Diff for /imach/src/imach.c between versions 1.3 and 1.84

version 1.3, 2001/05/02 17:21:42 version 1.84, 2003/06/13 21:44:43
Line 1 Line 1
      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.84  2003/06/13 21:44:43  brouard
   individuals from different ages are interviewed on their health status    * imach.c (Repository): Replace "freqsummary" at a correct
   or degree of  disability. At least a second wave of interviews    place. It differs from routine "prevalence" which may be called
   ("longitudinal") should  measure each new individual health status.    many times. Probs is memory consuming and must be used with
   Health expectancies are computed from the transistions observed between    parcimony.
   waves and are computed for each degree of severity of disability (number    Version 0.95a2 (should output exactly the same maximization than 0.8a2)
   of life states). More degrees you consider, more time is necessary to  
   reach the Maximum Likelihood of the parameters involved in the model.    Revision 1.83  2003/06/10 13:39:11  lievre
   The simplest model is the multinomial logistic model where pij is    *** empty log message ***
   the probabibility to be observed in state j at the second wave conditional  
   to be observed in state i at the first wave. Therefore the model is:    Revision 1.82  2003/06/05 15:57:20  brouard
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Add log in  imach.c and  fullversion number is now printed.
   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 you to do it.  /*
   More covariates you add, less is the speed of the convergence.     Interpolated Markov Chain
   
   The advantage that this computer programme claims, comes from that if the    Short summary of the programme:
   delay between waves is not identical for each individual, or if some    
   individual missed an interview, the information is not rounded or lost, but    This program computes Healthy Life Expectancies from
   taken into account using an interpolation or extrapolation.    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   hPijx is the probability to be    first survey ("cross") where individuals from different ages are
   observed in state i at age x+h conditional to the observed state i at age    interviewed on their health status or degree of disability (in the
   x. The delay 'h' can be split into an exact number (nh*stepm) of    case of a health survey which is our main interest) -2- at least a
   unobserved intermediate  states. This elementary transition (by month or    second wave of interviews ("longitudinal") which measure each change
   quarter trimester, semester or year) is model as a multinomial logistic.    (if any) in individual health status.  Health expectancies are
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    computed from the time spent in each health state according to a
   and the contribution of each individual to the likelihood is simply hPijx.    model. More health states you consider, more time is necessary to reach the
     Maximum Likelihood of the parameters involved in the model.  The
   Also this programme outputs the covariance matrix of the parameters but also    simplest model is the multinomial logistic model where pij is the
   of the life expectancies. It also computes the prevalence limits.    probability to be observed in state j at the second wave
      conditional to be observed in state i at the first wave. Therefore
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
            Institut national d'études démographiques, Paris.    'age' is age and 'sex' is a covariate. If you want to have a more
   This software have been partly granted by Euro-REVES, a concerted action    complex model than "constant and age", you should modify the program
   from the European Union.    where the markup *Covariates have to be included here again* invites
   It is copyrighted identically to a GNU software product, ie programme and    you to do it.  More covariates you add, slower the
   software can be distributed freely for non commercial use. Latest version    convergence.
   can be accessed at http://euroreves.ined.fr/imach .  
   **********************************************************************/    The advantage of this computer programme, compared to a simple
      multinomial logistic model, is clear when the delay between waves is not
 #include <math.h>    identical for each individual. Also, if a individual missed an
 #include <stdio.h>    intermediate interview, the information is lost, but taken into
 #include <stdlib.h>    account using an interpolation or extrapolation.  
 #include <unistd.h>  
     hPijx is the probability to be observed in state i at age x+h
 #define MAXLINE 256    conditional to the observed state i at age x. The delay 'h' can be
 #define FILENAMELENGTH 80    split into an exact number (nh*stepm) of unobserved intermediate
 /*#define DEBUG*/    states. This elementary transition (by month, quarter,
 #define windows    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 nvar;  
 static int cptcov;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 int cptcovn;    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, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    main
     read parameterfile
 int *wav; /* Number of waves for this individuual 0 is possible */    read datafile
 int maxwav; /* Maxim number of waves */    concatwav
 int mle, weightopt;    freqsummary
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    if (mle >= 1)
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */      mlikeli
 double **oldm, **newm, **savm; /* Working pointers to matrices */    print results files
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    if mle==1 
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;       computes hessian
 FILE *ficgp, *fichtm;    read end of parameter file: agemin, agemax, bage, fage, estepm
 FILE *ficreseij;        begin-prev-date,...
   char filerese[FILENAMELENGTH];    open gnuplot file
  FILE  *ficresvij;    open html file
   char fileresv[FILENAMELENGTH];    stable prevalence
  FILE  *ficresvpl;     for age prevalim()
   char fileresvpl[FILENAMELENGTH];    h Pij x
     variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
     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 80
 #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 m,nb;  #define NCOVMAX 8 /* Maximum number of covariates */
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  #define MAXN 20000
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  #define YEARM 12. /* Number of months per year */
 double **pmmij;  #define AGESUP 130
   #define AGEBASE 40
 double *weight;  #ifdef windows
 int **s; /* Status */  #define DIRSEPARATOR '\\'
 double *agedc, **covar, idx;  #define ODIRSEPARATOR '/'
 int **nbcode, *Tcode, *Tvar, **codtab;  #else
   #define DIRSEPARATOR '/'
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  #define ODIRSEPARATOR '\\'
 double ftolhess; /* Tolerance for computing hessian */  #endif
   
   /* $Id$ */
 /******************************************/  /* $State$ */
   
 void replace(char *s, char*t)  char version[]="Imach version 0.95a2, June 2003, INED-EUROREVES ";
 {  char fullversion[]="$Revision$ $Date$"; 
   int i;  int erreur; /* Error number */
   int lg=20;  int nvar;
   i=0;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   lg=strlen(t);  int npar=NPARMAX;
   for(i=0; i<= lg; i++) {  int nlstate=2; /* Number of live states */
     (s[i] = t[i]);  int ndeath=1; /* Number of dead states */
     if (t[i]== '\\') s[i]='/';  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   }  int popbased=0;
 }  
   int *wav; /* Number of waves for this individuual 0 is possible */
 int nbocc(char *s, char occ)  int maxwav; /* Maxim number of waves */
 {  int jmin, jmax; /* min, max spacing between 2 waves */
   int i,j=0;  int mle, weightopt;
   int lg=20;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   i=0;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   lg=strlen(s);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   for(i=0; i<= lg; i++) {             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   if  (s[i] == occ ) j++;  double jmean; /* Mean space between 2 waves */
   }  double **oldm, **newm, **savm; /* Working pointers to matrices */
   return j;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 }  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   FILE *ficlog, *ficrespow;
 void cutv(char *u,char *v, char*t, char occ)  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 {  FILE *ficresprobmorprev;
   int i,lg,j,p;  FILE *fichtm; /* Html File */
   i=0;  FILE *ficreseij;
   for(j=0; j<=strlen(t)-1; j++) {  char filerese[FILENAMELENGTH];
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  FILE  *ficresvij;
   }  char fileresv[FILENAMELENGTH];
   FILE  *ficresvpl;
   lg=strlen(t);  char fileresvpl[FILENAMELENGTH];
   for(j=0; j<p; j++) {  char title[MAXLINE];
     (u[j] = t[j]);  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     u[p]='\0';  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   }  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
    for(j=0; j<= lg; j++) {  char filelog[FILENAMELENGTH]; /* Log file */
     if (j>=(p+1))(v[j-p-1] = t[j]);  char filerest[FILENAMELENGTH];
   }  char fileregp[FILENAMELENGTH];
 }  char popfile[FILENAMELENGTH];
   
 /********************** nrerror ********************/  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];
   
 void nrerror(char error_text[])  #define NR_END 1
 {  #define FREE_ARG char*
   fprintf(stderr,"ERREUR ...\n");  #define FTOL 1.0e-10
   fprintf(stderr,"%s\n",error_text);  
   exit(1);  #define NRANSI 
 }  #define ITMAX 200 
 /*********************** vector *******************/  
 double *vector(int nl, int nh)  #define TOL 2.0e-4 
 {  
   double *v;  #define CGOLD 0.3819660 
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #define ZEPS 1.0e-10 
   if (!v) nrerror("allocation failure in vector");  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   return v-nl+NR_END;  
 }  #define GOLD 1.618034 
   #define GLIMIT 100.0 
 /************************ free vector ******************/  #define TINY 1.0e-20 
 void free_vector(double*v, int nl, int nh)  
 {  static double maxarg1,maxarg2;
   free((FREE_ARG)(v+nl-NR_END));  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     
 /************************ivector *******************************/  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 int *ivector(long nl,long nh)  #define rint(a) floor(a+0.5)
 {  
   int *v;  static double sqrarg;
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   if (!v) nrerror("allocation failure in ivector");  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   return v-nl+NR_END;  
 }  int imx; 
   int stepm;
 /******************free ivector **************************/  /* Stepm, step in month: minimum step interpolation*/
 void free_ivector(int *v, long nl, long nh)  
 {  int estepm;
   free((FREE_ARG)(v+nl-NR_END));  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 }  
   int m,nb;
 /******************* imatrix *******************************/  int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;
 int **imatrix(long nrl, long nrh, long ncl, long nch)  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  double **pmmij, ***probs;
 {  double dateintmean=0;
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  
   int **m;  double *weight;
    int **s; /* Status */
   /* allocate pointers to rows */  double *agedc, **covar, idx;
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   m -= nrl;  double ftolhess; /* Tolerance for computing hessian */
    
    /**************** split *************************/
   /* allocate rows and set pointers to them */  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  {
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    char  *ss;                            /* pointer */
   m[nrl] += NR_END;    int   l1, l2;                         /* length counters */
   m[nrl] -= ncl;  
      l1 = strlen(path );                   /* length of path */
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
      ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   /* return pointer to array of pointers to rows */    if ( ss == NULL ) {                   /* no directory, so use current */
   return m;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
 }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       /* get current working directory */
 /****************** free_imatrix *************************/      /*    extern  char* getcwd ( char *buf , int len);*/
 void free_imatrix(m,nrl,nrh,ncl,nch)      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       int **m;        return( GLOCK_ERROR_GETCWD );
       long nch,ncl,nrh,nrl;      }
      /* free an int matrix allocated by imatrix() */      strcpy( name, path );               /* we've got it */
 {    } else {                              /* strip direcotry from path */
   free((FREE_ARG) (m[nrl]+ncl-NR_END));      ss++;                               /* after this, the filename */
   free((FREE_ARG) (m+nrl-NR_END));      l2 = strlen( ss );                  /* length of filename */
 }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       strcpy( name, ss );         /* save file name */
 /******************* matrix *******************************/      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 double **matrix(long nrl, long nrh, long ncl, long nch)      dirc[l1-l2] = 0;                    /* add zero */
 {    }
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    l1 = strlen( dirc );                  /* length of directory */
   double **m;  #ifdef windows
     if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #else
   if (!m) nrerror("allocation failure 1 in matrix()");    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   m += NR_END;  #endif
   m -= nrl;    ss = strrchr( name, '.' );            /* find last / */
     ss++;
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    strcpy(ext,ss);                       /* save extension */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    l1= strlen( name);
   m[nrl] += NR_END;    l2= strlen(ss)+1;
   m[nrl] -= ncl;    strncpy( finame, name, l1-l2);
     finame[l1-l2]= 0;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    return( 0 );                          /* we're done */
   return m;  }
 }  
   
 /*************************free matrix ************************/  /******************************************/
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  
 {  void replace(char *s, char*t)
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  {
   free((FREE_ARG)(m+nrl-NR_END));    int i;
 }    int lg=20;
     i=0;
 /******************* ma3x *******************************/    lg=strlen(t);
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    for(i=0; i<= lg; i++) {
 {      (s[i] = t[i]);
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;      if (t[i]== '\\') s[i]='/';
   double ***m;    }
   }
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  int nbocc(char *s, char occ)
   m += NR_END;  {
   m -= nrl;    int i,j=0;
     int lg=20;
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    i=0;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    lg=strlen(s);
   m[nrl] += NR_END;    for(i=0; i<= lg; i++) {
   m[nrl] -= ncl;    if  (s[i] == occ ) j++;
     }
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    return j;
   }
   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 cutv(char *u,char *v, char*t, char occ)
   m[nrl][ncl] += NR_END;  {
   m[nrl][ncl] -= nll;    /* cuts string t into u and v where u is ended by char occ excluding it
   for (j=ncl+1; j<=nch; j++)       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
     m[nrl][j]=m[nrl][j-1]+nlay;       gives u="abcedf" and v="ghi2j" */
      int i,lg,j,p=0;
   for (i=nrl+1; i<=nrh; i++) {    i=0;
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    for(j=0; j<=strlen(t)-1; j++) {
     for (j=ncl+1; j<=nch; j++)      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
       m[i][j]=m[i][j-1]+nlay;    }
   }  
   return m;    lg=strlen(t);
 }    for(j=0; j<p; j++) {
       (u[j] = t[j]);
 /*************************free ma3x ************************/    }
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)       u[p]='\0';
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));     for(j=0; j<= lg; j++) {
   free((FREE_ARG)(m[nrl]+ncl-NR_END));      if (j>=(p+1))(v[j-p-1] = t[j]);
   free((FREE_ARG)(m+nrl-NR_END));    }
 }  }
   
 /***************** f1dim *************************/  /********************** nrerror ********************/
 extern int ncom;  
 extern double *pcom,*xicom;  void nrerror(char error_text[])
 extern double (*nrfunc)(double []);  {
      fprintf(stderr,"ERREUR ...\n");
 double f1dim(double x)    fprintf(stderr,"%s\n",error_text);
 {    exit(EXIT_FAILURE);
   int j;  }
   double f;  /*********************** vector *******************/
   double *xt;  double *vector(int nl, int nh)
    {
   xt=vector(1,ncom);    double *v;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   f=(*nrfunc)(xt);    if (!v) nrerror("allocation failure in vector");
   free_vector(xt,1,ncom);    return v-nl+NR_END;
   return f;  }
 }  
   /************************ free vector ******************/
 /*****************brent *************************/  void free_vector(double*v, int nl, int nh)
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  {
 {    free((FREE_ARG)(v+nl-NR_END));
   int iter;  }
   double a,b,d,etemp;  
   double fu,fv,fw,fx;  /************************ivector *******************************/
   double ftemp;  char *cvector(long nl,long nh)
   double p,q,r,tol1,tol2,u,v,w,x,xm;  {
   double e=0.0;    char *v;
      v=(char *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(char)));
   a=(ax < cx ? ax : cx);    if (!v) nrerror("allocation failure in cvector");
   b=(ax > cx ? ax : cx);    return v-nl+NR_END;
   x=w=v=bx;  }
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {  /******************free ivector **************************/
     xm=0.5*(a+b);  void free_cvector(char *v, long nl, long nh)
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  {
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    free((FREE_ARG)(v+nl-NR_END));
     printf(".");fflush(stdout);  }
 #ifdef DEBUG  
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  /************************ivector *******************************/
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int *ivector(long nl,long nh)
 #endif  {
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    int *v;
       *xmin=x;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       return fx;    if (!v) nrerror("allocation failure in ivector");
     }    return v-nl+NR_END;
     ftemp=fu;  }
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  /******************free ivector **************************/
       q=(x-v)*(fx-fw);  void free_ivector(int *v, long nl, long nh)
       p=(x-v)*q-(x-w)*r;  {
       q=2.0*(q-r);    free((FREE_ARG)(v+nl-NR_END));
       if (q > 0.0) p = -p;  }
       q=fabs(q);  
       etemp=e;  /******************* imatrix *******************************/
       e=d;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  { 
       else {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         d=p/q;    int **m; 
         u=x+d;    
         if (u-a < tol2 || b-u < tol2)    /* allocate pointers to rows */ 
           d=SIGN(tol1,xm-x);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     } else {    m += NR_END; 
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    m -= nrl; 
     }    
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    
     fu=(*f)(u);    /* allocate rows and set pointers to them */ 
     if (fu <= fx) {    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       if (u >= x) a=x; else b=x;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       SHFT(v,w,x,u)    m[nrl] += NR_END; 
         SHFT(fv,fw,fx,fu)    m[nrl] -= ncl; 
         } else {    
           if (u < x) a=u; else b=u;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
           if (fu <= fw || w == x) {    
             v=w;    /* return pointer to array of pointers to rows */ 
             w=u;    return m; 
             fv=fw;  } 
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {  /****************** free_imatrix *************************/
             v=u;  void free_imatrix(m,nrl,nrh,ncl,nch)
             fv=fu;        int **m;
           }        long nch,ncl,nrh,nrl; 
         }       /* free an int matrix allocated by imatrix() */ 
   }  { 
   nrerror("Too many iterations in brent");    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   *xmin=x;    free((FREE_ARG) (m+nrl-NR_END)); 
   return fx;  } 
 }  
   /******************* matrix *******************************/
 /****************** mnbrak ***********************/  double **matrix(long nrl, long nrh, long ncl, long nch)
   {
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
             double (*func)(double))    double **m;
 {  
   double ulim,u,r,q, dum;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double fu;    if (!m) nrerror("allocation failure 1 in matrix()");
      m += NR_END;
   *fa=(*func)(*ax);    m -= nrl;
   *fb=(*func)(*bx);  
   if (*fb > *fa) {    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     SHFT(dum,*ax,*bx,dum)    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       SHFT(dum,*fb,*fa,dum)    m[nrl] += NR_END;
       }    m[nrl] -= ncl;
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   while (*fb > *fc) {    return m;
     r=(*bx-*ax)*(*fb-*fc);    /* print *(*(m+1)+70) ou print m[1][70]; print m+1 or print &(m[1]) 
     q=(*bx-*cx)*(*fb-*fa);     */
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  }
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);  /*************************free matrix ************************/
     if ((*bx-u)*(u-*cx) > 0.0) {  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       fu=(*func)(u);  {
     } else if ((*cx-u)*(u-ulim) > 0.0) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       fu=(*func)(u);    free((FREE_ARG)(m+nrl-NR_END));
       if (fu < *fc) {  }
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))  /******************* ma3x *******************************/
           }  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  {
       u=ulim;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       fu=(*func)(u);    double ***m;
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       fu=(*func)(u);    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
     SHFT(*ax,*bx,*cx,u)    m -= nrl;
       SHFT(*fa,*fb,*fc,fu)  
       }    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
 /*************** linmin ************************/    m[nrl] -= ncl;
   
 int ncom;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 double *pcom,*xicom;  
 double (*nrfunc)(double []);    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 linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    m[nrl][ncl] += NR_END;
 {    m[nrl][ncl] -= nll;
   double brent(double ax, double bx, double cx,    for (j=ncl+1; j<=nch; j++) 
                double (*f)(double), double tol, double *xmin);      m[nrl][j]=m[nrl][j-1]+nlay;
   double f1dim(double x);    
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    for (i=nrl+1; i<=nrh; i++) {
               double *fc, double (*func)(double));      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   int j;      for (j=ncl+1; j<=nch; j++) 
   double xx,xmin,bx,ax;        m[i][j]=m[i][j-1]+nlay;
   double fx,fb,fa;    }
      return m; 
   ncom=n;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   pcom=vector(1,n);             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   xicom=vector(1,n);    */
   nrfunc=func;  }
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  /*************************free ma3x ************************/
     xicom[j]=xi[j];  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   }  {
   ax=0.0;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   xx=1.0;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    free((FREE_ARG)(m+nrl-NR_END));
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  }
 #ifdef DEBUG  
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  /***************** f1dim *************************/
 #endif  extern int ncom; 
   for (j=1;j<=n;j++) {  extern double *pcom,*xicom;
     xi[j] *= xmin;  extern double (*nrfunc)(double []); 
     p[j] += xi[j];   
   }  double f1dim(double x) 
   free_vector(xicom,1,n);  { 
   free_vector(pcom,1,n);    int j; 
 }    double f;
     double *xt; 
 /*************** powell ************************/   
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    xt=vector(1,ncom); 
             double (*func)(double []))    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
 {    f=(*nrfunc)(xt); 
   void linmin(double p[], double xi[], int n, double *fret,    free_vector(xt,1,ncom); 
               double (*func)(double []));    return f; 
   int i,ibig,j;  } 
   double del,t,*pt,*ptt,*xit;  
   double fp,fptt;  /*****************brent *************************/
   double *xits;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   pt=vector(1,n);  { 
   ptt=vector(1,n);    int iter; 
   xit=vector(1,n);    double a,b,d,etemp;
   xits=vector(1,n);    double fu,fv,fw,fx;
   *fret=(*func)(p);    double ftemp;
   for (j=1;j<=n;j++) pt[j]=p[j];    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   for (*iter=1;;++(*iter)) {    double e=0.0; 
     fp=(*fret);   
     ibig=0;    a=(ax < cx ? ax : cx); 
     del=0.0;    b=(ax > cx ? ax : cx); 
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    x=w=v=bx; 
     for (i=1;i<=n;i++)    fw=fv=fx=(*f)(x); 
       printf(" %d %.12f",i, p[i]);    for (iter=1;iter<=ITMAX;iter++) { 
     printf("\n");      xm=0.5*(a+b); 
     for (i=1;i<=n;i++) {      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       fptt=(*fret);      printf(".");fflush(stdout);
 #ifdef DEBUG      fprintf(ficlog,".");fflush(ficlog);
       printf("fret=%lf \n",*fret);  #ifdef DEBUG
 #endif      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       printf("%d",i);fflush(stdout);      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);
       linmin(p,xit,n,fret,func);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
       if (fabs(fptt-(*fret)) > del) {  #endif
         del=fabs(fptt-(*fret));      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
         ibig=i;        *xmin=x; 
       }        return fx; 
 #ifdef DEBUG      } 
       printf("%d %.12e",i,(*fret));      ftemp=fu;
       for (j=1;j<=n;j++) {      if (fabs(e) > tol1) { 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);        r=(x-w)*(fx-fv); 
         printf(" x(%d)=%.12e",j,xit[j]);        q=(x-v)*(fx-fw); 
       }        p=(x-v)*q-(x-w)*r; 
       for(j=1;j<=n;j++)        q=2.0*(q-r); 
         printf(" p=%.12e",p[j]);        if (q > 0.0) p = -p; 
       printf("\n");        q=fabs(q); 
 #endif        etemp=e; 
     }        e=d; 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
 #ifdef DEBUG          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       int k[2],l;        else { 
       k[0]=1;          d=p/q; 
       k[1]=-1;          u=x+d; 
       printf("Max: %.12e",(*func)(p));          if (u-a < tol2 || b-u < tol2) 
       for (j=1;j<=n;j++)            d=SIGN(tol1,xm-x); 
         printf(" %.12e",p[j]);        } 
       printf("\n");      } else { 
       for(l=0;l<=1;l++) {        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         for (j=1;j<=n;j++) {      } 
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);      fu=(*f)(u); 
         }      if (fu <= fx) { 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));        if (u >= x) a=x; else b=x; 
       }        SHFT(v,w,x,u) 
 #endif          SHFT(fv,fw,fx,fu) 
           } else { 
             if (u < x) a=u; else b=u; 
       free_vector(xit,1,n);            if (fu <= fw || w == x) { 
       free_vector(xits,1,n);              v=w; 
       free_vector(ptt,1,n);              w=u; 
       free_vector(pt,1,n);              fv=fw; 
       return;              fw=fu; 
     }            } else if (fu <= fv || v == x || v == w) { 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");              v=u; 
     for (j=1;j<=n;j++) {              fv=fu; 
       ptt[j]=2.0*p[j]-pt[j];            } 
       xit[j]=p[j]-pt[j];          } 
       pt[j]=p[j];    } 
     }    nrerror("Too many iterations in brent"); 
     fptt=(*func)(ptt);    *xmin=x; 
     if (fptt < fp) {    return fx; 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  } 
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);  /****************** mnbrak ***********************/
         for (j=1;j<=n;j++) {  
           xi[j][ibig]=xi[j][n];  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
           xi[j][n]=xit[j];              double (*func)(double)) 
         }  { 
 #ifdef DEBUG    double ulim,u,r,q, dum;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    double fu; 
         for(j=1;j<=n;j++)   
           printf(" %.12e",xit[j]);    *fa=(*func)(*ax); 
         printf("\n");    *fb=(*func)(*bx); 
 #endif    if (*fb > *fa) { 
       }      SHFT(dum,*ax,*bx,dum) 
     }        SHFT(dum,*fb,*fa,dum) 
   }        } 
 }    *cx=(*bx)+GOLD*(*bx-*ax); 
     *fc=(*func)(*cx); 
 /**** Prevalence limit ****************/    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      q=(*bx-*cx)*(*fb-*fa); 
 {      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
      matrix by transitions matrix until convergence is reached */      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if ((*bx-u)*(u-*cx) > 0.0) { 
   int i, ii,j,k;        fu=(*func)(u); 
   double min, max, maxmin, maxmax,sumnew=0.;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
   double **matprod2();        fu=(*func)(u); 
   double **out, cov[NCOVMAX], **pmij();        if (fu < *fc) { 
   double **newm;          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   double agefin, delaymax=50 ; /* Max number of years to converge */            SHFT(*fb,*fc,fu,(*func)(u)) 
             } 
   for (ii=1;ii<=nlstate+ndeath;ii++)      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     for (j=1;j<=nlstate+ndeath;j++){        u=ulim; 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);        fu=(*func)(u); 
     }      } else { 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        u=(*cx)+GOLD*(*cx-*bx); 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){        fu=(*func)(u); 
     newm=savm;      } 
     /* Covariates have to be included here again */      SHFT(*ax,*bx,*cx,u) 
     cov[1]=1.;        SHFT(*fa,*fb,*fc,fu) 
     cov[2]=agefin;        } 
     if (cptcovn>0){  } 
       for (k=1; k<=cptcovn;k++) {cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];/*printf("Tcode[ij]=%d nbcode=%d\n",Tcode[ij],nbcode[k][Tcode[ij]]);*/}  
     }  /*************** linmin ************************/
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  
   int ncom; 
     savm=oldm;  double *pcom,*xicom;
     oldm=newm;  double (*nrfunc)(double []); 
     maxmax=0.;   
     for(j=1;j<=nlstate;j++){  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       min=1.;  { 
       max=0.;    double brent(double ax, double bx, double cx, 
       for(i=1; i<=nlstate; i++) {                 double (*f)(double), double tol, double *xmin); 
         sumnew=0;    double f1dim(double x); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
         prlim[i][j]= newm[i][j]/(1-sumnew);                double *fc, double (*func)(double)); 
         max=FMAX(max,prlim[i][j]);    int j; 
         min=FMIN(min,prlim[i][j]);    double xx,xmin,bx,ax; 
       }    double fx,fb,fa;
       maxmin=max-min;   
       maxmax=FMAX(maxmax,maxmin);    ncom=n; 
     }    pcom=vector(1,n); 
     if(maxmax < ftolpl){    xicom=vector(1,n); 
       return prlim;    nrfunc=func; 
     }    for (j=1;j<=n;j++) { 
   }      pcom[j]=p[j]; 
 }      xicom[j]=xi[j]; 
     } 
 /*************** transition probabilities **********/    ax=0.0; 
     xx=1.0; 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
 {    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   double s1, s2;  #ifdef DEBUG
   /*double t34;*/    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   int i,j,j1, nc, ii, jj;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
     for(i=1; i<= nlstate; i++){    for (j=1;j<=n;j++) { 
     for(j=1; j<i;j++){      xi[j] *= xmin; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      p[j] += xi[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];    free_vector(xicom,1,n); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    free_vector(pcom,1,n); 
       }  } 
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  /*************** powell ************************/
     }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     for(j=i+1; j<=nlstate+ndeath;j++){              double (*func)(double [])) 
       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];    void linmin(double p[], double xi[], int n, double *fret, 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/                double (*func)(double [])); 
       }    int i,ibig,j; 
       ps[i][j]=s2;    double del,t,*pt,*ptt,*xit;
     }    double fp,fptt;
   }    double *xits;
   for(i=1; i<= nlstate; i++){    pt=vector(1,n); 
      s1=0;    ptt=vector(1,n); 
     for(j=1; j<i; j++)    xit=vector(1,n); 
       s1+=exp(ps[i][j]);    xits=vector(1,n); 
     for(j=i+1; j<=nlstate+ndeath; j++)    *fret=(*func)(p); 
       s1+=exp(ps[i][j]);    for (j=1;j<=n;j++) pt[j]=p[j]; 
     ps[i][i]=1./(s1+1.);    for (*iter=1;;++(*iter)) { 
     for(j=1; j<i; j++)      fp=(*fret); 
       ps[i][j]= exp(ps[i][j])*ps[i][i];      ibig=0; 
     for(j=i+1; j<=nlstate+ndeath; j++)      del=0.0; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];      printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
   } /* end i */      fprintf(ficrespow,"%d %.12f",*iter,*fret);
       for (i=1;i<=n;i++) {
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){        printf(" %d %.12f",i, p[i]);
     for(jj=1; jj<= nlstate+ndeath; jj++){        fprintf(ficlog," %d %.12lf",i, p[i]);
       ps[ii][jj]=0;        fprintf(ficrespow," %.12lf", p[i]);
       ps[ii][ii]=1;      }
     }      printf("\n");
   }      fprintf(ficlog,"\n");
       fprintf(ficrespow,"\n");
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      for (i=1;i<=n;i++) { 
     for(jj=1; jj<= nlstate+ndeath; jj++){        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
      printf("%lf ",ps[ii][jj]);        fptt=(*fret); 
    }  #ifdef DEBUG
     printf("\n ");        printf("fret=%lf \n",*fret);
     }        fprintf(ficlog,"fret=%lf \n",*fret);
     printf("\n ");printf("%lf ",cov[2]);*/  #endif
 /*        printf("%d",i);fflush(stdout);
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        fprintf(ficlog,"%d",i);fflush(ficlog);
   goto end;*/        linmin(p,xit,n,fret,func); 
     return ps;        if (fabs(fptt-(*fret)) > del) { 
 }          del=fabs(fptt-(*fret)); 
           ibig=i; 
 /**************** Product of 2 matrices ******************/        } 
   #ifdef DEBUG
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)        printf("%d %.12e",i,(*fret));
 {        fprintf(ficlog,"%d %.12e",i,(*fret));
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        for (j=1;j<=n;j++) {
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   /* in, b, out are matrice of pointers which should have been initialized          printf(" x(%d)=%.12e",j,xit[j]);
      before: only the contents of out is modified. The function returns          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
      a pointer to pointers identical to out */        }
   long i, j, k;        for(j=1;j<=n;j++) {
   for(i=nrl; i<= nrh; i++)          printf(" p=%.12e",p[j]);
     for(k=ncolol; k<=ncoloh; k++)          fprintf(ficlog," p=%.12e",p[j]);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        }
         out[i][k] +=in[i][j]*b[j][k];        printf("\n");
         fprintf(ficlog,"\n");
   return out;  #endif
 }      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   #ifdef DEBUG
 /************* Higher Matrix Product ***************/        int k[2],l;
         k[0]=1;
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )        k[1]=-1;
 {        printf("Max: %.12e",(*func)(p));
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        fprintf(ficlog,"Max: %.12e",(*func)(p));
      duration (i.e. until        for (j=1;j<=n;j++) {
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.          printf(" %.12e",p[j]);
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step          fprintf(ficlog," %.12e",p[j]);
      (typically every 2 years instead of every month which is too big).        }
      Model is determined by parameters x and covariates have to be        printf("\n");
      included manually here.        fprintf(ficlog,"\n");
         for(l=0;l<=1;l++) {
      */          for (j=1;j<=n;j++) {
             ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   int i, j, d, h, k;            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   double **out, cov[NCOVMAX];            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   double **newm;          }
           printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   /* Hstepm could be zero and should return the unit matrix */          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   for (i=1;i<=nlstate+ndeath;i++)        }
     for (j=1;j<=nlstate+ndeath;j++){  #endif
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }        free_vector(xit,1,n); 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        free_vector(xits,1,n); 
   for(h=1; h <=nhstepm; h++){        free_vector(ptt,1,n); 
     for(d=1; d <=hstepm; d++){        free_vector(pt,1,n); 
       newm=savm;        return; 
       /* Covariates have to be included here again */      } 
       cov[1]=1.;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      for (j=1;j<=n;j++) { 
       if (cptcovn>0){        ptt[j]=2.0*p[j]-pt[j]; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];        xit[j]=p[j]-pt[j]; 
     }        pt[j]=p[j]; 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/      } 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/      fptt=(*func)(ptt); 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,      if (fptt < fp) { 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       savm=oldm;        if (t < 0.0) { 
       oldm=newm;          linmin(p,xit,n,fret,func); 
     }          for (j=1;j<=n;j++) { 
     for(i=1; i<=nlstate+ndeath; i++)            xi[j][ibig]=xi[j][n]; 
       for(j=1;j<=nlstate+ndeath;j++) {            xi[j][n]=xit[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]);  #ifdef DEBUG
          */          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   } /* end h */          for(j=1;j<=n;j++){
   return po;            printf(" %.12e",xit[j]);
 }            fprintf(ficlog," %.12e",xit[j]);
           }
           printf("\n");
 /*************** log-likelihood *************/          fprintf(ficlog,"\n");
 double func( double *x)  #endif
 {        }
   int i, ii, j, k, mi, d;      } 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    } 
   double **out;  } 
   double sw; /* Sum of weights */  
   double lli; /* Individual log likelihood */  /**** Prevalence limit (stable prevalence)  ****************/
   long ipmx;  
   /*extern weight */  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   /* We are differentiating ll according to initial status */  {
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   /*for(i=1;i<imx;i++)       matrix by transitions matrix until convergence is reached */
 printf(" %d\n",s[4][i]);  
   */    int i, ii,j,k;
     double min, max, maxmin, maxmax,sumnew=0.;
   for(k=1; k<=nlstate; k++) ll[k]=0.;    double **matprod2();
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    double **out, cov[NCOVMAX], **pmij();
        for(mi=1; mi<= wav[i]-1; mi++){    double **newm;
       for (ii=1;ii<=nlstate+ndeath;ii++)    double agefin, delaymax=50 ; /* Max number of years to converge */
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
             for(d=0; d<dh[mi][i]; d++){    for (ii=1;ii<=nlstate+ndeath;ii++)
         newm=savm;      for (j=1;j<=nlstate+ndeath;j++){
           cov[1]=1.;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      }
           if (cptcovn>0){  
             for (k=1; k<=cptcovn;k++) cov[2+k]=covar[1+k-1][i];     cov[1]=1.;
             }   
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           savm=oldm;      newm=savm;
           oldm=newm;      /* Covariates have to be included here again */
        cov[2]=agefin;
     
       } /* end mult */        for (k=1; k<=cptcovn;k++) {
              cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        }
       ipmx +=1;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       sw += weight[i];        for (k=1; k<=cptcovprod;k++)
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     } /* end of wave */  
   } /* end of individual */        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  
   return -l;      savm=oldm;
 }      oldm=newm;
       maxmax=0.;
       for(j=1;j<=nlstate;j++){
 /*********** Maximum Likelihood Estimation ***************/        min=1.;
         max=0.;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        for(i=1; i<=nlstate; i++) {
 {          sumnew=0;
   int i,j, iter;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   double **xi,*delti;          prlim[i][j]= newm[i][j]/(1-sumnew);
   double fret;          max=FMAX(max,prlim[i][j]);
   xi=matrix(1,npar,1,npar);          min=FMIN(min,prlim[i][j]);
   for (i=1;i<=npar;i++)        }
     for (j=1;j<=npar;j++)        maxmin=max-min;
       xi[i][j]=(i==j ? 1.0 : 0.0);        maxmax=FMAX(maxmax,maxmin);
   printf("Powell\n");      }
   powell(p,xi,npar,ftol,&iter,&fret,func);      if(maxmax < ftolpl){
         return prlim;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));      }
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    }
   }
 }  
   /*************** transition probabilities ***************/ 
 /**** Computes Hessian and covariance matrix ***/  
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
 {  {
   double  **a,**y,*x,pd;    double s1, s2;
   double **hess;    /*double t34;*/
   int i, j,jk;    int i,j,j1, nc, ii, jj;
   int *indx;  
       for(i=1; i<= nlstate; i++){
   double hessii(double p[], double delta, int theta, double delti[]);      for(j=1; j<i;j++){
   double hessij(double p[], double delti[], int i, int j);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   void lubksb(double **a, int npar, int *indx, double b[]) ;          /*s2 += param[i][j][nc]*cov[nc];*/
   void ludcmp(double **a, int npar, int *indx, double *d) ;          s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
           /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
         }
   hess=matrix(1,npar,1,npar);        ps[i][j]=s2;
         /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
   printf("\nCalculation of the hessian matrix. Wait...\n");      }
   for (i=1;i<=npar;i++){      for(j=i+1; j<=nlstate+ndeath;j++){
     printf("%d",i);fflush(stdout);        for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     hess[i][i]=hessii(p,ftolhess,i,delti);          s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     /*printf(" %f ",p[i]);*/          /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
   }        }
         ps[i][j]=s2;
   for (i=1;i<=npar;i++) {      }
     for (j=1;j<=npar;j++)  {    }
       if (j>i) {      /*ps[3][2]=1;*/
         printf(".%d%d",i,j);fflush(stdout);  
         hess[i][j]=hessij(p,delti,i,j);    for(i=1; i<= nlstate; i++){
         hess[j][i]=hess[i][j];       s1=0;
       }      for(j=1; j<i; j++)
     }        s1+=exp(ps[i][j]);
   }      for(j=i+1; j<=nlstate+ndeath; j++)
   printf("\n");        s1+=exp(ps[i][j]);
       ps[i][i]=1./(s1+1.);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");      for(j=1; j<i; j++)
          ps[i][j]= exp(ps[i][j])*ps[i][i];
   a=matrix(1,npar,1,npar);      for(j=i+1; j<=nlstate+ndeath; j++)
   y=matrix(1,npar,1,npar);        ps[i][j]= exp(ps[i][j])*ps[i][i];
   x=vector(1,npar);      /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   indx=ivector(1,npar);    } /* end i */
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   ludcmp(a,npar,indx,&pd);      for(jj=1; jj<= nlstate+ndeath; jj++){
         ps[ii][jj]=0;
   for (j=1;j<=npar;j++) {        ps[ii][ii]=1;
     for (i=1;i<=npar;i++) x[i]=0;      }
     x[j]=1;    }
     lubksb(a,npar,indx,x);  
     for (i=1;i<=npar;i++){  
       matcov[i][j]=x[i];    /*   for(ii=1; ii<= nlstate+ndeath; ii++){
     }      for(jj=1; jj<= nlstate+ndeath; jj++){
   }       printf("%lf ",ps[ii][jj]);
      }
   printf("\n#Hessian matrix#\n");      printf("\n ");
   for (i=1;i<=npar;i++) {      }
     for (j=1;j<=npar;j++) {      printf("\n ");printf("%lf ",cov[2]);*/
       printf("%.3e ",hess[i][j]);  /*
     }    for(i=1; i<= npar; i++) printf("%f ",x[i]);
     printf("\n");    goto end;*/
   }      return ps;
   }
   /* Recompute Inverse */  
   for (i=1;i<=npar;i++)  /**************** Product of 2 matrices ******************/
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  
   ludcmp(a,npar,indx,&pd);  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   {
   /*  printf("\n#Hessian matrix recomputed#\n");    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
        b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   for (j=1;j<=npar;j++) {    /* in, b, out are matrice of pointers which should have been initialized 
     for (i=1;i<=npar;i++) x[i]=0;       before: only the contents of out is modified. The function returns
     x[j]=1;       a pointer to pointers identical to out */
     lubksb(a,npar,indx,x);    long i, j, k;
     for (i=1;i<=npar;i++){    for(i=nrl; i<= nrh; i++)
       y[i][j]=x[i];      for(k=ncolol; k<=ncoloh; k++)
       printf("%.3e ",y[i][j]);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     }          out[i][k] +=in[i][j]*b[j][k];
     printf("\n");  
   }    return out;
   */  }
   
   free_matrix(a,1,npar,1,npar);  
   free_matrix(y,1,npar,1,npar);  /************* Higher Matrix Product ***************/
   free_vector(x,1,npar);  
   free_ivector(indx,1,npar);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   free_matrix(hess,1,npar,1,npar);  {
     /* Computes the transition matrix starting at age 'age' over 
        'nhstepm*hstepm*stepm' months (i.e. until
 }       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
 /*************** hessian matrix ****************/       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
 double hessii( double x[], double delta, int theta, double delti[])       (typically every 2 years instead of every month which is too big 
 {       for the memory).
   int i;       Model is determined by parameters x and covariates have to be 
   int l=1, lmax=20;       included manually here. 
   double k1,k2;  
   double p2[NPARMAX+1];       */
   double res;  
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    int i, j, d, h, k;
   double fx;    double **out, cov[NCOVMAX];
   int k=0,kmax=10;    double **newm;
   double l1;  
     /* Hstepm could be zero and should return the unit matrix */
   fx=func(x);    for (i=1;i<=nlstate+ndeath;i++)
   for (i=1;i<=npar;i++) p2[i]=x[i];      for (j=1;j<=nlstate+ndeath;j++){
   for(l=0 ; l <=lmax; l++){        oldm[i][j]=(i==j ? 1.0 : 0.0);
     l1=pow(10,l);        po[i][j][0]=(i==j ? 1.0 : 0.0);
     delts=delt;      }
     for(k=1 ; k <kmax; k=k+1){    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       delt = delta*(l1*k);    for(h=1; h <=nhstepm; h++){
       p2[theta]=x[theta] +delt;      for(d=1; d <=hstepm; d++){
       k1=func(p2)-fx;        newm=savm;
       p2[theta]=x[theta]-delt;        /* Covariates have to be included here again */
       k2=func(p2)-fx;        cov[1]=1.;
       /*res= (k1-2.0*fx+k2)/delt/delt; */        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
              for (k=1; k<=cptcovage;k++)
 #ifdef DEBUG          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       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=1; k<=cptcovprod;k++)
 #endif          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  
         k=kmax;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
       }        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         k=kmax; l=lmax*10.;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       }        savm=oldm;
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        oldm=newm;
         delts=delt;      }
       }      for(i=1; i<=nlstate+ndeath; i++)
     }        for(j=1;j<=nlstate+ndeath;j++) {
   }          po[i][j][h]=newm[i][j];
   delti[theta]=delts;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
   return res;           */
          }
 }    } /* end h */
     return po;
 double hessij( double x[], double delti[], int thetai,int thetaj)  }
 {  
   int i;  
   int l=1, l1, lmax=20;  /*************** log-likelihood *************/
   double k1,k2,k3,k4,res,fx;  double func( double *x)
   double p2[NPARMAX+1];  {
   int k;    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX], cov[NCOVMAX];
   fx=func(x);    double **out;
   for (k=1; k<=2; k++) {    double sw; /* Sum of weights */
     for (i=1;i<=npar;i++) p2[i]=x[i];    double lli; /* Individual log likelihood */
     p2[thetai]=x[thetai]+delti[thetai]/k;    int s1, s2;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    double bbh, survp;
     k1=func(p2)-fx;    long ipmx;
      /*extern weight */
     p2[thetai]=x[thetai]+delti[thetai]/k;    /* We are differentiating ll according to initial status */
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     k2=func(p2)-fx;    /*for(i=1;i<imx;i++) 
        printf(" %d\n",s[4][i]);
     p2[thetai]=x[thetai]-delti[thetai]/k;    */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    cov[1]=1.;
     k3=func(p2)-fx;  
      for(k=1; k<=nlstate; k++) ll[k]=0.;
     p2[thetai]=x[thetai]-delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    if(mle==1){
     k4=func(p2)-fx;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 #ifdef DEBUG        for(mi=1; mi<= wav[i]-1; mi++){
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);          for (ii=1;ii<=nlstate+ndeath;ii++)
 #endif            for (j=1;j<=nlstate+ndeath;j++){
   }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   return res;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
 }            }
           for(d=0; d<dh[mi][i]; d++){
 /************** Inverse of matrix **************/            newm=savm;
 void ludcmp(double **a, int n, int *indx, double *d)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 {            for (kk=1; kk<=cptcovage;kk++) {
   int i,imax,j,k;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double big,dum,sum,temp;            }
   double *vv;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   vv=vector(1,n);            savm=oldm;
   *d=1.0;            oldm=newm;
   for (i=1;i<=n;i++) {          } /* end mult */
     big=0.0;        
     for (j=1;j<=n;j++)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       if ((temp=fabs(a[i][j])) > big) big=temp;          /* But now since version 0.9 we anticipate for bias and large stepm.
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     vv[i]=1.0/big;           * (in months) between two waves is not a multiple of stepm, we rounded to 
   }           * the nearest (and in case of equal distance, to the lowest) interval but now
   for (j=1;j<=n;j++) {           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     for (i=1;i<j;i++) {           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       sum=a[i][j];           * probability in order to take into account the bias as a fraction of the way
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
       a[i][j]=sum;           * -stepm/2 to stepm/2 .
     }           * For stepm=1 the results are the same as for previous versions of Imach.
     big=0.0;           * For stepm > 1 the results are less biased than in previous versions. 
     for (i=j;i<=n;i++) {           */
       sum=a[i][j];          s1=s[mw[mi][i]][i];
       for (k=1;k<j;k++)          s2=s[mw[mi+1][i]][i];
         sum -= a[i][k]*a[k][j];          bbh=(double)bh[mi][i]/(double)stepm; 
       a[i][j]=sum;          /* bias is positive if real duration
       if ( (dum=vv[i]*fabs(sum)) >= big) {           * is higher than the multiple of stepm and negative otherwise.
         big=dum;           */
         imax=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]));*/
       }          if( s2 > nlstate){ 
     }            /* i.e. if s2 is a death state and if the date of death is known then the contribution
     if (j != imax) {               to the likelihood is the probability to die between last step unit time and current 
       for (k=1;k<=n;k++) {               step unit time, which is also the differences between probability to die before dh 
         dum=a[imax][k];               and probability to die before dh-stepm . 
         a[imax][k]=a[j][k];               In version up to 0.92 likelihood was computed
         a[j][k]=dum;          as if date of death was unknown. Death was treated as any other
       }          health state: the date of the interview describes the actual state
       *d = -(*d);          and not the date of a change in health state. The former idea was
       vv[imax]=vv[j];          to consider that at each interview the state was recorded
     }          (healthy, disable or death) and IMaCh was corrected; but when we
     indx[j]=imax;          introduced the exact date of death then we should have modified
     if (a[j][j] == 0.0) a[j][j]=TINY;          the contribution of an exact death to the likelihood. This new
     if (j != n) {          contribution is smaller and very dependent of the step unit
       dum=1.0/(a[j][j]);          stepm. It is no more the probability to die between last interview
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          and month of death but the probability to survive from last
     }          interview up to one month before death multiplied by the
   }          probability to die within a month. Thanks to Chris
   free_vector(vv,1,n);  /* Doesn't work */          Jackson for correcting this bug.  Former versions increased
 ;          mortality artificially. The bad side is that we add another loop
 }          which slows down the processing. The difference can be up to 10%
           lower mortality.
 void lubksb(double **a, int n, int *indx, double b[])            */
 {            lli=log(out[s1][s2] - savm[s1][s2]);
   int i,ii=0,ip,j;          }else{
   double sum;            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
              /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
   for (i=1;i<=n;i++) {          } 
     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==2){
     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)            }
 {  /* 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;            }
   FILE *ficresp;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   char fileresp[FILENAMELENGTH];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   pp=vector(1,nlstate);            oldm=newm;
           } /* end mult */
   strcpy(fileresp,"p");        
   strcat(fileresp,fileres);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   if((ficresp=fopen(fileresp,"w"))==NULL) {          /* But now since version 0.9 we anticipate for bias and large stepm.
     printf("Problem with prevalence resultfile: %s\n", fileresp);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     exit(0);           * (in months) between two waves is not a multiple of stepm, we rounded to 
   }           * the nearest (and in case of equal distance, to the lowest) interval but now
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   j1=0;           * (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
   j=cptcovn;           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
   if (cptcovn<1) {j=1;ncodemax[1]=1;}           * -stepm/2 to stepm/2 .
            * For stepm=1 the results are the same as for previous versions of Imach.
   for(k1=1; k1<=j;k1++){           * For stepm > 1 the results are less biased than in previous versions. 
    for(i1=1; i1<=ncodemax[k1];i1++){           */
        j1++;          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
         for (i=-1; i<=nlstate+ndeath; i++)            bbh=(double)bh[mi][i]/(double)stepm; 
          for (jk=-1; jk<=nlstate+ndeath; jk++)            /* bias is positive if real duration
            for(m=agemin; m <= agemax+3; m++)           * is higher than the multiple of stepm and negative otherwise.
              freq[i][jk][m]=0;           */
                  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
        for (i=1; i<=imx; 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]));*/
          bool=1;          /*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 */
          if  (cptcovn>0) {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
            for (z1=1; z1<=cptcovn; z1++)          /*if(lli ==000.0)*/
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
          }          ipmx +=1;
           if (bool==1) {          sw += weight[i];
            for(m=firstpass; m<=lastpass-1; m++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
              if(agev[m][i]==0) agev[m][i]=agemax+1;        } /* end of wave */
              if(agev[m][i]==1) agev[m][i]=agemax+2;      } /* end of individual */
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    }  else if(mle==3){  /* exponential inter-extrapolation */
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
            }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          }        for(mi=1; mi<= wav[i]-1; mi++){
        }          for (ii=1;ii<=nlstate+ndeath;ii++)
         if  (cptcovn>0) {            for (j=1;j<=nlstate+ndeath;j++){
          fprintf(ficresp, "\n#Variable");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
        }            }
        fprintf(ficresp, "\n#");          for(d=0; d<dh[mi][i]; d++){
        for(i=1; i<=nlstate;i++)            newm=savm;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
        fprintf(ficresp, "\n");            for (kk=1; kk<=cptcovage;kk++) {
                      cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   for(i=(int)agemin; i <= (int)agemax+3; i++){            }
     if(i==(int)agemax+3)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       printf("Total");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     else            savm=oldm;
       printf("Age %d", i);            oldm=newm;
     for(jk=1; jk <=nlstate ; jk++){          } /* end mult */
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        
         pp[jk] += freq[jk][m][i];          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     }          /* But now since version 0.9 we anticipate for bias and large stepm.
     for(jk=1; jk <=nlstate ; jk++){           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       for(m=-1, pos=0; m <=0 ; m++)           * (in months) between two waves is not a multiple of stepm, we rounded to 
         pos += freq[jk][m][i];           * the nearest (and in case of equal distance, to the lowest) interval but now
       if(pp[jk]>=1.e-10)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
       else           * probability in order to take into account the bias as a fraction of the way
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
     }           * -stepm/2 to stepm/2 .
     for(jk=1; jk <=nlstate ; jk++){           * For stepm=1 the results are the same as for previous versions of Imach.
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)           * For stepm > 1 the results are less biased than in previous versions. 
         pp[jk] += freq[jk][m][i];           */
     }          s1=s[mw[mi][i]][i];
     for(jk=1,pos=0; jk <=nlstate ; jk++)          s2=s[mw[mi+1][i]][i];
       pos += pp[jk];          bbh=(double)bh[mi][i]/(double)stepm; 
     for(jk=1; jk <=nlstate ; jk++){          /* bias is positive if real duration
       if(pos>=1.e-5)           * is higher than the multiple of stepm and negative otherwise.
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);           */
       else          /* lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); */ /* linear interpolation */
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       if( i <= (int) agemax){          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         if(pos>=1.e-5)          /*if(lli ==000.0)*/
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);          /*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); */
       else          ipmx +=1;
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);          sw += weight[i];
       }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        } /* end of wave */
     for(jk=-1; jk <=nlstate+ndeath; jk++)      } /* end of individual */
       for(m=-1; m <=nlstate+ndeath; m++)    }else if (mle==4){  /* ml=4 no inter-extrapolation */
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     if(i <= (int) agemax)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       fprintf(ficresp,"\n");        for(mi=1; mi<= wav[i]-1; mi++){
     printf("\n");          for (ii=1;ii<=nlstate+ndeath;ii++)
     }            for (j=1;j<=nlstate+ndeath;j++){
     }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
   fclose(ficresp);          for(d=0; d<dh[mi][i]; d++){
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);            newm=savm;
   free_vector(pp,1,nlstate);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
 }  /* End of Freq */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
 /************* Waves Concatenation ***************/          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 {            savm=oldm;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.            oldm=newm;
      Death is a valid wave (if date is known).          } /* end mult */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          s1=s[mw[mi][i]][i];
      and mw[mi+1][i]. dh depends on stepm.          s2=s[mw[mi+1][i]][i];
      */          if( s2 > nlstate){ 
             lli=log(out[s1][s2] - savm[s1][s2]);
   int i, mi, m;          }else{
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 float sum=0.;          }
           ipmx +=1;
   for(i=1; i<=imx; i++){          sw += weight[i];
     mi=0;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     m=firstpass;          /*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]);*/
     while(s[m][i] <= nlstate){        } /* end of wave */
       if(s[m][i]>=1)      } /* end of individual */
         mw[++mi][i]=m;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
       if(m >=lastpass)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         break;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       else        for(mi=1; mi<= wav[i]-1; mi++){
         m++;          for (ii=1;ii<=nlstate+ndeath;ii++)
     }/* end while */            for (j=1;j<=nlstate+ndeath;j++){
     if (s[m][i] > nlstate){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       mi++;     /* Death is another wave */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       /* if(mi==0)  never been interviewed correctly before death */            }
          /* Only death is a correct wave */          for(d=0; d<dh[mi][i]; d++){
       mw[mi][i]=m;            newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
     wav[i]=mi;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     if(mi==0)            }
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          
   }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   for(i=1; i<=imx; i++){            savm=oldm;
     for(mi=1; mi<wav[i];mi++){            oldm=newm;
       if (stepm <=0)          } /* end mult */
         dh[mi][i]=1;        
       else{          s1=s[mw[mi][i]][i];
         if (s[mw[mi+1][i]][i] > nlstate) {          s2=s[mw[mi+1][i]][i];
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
           if(j=0) j=1;  /* Survives at least one month after exam */          ipmx +=1;
         }          sw += weight[i];
         else{          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          /*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]);*/
           k=k+1;        } /* end of wave */
           if (j >= jmax) jmax=j;      } /* end of individual */
           else if (j <= jmin)jmin=j;    } /* End of if */
           sum=sum+j;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         jk= j/stepm;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
         jl= j -jk*stepm;    /*exit(0); */
         ju= j -(jk+1)*stepm;    return -l;
         if(jl <= -ju)  }
           dh[mi][i]=jk;  
         else  
           dh[mi][i]=jk+1;  /*********** Maximum Likelihood Estimation ***************/
         if(dh[mi][i]==0)  
           dh[mi][i]=1; /* At least one step */  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       }  {
     }    int i,j, iter;
   }    double **xi;
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);    double fret;
 }    char filerespow[FILENAMELENGTH];
 /*********** Tricode ****************************/    xi=matrix(1,npar,1,npar);
 void tricode(int *Tvar, int **nbcode, int imx)    for (i=1;i<=npar;i++)
 {      for (j=1;j<=npar;j++)
   int Ndum[80],ij, k, j, i;        xi[i][j]=(i==j ? 1.0 : 0.0);
   int cptcode=0;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   for (k=0; k<79; k++) Ndum[k]=0;    strcpy(filerespow,"pow"); 
   for (k=1; k<=7; k++) ncodemax[k]=0;    strcat(filerespow,fileres);
      if((ficrespow=fopen(filerespow,"w"))==NULL) {
   for (j=1; j<=cptcovn; j++) {      printf("Problem with resultfile: %s\n", filerespow);
     for (i=1; i<=imx; i++) {      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       ij=(int)(covar[Tvar[j]][i]);    }
       Ndum[ij]++;    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       if (ij > cptcode) cptcode=ij;    for (i=1;i<=nlstate;i++)
     }      for(j=1;j<=nlstate+ndeath;j++)
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for (i=0; i<=cptcode; i++) {    fprintf(ficrespow,"\n");
       if(Ndum[i]!=0) ncodemax[j]++;    powell(p,xi,npar,ftol,&iter,&fret,func);
     }  
      fclose(ficrespow);
     ij=1;    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     for (i=1; i<=ncodemax[j]; i++) {    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       for (k=0; k<=79; k++) {    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         if (Ndum[k] != 0) {  
           nbcode[Tvar[j]][ij]=k;  }
           ij++;  
         }  /**** Computes Hessian and covariance matrix ***/
         if (ij > ncodemax[j]) break;  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;
   }    int *indx;
   
 /*********** Health Expectancies ****************/    double hessii(double p[], double delta, int theta, double delti[]);
     double hessij(double p[], double delti[], int i, int j);
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)    void lubksb(double **a, int npar, int *indx, double b[]) ;
 {    void ludcmp(double **a, int npar, int *indx, double *d) ;
   /* Health expectancies */  
   int i, j, nhstepm, hstepm, h;    hess=matrix(1,npar,1,npar);
   double age, agelim,hf;  
   double ***p3mat;    printf("\nCalculation of the hessian matrix. Wait...\n");
      fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   fprintf(ficreseij,"# Health expectancies\n");    for (i=1;i<=npar;i++){
   fprintf(ficreseij,"# Age");      printf("%d",i);fflush(stdout);
   for(i=1; i<=nlstate;i++)      fprintf(ficlog,"%d",i);fflush(ficlog);
     for(j=1; j<=nlstate;j++)      hess[i][i]=hessii(p,ftolhess,i,delti);
       fprintf(ficreseij," %1d-%1d",i,j);      /*printf(" %f ",p[i]);*/
   fprintf(ficreseij,"\n");      /*printf(" %lf ",hess[i][i]);*/
     }
   hstepm=1*YEARM; /*  Every j years of age (in month) */    
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for (i=1;i<=npar;i++) {
       for (j=1;j<=npar;j++)  {
   agelim=AGESUP;        if (j>i) { 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          printf(".%d%d",i,j);fflush(stdout);
     /* nhstepm age range expressed in number of stepm */          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          hess[i][j]=hessij(p,delti,i,j);
     /* Typically if 20 years = 20*12/6=40 stepm */          hess[j][i]=hess[i][j];    
     if (stepm >= YEARM) hstepm=1;          /*printf(" %lf ",hess[i][j]);*/
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */        }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      }
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    }
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    printf("\n");
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      fprintf(ficlog,"\n");
   
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     for(i=1; i<=nlstate;i++)    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
       for(j=1; j<=nlstate;j++)    
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){    a=matrix(1,npar,1,npar);
           eij[i][j][(int)age] +=p3mat[i][j][h];    y=matrix(1,npar,1,npar);
         }    x=vector(1,npar);
        indx=ivector(1,npar);
     hf=1;    for (i=1;i<=npar;i++)
     if (stepm >= YEARM) hf=stepm/YEARM;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     fprintf(ficreseij,"%.0f",age );    ludcmp(a,npar,indx,&pd);
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++){    for (j=1;j<=npar;j++) {
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);      for (i=1;i<=npar;i++) x[i]=0;
       }      x[j]=1;
     fprintf(ficreseij,"\n");      lubksb(a,npar,indx,x);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for (i=1;i<=npar;i++){ 
   }        matcov[i][j]=x[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)    printf("\n#Hessian matrix#\n");
 {    fprintf(ficlog,"\n#Hessian matrix#\n");
   /* Variance of health expectancies */    for (i=1;i<=npar;i++) { 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      for (j=1;j<=npar;j++) { 
   double **newm;        printf("%.3e ",hess[i][j]);
   double **dnewm,**doldm;        fprintf(ficlog,"%.3e ",hess[i][j]);
   int i, j, nhstepm, hstepm, h;      }
   int k, cptcode;      printf("\n");
    double *xp;      fprintf(ficlog,"\n");
   double **gp, **gm;    }
   double ***gradg, ***trgradg;  
   double ***p3mat;    /* Recompute Inverse */
   double age,agelim;    for (i=1;i<=npar;i++)
   int theta;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     ludcmp(a,npar,indx,&pd);
    fprintf(ficresvij,"# Covariances of life expectancies\n");  
   fprintf(ficresvij,"# Age");    /*  printf("\n#Hessian matrix recomputed#\n");
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)    for (j=1;j<=npar;j++) {
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);      for (i=1;i<=npar;i++) x[i]=0;
   fprintf(ficresvij,"\n");      x[j]=1;
       lubksb(a,npar,indx,x);
   xp=vector(1,npar);      for (i=1;i<=npar;i++){ 
   dnewm=matrix(1,nlstate,1,npar);        y[i][j]=x[i];
   doldm=matrix(1,nlstate,1,nlstate);        printf("%.3e ",y[i][j]);
          fprintf(ficlog,"%.3e ",y[i][j]);
   hstepm=1*YEARM; /* Every year of age */      }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */      printf("\n");
   agelim = AGESUP;      fprintf(ficlog,"\n");
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    */
     if (stepm >= YEARM) hstepm=1;  
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    free_matrix(a,1,npar,1,npar);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_matrix(y,1,npar,1,npar);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    free_vector(x,1,npar);
     gp=matrix(0,nhstepm,1,nlstate);    free_ivector(indx,1,npar);
     gm=matrix(0,nhstepm,1,nlstate);    free_matrix(hess,1,npar,1,npar);
   
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */  }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }  /*************** hessian matrix ****************/
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    double hessii( double x[], double delta, int theta, double delti[])
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  {
       for(j=1; j<= nlstate; j++){    int i;
         for(h=0; h<=nhstepm; h++){    int l=1, lmax=20;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    double k1,k2;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    double p2[NPARMAX+1];
         }    double res;
       }    double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
        double fx;
       for(i=1; i<=npar; i++) /* Computes gradient */    int k=0,kmax=10;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double l1;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fx=func(x);
       for(j=1; j<= nlstate; j++){    for (i=1;i<=npar;i++) p2[i]=x[i];
         for(h=0; h<=nhstepm; h++){    for(l=0 ; l <=lmax; l++){
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)      l1=pow(10,l);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];      delts=delt;
         }      for(k=1 ; k <kmax; k=k+1){
       }        delt = delta*(l1*k);
       for(j=1; j<= nlstate; j++)        p2[theta]=x[theta] +delt;
         for(h=0; h<=nhstepm; h++){        k1=func(p2)-fx;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        p2[theta]=x[theta]-delt;
         }        k2=func(p2)-fx;
     } /* End theta */        /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        
   #ifdef DEBUG
     for(h=0; h<=nhstepm; h++)        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       for(j=1; j<=nlstate;j++)        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);
         for(theta=1; theta <=npar; theta++)  #endif
           trgradg[h][j][theta]=gradg[h][theta][j];        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     for(i=1;i<=nlstate;i++)          k=kmax;
       for(j=1;j<=nlstate;j++)        }
         vareij[i][j][(int)age] =0.;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     for(h=0;h<=nhstepm;h++){          k=kmax; l=lmax*10.;
       for(k=0;k<=nhstepm;k++){        }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          delts=delt;
         for(i=1;i<=nlstate;i++)        }
           for(j=1;j<=nlstate;j++)      }
             vareij[i][j][(int)age] += doldm[i][j];    }
       }    delti[theta]=delts;
     }    return res; 
     h=1;    
     if (stepm >= YEARM) h=stepm/YEARM;  }
     fprintf(ficresvij,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)  double hessij( double x[], double delti[], int thetai,int thetaj)
       for(j=1; j<=nlstate;j++){  {
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);    int i;
       }    int l=1, l1, lmax=20;
     fprintf(ficresvij,"\n");    double k1,k2,k3,k4,res,fx;
     free_matrix(gp,0,nhstepm,1,nlstate);    double p2[NPARMAX+1];
     free_matrix(gm,0,nhstepm,1,nlstate);    int k;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);  
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    fx=func(x);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for (k=1; k<=2; k++) {
   } /* End age */      for (i=1;i<=npar;i++) p2[i]=x[i];
        p2[thetai]=x[thetai]+delti[thetai]/k;
   free_vector(xp,1,npar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   free_matrix(doldm,1,nlstate,1,npar);      k1=func(p2)-fx;
   free_matrix(dnewm,1,nlstate,1,nlstate);    
       p2[thetai]=x[thetai]+delti[thetai]/k;
 }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k2=func(p2)-fx;
 /************ Variance of prevlim ******************/    
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      p2[thetai]=x[thetai]-delti[thetai]/k;
 {      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   /* Variance of prevalence limit */      k3=func(p2)-fx;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    
   double **newm;      p2[thetai]=x[thetai]-delti[thetai]/k;
   double **dnewm,**doldm;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   int i, j, nhstepm, hstepm;      k4=func(p2)-fx;
   int k, cptcode;      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   double *xp;  #ifdef DEBUG
   double *gp, *gm;      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);
   double **gradg, **trgradg;      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   double age,agelim;  #endif
   int theta;    }
        return res;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  }
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)  /************** Inverse of matrix **************/
       fprintf(ficresvpl," %1d-%1d",i,i);  void ludcmp(double **a, int n, int *indx, double *d) 
   fprintf(ficresvpl,"\n");  { 
     int i,imax,j,k; 
   xp=vector(1,npar);    double big,dum,sum,temp; 
   dnewm=matrix(1,nlstate,1,npar);    double *vv; 
   doldm=matrix(1,nlstate,1,nlstate);   
      vv=vector(1,n); 
   hstepm=1*YEARM; /* Every year of age */    *d=1.0; 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for (i=1;i<=n;i++) { 
   agelim = AGESUP;      big=0.0; 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (j=1;j<=n;j++) 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        if ((temp=fabs(a[i][j])) > big) big=temp; 
     if (stepm >= YEARM) hstepm=1;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      vv[i]=1.0/big; 
     gradg=matrix(1,npar,1,nlstate);    } 
     gp=vector(1,nlstate);    for (j=1;j<=n;j++) { 
     gm=vector(1,nlstate);      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
     for(theta=1; theta <=npar; theta++){        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
       for(i=1; i<=npar; i++){ /* Computes gradient */        a[i][j]=sum; 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      } 
       }      big=0.0; 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (i=j;i<=n;i++) { 
       for(i=1;i<=nlstate;i++)        sum=a[i][j]; 
         gp[i] = prlim[i][i];        for (k=1;k<j;k++) 
              sum -= a[i][k]*a[k][j]; 
       for(i=1; i<=npar; i++) /* Computes gradient */        a[i][j]=sum; 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          big=dum; 
       for(i=1;i<=nlstate;i++)          imax=i; 
         gm[i] = prlim[i][i];        } 
       } 
       for(i=1;i<=nlstate;i++)      if (j != imax) { 
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        for (k=1;k<=n;k++) { 
     } /* End theta */          dum=a[imax][k]; 
           a[imax][k]=a[j][k]; 
     trgradg =matrix(1,nlstate,1,npar);          a[j][k]=dum; 
         } 
     for(j=1; j<=nlstate;j++)        *d = -(*d); 
       for(theta=1; theta <=npar; theta++)        vv[imax]=vv[j]; 
         trgradg[j][theta]=gradg[theta][j];      } 
       indx[j]=imax; 
     for(i=1;i<=nlstate;i++)      if (a[j][j] == 0.0) a[j][j]=TINY; 
       varpl[i][(int)age] =0.;      if (j != n) { 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);        dum=1.0/(a[j][j]); 
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
     for(i=1;i<=nlstate;i++)      } 
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    } 
     free_vector(vv,1,n);  /* Doesn't work */
     fprintf(ficresvpl,"%.0f ",age );  ;
     for(i=1; i<=nlstate;i++)  } 
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));  
     fprintf(ficresvpl,"\n");  void lubksb(double **a, int n, int *indx, double b[]) 
     free_vector(gp,1,nlstate);  { 
     free_vector(gm,1,nlstate);    int i,ii=0,ip,j; 
     free_matrix(gradg,1,npar,1,nlstate);    double sum; 
     free_matrix(trgradg,1,nlstate,1,npar);   
   } /* End age */    for (i=1;i<=n;i++) { 
       ip=indx[i]; 
   free_vector(xp,1,npar);      sum=b[ip]; 
   free_matrix(doldm,1,nlstate,1,npar);      b[ip]=b[i]; 
   free_matrix(dnewm,1,nlstate,1,nlstate);      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
 }      else if (sum) ii=i; 
       b[i]=sum; 
     } 
     for (i=n;i>=1;i--) { 
 /***********************************************/      sum=b[i]; 
 /**************** Main Program *****************/      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
 /***********************************************/      b[i]=sum/a[i][i]; 
     } 
 /*int main(int argc, char *argv[])*/  } 
 int main()  
 {  /************ Frequencies ********************/
   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)
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;  {  /* Some frequencies */
   double agedeb, agefin,hf;    
   double agemin=1.e20, agemax=-1.e20;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     int first;
   double fret;    double ***freq; /* Frequencies */
   double **xi,tmp,delta;    double *pp, **prop;
     double pos,posprop, k2, dateintsum=0,k2cpt=0;
   double dum; /* Dummy variable */    FILE *ficresp;
   double ***p3mat;    char fileresp[FILENAMELENGTH];
   int *indx;    
   char line[MAXLINE], linepar[MAXLINE];    pp=vector(1,nlstate);
   char title[MAXLINE];    prop=matrix(1,nlstate,iagemin,iagemax+3);
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    strcpy(fileresp,"p");
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];    strcat(fileresp,fileres);
   char filerest[FILENAMELENGTH];    if((ficresp=fopen(fileresp,"w"))==NULL) {
   char fileregp[FILENAMELENGTH];      printf("Problem with prevalence resultfile: %s\n", fileresp);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   int firstobs=1, lastobs=10;      exit(0);
   int sdeb, sfin; /* Status at beginning and end */    }
   int c,  h , cpt,l;    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
   int ju,jl, mi;    j1=0;
   int i1,j1, k1,jk,aa,bb, stepsize;    
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    j=cptcoveff;
      if (cptcovn<1) {j=1;ncodemax[1]=1;}
   int hstepm, nhstepm;  
   double bage, fage, age, agelim, agebase;    first=1;
   double ftolpl=FTOL;  
   double **prlim;    for(k1=1; k1<=j;k1++){
   double *severity;      for(i1=1; i1<=ncodemax[k1];i1++){
   double ***param; /* Matrix of parameters */        j1++;
   double  *p;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   double **matcov; /* Matrix of covariance */          scanf("%d", i);*/
   double ***delti3; /* Scale */        for (i=-1; i<=nlstate+ndeath; i++)  
   double *delti; /* Scale */          for (jk=-1; jk<=nlstate+ndeath; jk++)  
   double ***eij, ***vareij;            for(m=iagemin; m <= iagemax+3; m++)
   double **varpl; /* Variances of prevalence limits by age */              freq[i][jk][m]=0;
   double *epj, vepp;  
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";      for (i=1; i<=nlstate; i++)  
   char *alph[]={"a","a","b","c","d","e"}, str[4];        for(m=iagemin; m <= iagemax+3; m++)
   char z[1]="c", occ;          prop[i][m]=0;
 #include <sys/time.h>        
 #include <time.h>        dateintsum=0;
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];        k2cpt=0;
   /* long total_usecs;        for (i=1; i<=imx; i++) {
   struct timeval start_time, end_time;          bool=1;
            if  (cptcovn>0) {
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */            for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
   printf("\nIMACH, Version 0.63");          }
   printf("\nEnter the parameter file name: ");          if (bool==1){
             for(m=firstpass; m<=lastpass; m++){
 #ifdef windows              k2=anint[m][i]+(mint[m][i]/12.);
   scanf("%s",pathtot);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   getcwd(pathcd, size);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   cutv(path,optionfile,pathtot,'\\');                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   chdir(path);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   replace(pathc,path);                if (m<lastpass) {
 #endif                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
 #ifdef unix                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
   scanf("%s",optionfile);                }
 #endif                
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
 /*-------- arguments in the command line --------*/                  dateintsum=dateintsum+k2;
                   k2cpt++;
   strcpy(fileres,"r");                }
   strcat(fileres, optionfile);                /*}*/
             }
   /*---------arguments file --------*/          }
         }
   if((ficpar=fopen(optionfile,"r"))==NULL)    {         
     printf("Problem with optionfile %s\n",optionfile);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
     goto end;  
   }        if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
   strcpy(filereso,"o");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcat(filereso,fileres);          fprintf(ficresp, "**********\n#");
   if((ficparo=fopen(filereso,"w"))==NULL) {        }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        for(i=1; i<=nlstate;i++) 
   }          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
   /* Reads comments: lines beginning with '#' */        
   while((c=getc(ficpar))=='#' && c!= EOF){        for(i=iagemin; i <= iagemax+3; i++){
     ungetc(c,ficpar);          if(i==iagemax+3){
     fgets(line, MAXLINE, ficpar);            fprintf(ficlog,"Total");
     puts(line);          }else{
     fputs(line,ficparo);            if(first==1){
   }              first=0;
   ungetc(c,ficpar);              printf("See log file for details...\n");
             }
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);            fprintf(ficlog,"Age %d", i);
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);          }
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   covar=matrix(1,NCOVMAX,1,n);                  pp[jk] += freq[jk][m][i]; 
   if (strlen(model)<=1) cptcovn=0;          }
   else {          for(jk=1; jk <=nlstate ; jk++){
     j=0;            for(m=-1, pos=0; m <=0 ; m++)
     j=nbocc(model,'+');              pos += freq[jk][m][i];
     cptcovn=j+1;            if(pp[jk]>=1.e-10){
   }              if(first==1){
               printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   ncovmodel=2+cptcovn;              }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
              }else{
   /* Read guess parameters */              if(first==1)
   /* Reads comments: lines beginning with '#' */                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   while((c=getc(ficpar))=='#' && c!= EOF){              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     ungetc(c,ficpar);            }
     fgets(line, MAXLINE, ficpar);          }
     puts(line);  
     fputs(line,ficparo);          for(jk=1; jk <=nlstate ; jk++){
   }            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   ungetc(c,ficpar);              pp[jk] += freq[jk][m][i];
            }       
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     for(i=1; i <=nlstate; i++)            pos += pp[jk];
     for(j=1; j <=nlstate+ndeath-1; j++){            posprop += prop[jk][i];
       fscanf(ficpar,"%1d%1d",&i1,&j1);          }
       fprintf(ficparo,"%1d%1d",i1,j1);          for(jk=1; jk <=nlstate ; jk++){
       printf("%1d%1d",i,j);            if(pos>=1.e-5){
       for(k=1; k<=ncovmodel;k++){              if(first==1)
         fscanf(ficpar," %lf",&param[i][j][k]);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         printf(" %lf",param[i][j][k]);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         fprintf(ficparo," %lf",param[i][j][k]);            }else{
       }              if(first==1)
       fscanf(ficpar,"\n");                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       printf("\n");              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficparo,"\n");            }
     }            if( i <= iagemax){
                if(pos>=1.e-5){
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   p=param[1][1];                /*probs[i][jk][j1]= pp[jk]/pos;*/
                  /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   /* Reads comments: lines beginning with '#' */              }
   while((c=getc(ficpar))=='#' && c!= EOF){              else
     ungetc(c,ficpar);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     fgets(line, MAXLINE, ficpar);            }
     puts(line);          }
     fputs(line,ficparo);          
   }          for(jk=-1; jk <=nlstate+ndeath; jk++)
   ungetc(c,ficpar);            for(m=-1; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);              if(first==1)
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   for(i=1; i <=nlstate; i++){                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     for(j=1; j <=nlstate+ndeath-1; j++){              }
       fscanf(ficpar,"%1d%1d",&i1,&j1);          if(i <= iagemax)
       printf("%1d%1d",i,j);            fprintf(ficresp,"\n");
       fprintf(ficparo,"%1d%1d",i1,j1);          if(first==1)
       for(k=1; k<=ncovmodel;k++){            printf("Others in log...\n");
         fscanf(ficpar,"%le",&delti3[i][j][k]);          fprintf(ficlog,"\n");
         printf(" %le",delti3[i][j][k]);        }
         fprintf(ficparo," %le",delti3[i][j][k]);      }
       }    }
       fscanf(ficpar,"\n");    dateintmean=dateintsum/k2cpt; 
       printf("\n");   
       fprintf(ficparo,"\n");    fclose(ficresp);
     }    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
   }    free_vector(pp,1,nlstate);
   delti=delti3[1][1];    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
      /* End of Freq */
   /* Reads comments: lines beginning with '#' */  }
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);  /************ Prevalence ********************/
     fgets(line, MAXLINE, ficpar);  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)
     puts(line);  {  
     fputs(line,ficparo);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   }       in each health status at the date of interview (if between dateprev1 and dateprev2).
   ungetc(c,ficpar);       We still use firstpass and lastpass as another selection.
      */
   matcov=matrix(1,npar,1,npar);   
   for(i=1; i <=npar; i++){    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     fscanf(ficpar,"%s",&str);    double ***freq; /* Frequencies */
     printf("%s",str);    double *pp, **prop;
     fprintf(ficparo,"%s",str);    double pos,posprop; 
     for(j=1; j <=i; j++){    double  y2; /* in fractional years */
       fscanf(ficpar," %le",&matcov[i][j]);    int iagemin, iagemax;
       printf(" %.5le",matcov[i][j]);  
       fprintf(ficparo," %.5le",matcov[i][j]);    iagemin= (int) agemin;
     }    iagemax= (int) agemax;
     fscanf(ficpar,"\n");    /*pp=vector(1,nlstate);*/
     printf("\n");    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     fprintf(ficparo,"\n");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   }    j1=0;
   for(i=1; i <=npar; i++)    
     for(j=i+1;j<=npar;j++)    j=cptcoveff;
       matcov[i][j]=matcov[j][i];    if (cptcovn<1) {j=1;ncodemax[1]=1;}
        
   printf("\n");    for(k1=1; k1<=j;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
    if(mle==1){        
     /*-------- data file ----------*/        for (i=1; i<=nlstate; i++)  
     if((ficres =fopen(fileres,"w"))==NULL) {          for(m=iagemin; m <= iagemax+3; m++)
       printf("Problem with resultfile: %s\n", fileres);goto end;            prop[i][m]=0.0;
     }       
     fprintf(ficres,"#%s\n",version);        for (i=1; i<=imx; i++) { /* Each individual */
              bool=1;
     if((fic=fopen(datafile,"r"))==NULL)    {          if  (cptcovn>0) {
       printf("Problem with datafile: %s\n", datafile);goto end;            for (z1=1; z1<=cptcoveff; z1++) 
     }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
     n= lastobs;          } 
     severity = vector(1,maxwav);          if (bool==1) { 
     outcome=imatrix(1,maxwav+1,1,n);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     num=ivector(1,n);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     moisnais=vector(1,n);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     annais=vector(1,n);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     moisdc=vector(1,n);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     andc=vector(1,n);                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); 
     agedc=vector(1,n);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     cod=ivector(1,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]]);*/
     weight=vector(1,n);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */                  prop[s[m][i]][iagemax+3] += weight[i]; 
     mint=matrix(1,maxwav,1,n);                } 
     anint=matrix(1,maxwav,1,n);              }
     s=imatrix(1,maxwav+1,1,n);            } /* end selection of waves */
     adl=imatrix(1,maxwav+1,1,n);              }
     tab=ivector(1,NCOVMAX);        }
     ncodemax=ivector(1,8);        for(i=iagemin; i <= iagemax+3; i++){  
           
     i=1;          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
     while (fgets(line, MAXLINE, fic) != NULL)    {            posprop += prop[jk][i]; 
       if ((i >= firstobs) && (i <=lastobs)) {          } 
          
         for (j=maxwav;j>=1;j--){          for(jk=1; jk <=nlstate ; jk++){     
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);            if( i <=  iagemax){ 
           strcpy(line,stra);              if(posprop>=1.e-5){ 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);                probs[i][jk][j1]= prop[jk][i]/posprop;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);              } 
         }            } 
                  }/* end jk */ 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        }/* end i */ 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);      } /* end i1 */
     } /* end k1 */
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     /*free_vector(pp,1,nlstate);*/
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
         for (j=ncov;j>=1;j--){  }  /* End of prevalence */
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);  
         }  /************* Waves Concatenation ***************/
         num[i]=atol(stra);  
   void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
         /*printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]),  (mint[5][i]), (anint[5][i]), (s[5][i]),  (mint[6][i]), (anint[6][i]), (s[6][i]));*/  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
         i=i+1;       Death is a valid wave (if date is known).
       }       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
        and mw[mi+1][i]. dh depends on stepm.
     /*scanf("%d",i);*/       */
   imx=i-1; /* Number of individuals */  
     int i, mi, m;
   /* Calculation of the number of parameter from char model*/    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
   Tvar=ivector(1,8);           double sum=0., jmean=0.;*/
        int first;
   if (strlen(model) >1){    int j, k=0,jk, ju, jl;
     j=0;    double sum=0.;
     j=nbocc(model,'+');    first=0;
     cptcovn=j+1;    jmin=1e+5;
        jmax=-1;
     strcpy(modelsav,model);    jmean=0.;
     if (j==0) {    for(i=1; i<=imx; i++){
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);      mi=0;
     }      m=firstpass;
     else {      while(s[m][i] <= nlstate){
       for(i=j; i>=1;i--){        if(s[m][i]>=1)
         cutv(stra,strb,modelsav,'+');          mw[++mi][i]=m;
         if (strchr(strb,'*')) {        if(m >=lastpass)
           cutv(strd,strc,strb,'*');          break;
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;        else
           cutv(strb,strc,strd,'V');          m++;
           for (k=1; k<=lastobs;k++)      }/* end while */
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];      if (s[m][i] > nlstate){
         }        mi++;     /* Death is another wave */
         else {cutv(strd,strc,strb,'V');        /* if(mi==0)  never been interviewed correctly before death */
         Tvar[i+1]=atoi(strc);           /* Only death is a correct wave */
         }        mw[mi][i]=m;
         strcpy(modelsav,stra);        }
       }  
       cutv(strd,strc,stra,'V');      wav[i]=mi;
       Tvar[1]=atoi(strc);      if(mi==0){
     }        if(first==0){
   }          printf("Warning! None valid information for:%d line=%d (skipped) and may be others, see log file\n",num[i],i);
   /*printf("tvar=%d ",Tvar[1]);          first=1;
   scanf("%d ",i);*/        }
     fclose(fic);        if(first==1){
           fprintf(ficlog,"Warning! None valid information for:%d line=%d (skipped)\n",num[i],i);
     if (weightopt != 1) { /* Maximisation without weights*/        }
       for(i=1;i<=n;i++) weight[i]=1.0;      } /* end mi==0 */
     }    } /* End individuals */
     /*-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(mi=1; mi<wav[i];mi++){
     for (i=1; i<=imx; i++)  {        if (stepm <=0)
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          dh[mi][i]=1;
       for(m=1; (m<= maxwav); m++){        else{
         if(s[m][i] >0){          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
           if (s[m][i] == nlstate+1) {            if (agedc[i] < 2*AGESUP) {
             if(agedc[i]>0)            j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
               if(moisdc[i]!=99 && andc[i]!=9999)            if(j==0) j=1;  /* Survives at least one month after exam */
               agev[m][i]=agedc[i];            k=k+1;
             else{            if (j >= jmax) jmax=j;
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            if (j <= jmin) jmin=j;
               agev[m][i]=-1;            sum=sum+j;
             }            /*if (j<0) printf("j=%d num=%d \n",j,i);*/
           }            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
           else if(s[m][i] !=9){ /* Should no more exist */            if(j<0)printf("Error! Negative delay (%d to death) between waves %d and %d of individual %d 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]);
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);            }
             if(mint[m][i]==99 || anint[m][i]==9999)          }
               agev[m][i]=1;          else{
             else if(agev[m][i] <agemin){            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
               agemin=agev[m][i];            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/            k=k+1;
             }            if (j >= jmax) jmax=j;
             else if(agev[m][i] >agemax){            else if (j <= jmin)jmin=j;
               agemax=agev[m][i];            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
             }            if(j<0)printf("Error! Negative delay (%d) between waves %d and %d of individual %d 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]);
             /*agev[m][i]=anint[m][i]-annais[i];*/            sum=sum+j;
             /*   agev[m][i] = age[i]+2*m;*/          }
           }          jk= j/stepm;
           else { /* =9 */          jl= j -jk*stepm;
             agev[m][i]=1;          ju= j -(jk+1)*stepm;
             s[m][i]=-1;          if(mle <=1){ 
           }            if(jl==0){
         }              dh[mi][i]=jk;
         else /*= 0 Unknown */              bh[mi][i]=0;
           agev[m][i]=1;            }else{ /* We want a negative bias in order to only have interpolation ie
       }                    * at the price of an extra matrix product in likelihood */
                  dh[mi][i]=jk+1;
     }              bh[mi][i]=ju;
     for (i=1; i<=imx; i++)  {            }
       for(m=1; (m<= maxwav); m++){          }else{
         if (s[m][i] > (nlstate+ndeath)) {            if(jl <= -ju){
           printf("Error: Wrong value in nlstate or ndeath\n");                dh[mi][i]=jk;
           goto end;              bh[mi][i]=jl;       /* bias is positive if real duration
         }                                   * is higher than the multiple of stepm and negative otherwise.
       }                                   */
     }            }
             else{
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
     free_vector(severity,1,maxwav);            }
     free_imatrix(outcome,1,maxwav+1,1,n);            if(dh[mi][i]==0){
     free_vector(moisnais,1,n);              dh[mi][i]=1; /* At least one step */
     free_vector(annais,1,n);              bh[mi][i]=ju; /* At least one step */
     free_matrix(mint,1,maxwav,1,n);              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
     free_matrix(anint,1,maxwav,1,n);            }
     free_vector(moisdc,1,n);          }
     free_vector(andc,1,n);        } /* end if mle */
       } /* end wave */
        }
     wav=ivector(1,imx);    jmean=sum/k;
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       }
     /* Concatenates waves */  
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  /*********** Tricode ****************************/
   void tricode(int *Tvar, int **nbcode, int imx)
   {
 Tcode=ivector(1,100);    
    nbcode=imatrix(1,nvar,1,8);      int Ndum[20],ij=1, k, j, i, maxncov=19;
    ncodemax[1]=1;    int cptcode=0;
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);    cptcoveff=0; 
     
    codtab=imatrix(1,100,1,10);    for (k=0; k<maxncov; k++) Ndum[k]=0;
    h=0;    for (k=1; k<=7; k++) ncodemax[k]=0;
    m=pow(2,cptcovn);  
      for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
    for(k=1;k<=cptcovn; k++){      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
      for(i=1; i <=(m/pow(2,k));i++){                                 modality*/ 
        for(j=1; j <= ncodemax[k]; j++){        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){        Ndum[ij]++; /*store the modality */
            h++;        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
            if (h>m) h=1;codtab[h][k]=j;        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
          }                                         Tvar[j]. If V=sex and male is 0 and 
        }                                         female is 1, then  cptcode=1.*/
      }      }
    }  
       for (i=0; i<=cptcode; i++) {
    /*for(i=1; i <=m ;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 */
      for(k=1; k <=cptcovn; k++){      }
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);  
      }      ij=1; 
      printf("\n");      for (i=1; i<=ncodemax[j]; i++) {
    }*/        for (k=0; k<= maxncov; k++) {
    /*scanf("%d",i);*/          if (Ndum[k] != 0) {
                nbcode[Tvar[j]][ij]=k; 
    /* Calculates basic frequencies. Computes observed prevalence at single age            /* 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; */
        and prints on file fileres'p'. */            
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);            ij++;
           }
           if (ij > ncodemax[j]) break; 
   /*scanf("%d ",i);*/        }  
       } 
     }  
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   for (k=0; k< maxncov; k++) Ndum[k]=0;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   for (i=1; i<=ncovmodel-2; i++) { 
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
         ij=Tvar[i];
     /* For Powell, parameters are in a vector p[] starting at p[1]     Ndum[ij]++;
        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) */  
       ij=1;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);   for (i=1; i<= maxncov; i++) {
      if((Ndum[i]!=0) && (i<=ncovcol)){
           Tvaraff[ij]=i; /*For printing */
     /*--------- results files --------------*/       ij++;
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);     }
       }
    jk=1;   
    fprintf(ficres,"# Parameters\n");   cptcoveff=ij-1; /*Number of simple covariates*/
    printf("# Parameters\n");  }
    for(i=1,jk=1; i <=nlstate; i++){  
      for(k=1; k <=(nlstate+ndeath); k++){  /*********** Health Expectancies ****************/
        if (k != i)  
          {  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )
            printf("%d%d ",i,k);  
            fprintf(ficres,"%1d%1d ",i,k);  {
            for(j=1; j <=ncovmodel; j++){    /* Health expectancies */
              printf("%f ",p[jk]);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
              fprintf(ficres,"%f ",p[jk]);    double age, agelim, hf;
              jk++;    double ***p3mat,***varhe;
            }    double **dnewm,**doldm;
            printf("\n");    double *xp;
            fprintf(ficres,"\n");    double **gp, **gm;
          }    double ***gradg, ***trgradg;
      }    int theta;
    }  
     varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     /* Computing hessian and covariance matrix */    xp=vector(1,npar);
     ftolhess=ftol; /* Usually correct */    dnewm=matrix(1,nlstate*nlstate,1,npar);
     hesscov(matcov, p, npar, delti, ftolhess, func);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     fprintf(ficres,"# Scales\n");    
     printf("# Scales\n");    fprintf(ficreseij,"# Health expectancies\n");
      for(i=1,jk=1; i <=nlstate; i++){    fprintf(ficreseij,"# Age");
       for(j=1; j <=nlstate+ndeath; j++){    for(i=1; i<=nlstate;i++)
         if (j!=i) {      for(j=1; j<=nlstate;j++)
           fprintf(ficres,"%1d%1d",i,j);        fprintf(ficreseij," %1d-%1d (SE)",i,j);
           printf("%1d%1d",i,j);    fprintf(ficreseij,"\n");
           for(k=1; k<=ncovmodel;k++){  
             printf(" %.5e",delti[jk]);    if(estepm < stepm){
             fprintf(ficres," %.5e",delti[jk]);      printf ("Problem %d lower than %d\n",estepm, stepm);
             jk++;    }
           }    else  hstepm=estepm;   
           printf("\n");    /* We compute the life expectancy from trapezoids spaced every estepm months
           fprintf(ficres,"\n");     * This is mainly to measure the difference between two models: for example
         }     * if stepm=24 months pijx are given only every 2 years and by summing them
       }     * we are calculating an estimate of the Life Expectancy assuming a linear 
       }     * progression in between and thus overestimating or underestimating according
         * to the curvature of the survival function. If, for the same date, we 
     k=1;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     fprintf(ficres,"# Covariance\n");     * to compare the new estimate of Life expectancy with the same linear 
     printf("# Covariance\n");     * hypothesis. A more precise result, taking into account a more precise
     for(i=1;i<=npar;i++){     * curvature will be obtained if estepm is as small as stepm. */
       /*  if (k>nlstate) k=1;  
       i1=(i-1)/(ncovmodel*nlstate)+1;    /* For example we decided to compute the life expectancy with the smallest unit */
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       printf("%s%d%d",alph[k],i1,tab[i]);*/       nhstepm is the number of hstepm from age to agelim 
       fprintf(ficres,"%3d",i);       nstepm is the number of stepm from age to agelin. 
       printf("%3d",i);       Look at hpijx to understand the reason of that which relies in memory size
       for(j=1; j<=i;j++){       and note for a fixed period like estepm months */
         fprintf(ficres," %.5e",matcov[i][j]);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         printf(" %.5e",matcov[i][j]);       survival function given by stepm (the optimization length). Unfortunately it
       }       means that if the survival funtion is printed only each two years of age and if
       fprintf(ficres,"\n");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       printf("\n");       results. So we changed our mind and took the option of the best precision.
       k++;    */
     }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
      
     while((c=getc(ficpar))=='#' && c!= EOF){    agelim=AGESUP;
       ungetc(c,ficpar);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       fgets(line, MAXLINE, ficpar);      /* nhstepm age range expressed in number of stepm */
       puts(line);      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
       fputs(line,ficparo);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     }      /* if (stepm >= YEARM) hstepm=1;*/
     ungetc(c,ficpar);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
          gp=matrix(0,nhstepm,1,nlstate*nlstate);
     if (fage <= 2) {      gm=matrix(0,nhstepm,1,nlstate*nlstate);
       bage = agemin;  
       fage = agemax;      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");   
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  
 /*------------ gnuplot -------------*/      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 chdir(pathcd);  
   if((ficgp=fopen("graph.plt","w"))==NULL) {      /* Computing Variances of health expectancies */
     printf("Problem with file graph.gp");goto end;  
   }       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,cptcovn);        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;
 #ifdef windows            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
 #endif            }
 #ifdef unix          }
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);        }
 #endif       
        
 for (i=1; i<= 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\"Stationary prevalence\" w l 0,\"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\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  
      for (i=1; i<= nlstate ; i ++) {              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          }
 }          }
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));        for(j=1; j<= nlstate*nlstate; j++)
 #ifdef unix          for(h=0; h<=nhstepm-1; h++){
 fprintf(ficgp,"\nset ter gif small size 400,300");            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 #endif          }
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);       } 
    }     
   }  /* End theta */
   /*2 eme*/  
        trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   for (k1=1; k1<= m ; k1 ++) {  
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);       for(h=0; h<=nhstepm-1; h++)
            for(j=1; j<=nlstate*nlstate;j++)
     for (i=1; i<= nlstate+1 ; i ++) {          for(theta=1; theta <=npar; theta++)
       k=2*i;            trgradg[h][j][theta]=gradg[h][theta][j];
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);       
       for (j=1; j<= nlstate+1 ; j ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       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.;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);       printf("%d|",(int)age);fflush(stdout);
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       for (j=1; j<= nlstate+1 ; j ++) {       for(h=0;h<=nhstepm-1;h++){
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        for(k=0;k<=nhstepm-1;k++){
         else fprintf(ficgp," \%%*lf (\%%*lf)");          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
 }            matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       fprintf(ficgp,"\" t\"\" w l 0,");          for(i=1;i<=nlstate*nlstate;i++)
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            for(j=1;j<=nlstate*nlstate;j++)
       for (j=1; j<= nlstate+1 ; j ++) {              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        }
   else fprintf(ficgp," \%%*lf (\%%*lf)");      }
 }        /* Computing expectancies */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");      for(i=1; i<=nlstate;i++)
       else fprintf(ficgp,"\" t\"\" w l 0,");        for(j=1; j<=nlstate;j++)
     }          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
   }            
    /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   /*3eme*/  
           }
    for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<= nlstate ; cpt ++) {      fprintf(ficreseij,"%3.0f",age );
       k=2+nlstate*(cpt-1);      cptj=0;
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);      for(i=1; i<=nlstate;i++)
       for (i=1; i< nlstate ; i ++) {        for(j=1; j<=nlstate;j++){
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);          cptj++;
       }          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        }
     }      fprintf(ficreseij,"\n");
    }     
        free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   /* CV preval stat */      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     for (k1=1; k1<= m ; k1 ++) {      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     for (cpt=1; cpt<nlstate ; cpt ++) {      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       k=3;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);    }
       for (i=1; i< nlstate ; i ++)    printf("\n");
         fprintf(ficgp,"+$%d",k+i+1);    fprintf(ficlog,"\n");
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);  
          free_vector(xp,1,npar);
       l=3+(nlstate+ndeath)*cpt;    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       for (i=1; i< nlstate ; i ++) {    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
         l=3+(nlstate+ndeath)*cpt;  }
         fprintf(ficgp,"+$%d",l+i+1);  
       }  /************ Variance ******************/
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);    void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav)
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  {
     }    /* Variance of health expectancies */
   }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
      /* double **newm;*/
   /* proba elementaires */    double **dnewm,**doldm;
   for(i=1,jk=1; i <=nlstate; i++){    double **dnewmp,**doldmp;
     for(k=1; k <=(nlstate+ndeath); k++){    int i, j, nhstepm, hstepm, h, nstepm ;
       if (k != i) {    int k, cptcode;
         /*  fprintf(ficgp,"%1d%1d ",i,k);*/    double *xp;
         for(j=1; j <=ncovmodel; j++){    double **gp, **gm;  /* for var eij */
           fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);    double ***gradg, ***trgradg; /*for var eij */
           jk++;    double **gradgp, **trgradgp; /* for var p point j */
           fprintf(ficgp,"\n");    double *gpp, *gmp; /* for var p point j */
         }    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       }    double ***p3mat;
     }    double age,agelim, hf;
   }    double ***mobaverage;
   for(jk=1; jk <=m; jk++) {    int theta;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);    char digit[4];
   for(i=1; i <=nlstate; i++) {    char digitp[25];
     for(k=1; k <=(nlstate+ndeath); k++){  
       if (k != i) {    char fileresprobmorprev[FILENAMELENGTH];
         fprintf(ficgp," exp(a%d%d+b%d%d*x",i,k,i,k);  
         for(j=3; j <=ncovmodel; j++)    if(popbased==1){
           fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      if(mobilav!=0)
         fprintf(ficgp,")/(1");        strcpy(digitp,"-populbased-mobilav-");
         for(k1=1; k1 <=(nlstate+ndeath); k1++)      else strcpy(digitp,"-populbased-nomobil-");
           if (k1 != i) {    }
             fprintf(ficgp,"+exp(a%d%d+b%d%d*x",i,k1,i,k1);    else 
             for(j=3; j <=ncovmodel; j++)      strcpy(digitp,"-stablbased-");
               fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  
             fprintf(ficgp,")");    if (mobilav!=0) {
           }      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         fprintf(ficgp,") t \"p%d%d\" ", i,k);      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
       if ((i+k)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
       }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     }      }
   }    }
 fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    
   }    strcpy(fileresprobmorprev,"prmorprev"); 
      sprintf(digit,"%-d",ij);
  fclose(ficgp);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
     chdir(path);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     free_matrix(agev,1,maxwav,1,imx);    strcat(fileresprobmorprev,fileres);
     free_ivector(wav,1,imx);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
        }
     free_imatrix(s,1,maxwav+1,1,n);    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(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);
     free_ivector(num,1,n);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     free_vector(agedc,1,n);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     free_vector(weight,1,n);      fprintf(ficresprobmorprev," p.%-d SE",j);
     /*free_matrix(covar,1,NCOVMAX,1,n);*/      for(i=1; i<=nlstate;i++)
     fclose(ficparo);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     fclose(ficres);    }  
    }    fprintf(ficresprobmorprev,"\n");
        if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
    /*________fin mle=1_________*/      printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
          fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
       exit(0);
      }
     /* No more information from the sample is required now */    else{
   /* Reads comments: lines beginning with '#' */      fprintf(ficgp,"\n# Routine varevsij");
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
     fgets(line, MAXLINE, ficpar);      printf("Problem with html file: %s\n", optionfilehtm);
     puts(line);      fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
     fputs(line,ficparo);      exit(0);
   }    }
   ungetc(c,ficpar);    else{
        fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
       fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    }
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  
 /*--------- index.htm --------*/    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");
     fprintf(ficresvij,"# Age");
   if((fichtm=fopen("index.htm","w"))==NULL)    {    for(i=1; i<=nlstate;i++)
     printf("Problem with index.htm \n");goto end;      for(j=1; j<=nlstate;j++)
   }        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
     fprintf(ficresvij,"\n");
  fprintf(fichtm,"<body><ul> Imach, Version 0.63<hr> <li>Outputs files<br><br>\n  
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    xp=vector(1,npar);
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>    dnewm=matrix(1,nlstate,1,npar);
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>    doldm=matrix(1,nlstate,1,nlstate);
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>  
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    gpp=vector(nlstate+1,nlstate+ndeath);
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);    gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
  fprintf(fichtm," <li>Graphs</li>\n<p>");    
     if(estepm < stepm){
  m=cptcovn;      printf ("Problem %d lower than %d\n",estepm, stepm);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    }
     else  hstepm=estepm;   
  j1=0;    /* For example we decided to compute the life expectancy with the smallest unit */
  for(k1=1; k1<=m;k1++){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
    for(i1=1; i1<=ncodemax[k1];i1++){       nhstepm is the number of hstepm from age to agelim 
        j1++;       nstepm is the number of stepm from age to agelin. 
        if (cptcovn > 0) {       Look at hpijx to understand the reason of that which relies in memory size
          fprintf(fichtm,"<hr>************ Results for covariates");       and note for a fixed period like k years */
          for (cpt=1; cpt<=cptcovn;cpt++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);       survival function given by stepm (the optimization length). Unfortunately it
          fprintf(fichtm," ************\n<hr>");       means that if the survival funtion is printed every two years of age and if
        }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>       results. So we changed our mind and took the option of the best precision.
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);        */
        for(cpt=1; cpt<nlstate;cpt++){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    agelim = AGESUP;
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
        }      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     for(cpt=1; cpt<=nlstate;cpt++) {      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 interval) in state (%d): v%s%d%d.gif <br>      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        gp=matrix(0,nhstepm,1,nlstate);
      }      gm=matrix(0,nhstepm,1,nlstate);
      for(cpt=1; cpt<=nlstate;cpt++) {  
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>  
 <img src=\"ex%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      for(theta=1; theta <=npar; theta++){
      }        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 health expectancies in states (1) and (2): e%s%d.gif<br>        }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 fprintf(fichtm,"\n</body>");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    }  
  }        if (popbased==1) {
 fclose(fichtm);          if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
   /*--------------- Prevalence limit --------------*/              prlim[i][i]=probs[(int)age][i][ij];
            }else{ /* mobilav */ 
   strcpy(filerespl,"pl");            for(i=1; i<=nlstate;i++)
   strcat(filerespl,fileres);              prlim[i][i]=mobaverage[(int)age][i][ij];
   if((ficrespl=fopen(filerespl,"w"))==NULL) {          }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        }
   }    
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);        for(j=1; j<= nlstate; j++){
   fprintf(ficrespl,"#Prevalence limit\n");          for(h=0; h<=nhstepm; h++){
   fprintf(ficrespl,"#Age ");            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
   fprintf(ficrespl,"\n");          }
          }
   prlim=matrix(1,nlstate,1,nlstate);        /* This for computing probability of death (h=1 means
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           computed over hstepm matrices product = hstepm*stepm months) 
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           as a weighted average of prlim.
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        */
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          for(i=1,gpp[j]=0.; i<= nlstate; i++)
   k=0;            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   agebase=agemin;        }    
   agelim=agemax;        /* end probability of death */
   ftolpl=1.e-10;  
   i1=cptcovn;        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   if (cptcovn < 1){i1=1;}          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   for(cptcov=1;cptcov<=i1;cptcov++){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   
         k=k+1;        if (popbased==1) {
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/          if(mobilav ==0){
         fprintf(ficrespl,"\n#****** ");            for(i=1; i<=nlstate;i++)
         for(j=1;j<=cptcovn;j++)              prlim[i][i]=probs[(int)age][i][ij];
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);          }else{ /* mobilav */ 
         fprintf(ficrespl,"******\n");            for(i=1; i<=nlstate;i++)
                      prlim[i][i]=mobaverage[(int)age][i][ij];
         for (age=agebase; age<=agelim; age++){          }
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        }
           fprintf(ficrespl,"%.0f",age );  
           for(i=1; i<=nlstate;i++)        for(j=1; j<= nlstate; j++){
           fprintf(ficrespl," %.5f", prlim[i][i]);          for(h=0; h<=nhstepm; h++){
           fprintf(ficrespl,"\n");            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
         }              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
       }          }
     }        }
   fclose(ficrespl);        /* This for computing probability of death (h=1 means
   /*------------- h Pij x at various ages ------------*/           computed over hstepm matrices product = hstepm*stepm months) 
             as a weighted average of prlim.
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        */
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
   }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
   printf("Computing pij: result on file '%s' \n", filerespij);        }    
          /* end probability of death */
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=24) stepsize=2;        for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
   agelim=AGESUP;            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   hstepm=stepsize*YEARM; /* Every year of age */          }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
          for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   k=0;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
   for(cptcov=1;cptcov<=i1;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;      } /* End theta */
         fprintf(ficrespij,"\n#****** ");  
         for(j=1;j<=cptcovn;j++)      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);  
         fprintf(ficrespij,"******\n");      for(h=0; h<=nhstepm; h++) /* veij */
                for(j=1; j<=nlstate;j++)
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */          for(theta=1; theta <=npar; theta++)
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */            trgradg[h][j][theta]=gradg[h][theta][j];
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
           oldm=oldms;savm=savms;        for(theta=1; theta <=npar; theta++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            trgradgp[j][theta]=gradgp[theta][j];
           fprintf(ficrespij,"# Age");    
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
               fprintf(ficrespij," %1d-%1d",i,j);      for(i=1;i<=nlstate;i++)
           fprintf(ficrespij,"\n");        for(j=1;j<=nlstate;j++)
           for (h=0; h<=nhstepm; h++){          vareij[i][j][(int)age] =0.;
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );  
             for(i=1; i<=nlstate;i++)      for(h=0;h<=nhstepm;h++){
               for(j=1; j<=nlstate+ndeath;j++)        for(k=0;k<=nhstepm;k++){
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
             fprintf(ficrespij,"\n");          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           }          for(i=1;i<=nlstate;i++)
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for(j=1;j<=nlstate;j++)
           fprintf(ficrespij,"\n");              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }        }
     }      }
   }    
       /* pptj */
   fclose(ficrespij);      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);
   /*---------- Health expectancies and variances ------------*/      for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
   strcpy(filerest,"t");          varppt[j][i]=doldmp[j][i];
   strcat(filerest,fileres);      /* end ppptj */
   if((ficrest=fopen(filerest,"w"))==NULL) {      /*  x centered again */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
   }      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);   
       if (popbased==1) {
         if(mobilav ==0){
   strcpy(filerese,"e");          for(i=1; i<=nlstate;i++)
   strcat(filerese,fileres);            prlim[i][i]=probs[(int)age][i][ij];
   if((ficreseij=fopen(filerese,"w"))==NULL) {        }else{ /* mobilav */ 
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          for(i=1; i<=nlstate;i++)
   }            prlim[i][i]=mobaverage[(int)age][i][ij];
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);        }
       }
  strcpy(fileresv,"v");               
   strcat(fileresv,fileres);      /* This for computing probability of death (h=1 means
   if((ficresvij=fopen(fileresv,"w"))==NULL) {         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);         as a weighted average of prlim.
   }      */
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
   k=0;          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   for(cptcov=1;cptcov<=i1;cptcov++){      }    
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      /* end probability of death */
       k=k+1;  
       fprintf(ficrest,"\n#****** ");      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=1;j<=cptcovn;j++)      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
       fprintf(ficrest,"******\n");        for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
       fprintf(ficreseij,"\n#****** ");        }
       for(j=1;j<=cptcovn;j++)      } 
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      fprintf(ficresprobmorprev,"\n");
       fprintf(ficreseij,"******\n");  
       fprintf(ficresvij,"%.0f ",age );
       fprintf(ficresvij,"\n#****** ");      for(i=1; i<=nlstate;i++)
       for(j=1;j<=cptcovn;j++)        for(j=1; j<=nlstate;j++){
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       fprintf(ficresvij,"******\n");        }
       fprintf(ficresvij,"\n");
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      free_matrix(gp,0,nhstepm,1,nlstate);
       oldm=oldms;savm=savms;      free_matrix(gm,0,nhstepm,1,nlstate);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);        free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       oldm=oldms;savm=savms;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    } /* End age */
          free_vector(gpp,nlstate+1,nlstate+ndeath);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    free_vector(gmp,nlstate+1,nlstate+ndeath);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
       fprintf(ficrest,"\n");    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");
       hf=1;    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
       if (stepm >= YEARM) hf=stepm/YEARM;    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
       epj=vector(1,nlstate+1);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
       for(age=bage; age <=fage ;age++){  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
         fprintf(ficrest," %.0f",age);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",fileresprobmorprev);
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",fileresprobmorprev);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",fileresprobmorprev);
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);
           }    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s%s.png\"> <br>\n", estepm,digitp,optionfilefiname,digit);
           epj[nlstate+1] +=epj[j];    /*  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);
         }  */
         for(i=1, vepp=0.;i <=nlstate;i++)    fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit);
           for(j=1;j <=nlstate;j++)  
             vepp += vareij[i][j][(int)age];    free_vector(xp,1,npar);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    free_matrix(doldm,1,nlstate,1,nlstate);
         for(j=1;j <=nlstate;j++){    free_matrix(dnewm,1,nlstate,1,npar);
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         }    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
         fprintf(ficrest,"\n");    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       }    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }    fclose(ficresprobmorprev);
   }    fclose(ficgp);
            fclose(fichtm);
  fclose(ficreseij);  }  /* end varevsij */
  fclose(ficresvij);  
   fclose(ficrest);  /************ Variance of prevlim ******************/
   fclose(ficpar);  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)
   free_vector(epj,1,nlstate+1);  {
   /*scanf("%d ",i); */    /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   /*------- Variance limit prevalence------*/      double **newm;
     double **dnewm,**doldm;
 strcpy(fileresvpl,"vpl");    int i, j, nhstepm, hstepm;
   strcat(fileresvpl,fileres);    int k, cptcode;
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    double *xp;
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    double *gp, *gm;
     exit(0);    double **gradg, **trgradg;
   }    double age,agelim;
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    int theta;
      
  k=0;    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
  for(cptcov=1;cptcov<=i1;cptcov++){    fprintf(ficresvpl,"# Age");
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    for(i=1; i<=nlstate;i++)
      k=k+1;        fprintf(ficresvpl," %1d-%1d",i,i);
      fprintf(ficresvpl,"\n#****** ");    fprintf(ficresvpl,"\n");
      for(j=1;j<=cptcovn;j++)  
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    xp=vector(1,npar);
      fprintf(ficresvpl,"******\n");    dnewm=matrix(1,nlstate,1,npar);
          doldm=matrix(1,nlstate,1,nlstate);
      varpl=matrix(1,nlstate,(int) bage, (int) fage);    
      oldm=oldms;savm=savms;    hstepm=1*YEARM; /* Every year of age */
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
    }    agelim = AGESUP;
  }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   fclose(ficresvpl);      if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   /*---------- End : free ----------------*/      gradg=matrix(1,npar,1,nlstate);
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      gp=vector(1,nlstate);
        gm=vector(1,nlstate);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      for(theta=1; theta <=npar; theta++){
          for(i=1; i<=npar; i++){ /* Computes gradient */
            xp[i] = x[i] + (i==theta ?delti[theta]:0);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        }
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(i=1;i<=nlstate;i++)
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          gp[i] = prlim[i][i];
        
   free_matrix(matcov,1,npar,1,npar);        for(i=1; i<=npar; i++) /* Computes gradient */
   free_vector(delti,1,npar);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
          prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   printf("End of Imach\n");  
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        for(i=1;i<=nlstate;i++)
            gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
   /* 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);*/      } /* End theta */
   /*printf("Total time was %d uSec.\n", total_usecs);*/  
   /*------ End -----------*/      trgradg =matrix(1,nlstate,1,npar);
   
  end:      for(j=1; j<=nlstate;j++)
 #ifdef windows        for(theta=1; theta <=npar; theta++)
  chdir(pathcd);          trgradg[j][theta]=gradg[theta][j];
 #endif  
  system("wgnuplot graph.plt");      for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
 #ifdef windows      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
   while (z[0] != 'q') {      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
     chdir(pathcd);      for(i=1;i<=nlstate;i++)
     printf("\nType e to edit output files, c to start again, and q for exiting: ");        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     scanf("%s",z);  
     if (z[0] == 'c') system("./imach");      fprintf(ficresvpl,"%.0f ",age );
     else if (z[0] == 'e') {      for(i=1; i<=nlstate;i++)
       chdir(path);        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       system("index.htm");      fprintf(ficresvpl,"\n");
     }      free_vector(gp,1,nlstate);
     else if (z[0] == 'q') exit(0);      free_vector(gm,1,nlstate);
   }      free_matrix(gradg,1,npar,1,nlstate);
 #endif      free_matrix(trgradg,1,nlstate,1,npar);
 }    } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcov,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with gnuplot file: %s\n", optionfilegnuplot);
       fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);
       exit(0);
     }
     else{
       fprintf(ficgp,"\n# Routine varprob");
     }
     if((fichtm=fopen(optionfilehtm,"a"))==NULL) {
       printf("Problem with html file: %s\n", optionfilehtm);
       fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);
       exit(0);
     }
     else{
       fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
       fprintf(fichtm,"\n");
   
       fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");
       fprintf(fichtm,"\nWe have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
       fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");
   
     }
   
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(fichtm,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtm," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fclose(ficgp);
     fclose(fichtm);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
     /*char optionfilehtm[FILENAMELENGTH];*/
     if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
       fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);
     }
   
      fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n
    - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n
    - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n
    - Life expectancies by age and initial health status (estepm=%2d months): 
      <a href=\"e%s\">e%s</a> <br>\n</li>", \
     jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: pe%s%d1.png<br>
   <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>
   <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1); 
          /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>
   <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>
   <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and
   health expectancies in states (1) and (2): e%s%d.png<br>
   <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n
    - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n
    - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n
    - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n 
    - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n
    - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed and period prevalence (with confident
   interval) in state (%d): v%s%d%d.png <br>
   <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   fclose(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
     if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
       fprintf(ficlog,"Problem with file %s",optionfilegnuplot);
     }
   
     /*#ifdef windows */
       fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   m=pow(2,cptcoveff);
     
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Stable prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",fileres,k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",fileres,k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
         fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);
           
         } 
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fclose(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[80],pathc[80],pathcd[80],pathtot[80],model[80];
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     double jprev1=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];
    
     /* long total_usecs;
        struct timeval start_time, end_time;
     
        gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     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, 80)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     replace(pathc,path);
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s",version);
     fprintf(ficlog,"\nEnter the parameter file name: ");
     fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     fflush(ficlog);
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       goto end;
     }
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) {
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     
     /* Read guess parameters */
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
     param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     for(i=1; i <=nlstate; i++)
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         fprintf(ficparo,"%1d%1d",i1,j1);
         if(mle==1)
           printf("%1d%1d",i,j);
         fprintf(ficlog,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar," %lf",&param[i][j][k]);
           if(mle==1){
             printf(" %lf",param[i][j][k]);
             fprintf(ficlog," %lf",param[i][j][k]);
           }
           else
             fprintf(ficlog," %lf",param[i][j][k]);
           fprintf(ficparo," %lf",param[i][j][k]);
         }
         fscanf(ficpar,"\n");
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
     
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     p=param[1][1];
     
     /* Reads comments: lines beginning with '#' */
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     /* delti=vector(1,npar); *//* Scale of each paramater (output from hesscov) */
     for(i=1; i <=nlstate; i++){
       for(j=1; j <=nlstate+ndeath-1; j++){
         fscanf(ficpar,"%1d%1d",&i1,&j1);
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i1,j1);
         for(k=1; k<=ncovmodel;k++){
           fscanf(ficpar,"%le",&delti3[i][j][k]);
           printf(" %le",delti3[i][j][k]);
           fprintf(ficparo," %le",delti3[i][j][k]);
         }
         fscanf(ficpar,"\n");
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     delti=delti3[1][1];
   
   
     /* 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);
       puts(line);
       fputs(line,ficparo);
     }
     ungetc(c,ficpar);
     
     matcov=matrix(1,npar,1,npar);
     for(i=1; i <=npar; i++){
       fscanf(ficpar,"%s",&str);
       if(mle==1)
         printf("%s",str);
       fprintf(ficlog,"%s",str);
       fprintf(ficparo,"%s",str);
       for(j=1; j <=i; j++){
         fscanf(ficpar," %le",&matcov[i][j]);
         if(mle==1){
           printf(" %.5le",matcov[i][j]);
           fprintf(ficlog," %.5le",matcov[i][j]);
         }
         else
           fprintf(ficlog," %.5le",matcov[i][j]);
         fprintf(ficparo," %.5le",matcov[i][j]);
       }
       fscanf(ficpar,"\n");
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       fprintf(ficparo,"\n");
     }
     for(i=1; i <=npar; i++)
       for(j=i+1;j<=npar;j++)
         matcov[i][j]=matcov[j][i];
      
     if(mle==1)
       printf("\n");
     fprintf(ficlog,"\n");
   
   
     /*-------- Rewriting paramater file ----------*/
     strcpy(rfileres,"r");    /* "Rparameterfile */
     strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
     strcat(rfileres,".");    /* */
     strcat(rfileres,optionfilext);    /* Other files have txt extension */
     if((ficres =fopen(rfileres,"w"))==NULL) {
       printf("Problem writing new parameter file: %s\n", fileres);goto end;
       fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
     }
     fprintf(ficres,"#%s\n",version);
       
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=ivector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     while (fgets(line, MAXLINE, fic) != NULL)    {
       if ((i >= firstobs) && (i <=lastobs)) {
           
         for (j=maxwav;j>=1;j--){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb); 
           strcpy(line,stra);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         }
           
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);
         for (j=ncovcol;j>=1;j--){
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         } 
         num[i]=atol(stra);
           
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
   
         i=i+1;
       }
     }
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
    for (i=1; i<=imx; i++)
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameter from char model*/
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);
     fclose(fic);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((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 %d 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 %d 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 %d 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 %d 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: %d line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a
                                    month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((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("%d %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     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) */
   
     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_ivector(num,1,n);
     free_vector(agedc,1,n);
     /*free_matrix(covar,0,NCOVMAX,1,n);*/
     /*free_matrix(covar,1,NCOVMAX,1,n);*/
     fclose(ficparo);
     fclose(ficres);
   
   
     /*--------------- Prevalence limit  (stable prevalence) --------------*/
     
     strcpy(filerespl,"pl");
     strcat(filerespl,fileres);
     if((ficrespl=fopen(filerespl,"w"))==NULL) {
       printf("Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
       fprintf(ficlog,"Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
     }
     printf("Computing stable prevalence: result on file '%s' \n", filerespl);
     fprintf(ficlog,"Computing stable prevalence: result on file '%s' \n", filerespl);
     fprintf(ficrespl,"#Stable prevalence \n");
     fprintf(ficrespl,"#Age ");
     for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
     fprintf(ficrespl,"\n");
     
     prlim=matrix(1,nlstate,1,nlstate);
   
     agebase=ageminpar;
     agelim=agemaxpar;
     ftolpl=1.e-10;
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
   
     for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
         fprintf(ficrespl,"\n#******");
         printf("\n#******");
         fprintf(ficlog,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespl,"******\n");
         printf("******\n");
         fprintf(ficlog,"******\n");
           
         for (age=agebase; age<=agelim; age++){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
           fprintf(ficrespl,"%.0f ",age );
           for(j=1;j<=cptcoveff;j++)
             fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           for(i=1; i<=nlstate;i++)
             fprintf(ficrespl," %.5f", prlim[i][i]);
           fprintf(ficrespl,"\n");
         }
       }
     }
     fclose(ficrespl);
   
     /*------------- h Pij x at various ages ------------*/
     
     strcpy(filerespij,"pij");  strcat(filerespij,fileres);
     if((ficrespij=fopen(filerespij,"w"))==NULL) {
       printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
       fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
     }
     printf("Computing pij: result on file '%s' \n", filerespij);
     fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     /*if (stepm<=24) stepsize=2;*/
   
     agelim=AGESUP;
     hstepm=stepsize*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
     /* hstepm=1;   aff par mois*/
   
     fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
     for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
         k=k+1;
         fprintf(ficrespij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficrespij,"******\n");
           
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
           /*        nhstepm=nhstepm*YEARM; aff par mois*/
   
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           oldm=oldms;savm=savms;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
           for(i=1; i<=nlstate;i++)
             for(j=1; j<=nlstate+ndeath;j++)
               fprintf(ficrespij," %1d-%1d",i,j);
           fprintf(ficrespij,"\n");
           for (h=0; h<=nhstepm; h++){
             fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);
             fprintf(ficrespij,"\n");
           }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"\n");
         }
       }
     }
   
     varprob(optionfilefiname, matcov, p, delti, nlstate, 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 */
     
     /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/
     /*printf("Total time was %d uSec.\n", total_usecs);*/
     /*------ End -----------*/
   
     end:
   #ifdef windows
     /* chdir(pathcd);*/
   #endif 
    /*system("wgnuplot graph.plt");*/
    /*system("../gp37mgw/wgnuplot graph.plt");*/
    /*system("cd ../gp37mgw");*/
    /* system("..\\gp37mgw\\wgnuplot graph.plt");*/
     strcpy(plotcmd,GNUPLOTPROGRAM);
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting graphs with: %s",plotcmd);fflush(stdout);
     system(plotcmd);
     printf(" Wait...");
   
    /*#ifdef windows*/
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");
       scanf("%s",z);
       if (z[0] == 'c') system("./imach");
       else if (z[0] == 'e') system(optionfilehtm);
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     /*#endif */
   }
   
   

Removed from v.1.3  
changed lines
  Added in v.1.84


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