note for a fixed period like k years */            for(m=-1, pos=0; m <=0 ; m++)
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the              pos += freq[jk][m][i];
      survival function given by stepm (the optimization length). Unfortunately it            if(pp[jk]>=1.e-10){
      means that if the survival funtion is printed only each two years of age and if              if(first==1){
      you sum them up and add 1 year (area under the trapezoids) you won't get the same              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
      results. So we changed our mind and took the option of the best precision.              }
   */              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */            }else{
   agelim = AGESUP;              if(first==1)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          }
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  
     gp=matrix(0,nhstepm,1,nlstate);          for(jk=1; jk <=nlstate ; jk++){
     gm=matrix(0,nhstepm,1,nlstate);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
               pp[jk] += freq[jk][m][i];
     for(theta=1; theta <=npar; theta++){          }       
       for(i=1; i<=npar; i++){ /* Computes gradient */          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            pos += pp[jk];
       }            posprop += prop[jk][i];
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          for(jk=1; jk <=nlstate ; jk++){
             if(pos>=1.e-5){
       if (popbased==1) {              if(first==1)
         for(i=1; i<=nlstate;i++)                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           prlim[i][i]=probs[(int)age][i][ij];              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       }            }else{
                if(first==1)
       for(j=1; j<= nlstate; j++){                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
         for(h=0; h<=nhstepm; h++){              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)            }
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];            if( i <= iagemax){
         }              if(pos>=1.e-5){
       }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                    /*probs[i][jk][j1]= pp[jk]/pos;*/
       for(i=1; i<=npar; i++) /* Computes gradient */                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
         xp[i] = x[i] - (i==theta ?delti[theta]:0);              }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                else
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
              }
       if (popbased==1) {          }
         for(i=1; i<=nlstate;i++)          
           prlim[i][i]=probs[(int)age][i][ij];          for(jk=-1; jk <=nlstate+ndeath; jk++)
       }            for(m=-1; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
       for(j=1; j<= nlstate; j++){              if(first==1)
         for(h=0; h<=nhstepm; h++){                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];              }
         }          if(i <= iagemax)
       }            fprintf(ficresp,"\n");
           if(first==1)
       for(j=1; j<= nlstate; j++)            printf("Others in log...\n");
         for(h=0; h<=nhstepm; h++){          fprintf(ficlog,"\n");
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        }
         }      }
     } /* End theta */    }
     dateintmean=dateintsum/k2cpt; 
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);   
     fclose(ficresp);
     for(h=0; h<=nhstepm; h++)    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
       for(j=1; j<=nlstate;j++)    free_vector(pp,1,nlstate);
         for(theta=1; theta <=npar; theta++)    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
           trgradg[h][j][theta]=gradg[h][theta][j];    /* End of Freq */
   }
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */  
     for(i=1;i<=nlstate;i++)  /************ Prevalence ********************/
       for(j=1;j<=nlstate;j++)  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)
         vareij[i][j][(int)age] =0.;  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
     for(h=0;h<=nhstepm;h++){       in each health status at the date of interview (if between dateprev1 and dateprev2).
       for(k=0;k<=nhstepm;k++){       We still use firstpass and lastpass as another selection.
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);   
         for(i=1;i<=nlstate;i++)    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
           for(j=1;j<=nlstate;j++)    double ***freq; /* Frequencies */
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    double *pp, **prop;
       }    double pos,posprop; 
     }    double  y2; /* in fractional years */
     int iagemin, iagemax;
     fprintf(ficresvij,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)    iagemin= (int) agemin;
       for(j=1; j<=nlstate;j++){    iagemax= (int) agemax;
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    /*pp=vector(1,nlstate);*/
       }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     fprintf(ficresvij,"\n");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     free_matrix(gp,0,nhstepm,1,nlstate);    j1=0;
     free_matrix(gm,0,nhstepm,1,nlstate);    
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    j=cptcoveff;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    
   } /* End age */    for(k1=1; k1<=j;k1++){
        for(i1=1; i1<=ncodemax[k1];i1++){
   free_vector(xp,1,npar);        j1++;
   free_matrix(doldm,1,nlstate,1,npar);        
   free_matrix(dnewm,1,nlstate,1,nlstate);        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
 }            prop[i][m]=0.0;
        
 /************ Variance of prevlim ******************/        for (i=1; i<=imx; i++) { /* Each individual */
 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)          bool=1;
 {          if  (cptcovn>0) {
   /* Variance of prevalence limit */            for (z1=1; z1<=cptcoveff; z1++) 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   double **newm;                bool=0;
   double **dnewm,**doldm;          } 
   int i, j, nhstepm, hstepm;          if (bool==1) { 
   int k, cptcode;            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
   double *xp;              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
   double *gp, *gm;              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
   double **gradg, **trgradg;                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   double age,agelim;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   int theta;                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) { 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");                  /*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]]);*/
   fprintf(ficresvpl,"# Age");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   for(i=1; i<=nlstate;i++)                  prop[s[m][i]][iagemax+3] += weight[i]; 
       fprintf(ficresvpl," %1d-%1d",i,i);                } 
   fprintf(ficresvpl,"\n");              }
             } /* end selection of waves */
   xp=vector(1,npar);          }
   dnewm=matrix(1,nlstate,1,npar);        }
   doldm=matrix(1,nlstate,1,nlstate);        for(i=iagemin; i <= iagemax+3; i++){  
            
   hstepm=1*YEARM; /* Every year of age */          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            posprop += prop[jk][i]; 
   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 */          for(jk=1; jk <=nlstate ; jk++){     
     if (stepm >= YEARM) hstepm=1;            if( i <=  iagemax){ 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */              if(posprop>=1.e-5){ 
     gradg=matrix(1,npar,1,nlstate);                probs[i][jk][j1]= prop[jk][i]/posprop;
     gp=vector(1,nlstate);              } 
     gm=vector(1,nlstate);            } 
           }/* end jk */ 
     for(theta=1; theta <=npar; theta++){        }/* end i */ 
       for(i=1; i<=npar; i++){ /* Computes gradient */      } /* end i1 */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    } /* end k1 */
       }    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
       for(i=1;i<=nlstate;i++)    /*free_vector(pp,1,nlstate);*/
         gp[i] = prlim[i][i];    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
      }  /* End of prevalence */
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  /************* Waves Concatenation ***************/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)  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)
         gm[i] = prlim[i][i];  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       for(i=1;i<=nlstate;i++)       Death is a valid wave (if date is known).
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     } /* End theta */       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
        and mw[mi+1][i]. dh depends on stepm.
     trgradg =matrix(1,nlstate,1,npar);       */
   
     for(j=1; j<=nlstate;j++)    int i, mi, m;
       for(theta=1; theta <=npar; theta++)    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
         trgradg[j][theta]=gradg[theta][j];       double sum=0., jmean=0.;*/
     int first;
     for(i=1;i<=nlstate;i++)    int j, k=0,jk, ju, jl;
       varpl[i][(int)age] =0.;    double sum=0.;
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    first=0;
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    jmin=1e+5;
     for(i=1;i<=nlstate;i++)    jmax=-1;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    jmean=0.;
     for(i=1; i<=imx; i++){
     fprintf(ficresvpl,"%.0f ",age );      mi=0;
     for(i=1; i<=nlstate;i++)      m=firstpass;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      while(s[m][i] <= nlstate){
     fprintf(ficresvpl,"\n");        if(s[m][i]>=1)
     free_vector(gp,1,nlstate);          mw[++mi][i]=m;
     free_vector(gm,1,nlstate);        if(m >=lastpass)
     free_matrix(gradg,1,npar,1,nlstate);          break;
     free_matrix(trgradg,1,nlstate,1,npar);        else
   } /* End age */          m++;
       }/* end while */
   free_vector(xp,1,npar);      if (s[m][i] > nlstate){
   free_matrix(doldm,1,nlstate,1,npar);        mi++;     /* Death is another wave */
   free_matrix(dnewm,1,nlstate,1,nlstate);        /* if(mi==0)  never been interviewed correctly before death */
            /* Only death is a correct wave */
 }        mw[mi][i]=m;
       }
 /************ Variance of one-step probabilities  ******************/  
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)      wav[i]=mi;
 {      if(mi==0){
   int i, j, i1, k1, j1, z1;        if(first==0){
   int k=0, cptcode;          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   double **dnewm,**doldm;          first=1;
   double *xp;        }
   double *gp, *gm;        if(first==1){
   double **gradg, **trgradg;          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
   double age,agelim, cov[NCOVMAX];        }
   int theta;      } /* end mi==0 */
   char fileresprob[FILENAMELENGTH];    } /* End individuals */
   
   strcpy(fileresprob,"prob");    for(i=1; i<=imx; i++){
   strcat(fileresprob,fileres);      for(mi=1; mi<wav[i];mi++){
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {        if (stepm <=0)
     printf("Problem with resultfile: %s\n", fileresprob);          dh[mi][i]=1;
   }        else{
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
              if (agedc[i] < 2*AGESUP) {
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   fprintf(ficresprob,"# Age");              if(j==0) j=1;  /* Survives at least one month after exam */
   for(i=1; i<=nlstate;i++)              else if(j<0){
     for(j=1; j<=(nlstate+ndeath);j++)                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);                j=1; /* Careful Patch */
                 printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST 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]);
   fprintf(ficresprob,"\n");                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
               }
               k=k+1;
   xp=vector(1,npar);              if (j >= jmax) jmax=j;
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);              if (j <= jmin) jmin=j;
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));              sum=sum+j;
                /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   cov[1]=1;              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
   j=cptcoveff;            }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          }
   j1=0;          else{
   for(k1=1; k1<=1;k1++){            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     for(i1=1; i1<=ncodemax[k1];i1++){            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     j1++;            k=k+1;
             if (j >= jmax) jmax=j;
     if  (cptcovn>0) {            else if (j <= jmin)jmin=j;
       fprintf(ficresprob, "\n#********** Variable ");            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);            /*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(ficresprob, "**********\n#");            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]);
                  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]);
       for (age=bage; age<=fage; age ++){            }
         cov[2]=age;            sum=sum+j;
         for (k=1; k<=cptcovn;k++) {          }
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];          jk= j/stepm;
                    jl= j -jk*stepm;
         }          ju= j -(jk+1)*stepm;
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
         for (k=1; k<=cptcovprod;k++)            if(jl==0){
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];              dh[mi][i]=jk;
                      bh[mi][i]=0;
         gradg=matrix(1,npar,1,9);            }else{ /* We want a negative bias in order to only have interpolation ie
         trgradg=matrix(1,9,1,npar);                    * at the price of an extra matrix product in likelihood */
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));              dh[mi][i]=jk+1;
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));              bh[mi][i]=ju;
                }
         for(theta=1; theta <=npar; theta++){          }else{
           for(i=1; i<=npar; i++)            if(jl <= -ju){
             xp[i] = x[i] + (i==theta ?delti[theta]:0);              dh[mi][i]=jk;
                        bh[mi][i]=jl;       /* bias is positive if real duration
           pmij(pmmij,cov,ncovmodel,xp,nlstate);                                   * is higher than the multiple of stepm and negative otherwise.
                                             */
           k=0;            }
           for(i=1; i<= (nlstate+ndeath); i++){            else{
             for(j=1; j<=(nlstate+ndeath);j++){              dh[mi][i]=jk+1;
               k=k+1;              bh[mi][i]=ju;
               gp[k]=pmmij[i][j];            }
             }            if(dh[mi][i]==0){
           }              dh[mi][i]=1; /* At least one step */
                        bh[mi][i]=ju; /* At least one step */
           for(i=1; i<=npar; i++)              /*  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);*/
             xp[i] = x[i] - (i==theta ?delti[theta]:0);            }
              } /* end if mle */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);        }
           k=0;      } /* end wave */
           for(i=1; i<=(nlstate+ndeath); i++){    }
             for(j=1; j<=(nlstate+ndeath);j++){    jmean=sum/k;
               k=k+1;    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
               gm[k]=pmmij[i][j];    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
             }   }
           }  
        /*********** Tricode ****************************/
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)  void tricode(int *Tvar, int **nbcode, int imx)
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];    {
         }    
     int Ndum[20],ij=1, k, j, i, maxncov=19;
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    int cptcode=0;
           for(theta=1; theta <=npar; theta++)    cptcoveff=0; 
             trgradg[j][theta]=gradg[theta][j];   
            for (k=0; k<maxncov; k++) Ndum[k]=0;
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    for (k=1; k<=7; k++) ncodemax[k]=0;
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);  
            for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
         pmij(pmmij,cov,ncovmodel,x,nlstate);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
                                         modality*/ 
         k=0;        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
         for(i=1; i<=(nlstate+ndeath); i++){        Ndum[ij]++; /*store the modality */
           for(j=1; j<=(nlstate+ndeath);j++){        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
             k=k+1;        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
             gm[k]=pmmij[i][j];                                         Tvar[j]. If V=sex and male is 0 and 
           }                                         female is 1, then  cptcode=1.*/
         }      }
        
      /*printf("\n%d ",(int)age);      for (i=0; i<=cptcode; i++) {
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      }
      }*/  
       ij=1; 
         fprintf(ficresprob,"\n%d ",(int)age);      for (i=1; i<=ncodemax[j]; i++) {
         for (k=0; k<= maxncov; k++) {
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)          if (Ndum[k] != 0) {
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));            nbcode[Tvar[j]][ij]=k; 
              /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
       }            
     }            ij++;
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          }
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));          if (ij > ncodemax[j]) break; 
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        }  
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      } 
   }    }  
   free_vector(xp,1,npar);  
   fclose(ficresprob);   for (k=0; k< maxncov; k++) Ndum[k]=0;
    
 }   for (i=1; i<=ncovmodel-2; i++) { 
      /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
 /******************* Printing html file ***********/     ij=Tvar[i];
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \     Ndum[ij]++;
  int lastpass, int stepm, int weightopt, char model[],\   }
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \  
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\   ij=1;
  char version[], int popforecast, int estepm ){   for (i=1; i<= maxncov; i++) {
   int jj1, k1, i1, cpt;     if((Ndum[i]!=0) && (i<=ncovcol)){
   FILE *fichtm;       Tvaraff[ij]=i; /*For printing */
   /*char optionfilehtm[FILENAMELENGTH];*/       ij++;
      }
   strcpy(optionfilehtm,optionfile);   }
   strcat(optionfilehtm,".htm");   
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {   cptcoveff=ij-1; /*Number of simple covariates*/
     printf("Problem with %s \n",optionfilehtm), exit(0);  }
   }  
   /*********** Health Expectancies ****************/
  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  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 )
 \n  
 Total number of observations=%d <br>\n  {
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    /* Health expectancies */
 <hr  size=\"2\" color=\"#EC5E5E\">    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
  <ul><li>Outputs files<br>\n    double age, agelim, hf;
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n    double ***p3mat,***varhe;
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n    double **dnewm,**doldm;
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    double *xp;
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n    double **gp, **gm;
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n    double ***gradg, ***trgradg;
  - Life expectancies by age and initial health status (estepm=%2d months): <a href=\"e%s\">e%s</a> <br>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot,fileres,fileres,fileres,fileres,fileres,fileres,estepm,fileres,fileres);    int theta;
   
  fprintf(fichtm,"\n    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n    xp=vector(1,npar);
   - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n    dnewm=matrix(1,nlstate*nlstate,1,npar);
  - Variances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
  - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>\n    
  - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);    fprintf(ficreseij,"# Health expectancies\n");
     fprintf(ficreseij,"# Age");
  if(popforecast==1) fprintf(fichtm,"\n    for(i=1; i<=nlstate;i++)
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n      for(j=1; j<=nlstate;j++)
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n        fprintf(ficreseij," %1d-%1d (SE)",i,j);
         <br>",fileres,fileres,fileres,fileres);    fprintf(ficreseij,"\n");
  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);    if(estepm < stepm){
 fprintf(fichtm," <li>Graphs</li><p>");      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
  m=cptcoveff;    else  hstepm=estepm;   
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
  jj1=0;     * if stepm=24 months pijx are given only every 2 years and by summing them
  for(k1=1; k1<=m;k1++){     * we are calculating an estimate of the Life Expectancy assuming a linear 
    for(i1=1; i1<=ncodemax[k1];i1++){     * progression in between and thus overestimating or underestimating according
        jj1++;     * to the curvature of the survival function. If, for the same date, we 
        if (cptcovn > 0) {     * estimate the model with stepm=1 month, we can keep estepm to 24 months
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");     * to compare the new estimate of Life expectancy with the same linear 
          for (cpt=1; cpt<=cptcoveff;cpt++)     * hypothesis. A more precise result, taking into account a more precise
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);     * curvature will be obtained if estepm is as small as stepm. */
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");  
        }    /* For example we decided to compute the life expectancy with the smallest unit */
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);           nhstepm is the number of hstepm from age to agelim 
        for(cpt=1; cpt<nlstate;cpt++){       nstepm is the number of stepm from age to agelin. 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>       Look at hpijx to understand the reason of that which relies in memory size
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);       and note for a fixed period like estepm months */
        }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     for(cpt=1; cpt<=nlstate;cpt++) {       survival function given by stepm (the optimization length). Unfortunately it
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident       means that if the survival funtion is printed only each two years of age and if
 interval) in state (%d): v%s%d%d.gif <br>       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);         results. So we changed our mind and took the option of the best precision.
      }    */
      for(cpt=1; cpt<=nlstate;cpt++) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>  
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    agelim=AGESUP;
      }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      /* nhstepm age range expressed in number of stepm */
 health expectancies in states (1) and (2): e%s%d.gif<br>      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
 fprintf(fichtm,"\n</body>");      /* if (stepm >= YEARM) hstepm=1;*/
    }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
    }      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 fclose(fichtm);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
 }      gp=matrix(0,nhstepm,1,nlstate*nlstate);
       gm=matrix(0,nhstepm,1,nlstate*nlstate);
 /******************* Gnuplot file **************/  
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){      /* Computed by stepm unit matrices, product of hstepm matrices, stored
          in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
    
   strcpy(optionfilegnuplot,optionfilefiname);  
   strcat(optionfilegnuplot,".gp.txt");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {  
     printf("Problem with file %s",optionfilegnuplot);      /* Computing Variances of health expectancies */
   }  
        for(theta=1; theta <=npar; theta++){
 #ifdef windows        for(i=1; i<=npar; i++){ 
     fprintf(ficgp,"cd \"%s\" \n",pathc);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 #endif        }
 m=pow(2,cptcoveff);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
      
  /* 1eme*/        cptj=0;
   for (cpt=1; cpt<= nlstate ; cpt ++) {        for(j=1; j<= nlstate; j++){
    for (k1=1; k1<= m ; k1 ++) {          for(i=1; i<=nlstate; i++){
             cptj=cptj+1;
      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",ageminpar,fage,fileres,k1-1,k1-1);            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
               gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
 for (i=1; i<= nlstate ; i ++) {            }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          }
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }       
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);       
     for (i=1; i<= nlstate ; i ++) {        for(i=1; i<=npar; i++) 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   else fprintf(ficgp," \%%*lf (\%%*lf)");        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 }        
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        cptj=0;
      for (i=1; i<= nlstate ; i ++) {        for(j=1; j<= nlstate; j++){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          for(i=1;i<=nlstate;i++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");            cptj=cptj+1;
 }              for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));  
               gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            }
    }          }
   }        }
   /*2 eme*/        for(j=1; j<= nlstate*nlstate; j++)
           for(h=0; h<=nhstepm-1; h++){
   for (k1=1; k1<= m ; k1 ++) {            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",ageminpar,fage);          }
           } 
     for (i=1; i<= nlstate+1 ; i ++) {     
       k=2*i;  /* End theta */
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");       for(h=0; h<=nhstepm-1; h++)
 }          for(j=1; j<=nlstate*nlstate;j++)
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");          for(theta=1; theta <=npar; theta++)
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);            trgradg[h][j][theta]=gradg[h][theta][j];
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);       
       for (j=1; j<= nlstate+1 ; j ++) {  
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       for(i=1;i<=nlstate*nlstate;i++)
         else fprintf(ficgp," \%%*lf (\%%*lf)");        for(j=1;j<=nlstate*nlstate;j++)
 }            varhe[i][j][(int)age] =0.;
       fprintf(ficgp,"\" t\"\" w l 0,");  
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);       printf("%d|",(int)age);fflush(stdout);
       for (j=1; j<= nlstate+1 ; j ++) {       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       for(h=0;h<=nhstepm-1;h++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");        for(k=0;k<=nhstepm-1;k++){
 }            matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       else fprintf(ficgp,"\" t\"\" w l 0,");          for(i=1;i<=nlstate*nlstate;i++)
     }            for(j=1;j<=nlstate*nlstate;j++)
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
   }        }
        }
   /*3eme*/      /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
   for (k1=1; k1<= m ; k1 ++) {        for(j=1; j<=nlstate;j++)
     for (cpt=1; cpt<= nlstate ; cpt ++) {          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       k=2+nlstate*(2*cpt-2);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);            
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);  /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");  
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          }
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);  
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");      fprintf(ficreseij,"%3.0f",age );
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);      cptj=0;
       for(i=1; i<=nlstate;i++)
 */        for(j=1; j<=nlstate;j++){
       for (i=1; i< nlstate ; i ++) {          cptj++;
         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);          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
         }
       }      fprintf(ficreseij,"\n");
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);     
     }      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     }      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
        free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   /* CV preval stat */      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     for (k1=1; k1<= m ; k1 ++) {      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for (cpt=1; cpt<nlstate ; cpt ++) {    }
       k=3;    printf("\n");
       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",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);    fprintf(ficlog,"\n");
   
       for (i=1; i< nlstate ; i ++)    free_vector(xp,1,npar);
         fprintf(ficgp,"+$%d",k+i+1);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
          free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
       l=3+(nlstate+ndeath)*cpt;  }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  
       for (i=1; i< nlstate ; i ++) {  /************ Variance ******************/
         l=3+(nlstate+ndeath)*cpt;  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav)
         fprintf(ficgp,"+$%d",l+i+1);  {
       }    /* Variance of health expectancies */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    /* double **newm;*/
     }    double **dnewm,**doldm;
   }      double **dnewmp,**doldmp;
      int i, j, nhstepm, hstepm, h, nstepm ;
   /* proba elementaires */    int k, cptcode;
    for(i=1,jk=1; i <=nlstate; i++){    double *xp;
     for(k=1; k <=(nlstate+ndeath); k++){    double **gp, **gm;  /* for var eij */
       if (k != i) {    double ***gradg, ***trgradg; /*for var eij */
         for(j=1; j <=ncovmodel; j++){    double **gradgp, **trgradgp; /* for var p point j */
            double *gpp, *gmp; /* for var p point j */
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
           jk++;    double ***p3mat;
           fprintf(ficgp,"\n");    double age,agelim, hf;
         }    double ***mobaverage;
       }    int theta;
     }    char digit[4];
     }    char digitp[25];
   
     for(jk=1; jk <=m; jk++) {    char fileresprobmorprev[FILENAMELENGTH];
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);  
    i=1;    if(popbased==1){
    for(k2=1; k2<=nlstate; k2++) {      if(mobilav!=0)
      k3=i;        strcpy(digitp,"-populbased-mobilav-");
      for(k=1; k<=(nlstate+ndeath); k++) {      else strcpy(digitp,"-populbased-nomobil-");
        if (k != k2){    }
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    else 
 ij=1;      strcpy(digitp,"-stablbased-");
         for(j=3; j <=ncovmodel; j++) {  
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    if (mobilav!=0) {
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
             ij++;      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           }        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           else        printf(" Error in movingaverage mobilav=%d\n",mobilav);
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      }
         }    }
           fprintf(ficgp,")/(1");  
            strcpy(fileresprobmorprev,"prmorprev"); 
         for(k1=1; k1 <=nlstate; k1++){      sprintf(digit,"%-d",ij);
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
 ij=1;    strcat(fileresprobmorprev,digit); /* Tvar to be done */
           for(j=3; j <=ncovmodel; j++){    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    strcat(fileresprobmorprev,fileres);
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
             ij++;      printf("Problem with resultfile: %s\n", fileresprobmorprev);
           }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           else    }
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           }    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           fprintf(ficgp,")");    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(ficresprobmorprev,"# Age cov=%-d",ij);
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      fprintf(ficresprobmorprev," p.%-d SE",j);
         i=i+ncovmodel;      for(i=1; i<=nlstate;i++)
        }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
      }    }  
    }    fprintf(ficresprobmorprev,"\n");
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
    }      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
          fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
   fclose(ficgp);      exit(0);
 }  /* end gnuplot */    }
     else{
       fprintf(ficgp,"\n# Routine varevsij");
 /*************** Moving average **************/    }
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
   int i, cpt, cptcod;      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)      exit(0);
       for (i=1; i<=nlstate;i++)    }
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    else{
           mobaverage[(int)agedeb][i][cptcod]=0.;      fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
          fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){    }
       for (i=1; i<=nlstate;i++){    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
           for (cpt=0;cpt<=4;cpt++){    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");
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    fprintf(ficresvij,"# Age");
           }    for(i=1; i<=nlstate;i++)
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      for(j=1; j<=nlstate;j++)
         }        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
       }    fprintf(ficresvij,"\n");
     }  
        xp=vector(1,npar);
 }    dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
 /************** Forecasting ******************/    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){  
      gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    gpp=vector(nlstate+1,nlstate+ndeath);
   int *popage;    gmp=vector(nlstate+1,nlstate+ndeath);
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   double *popeffectif,*popcount;    
   double ***p3mat;    if(estepm < stepm){
   char fileresf[FILENAMELENGTH];      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
  agelim=AGESUP;    else  hstepm=estepm;   
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    /* 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. 
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);       nhstepm is the number of hstepm from age to agelim 
         nstepm is the number of stepm from age to agelin. 
         Look at hpijx to understand the reason of that which relies in memory size
   strcpy(fileresf,"f");       and note for a fixed period like k years */
   strcat(fileresf,fileres);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   if((ficresf=fopen(fileresf,"w"))==NULL) {       survival function given by stepm (the optimization length). Unfortunately it
     printf("Problem with forecast resultfile: %s\n", fileresf);       means that if the survival funtion is printed every two years of age and if
   }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   printf("Computing forecasting: result on file '%s' \n", fileresf);       results. So we changed our mind and took the option of the best precision.
     */
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
   if (mobilav==1) {    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     movingaverage(agedeb, fage, ageminpar, mobaverage);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   stepsize=(int) (stepm+YEARM-1)/YEARM;      gp=matrix(0,nhstepm,1,nlstate);
   if (stepm<=12) stepsize=1;      gm=matrix(0,nhstepm,1,nlstate);
    
   agelim=AGESUP;  
        for(theta=1; theta <=npar; theta++){
   hstepm=1;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   hstepm=hstepm/stepm;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   yp1=modf(dateintmean,&yp);        }
   anprojmean=yp;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   yp2=modf((yp1*12),&yp);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   mprojmean=yp;  
   yp1=modf((yp2*30.5),&yp);        if (popbased==1) {
   jprojmean=yp;          if(mobilav ==0){
   if(jprojmean==0) jprojmean=1;            for(i=1; i<=nlstate;i++)
   if(mprojmean==0) jprojmean=1;              prlim[i][i]=probs[(int)age][i][ij];
            }else{ /* mobilav */ 
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);            for(i=1; i<=nlstate;i++)
                prlim[i][i]=mobaverage[(int)age][i][ij];
   for(cptcov=1;cptcov<=i2;cptcov++){          }
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        }
       k=k+1;    
       fprintf(ficresf,"\n#******");        for(j=1; j<= nlstate; j++){
       for(j=1;j<=cptcoveff;j++) {          for(h=0; h<=nhstepm; h++){
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       }              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       fprintf(ficresf,"******\n");          }
       fprintf(ficresf,"# StartingAge FinalAge");        }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);        /* This for computing probability of death (h=1 means
                 computed over hstepm matrices product = hstepm*stepm months) 
                 as a weighted average of prlim.
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {        */
         fprintf(ficresf,"\n");        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);            for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        }    
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        /* end probability of death */
           nhstepm = nhstepm/hstepm;  
                  for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           oldm=oldms;savm=savms;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           
           for (h=0; h<=nhstepm; h++){        if (popbased==1) {
             if (h==(int) (calagedate+YEARM*cpt)) {          if(mobilav ==0){
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);            for(i=1; i<=nlstate;i++)
             }              prlim[i][i]=probs[(int)age][i][ij];
             for(j=1; j<=nlstate+ndeath;j++) {          }else{ /* mobilav */ 
               kk1=0.;kk2=0;            for(i=1; i<=nlstate;i++)
               for(i=1; i<=nlstate;i++) {                            prlim[i][i]=mobaverage[(int)age][i][ij];
                 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];        for(j=1; j<= nlstate; j++){
                 }          for(h=0; h<=nhstepm; h++){
                            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               }              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
               if (h==(int)(calagedate+12*cpt)){          }
                 fprintf(ficresf," %.3f", kk1);        }
                                /* This for computing probability of death (h=1 means
               }           computed over hstepm matrices product = hstepm*stepm months) 
             }           as a weighted average of prlim.
           }        */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         }          for(i=1,gmp[j]=0.; i<= nlstate; i++)
       }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     }        }    
   }        /* end probability of death */
          
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
   fclose(ficresf);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 }          }
 /************** Forecasting ******************/  
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
            gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;        }
   int *popage;  
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;      } /* End theta */
   double *popeffectif,*popcount;  
   double ***p3mat,***tabpop,***tabpopprev;      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   char filerespop[FILENAMELENGTH];  
       for(h=0; h<=nhstepm; h++) /* veij */
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(j=1; j<=nlstate;j++)
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          for(theta=1; theta <=npar; theta++)
   agelim=AGESUP;            trgradg[h][j][theta]=gradg[h][theta][j];
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;  
        for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        for(theta=1; theta <=npar; theta++)
            trgradgp[j][theta]=gradgp[theta][j];
      
   strcpy(filerespop,"pop");  
   strcat(filerespop,fileres);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   if((ficrespop=fopen(filerespop,"w"))==NULL) {      for(i=1;i<=nlstate;i++)
     printf("Problem with forecast resultfile: %s\n", filerespop);        for(j=1;j<=nlstate;j++)
   }          vareij[i][j][(int)age] =0.;
   printf("Computing forecasting: result on file '%s' \n", filerespop);  
       for(h=0;h<=nhstepm;h++){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
   if (mobilav==1) {          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          for(i=1;i<=nlstate;i++)
     movingaverage(agedeb, fage, ageminpar, mobaverage);            for(j=1;j<=nlstate;j++)
   }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
   stepsize=(int) (stepm+YEARM-1)/YEARM;      }
   if (stepm<=12) stepsize=1;    
        /* pptj */
   agelim=AGESUP;      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
        matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
   hstepm=1;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
   hstepm=hstepm/stepm;        for(i=nlstate+1;i<=nlstate+ndeath;i++)
            varppt[j][i]=doldmp[j][i];
   if (popforecast==1) {      /* end ppptj */
     if((ficpop=fopen(popfile,"r"))==NULL) {      /*  x centered again */
       printf("Problem with population file : %s\n",popfile);exit(0);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     }      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     popage=ivector(0,AGESUP);   
     popeffectif=vector(0,AGESUP);      if (popbased==1) {
     popcount=vector(0,AGESUP);        if(mobilav ==0){
              for(i=1; i<=nlstate;i++)
     i=1;              prlim[i][i]=probs[(int)age][i][ij];
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;        }else{ /* mobilav */ 
              for(i=1; i<=nlstate;i++)
     imx=i;            prlim[i][i]=mobaverage[(int)age][i][ij];
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];        }
   }      }
                
   for(cptcov=1;cptcov<=i2;cptcov++){      /* This for computing probability of death (h=1 means
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
       k=k+1;         as a weighted average of prlim.
       fprintf(ficrespop,"\n#******");      */
       for(j=1;j<=cptcoveff;j++) {      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
       }          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       fprintf(ficrespop,"******\n");      }    
       fprintf(ficrespop,"# Age");      /* end probability of death */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);  
       if (popforecast==1)  fprintf(ficrespop," [Population]");      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
            for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       for (cpt=0; cpt<=0;cpt++) {        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);          for(i=1; i<=nlstate;i++){
                  fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        }
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      } 
           nhstepm = nhstepm/hstepm;      fprintf(ficresprobmorprev,"\n");
            
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficresvij,"%.0f ",age );
           oldm=oldms;savm=savms;      for(i=1; i<=nlstate;i++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          for(j=1; j<=nlstate;j++){
                  fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
           for (h=0; h<=nhstepm; h++){        }
             if (h==(int) (calagedate+YEARM*cpt)) {      fprintf(ficresvij,"\n");
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);      free_matrix(gp,0,nhstepm,1,nlstate);
             }      free_matrix(gm,0,nhstepm,1,nlstate);
             for(j=1; j<=nlstate+ndeath;j++) {      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
               kk1=0.;kk2=0;      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
               for(i=1; i<=nlstate;i++) {                    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                 if (mobilav==1)    } /* End age */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    free_vector(gpp,nlstate+1,nlstate+ndeath);
                 else {    free_vector(gmp,nlstate+1,nlstate+ndeath);
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
                 }    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
               }    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
               if (h==(int)(calagedate+12*cpt)){    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
                   /*fprintf(ficrespop," %.3f", kk1);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
               }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
             }    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
             for(i=1; i<=nlstate;i++){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",fileresprobmorprev);
               kk1=0.;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",fileresprobmorprev);
                 for(j=1; j<=nlstate;j++){    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s%s.png\"> <br>\n", estepm,digitp,optionfilefiname,digit);
                 }    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];  */
             }    fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit);
   
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    free_vector(xp,1,npar);
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);    free_matrix(doldm,1,nlstate,1,nlstate);
           }    free_matrix(dnewm,1,nlstate,1,npar);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    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);
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    fclose(fichtm);
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);    }  /* end varevsij */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  /************ Variance of prevlim ******************/
           nhstepm = nhstepm/hstepm;  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)
            {
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* Variance of prevalence limit */
           oldm=oldms;savm=savms;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double **newm;
           for (h=0; h<=nhstepm; h++){    double **dnewm,**doldm;
             if (h==(int) (calagedate+YEARM*cpt)) {    int i, j, nhstepm, hstepm;
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    int k, cptcode;
             }    double *xp;
             for(j=1; j<=nlstate+ndeath;j++) {    double *gp, *gm;
               kk1=0.;kk2=0;    double **gradg, **trgradg;
               for(i=1; i<=nlstate;i++) {                  double age,agelim;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        int theta;
               }     
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
             }    fprintf(ficresvpl,"# Age");
           }    for(i=1; i<=nlstate;i++)
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        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);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    
     hstepm=1*YEARM; /* Every year of age */
   if (popforecast==1) {    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     free_ivector(popage,0,AGESUP);    agelim = AGESUP;
     free_vector(popeffectif,0,AGESUP);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     free_vector(popcount,0,AGESUP);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   }      if (stepm >= YEARM) hstepm=1;
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      gradg=matrix(1,npar,1,nlstate);
   fclose(ficrespop);      gp=vector(1,nlstate);
 }      gm=vector(1,nlstate);
   
 /***********************************************/      for(theta=1; theta <=npar; theta++){
 /**************** Main Program *****************/        for(i=1; i<=npar; i++){ /* Computes gradient */
 /***********************************************/          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
 int main(int argc, char *argv[])        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
 {        for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      
   double agedeb, agefin,hf;        for(i=1; i<=npar; i++) /* Computes gradient */
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   double fret;        for(i=1;i<=nlstate;i++)
   double **xi,tmp,delta;          gm[i] = prlim[i][i];
   
   double dum; /* Dummy variable */        for(i=1;i<=nlstate;i++)
   double ***p3mat;          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
   int *indx;      } /* End theta */
   char line[MAXLINE], linepar[MAXLINE];  
   char title[MAXLINE];      trgradg =matrix(1,nlstate,1,npar);
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];  
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];      for(j=1; j<=nlstate;j++)
          for(theta=1; theta <=npar; theta++)
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];          trgradg[j][theta]=gradg[theta][j];
   
   char filerest[FILENAMELENGTH];      for(i=1;i<=nlstate;i++)
   char fileregp[FILENAMELENGTH];        varpl[i][(int)age] =0.;
   char popfile[FILENAMELENGTH];      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
   int firstobs=1, lastobs=10;      for(i=1;i<=nlstate;i++)
   int sdeb, sfin; /* Status at beginning and end */        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   int c,  h , cpt,l;  
   int ju,jl, mi;      fprintf(ficresvpl,"%.0f ",age );
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      for(i=1; i<=nlstate;i++)
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
   int mobilav=0,popforecast=0;      fprintf(ficresvpl,"\n");
   int hstepm, nhstepm;      free_vector(gp,1,nlstate);
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;      free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
   double bage, fage, age, agelim, agebase;      free_matrix(trgradg,1,nlstate,1,npar);
   double ftolpl=FTOL;    } /* End age */
   double **prlim;  
   double *severity;    free_vector(xp,1,npar);
   double ***param; /* Matrix of parameters */    free_matrix(doldm,1,nlstate,1,npar);
   double  *p;    free_matrix(dnewm,1,nlstate,1,nlstate);
   double **matcov; /* Matrix of covariance */  
   double ***delti3; /* Scale */  }
   double *delti; /* Scale */  
   double ***eij, ***vareij;  /************ Variance of one-step probabilities  ******************/
   double **varpl; /* Variances of prevalence limits by age */  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   double *epj, vepp;  {
   double kk1, kk2;    int i, j=0,  i1, k1, l1, t, tj;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    int k2, l2, j1,  z1;
      int k=0,l, cptcode;
     int first=1, first1;
   char version[80]="Imach version 0.8a1, June 2003, INED-EUROREVES ";    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
   char *alph[]={"a","a","b","c","d","e"}, str[4];    double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
   char z[1]="c", occ;    double **gradg, **trgradg;
 #include <sys/time.h>    double **mu;
 #include <time.h>    double age,agelim, cov[NCOVMAX];
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
      int theta;
   /* long total_usecs;    char fileresprob[FILENAMELENGTH];
   struct timeval start_time, end_time;    char fileresprobcov[FILENAMELENGTH];
      char fileresprobcor[FILENAMELENGTH];
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   getcwd(pathcd, size);    double ***varpij;
   
   printf("\n%s",version);    strcpy(fileresprob,"prob"); 
   if(argc <=1){    strcat(fileresprob,fileres);
     printf("\nEnter the parameter file name: ");    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     scanf("%s",pathtot);      printf("Problem with resultfile: %s\n", fileresprob);
   }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
   else{    }
     strcpy(pathtot,argv[1]);    strcpy(fileresprobcov,"probcov"); 
   }    strcat(fileresprobcov,fileres);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
   /*cygwin_split_path(pathtot,path,optionfile);      printf("Problem with resultfile: %s\n", fileresprobcov);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   /* cutv(path,optionfile,pathtot,'\\');*/    }
     strcpy(fileresprobcor,"probcor"); 
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    strcat(fileresprobcor,fileres);
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
   chdir(path);      printf("Problem with resultfile: %s\n", fileresprobcor);
   replace(pathc,path);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
 /*-------- arguments in the command line --------*/    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);
   strcpy(fileres,"r");    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   strcat(fileres, optionfilefiname);    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   strcat(fileres,".txt");    /* Other files have txt extension */    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);
   /*---------arguments file --------*/    
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    fprintf(ficresprob,"# Age");
     printf("Problem with optionfile %s\n",optionfile);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     goto end;    fprintf(ficresprobcov,"# Age");
   }    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcov,"# Age");
   strcpy(filereso,"o");  
   strcat(filereso,fileres);  
   if((ficparo=fopen(filereso,"w"))==NULL) {    for(i=1; i<=nlstate;i++)
     printf("Problem with Output resultfile: %s\n", filereso);goto end;      for(j=1; j<=(nlstate+ndeath);j++){
   }        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
   /* Reads comments: lines beginning with '#' */        fprintf(ficresprobcor," p%1d-%1d ",i,j);
   while((c=getc(ficpar))=='#' && c!= EOF){      }  
     ungetc(c,ficpar);   /* fprintf(ficresprob,"\n");
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprobcov,"\n");
     puts(line);    fprintf(ficresprobcor,"\n");
     fputs(line,ficparo);   */
   }   xp=vector(1,npar);
   ungetc(c,ficpar);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
   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);    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
   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);    first=1;
 while((c=getc(ficpar))=='#' && c!= EOF){    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
     ungetc(c,ficpar);      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
     fgets(line, MAXLINE, ficpar);      fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
     puts(line);      exit(0);
     fputs(line,ficparo);    }
   }    else{
   ungetc(c,ficpar);      fprintf(ficgp,"\n# Routine varprob");
      }
        if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
   covar=matrix(0,NCOVMAX,1,n);      printf("Problem with html file: %s\n", optionfilehtm);
   cptcovn=0;      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      exit(0);
     }
   ncovmodel=2+cptcovn;    else{
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
        fprintf(fichtm,"\n");
   /* Read guess parameters */  
   /* Reads comments: lines beginning with '#' */      fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
   while((c=getc(ficpar))=='#' && c!= EOF){      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");
     ungetc(c,ficpar);      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");
     fgets(line, MAXLINE, ficpar);  
     puts(line);    }
     fputs(line,ficparo);  
   }    cov[1]=1;
   ungetc(c,ficpar);    tj=cptcoveff;
      if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    j1=0;
     for(i=1; i <=nlstate; i++)    for(t=1; t<=tj;t++){
     for(j=1; j <=nlstate+ndeath-1; j++){      for(i1=1; i1<=ncodemax[t];i1++){ 
       fscanf(ficpar,"%1d%1d",&i1,&j1);        j1++;
       fprintf(ficparo,"%1d%1d",i1,j1);        if  (cptcovn>0) {
       printf("%1d%1d",i,j);          fprintf(ficresprob, "\n#********** Variable "); 
       for(k=1; k<=ncovmodel;k++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         fscanf(ficpar," %lf",&param[i][j][k]);          fprintf(ficresprob, "**********\n#\n");
         printf(" %lf",param[i][j][k]);          fprintf(ficresprobcov, "\n#********** Variable "); 
         fprintf(ficparo," %lf",param[i][j][k]);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       }          fprintf(ficresprobcov, "**********\n#\n");
       fscanf(ficpar,"\n");          
       printf("\n");          fprintf(ficgp, "\n#********** Variable "); 
       fprintf(ficparo,"\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     }          fprintf(ficgp, "**********\n#\n");
            
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;          
           fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   p=param[1][1];          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\">");
   /* Reads comments: lines beginning with '#' */          
   while((c=getc(ficpar))=='#' && c!= EOF){          fprintf(ficresprobcor, "\n#********** Variable ");    
     ungetc(c,ficpar);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     fgets(line, MAXLINE, ficpar);          fprintf(ficresprobcor, "**********\n#");    
     puts(line);        }
     fputs(line,ficparo);        
   }        for (age=bage; age<=fage; age ++){ 
   ungetc(c,ficpar);          cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */          }
   for(i=1; i <=nlstate; i++){          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     for(j=1; j <=nlstate+ndeath-1; j++){          for (k=1; k<=cptcovprod;k++)
       fscanf(ficpar,"%1d%1d",&i1,&j1);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       printf("%1d%1d",i,j);          
       fprintf(ficparo,"%1d%1d",i1,j1);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
       for(k=1; k<=ncovmodel;k++){          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
         fscanf(ficpar,"%le",&delti3[i][j][k]);          gp=vector(1,(nlstate)*(nlstate+ndeath));
         printf(" %le",delti3[i][j][k]);          gm=vector(1,(nlstate)*(nlstate+ndeath));
         fprintf(ficparo," %le",delti3[i][j][k]);      
       }          for(theta=1; theta <=npar; theta++){
       fscanf(ficpar,"\n");            for(i=1; i<=npar; i++)
       printf("\n");              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
       fprintf(ficparo,"\n");            
     }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   }            
   delti=delti3[1][1];            k=0;
              for(i=1; i<= (nlstate); i++){
   /* Reads comments: lines beginning with '#' */              for(j=1; j<=(nlstate+ndeath);j++){
   while((c=getc(ficpar))=='#' && c!= EOF){                k=k+1;
     ungetc(c,ficpar);                gp[k]=pmmij[i][j];
     fgets(line, MAXLINE, ficpar);              }
     puts(line);            }
     fputs(line,ficparo);            
   }            for(i=1; i<=npar; i++)
   ungetc(c,ficpar);              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
        
   matcov=matrix(1,npar,1,npar);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   for(i=1; i <=npar; i++){            k=0;
     fscanf(ficpar,"%s",&str);            for(i=1; i<=(nlstate); i++){
     printf("%s",str);              for(j=1; j<=(nlstate+ndeath);j++){
     fprintf(ficparo,"%s",str);                k=k+1;
     for(j=1; j <=i; j++){                gm[k]=pmmij[i][j];
       fscanf(ficpar," %le",&matcov[i][j]);              }
       printf(" %.5le",matcov[i][j]);            }
       fprintf(ficparo," %.5le",matcov[i][j]);       
     }            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
     fscanf(ficpar,"\n");              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
     printf("\n");          }
     fprintf(ficparo,"\n");  
   }          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   for(i=1; i <=npar; i++)            for(theta=1; theta <=npar; theta++)
     for(j=i+1;j<=npar;j++)              trgradg[j][theta]=gradg[theta][j];
       matcov[i][j]=matcov[j][i];          
              matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
   printf("\n");          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));
     /*-------- Rewriting paramater file ----------*/          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
      strcpy(rfileres,"r");    /* "Rparameterfile */          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/  
      strcat(rfileres,".");    /* */          pmij(pmmij,cov,ncovmodel,x,nlstate);
      strcat(rfileres,optionfilext);    /* Other files have txt extension */          
     if((ficres =fopen(rfileres,"w"))==NULL) {          k=0;
       printf("Problem writing new parameter file: %s\n", fileres);goto end;          for(i=1; i<=(nlstate); i++){
     }            for(j=1; j<=(nlstate+ndeath);j++){
     fprintf(ficres,"#%s\n",version);              k=k+1;
                  mu[k][(int) age]=pmmij[i][j];
     /*-------- data file ----------*/            }
     if((fic=fopen(datafile,"r"))==NULL)    {          }
       printf("Problem with datafile: %s\n", datafile);goto end;          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
     }            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
     n= lastobs;  
     severity = vector(1,maxwav);          /*printf("\n%d ",(int)age);
     outcome=imatrix(1,maxwav+1,1,n);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     num=ivector(1,n);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     moisnais=vector(1,n);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     annais=vector(1,n);            }*/
     moisdc=vector(1,n);  
     andc=vector(1,n);          fprintf(ficresprob,"\n%d ",(int)age);
     agedc=vector(1,n);          fprintf(ficresprobcov,"\n%d ",(int)age);
     cod=ivector(1,n);          fprintf(ficresprobcor,"\n%d ",(int)age);
     weight=vector(1,n);  
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
     mint=matrix(1,maxwav,1,n);            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
     anint=matrix(1,maxwav,1,n);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     s=imatrix(1,maxwav+1,1,n);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
     adl=imatrix(1,maxwav+1,1,n);                fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
     tab=ivector(1,NCOVMAX);          }
     ncodemax=ivector(1,8);          i=0;
           for (k=1; k<=(nlstate);k++){
     i=1;            for (l=1; l<=(nlstate+ndeath);l++){ 
     while (fgets(line, MAXLINE, fic) != NULL)    {              i=i++;
       if ((i >= firstobs) && (i <=lastobs)) {              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
                      fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
         for (j=maxwav;j>=1;j--){              for (j=1; j<=i;j++){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
           strcpy(line,stra);                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
           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);            }
         }          }/* end of loop for state */
                } /* end of loop for age */
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        /* Confidence intervalle of pij  */
         /*
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);          fprintf(ficgp,"\nset noparametric;unset label");
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);          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");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);          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);
         for (j=ncovcol;j>=1;j--){          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
         }          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         num[i]=atol(stra);        */
          
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/        first1=1;
         for (k2=1; k2<=(nlstate);k2++){
         i=i+1;          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
       }            if(l2==k2) continue;
     }            j=(k2-1)*(nlstate+ndeath)+l2;
     /* printf("ii=%d", ij);            for (k1=1; k1<=(nlstate);k1++){
        scanf("%d",i);*/              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   imx=i-1; /* Number of individuals */                if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
   /* for (i=1; i<=imx; i++){                if(i<=j) continue;
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;                for (age=bage; age<=fage; age ++){ 
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;                  if ((int)age %5==0){
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
     }*/                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
    /*  for (i=1; i<=imx; i++){                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
      if (s[4][i]==9)  s[4][i]=-1;                    mu1=mu[i][(int) age]/stepm*YEARM ;
      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]));}*/                    mu2=mu[j][(int) age]/stepm*YEARM;
                      c12=cv12/sqrt(v1*v2);
                      /* Computing eigen value of matrix of covariance */
   /* Calculation of the number of parameter from char model*/                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   Tvar=ivector(1,15);                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   Tprod=ivector(1,15);                    /* Eigen vectors */
   Tvaraff=ivector(1,15);                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
   Tvard=imatrix(1,15,1,2);                    /*v21=sqrt(1.-v11*v11); *//* error */
   Tage=ivector(1,15);                          v21=(lc1-v1)/cv12*v11;
                        v12=-v21;
   if (strlen(model) >1){                    v22=v11;
     j=0, j1=0, k1=1, k2=1;                    tnalp=v21/v11;
     j=nbocc(model,'+');                    if(first1==1){
     j1=nbocc(model,'*');                      first1=0;
     cptcovn=j+1;                      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);
     cptcovprod=j1;                    }
                        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);
     strcpy(modelsav,model);                    /*printf(fignu*/
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
       printf("Error. Non available option model=%s ",model);                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
       goto end;                    if(first==1){
     }                      first=0;
                          fprintf(ficgp,"\nset parametric;unset label");
     for(i=(j+1); i>=1;i--){                      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);
       cutv(stra,strb,modelsav,'+');                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);                      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);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/                      fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);
       /*scanf("%d",i);*/                      fprintf(fichtm,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
       if (strchr(strb,'*')) {                      fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);
         cutv(strd,strc,strb,'*');                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
         if (strcmp(strc,"age")==0) {                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
           cptcovprod--;                      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",\
           cutv(strb,stre,strd,'V');                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
           Tvar[i]=atoi(stre);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
           cptcovage++;                    }else{
             Tage[cptcovage]=i;                      first=0;
             /*printf("stre=%s ", stre);*/                      fprintf(fichtm," %d (%.3f),",(int) age, c12);
         }                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
         else if (strcmp(strd,"age")==0) {                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
           cptcovprod--;                      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",\
           cutv(strb,stre,strc,'V');                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
           Tvar[i]=atoi(stre);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
           cptcovage++;                    }/* if first */
           Tage[cptcovage]=i;                  } /* age mod 5 */
         }                } /* end loop age */
         else {                fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);
           cutv(strb,stre,strc,'V');                first=1;
           Tvar[i]=ncovcol+k1;              } /*l12 */
           cutv(strb,strc,strd,'V');            } /* k12 */
           Tprod[k1]=i;          } /*l1 */
           Tvard[k1][1]=atoi(strc);        }/* k1 */
           Tvard[k1][2]=atoi(stre);      } /* loop covariates */
           Tvar[cptcovn+k2]=Tvard[k1][1];    }
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
           for (k=1; k<=lastobs;k++)    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    free_vector(xp,1,npar);
           k1++;    fclose(ficresprob);
           k2=k2+2;    fclose(ficresprobcov);
         }    fclose(ficresprobcor);
       }    fclose(ficgp);
       else {    fclose(fichtm);
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/  }
        /*  scanf("%d",i);*/  
       cutv(strd,strc,strb,'V');  
       Tvar[i]=atoi(strc);  /******************* Printing html file ***********/
       }  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
       strcpy(modelsav,stra);                      int lastpass, int stepm, int weightopt, char model[],\
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
         scanf("%d",i);*/                    int popforecast, int estepm ,\
     }                    double jprev1, double mprev1,double anprev1, \
 }                    double jprev2, double mprev2,double anprev2){
      int jj1, k1, i1, cpt;
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    /*char optionfilehtm[FILENAMELENGTH];*/
   printf("cptcovprod=%d ", cptcovprod);    if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {
   scanf("%d ",i);*/      printf("Problem with %s \n",optionfilehtm), exit(0);
     fclose(fic);      fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);
     }
     /*  if(mle==1){*/  
     if (weightopt != 1) { /* Maximisation without weights*/     fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n \
       for(i=1;i<=n;i++) weight[i]=1.0;   - 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 \
     /*-calculation of age at interview from date of interview and age at death -*/   - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n \
     agev=matrix(1,maxwav,1,imx);   - Life expectancies by age and initial health status (estepm=%2d months): \
      <a href=\"e%s\">e%s</a> <br>\n</li>", \
     for (i=1; i<=imx; i++) {    jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);
       for(m=2; (m<= maxwav); m++) {  
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
          anint[m][i]=9999;  
          s[m][i]=-1;   m=cptcoveff;
        }   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;  
       }   jj1=0;
     }   for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
     for (i=1; i<=imx; i++)  {       jj1++;
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);       if (cptcovn > 0) {
       for(m=1; (m<= maxwav); m++){         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
         if(s[m][i] >0){         for (cpt=1; cpt<=cptcoveff;cpt++) 
           if (s[m][i] >= nlstate+1) {           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
             if(agedc[i]>0)         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
               if(moisdc[i]!=99 && andc[i]!=9999)       }
                 agev[m][i]=agedc[i];       /* Pij */
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/       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> \
            else {  <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);     
               if (andc[i]!=9999){       /* Quasi-incidences */
               printf("Warning negative age at death: %d line:%d\n",num[i],i);       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
               agev[m][i]=-1;   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++){
           else if(s[m][i] !=9){ /* Should no more exist */           fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br> \
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);  <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
             if(mint[m][i]==99 || anint[m][i]==9999)         }
               agev[m][i]=1;       for(cpt=1; cpt<=nlstate;cpt++) {
             else if(agev[m][i] <agemin){          fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br> \
               agemin=agev[m][i];  <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/       }
             }       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
             else if(agev[m][i] >agemax){  health expectancies in states (1) and (2): e%s%d.png<br>\
               agemax=agev[m][i];  <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/     } /* end i1 */
             }   }/* End k1 */
             /*agev[m][i]=anint[m][i]-annais[i];*/   fprintf(fichtm,"</ul>");
             /*   agev[m][i] = age[i]+2*m;*/  
           }  
           else { /* =9 */   fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n\
             agev[m][i]=1;   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n\
             s[m][i]=-1;   - 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\
         else /*= 0 Unknown */   - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n\
           agev[m][i]=1;   - 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 */
     for (i=1; i<=imx; i++)  {  /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
       for(m=1; (m<= maxwav); m++){  /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
         if (s[m][i] > (nlstate+ndeath)) {  /*      <br>",fileres,fileres,fileres,fileres); */
           printf("Error: Wrong value in nlstate or ndeath\n");    /*  else  */
           goto end;  /*    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;}
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  
    jj1=0;
     free_vector(severity,1,maxwav);   for(k1=1; k1<=m;k1++){
     free_imatrix(outcome,1,maxwav+1,1,n);     for(i1=1; i1<=ncodemax[k1];i1++){
     free_vector(moisnais,1,n);       jj1++;
     free_vector(annais,1,n);       if (cptcovn > 0) {
     /* free_matrix(mint,1,maxwav,1,n);         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
        free_matrix(anint,1,maxwav,1,n);*/         for (cpt=1; cpt<=cptcoveff;cpt++) 
     free_vector(moisdc,1,n);           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
     free_vector(andc,1,n);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
           for(cpt=1; cpt<=nlstate;cpt++) {
     wav=ivector(1,imx);         fprintf(fichtm,"<br>- Observed and period prevalence (with confident\
     dh=imatrix(1,lastpass-firstpass+1,1,imx);  interval) in state (%d): v%s%d%d.png <br>\
     mw=imatrix(1,lastpass-firstpass+1,1,imx);  <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
           }
     /* Concatenates waves */     } /* end i1 */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);   }/* End k1 */
    fprintf(fichtm,"</ul>");
   fclose(fichtm);
       Tcode=ivector(1,100);  }
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);  
       ncodemax[1]=1;  /******************* Gnuplot file **************/
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);  void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
        
    codtab=imatrix(1,100,1,10);    int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
    h=0;    int ng;
    m=pow(2,cptcoveff);    if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
        printf("Problem with file %s",optionfilegnuplot);
    for(k=1;k<=cptcoveff; k++){      fprintf(ficlog,"Problem with file %s",optionfilegnuplot);
      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++){    /*#ifdef windows */
            h++;      fprintf(ficgp,"cd \"%s\" \n",pathc);
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;      /*#endif */
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/  m=pow(2,cptcoveff);
          }    
        }   /* 1eme*/
      }    for (cpt=1; cpt<= nlstate ; cpt ++) {
    }     for (k1=1; k1<= m ; k1 ++) {
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);       fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
       codtab[1][2]=1;codtab[2][2]=2; */       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 <=m ;i++){  
       for(k=1; k <=cptcovn; k++){       for (i=1; i<= nlstate ; i ++) {
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
       }         else fprintf(ficgp," \%%*lf (\%%*lf)");
       printf("\n");       }
       }       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);
       scanf("%d",i);*/       for (i=1; i<= nlstate ; i ++) {
             if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
    /* Calculates basic frequencies. Computes observed prevalence at single age         else fprintf(ficgp," \%%*lf (\%%*lf)");
        and prints on file fileres'p'. */       } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",fileres,k1-1,k1-1); 
           for (i=1; i<= nlstate ; i ++) {
             if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         else fprintf(ficgp," \%%*lf (\%%*lf)");
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       }  
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     }
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    }
          /*2 eme*/
     /* For Powell, parameters are in a vector p[] starting at p[1]    
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    for (k1=1; k1<= m ; k1 ++) { 
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */      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);
     if(mle==1){      
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      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);
     /*--------- results files --------------*/        for (j=1; j<= nlstate+1 ; j ++) {
     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);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
            else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
    jk=1;        if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");        else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");        fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);
    for(i=1,jk=1; i <=nlstate; i++){        for (j=1; j<= nlstate+1 ; j ++) {
      for(k=1; k <=(nlstate+ndeath); k++){          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
        if (k != i)          else fprintf(ficgp," \%%*lf (\%%*lf)");
          {        }   
            printf("%d%d ",i,k);        fprintf(ficgp,"\" t\"\" w l 0,");
            fprintf(ficres,"%1d%1d ",i,k);        fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);
            for(j=1; j <=ncovmodel; j++){        for (j=1; j<= nlstate+1 ; j ++) {
              printf("%f ",p[jk]);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
              fprintf(ficres,"%f ",p[jk]);          else fprintf(ficgp," \%%*lf (\%%*lf)");
              jk++;        }   
            }        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
            printf("\n");        else fprintf(ficgp,"\" t\"\" w l 0,");
            fprintf(ficres,"\n");      }
          }    }
      }    
    }    /*3eme*/
  if(mle==1){    
     /* Computing hessian and covariance matrix */    for (k1=1; k1<= m ; k1 ++) { 
     ftolhess=ftol; /* Usually correct */      for (cpt=1; cpt<= nlstate ; cpt ++) {
     hesscov(matcov, p, npar, delti, ftolhess, func);        k=2+nlstate*(2*cpt-2);
  }        fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");        fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);
     printf("# Scales (for hessian or gradient estimation)\n");        /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
      for(i=1,jk=1; i <=nlstate; i++){          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
       for(j=1; j <=nlstate+ndeath; j++){          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
         if (j!=i) {          fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           fprintf(ficres,"%1d%1d",i,j);          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           printf("%1d%1d",i,j);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           for(k=1; k<=ncovmodel;k++){          
             printf(" %.5e",delti[jk]);        */
             fprintf(ficres," %.5e",delti[jk]);        for (i=1; i< nlstate ; i ++) {
             jk++;          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);
           }          
           printf("\n");        } 
           fprintf(ficres,"\n");      }
         }    }
       }    
      }    /* CV preval stable (period) */
        for (k1=1; k1<= m ; k1 ++) { 
     k=1;      for (cpt=1; cpt<=nlstate ; cpt ++) {
     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");        k=3;
     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(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
     for(i=1;i<=npar;i++){        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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);
       /*  if (k>nlstate) k=1;        
       i1=(i-1)/(ncovmodel*nlstate)+1;        for (i=1; i< nlstate ; i ++)
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          fprintf(ficgp,"+$%d",k+i+1);
       printf("%s%d%d",alph[k],i1,tab[i]);*/        fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
       fprintf(ficres,"%3d",i);        
       printf("%3d",i);        l=3+(nlstate+ndeath)*cpt;
       for(j=1; j<=i;j++){        fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);
         fprintf(ficres," %.5e",matcov[i][j]);        for (i=1; i< nlstate ; i ++) {
         printf(" %.5e",matcov[i][j]);          l=3+(nlstate+ndeath)*cpt;
       }          fprintf(ficgp,"+$%d",l+i+1);
       fprintf(ficres,"\n");        }
       printf("\n");        fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       k++;      } 
     }    }  
        
     while((c=getc(ficpar))=='#' && c!= EOF){    /* proba elementaires */
       ungetc(c,ficpar);    for(i=1,jk=1; i <=nlstate; i++){
       fgets(line, MAXLINE, ficpar);      for(k=1; k <=(nlstate+ndeath); k++){
       puts(line);        if (k != i) {
       fputs(line,ficparo);          for(j=1; j <=ncovmodel; j++){
     }            fprintf(ficgp,"p%d=%f ",jk,p[jk]);
     ungetc(c,ficpar);            jk++; 
     estepm=0;            fprintf(ficgp,"\n");
     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;  
     }     for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
           for(jk=1; jk <=m; jk++) {
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");         fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng); 
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);         if (ng==2)
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);           fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
           else
     while((c=getc(ficpar))=='#' && c!= EOF){           fprintf(ficgp,"\nset title \"Probability\"\n");
     ungetc(c,ficpar);         fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
     fgets(line, MAXLINE, ficpar);         i=1;
     puts(line);         for(k2=1; k2<=nlstate; k2++) {
     fputs(line,ficparo);           k3=i;
   }           for(k=1; k<=(nlstate+ndeath); k++) {
   ungetc(c,ficpar);             if (k != k2){
                 if(ng==2)
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);                 fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);               else
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                 fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                     ij=1;
   while((c=getc(ficpar))=='#' && c!= EOF){               for(j=3; j <=ncovmodel; j++) {
     ungetc(c,ficpar);                 if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
     fgets(line, MAXLINE, ficpar);                   fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
     puts(line);                   ij++;
     fputs(line,ficparo);                 }
   }                 else
   ungetc(c,ficpar);                   fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                 }
                fprintf(ficgp,")/(1");
    dateprev1=anprev1+mprev1/12.+jprev1/365.;               
    dateprev2=anprev2+mprev2/12.+jprev2/365.;               for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
   fscanf(ficpar,"pop_based=%d\n",&popbased);                 ij=1;
   fprintf(ficparo,"pop_based=%d\n",popbased);                   for(j=3; j <=ncovmodel; j++){
   fprintf(ficres,"pop_based=%d\n",popbased);                     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]]]);
   while((c=getc(ficpar))=='#' && c!= EOF){                     ij++;
     ungetc(c,ficpar);                   }
     fgets(line, MAXLINE, ficpar);                   else
     puts(line);                     fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
     fputs(line,ficparo);                 }
   }                 fprintf(ficgp,")");
   ungetc(c,ficpar);               }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);               if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);               i=i+ncovmodel;
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);             }
            } /* end k */
          } /* end k2 */
 while((c=getc(ficpar))=='#' && c!= EOF){       } /* end jk */
     ungetc(c,ficpar);     } /* end ng */
     fgets(line, MAXLINE, ficpar);     fclose(ficgp); 
     puts(line);  }  /* end gnuplot */
     fputs(line,ficparo);  
   }  
   ungetc(c,ficpar);  /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   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);    int i, cpt, cptcod;
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    int modcovmax =1;
     int mobilavrange, mob;
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    double age;
   
 /*------------ gnuplot -------------*/    modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);                             a covariate has 2 modalities */
      if (cptcovn<1) modcovmax=1; /* At least 1 pass */
 /*------------ free_vector  -------------*/  
  chdir(path);    if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
        if(mobilav==1) mobilavrange=5; /* default */
  free_ivector(wav,1,imx);      else mobilavrange=mobilav;
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      for (age=bage; age<=fage; age++)
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          for (i=1; i<=nlstate;i++)
  free_ivector(num,1,n);          for (cptcod=1;cptcod<=modcovmax;cptcod++)
  free_vector(agedc,1,n);            mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
  /*free_matrix(covar,1,NCOVMAX,1,n);*/      /* We keep the original values on the extreme ages bage, fage and for 
  fclose(ficparo);         fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
  fclose(ficres);         we use a 5 terms etc. until the borders are no more concerned. 
       */ 
 /*--------- index.htm --------*/      for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);          for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
                mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
   /*--------------- Prevalence limit --------------*/                for (cpt=1;cpt<=(mob-1)/2;cpt++){
                    mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
   strcpy(filerespl,"pl");                  mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
   strcat(filerespl,fileres);                }
   if((ficrespl=fopen(filerespl,"w"))==NULL) {              mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;            }
   }          }
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);        }/* end age */
   fprintf(ficrespl,"#Prevalence limit\n");      }/* end mob */
   fprintf(ficrespl,"#Age ");    }else return -1;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    return 0;
   fprintf(ficrespl,"\n");  }/* End movingaverage */
    
   prlim=matrix(1,nlstate,1,nlstate);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /************** Forecasting ******************/
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  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){
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* proj1, year, month, day of starting projection 
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       agemin, agemax range of age
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */       dateprev1 dateprev2 range of dates during which prevalence is computed
   k=0;       anproj2 year of en of projection (same day and month as proj1).
   agebase=ageminpar;    */
   agelim=agemaxpar;    int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
   ftolpl=1.e-10;    int *popage;
   i1=cptcoveff;    double agec; /* generic age */
   if (cptcovn < 1){i1=1;}    double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
   for(cptcov=1;cptcov<=i1;cptcov++){    double ***p3mat;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double ***mobaverage;
         k=k+1;    char fileresf[FILENAMELENGTH];
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/  
         fprintf(ficrespl,"\n#******");    agelim=AGESUP;
         for(j=1;j<=cptcoveff;j++)    prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   
         fprintf(ficrespl,"******\n");    strcpy(fileresf,"f"); 
            strcat(fileresf,fileres);
         for (age=agebase; age<=agelim; age++){    if((ficresf=fopen(fileresf,"w"))==NULL) {
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      printf("Problem with forecast resultfile: %s\n", fileresf);
           fprintf(ficrespl,"%.0f",age );      fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
           for(i=1; i<=nlstate;i++)    }
           fprintf(ficrespl," %.5f", prlim[i][i]);    printf("Computing forecasting: result on file '%s' \n", fileresf);
           fprintf(ficrespl,"\n");    fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
         }  
       }    if (cptcoveff==0) ncodemax[cptcoveff]=1;
     }  
   fclose(ficrespl);    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   /*------------- h Pij x at various ages ------------*/      if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
          fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      }
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    }
   }  
   printf("Computing pij: result on file '%s' \n", filerespij);    stepsize=(int) (stepm+YEARM-1)/YEARM;
      if (stepm<=12) stepsize=1;
   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 */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    hstepm=hstepm/stepm; 
      yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
   k=0;                                 fractional in yp1 */
   for(cptcov=1;cptcov<=i1;cptcov++){    anprojmean=yp;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    yp2=modf((yp1*12),&yp);
       k=k+1;    mprojmean=yp;
         fprintf(ficrespij,"\n#****** ");    yp1=modf((yp2*30.5),&yp);
         for(j=1;j<=cptcoveff;j++)    jprojmean=yp;
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    if(jprojmean==0) jprojmean=1;
         fprintf(ficrespij,"******\n");    if(mprojmean==0) jprojmean=1;
          
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    i1=cptcoveff;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    if (cptcovn < 1){i1=1;}
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
           oldm=oldms;savm=savms;    
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      fprintf(ficresf,"#****** Routine prevforecast **\n");
           fprintf(ficrespij,"# Age");  
           for(i=1; i<=nlstate;i++)  /*            if (h==(int)(YEARM*yearp)){ */
             for(j=1; j<=nlstate+ndeath;j++)    for(cptcov=1, k=0;cptcov<=i1;cptcov++){
               fprintf(ficrespij," %1d-%1d",i,j);      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
           fprintf(ficrespij,"\n");        k=k+1;
            for (h=0; h<=nhstepm; h++){        fprintf(ficresf,"\n#******");
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        for(j=1;j<=cptcoveff;j++) {
             for(i=1; i<=nlstate;i++)          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]]);
               for(j=1; j<=nlstate+ndeath;j++)        }
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        fprintf(ficresf,"******\n");
             fprintf(ficrespij,"\n");        fprintf(ficresf,"# Covariate valuofcovar yearproj age");
              }        for(j=1; j<=nlstate+ndeath;j++){ 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for(i=1; i<=nlstate;i++)              
           fprintf(ficrespij,"\n");            fprintf(ficresf," p%d%d",i,j);
         }          fprintf(ficresf," p.%d",j);
     }        }
   }        for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);          fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
   fclose(ficrespij);          for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
   /*---------- Forecasting ------------------*/            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if((stepm == 1) && (strcmp(model,".")==0)){            oldm=oldms;savm=savms;
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);            hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);          
   }            for (h=0; h<=nhstepm; h++){
   else{              if (h*hstepm/YEARM*stepm ==yearp) {
     erreur=108;                fprintf(ficresf,"\n");
     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);                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);
               } 
   /*---------- Health expectancies and variances ------------*/              for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
   strcpy(filerest,"t");                for(i=1; i<=nlstate;i++) {
   strcat(filerest,fileres);                  if (mobilav==1) 
   if((ficrest=fopen(filerest,"w"))==NULL) {                    ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;                  else {
   }                    ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
   printf("Computing Total LEs with variances: file '%s' \n", filerest);                  }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
   strcpy(filerese,"e");                  }
   strcat(filerese,fileres);                } /* end i */
   if((ficreseij=fopen(filerese,"w"))==NULL) {                if (h*hstepm/YEARM*stepm==yearp) {
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);                  fprintf(ficresf," %.3f", ppij);
   }                }
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);              }/* end j */
             } /* end h */
  strcpy(fileresv,"v");            free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   strcat(fileresv,fileres);          } /* end agec */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {        } /* end yearp */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      } /* end cptcod */
   }    } /* end  cptcov */
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);         
   calagedate=-1;    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  
     fclose(ficresf);
   k=0;  }
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  /************** Forecasting *****not tested NB*************/
       k=k+1;  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){
       fprintf(ficrest,"\n#****** ");    
       for(j=1;j<=cptcoveff;j++)    int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    int *popage;
       fprintf(ficrest,"******\n");    double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
       fprintf(ficreseij,"\n#****** ");    double ***p3mat,***tabpop,***tabpopprev;
       for(j=1;j<=cptcoveff;j++)    double ***mobaverage;
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    char filerespop[FILENAMELENGTH];
       fprintf(ficreseij,"******\n");  
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       fprintf(ficresvij,"\n#****** ");    tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(j=1;j<=cptcoveff;j++)    agelim=AGESUP;
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
       fprintf(ficresvij,"******\n");    
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       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);      strcpy(filerespop,"pop"); 
      strcat(filerespop,fileres);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    if((ficrespop=fopen(filerespop,"w"))==NULL) {
       oldm=oldms;savm=savms;      printf("Problem with forecast resultfile: %s\n", filerespop);
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);      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);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");  
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    if (cptcoveff==0) ncodemax[cptcoveff]=1;
       fprintf(ficrest,"\n");  
     if (mobilav!=0) {
       epj=vector(1,nlstate+1);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(age=bage; age <=fage ;age++){      if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         if (popbased==1) {        printf(" Error in movingaverage mobilav=%d\n",mobilav);
           for(i=1; i<=nlstate;i++)      }
             prlim[i][i]=probs[(int)age][i][k];    }
         }  
            stepsize=(int) (stepm+YEARM-1)/YEARM;
         fprintf(ficrest," %4.0f",age);    if (stepm<=12) stepsize=1;
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    agelim=AGESUP;
             epj[j] += prlim[i][i]*eij[i][j][(int)age];    
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/    hstepm=1;
           }    hstepm=hstepm/stepm; 
           epj[nlstate+1] +=epj[j];    
         }    if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         for(i=1, vepp=0.;i <=nlstate;i++)        printf("Problem with population file : %s\n",popfile);exit(0);
           for(j=1;j <=nlstate;j++)        fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
             vepp += vareij[i][j][(int)age];      } 
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));      popage=ivector(0,AGESUP);
         for(j=1;j <=nlstate;j++){      popeffectif=vector(0,AGESUP);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));      popcount=vector(0,AGESUP);
         }      
         fprintf(ficrest,"\n");      i=1;   
       }      while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
     }     
   }      imx=i;
 free_matrix(mint,1,maxwav,1,n);      for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    }
     free_vector(weight,1,n);  
   fclose(ficreseij);    for(cptcov=1,k=0;cptcov<=i2;cptcov++){
   fclose(ficresvij);     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
   fclose(ficrest);        k=k+1;
   fclose(ficpar);        fprintf(ficrespop,"\n#******");
   free_vector(epj,1,nlstate+1);        for(j=1;j<=cptcoveff;j++) {
            fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
   /*------- Variance limit prevalence------*/          }
         fprintf(ficrespop,"******\n");
   strcpy(fileresvpl,"vpl");        fprintf(ficrespop,"# Age");
   strcat(fileresvpl,fileres);        for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        if (popforecast==1)  fprintf(ficrespop," [Population]");
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);        
     exit(0);        for (cpt=0; cpt<=0;cpt++) { 
   }          fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
   k=0;            nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
   for(cptcov=1;cptcov<=i1;cptcov++){            nhstepm = nhstepm/hstepm; 
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            
       k=k+1;            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficresvpl,"\n#****** ");            oldm=oldms;savm=savms;
       for(j=1;j<=cptcoveff;j++)            hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          
       fprintf(ficresvpl,"******\n");            for (h=0; h<=nhstepm; h++){
                    if (h==(int) (calagedatem+YEARM*cpt)) {
       varpl=matrix(1,nlstate,(int) bage, (int) fage);                fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
       oldm=oldms;savm=savms;              } 
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);              for(j=1; j<=nlstate+ndeath;j++) {
     }                kk1=0.;kk2=0;
  }                for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
   fclose(ficresvpl);                    kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
   /*---------- End : free ----------------*/                    kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);                  }
                  }
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                if (h==(int)(calagedatem+12*cpt)){
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);                  tabpop[(int)(agedeb)][j][cptcod]=kk1;
                      /*fprintf(ficrespop," %.3f", kk1);
                        if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
   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);              for(i=1; i<=nlstate;i++){
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);                kk1=0.;
                    for(j=1; j<=nlstate;j++){
   free_matrix(matcov,1,npar,1,npar);                    kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
   free_vector(delti,1,npar);                  }
   free_matrix(agev,1,maxwav,1,imx);                    tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);              }
   
   if(erreur >0)              if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
     printf("End of Imach with error or warning %d\n",erreur);                fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
   else   printf("End of Imach\n");            }
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */            free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
            }
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/        }
   /*printf("Total time was %d uSec.\n", total_usecs);*/   
   /*------ End -----------*/    /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
  end:          fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
   /* chdir(pathcd);*/          for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
  /*system("wgnuplot graph.plt");*/            nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
  /*system("../gp37mgw/wgnuplot graph.plt");*/            nhstepm = nhstepm/hstepm; 
  /*system("cd ../gp37mgw");*/            
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  strcpy(plotcmd,GNUPLOTPROGRAM);            oldm=oldms;savm=savms;
  strcat(plotcmd," ");            hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
  strcat(plotcmd,optionfilegnuplot);            for (h=0; h<=nhstepm; h++){
  system(plotcmd);              if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
  /*#ifdef windows*/              } 
   while (z[0] != 'q') {              for(j=1; j<=nlstate+ndeath;j++) {
     /* chdir(path); */                kk1=0.;kk2=0;
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");                for(i=1; i<=nlstate;i++) {              
     scanf("%s",z);                  kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
     if (z[0] == 'c') system("./imach");                }
     else if (z[0] == 'e') system(optionfilehtm);                if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
     else if (z[0] == 'g') system(plotcmd);              }
     else if (z[0] == 'q') exit(0);            }
   }            free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*#endif */          }
 }        }
      } 
     }
    
     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.1.41.2.2  
changed lines
  Added in v.1.85


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