Diff for /imach/src/imach.c between versions 1.8 and 1.99

version 1.8, 2001/05/02 17:54:31 version 1.99, 2004/06/05 08:57:40
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 1.99  2004/06/05 08:57:40  brouard
   individuals from different ages are interviewed on their health status    *** empty log message ***
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.98  2004/05/16 15:05:56  brouard
   Health expectancies are computed from the transistions observed between    New version 0.97 . First attempt to estimate force of mortality
   waves and are computed for each degree of severity of disability (number    directly from the data i.e. without the need of knowing the health
   of life states). More degrees you consider, more time is necessary to    state at each age, but using a Gompertz model: log u =a + b*age .
   reach the Maximum Likelihood of the parameters involved in the model.    This is the basic analysis of mortality and should be done before any
   The simplest model is the multinomial logistic model where pij is    other analysis, in order to test if the mortality estimated from the
   the probabibility to be observed in state j at the second wave conditional    cross-longitudinal survey is different from the mortality estimated
   to be observed in state i at the first wave. Therefore the model is:    from other sources like vital statistic data.
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'  
   is a covariate. If you want to have a more complex model than "constant and    The same imach parameter file can be used but the option for mle should be -3.
   age", you should modify the program where the markup  
     *Covariates have to be included here again* invites you to do it.    Agnès, who wrote this part of the code, tried to keep most of the
   More covariates you add, less is the speed of the convergence.    former routines in order to include the new code within the former code.
   
   The advantage that this computer programme claims, comes from that if the    The output is very simple: only an estimate of the intercept and of
   delay between waves is not identical for each individual, or if some    the slope with 95% confident intervals.
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    Current limitations:
   hPijx is the probability to be    A) Even if you enter covariates, i.e. with the
   observed in state i at age x+h conditional to the observed state i at age    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   x. The delay 'h' can be split into an exact number (nh*stepm) of    B) There is no computation of Life Expectancy nor Life Table.
   unobserved intermediate  states. This elementary transition (by month or  
   quarter trimester, semester or year) is model as a multinomial logistic.    Revision 1.97  2004/02/20 13:25:42  lievre
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Version 0.96d. Population forecasting command line is (temporarily)
   and the contribution of each individual to the likelihood is simply hPijx.    suppressed.
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.96  2003/07/15 15:38:55  brouard
   of the life expectancies. It also computes the prevalence limits.    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
      rewritten within the same printf. Workaround: many printfs.
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).  
            Institut national d'études démographiques, Paris.    Revision 1.95  2003/07/08 07:54:34  brouard
   This software have been partly granted by Euro-REVES, a concerted action    * imach.c (Repository):
   from the European Union.    (Repository): Using imachwizard code to output a more meaningful covariance
   It is copyrighted identically to a GNU software product, ie programme and    matrix (cov(a12,c31) instead of numbers.
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.94  2003/06/27 13:00:02  brouard
   **********************************************************************/    Just cleaning
    
 #include <math.h>    Revision 1.93  2003/06/25 16:33:55  brouard
 #include <stdio.h>    (Module): On windows (cygwin) function asctime_r doesn't
 #include <stdlib.h>    exist so I changed back to asctime which exists.
 #include <unistd.h>    (Module): Version 0.96b
   
 #define MAXLINE 256    Revision 1.92  2003/06/25 16:30:45  brouard
 #define FILENAMELENGTH 80    (Module): On windows (cygwin) function asctime_r doesn't
 /*#define DEBUG*/    exist so I changed back to asctime which exists.
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.91  2003/06/25 15:30:29  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    * imach.c (Repository): Duplicated warning errors corrected.
     (Repository): Elapsed time after each iteration is now output. It
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    helps to forecast when convergence will be reached. Elapsed time
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.90  2003/06/24 12:34:15  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    (Module): Some bugs corrected for windows. Also, when
 #define NCOVMAX 8 /* Maximum number of covariates */    mle=-1 a template is output in file "or"mypar.txt with the design
 #define MAXN 20000    of the covariance matrix to be input.
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.89  2003/06/24 12:30:52  brouard
 #define AGEBASE 40    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Revision 1.88  2003/06/23 17:54:56  brouard
 int npar=NPARMAX;    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.87  2003/06/18 12:26:01  brouard
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Version 0.96
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.86  2003/06/17 20:04:08  brouard
 int maxwav; /* Maxim number of waves */    (Module): Change position of html and gnuplot routines and added
 int jmin, jmax; /* min, max spacing between 2 waves */    routine fileappend.
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.85  2003/06/17 13:12:43  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    * imach.c (Repository): Check when date of death was earlier that
 double jmean; /* Mean space between 2 waves */    current date of interview. It may happen when the death was just
 double **oldm, **newm, **savm; /* Working pointers to matrices */    prior to the death. In this case, dh was negative and likelihood
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    was wrong (infinity). We still send an "Error" but patch by
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    assuming that the date of death was just one stepm after the
 FILE *ficgp, *fichtm;    interview.
 FILE *ficreseij;    (Repository): Because some people have very long ID (first column)
   char filerese[FILENAMELENGTH];    we changed int to long in num[] and we added a new lvector for
  FILE  *ficresvij;    memory allocation. But we also truncated to 8 characters (left
   char fileresv[FILENAMELENGTH];    truncation)
  FILE  *ficresvpl;    (Repository): No more line truncation errors.
   char fileresvpl[FILENAMELENGTH];  
     Revision 1.84  2003/06/13 21:44:43  brouard
 #define NR_END 1    * imach.c (Repository): Replace "freqsummary" at a correct
 #define FREE_ARG char*    place. It differs from routine "prevalence" which may be called
 #define FTOL 1.0e-10    many times. Probs is memory consuming and must be used with
     parcimony.
 #define NRANSI    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 #define ITMAX 200  
     Revision 1.83  2003/06/10 13:39:11  lievre
 #define TOL 2.0e-4    *** empty log message ***
   
 #define CGOLD 0.3819660    Revision 1.82  2003/06/05 15:57:20  brouard
 #define ZEPS 1.0e-10    Add log in  imach.c and  fullversion number is now printed.
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
   */
 #define GOLD 1.618034  /*
 #define GLIMIT 100.0     Interpolated Markov Chain
 #define TINY 1.0e-20  
     Short summary of the programme:
 static double maxarg1,maxarg2;    
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    This program computes Healthy Life Expectancies from
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
      first survey ("cross") where individuals from different ages are
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    interviewed on their health status or degree of disability (in the
 #define rint(a) floor(a+0.5)    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
 static double sqrarg;    (if any) in individual health status.  Health expectancies are
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    computed from the time spent in each health state according to a
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    model. More health states you consider, more time is necessary to reach the
     Maximum Likelihood of the parameters involved in the model.  The
 int imx;    simplest model is the multinomial logistic model where pij is the
 int stepm;    probability to be observed in state j at the second wave
 /* Stepm, step in month: minimum step interpolation*/    conditional to be observed in state i at the first wave. Therefore
     the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 int m,nb;    'age' is age and 'sex' is a covariate. If you want to have a more
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    complex model than "constant and age", you should modify the program
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    where the markup *Covariates have to be included here again* invites
 double **pmmij;    you to do it.  More covariates you add, slower the
     convergence.
 double *weight;  
 int **s; /* Status */    The advantage of this computer programme, compared to a simple
 double *agedc, **covar, idx;    multinomial logistic model, is clear when the delay between waves is not
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    identical for each individual. Also, if a individual missed an
     intermediate interview, the information is lost, but taken into
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    account using an interpolation or extrapolation.  
 double ftolhess; /* Tolerance for computing hessian */  
     hPijx is the probability to be observed in state i at age x+h
 /**************** split *************************/    conditional to the observed state i at age x. The delay 'h' can be
 static  int split( char *path, char *dirc, char *name )    split into an exact number (nh*stepm) of unobserved intermediate
 {    states. This elementary transition (by month, quarter,
    char *s;                             /* pointer */    semester or year) is modelled as a multinomial logistic.  The hPx
    int  l1, l2;                         /* length counters */    matrix is simply the matrix product of nh*stepm elementary matrices
     and the contribution of each individual to the likelihood is simply
    l1 = strlen( path );                 /* length of path */    hPijx.
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  
    s = strrchr( path, '\\' );           /* find last / */    Also this programme outputs the covariance matrix of the parameters but also
    if ( s == NULL ) {                   /* no directory, so use current */    of the life expectancies. It also computes the stable prevalence. 
 #if     defined(__bsd__)                /* get current working directory */    
       extern char       *getwd( );    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
              Institut national d'études démographiques, Paris.
       if ( getwd( dirc ) == NULL ) {    This software have been partly granted by Euro-REVES, a concerted action
 #else    from the European Union.
       extern char       *getcwd( );    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    can be accessed at http://euroreves.ined.fr/imach .
 #endif  
          return( GLOCK_ERROR_GETCWD );    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
       }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
       strcpy( name, path );             /* we've got it */    
    } else {                             /* strip direcotry from path */    **********************************************************************/
       s++;                              /* after this, the filename */  /*
       l2 = strlen( s );                 /* length of filename */    main
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    read parameterfile
       strcpy( name, s );                /* save file name */    read datafile
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    concatwav
       dirc[l1-l2] = 0;                  /* add zero */    freqsummary
    }    if (mle >= 1)
    l1 = strlen( dirc );                 /* length of directory */      mlikeli
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    print results files
    return( 0 );                         /* we're done */    if mle==1 
 }       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
         begin-prev-date,...
 /******************************************/    open gnuplot file
     open html file
 void replace(char *s, char*t)    stable prevalence
 {     for age prevalim()
   int i;    h Pij x
   int lg=20;    variance of p varprob
   i=0;    forecasting if prevfcast==1 prevforecast call prevalence()
   lg=strlen(t);    health expectancies
   for(i=0; i<= lg; i++) {    Variance-covariance of DFLE
     (s[i] = t[i]);    prevalence()
     if (t[i]== '\\') s[i]='/';     movingaverage()
   }    varevsij() 
 }    if popbased==1 varevsij(,popbased)
     total life expectancies
 int nbocc(char *s, char occ)    Variance of stable prevalence
 {   end
   int i,j=0;  */
   int lg=20;  
   i=0;  
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {   
   if  (s[i] == occ ) j++;  #include <math.h>
   }  #include <stdio.h>
   return j;  #include <stdlib.h>
 }  #include <unistd.h>
   
 void cutv(char *u,char *v, char*t, char occ)  /* #include <sys/time.h> */
 {  #include <time.h>
   int i,lg,j,p=0;  #include "timeval.h"
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {  /* #include <libintl.h> */
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  /* #define _(String) gettext (String) */
   }  
   #define MAXLINE 256
   lg=strlen(t);  #define GNUPLOTPROGRAM "gnuplot"
   for(j=0; j<p; j++) {  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
     (u[j] = t[j]);  #define FILENAMELENGTH 132
   }  /*#define DEBUG*/
      u[p]='\0';  /*#define windows*/
   #define GLOCK_ERROR_NOPATH              -1      /* empty path */
    for(j=0; j<= lg; j++) {  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 }  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   
 /********************** nrerror ********************/  #define NINTERVMAX 8
   #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 void nrerror(char error_text[])  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 {  #define NCOVMAX 8 /* Maximum number of covariates */
   fprintf(stderr,"ERREUR ...\n");  #define MAXN 20000
   fprintf(stderr,"%s\n",error_text);  #define YEARM 12. /* Number of months per year */
   exit(1);  #define AGESUP 130
 }  #define AGEBASE 40
 /*********************** vector *******************/  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 double *vector(int nl, int nh)  #ifdef unix
 {  #define DIRSEPARATOR '/'
   double *v;  #define ODIRSEPARATOR '\\'
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #else
   if (!v) nrerror("allocation failure in vector");  #define DIRSEPARATOR '\\'
   return v-nl+NR_END;  #define ODIRSEPARATOR '/'
 }  #endif
   
 /************************ free vector ******************/  /* $Id$ */
 void free_vector(double*v, int nl, int nh)  /* $State$ */
 {  
   free((FREE_ARG)(v+nl-NR_END));  char version[]="Imach version 0.97b, May 2004, INED-EUROREVES ";
 }  char fullversion[]="$Revision$ $Date$"; 
   int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 /************************ivector *******************************/  int nvar;
 int *ivector(long nl,long nh)  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
 {  int npar=NPARMAX;
   int *v;  int nlstate=2; /* Number of live states */
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  int ndeath=1; /* Number of dead states */
   if (!v) nrerror("allocation failure in ivector");  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   return v-nl+NR_END;  int popbased=0;
 }  
   int *wav; /* Number of waves for this individuual 0 is possible */
 /******************free ivector **************************/  int maxwav; /* Maxim number of waves */
 void free_ivector(int *v, long nl, long nh)  int jmin, jmax; /* min, max spacing between 2 waves */
 {  int gipmx, gsw; /* Global variables on the number of contributions 
   free((FREE_ARG)(v+nl-NR_END));                     to the likelihood and the sum of weights (done by funcone)*/
 }  int mle, weightopt;
   int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 /******************* imatrix *******************************/  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
 int **imatrix(long nrl, long nrh, long ncl, long nch)  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */             * wave mi and wave mi+1 is not an exact multiple of stepm. */
 {  double jmean; /* Mean space between 2 waves */
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  double **oldm, **newm, **savm; /* Working pointers to matrices */
   int **m;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
    FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   /* allocate pointers to rows */  FILE *ficlog, *ficrespow;
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  int globpr; /* Global variable for printing or not */
   if (!m) nrerror("allocation failure 1 in matrix()");  double fretone; /* Only one call to likelihood */
   m += NR_END;  long ipmx; /* Number of contributions */
   m -= nrl;  double sw; /* Sum of weights */
    char filerespow[FILENAMELENGTH];
    char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   /* allocate rows and set pointers to them */  FILE *ficresilk;
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  FILE *ficresprobmorprev;
   m[nrl] += NR_END;  FILE *fichtm, *fichtmcov; /* Html File */
   m[nrl] -= ncl;  FILE *ficreseij;
    char filerese[FILENAMELENGTH];
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  FILE  *ficresvij;
    char fileresv[FILENAMELENGTH];
   /* return pointer to array of pointers to rows */  FILE  *ficresvpl;
   return m;  char fileresvpl[FILENAMELENGTH];
 }  char title[MAXLINE];
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 /****************** free_imatrix *************************/  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
 void free_imatrix(m,nrl,nrh,ncl,nch)  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
       int **m;  char command[FILENAMELENGTH];
       long nch,ncl,nrh,nrl;  int  outcmd=0;
      /* free an int matrix allocated by imatrix() */  
 {  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));  char filelog[FILENAMELENGTH]; /* Log file */
 }  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 /******************* matrix *******************************/  char popfile[FILENAMELENGTH];
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  
   double **m;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   struct timezone tzp;
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  extern int gettimeofday();
   if (!m) nrerror("allocation failure 1 in matrix()");  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   m += NR_END;  long time_value;
   m -= nrl;  extern long time();
   char strcurr[80], strfor[80];
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define NR_END 1
   m[nrl] += NR_END;  #define FREE_ARG char*
   m[nrl] -= ncl;  #define FTOL 1.0e-10
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define NRANSI 
   return m;  #define ITMAX 200 
 }  
   #define TOL 2.0e-4 
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #define CGOLD 0.3819660 
 {  #define ZEPS 1.0e-10 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   free((FREE_ARG)(m+nrl-NR_END));  
 }  #define GOLD 1.618034 
   #define GLIMIT 100.0 
 /******************* ma3x *******************************/  #define TINY 1.0e-20 
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  
 {  static double maxarg1,maxarg2;
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   double ***m;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   if (!m) nrerror("allocation failure 1 in matrix()");  #define rint(a) floor(a+0.5)
   m += NR_END;  
   m -= nrl;  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  int agegomp= AGEGOMP;
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  int imx; 
   int stepm=1;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  /* Stepm, step in month: minimum step interpolation*/
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  int estepm;
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  int m,nb;
   for (j=ncl+1; j<=nch; j++)  long *num;
     m[nrl][j]=m[nrl][j-1]+nlay;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
    double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   for (i=nrl+1; i<=nrh; i++) {  double **pmmij, ***probs;
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  double *ageexmed,*agecens;
     for (j=ncl+1; j<=nch; j++)  double dateintmean=0;
       m[i][j]=m[i][j-1]+nlay;  
   }  double *weight;
   return m;  int **s; /* Status */
 }  double *agedc, **covar, idx;
   int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 {  double ftolhess; /* Tolerance for computing hessian */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  /**************** split *************************/
   free((FREE_ARG)(m+nrl-NR_END));  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 }  {
     /* From a file name with full path (either Unix or Windows) we extract the directory (dirc)
 /***************** f1dim *************************/       the name of the file (name), its extension only (ext) and its first part of the name (finame)
 extern int ncom;    */ 
 extern double *pcom,*xicom;    char  *ss;                            /* pointer */
 extern double (*nrfunc)(double []);    int   l1, l2;                         /* length counters */
    
 double f1dim(double x)    l1 = strlen(path );                   /* length of path */
 {    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   int j;    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   double f;    if ( ss == NULL ) {                   /* no directory, so use current */
   double *xt;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
          printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   xt=vector(1,ncom);      /* get current working directory */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];      /*    extern  char* getcwd ( char *buf , int len);*/
   f=(*nrfunc)(xt);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   free_vector(xt,1,ncom);        return( GLOCK_ERROR_GETCWD );
   return f;      }
 }      strcpy( name, path );               /* we've got it */
     } else {                              /* strip direcotry from path */
 /*****************brent *************************/      ss++;                               /* after this, the filename */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)      l2 = strlen( ss );                  /* length of filename */
 {      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   int iter;      strcpy( name, ss );         /* save file name */
   double a,b,d,etemp;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   double fu,fv,fw,fx;      dirc[l1-l2] = 0;                    /* add zero */
   double ftemp;    }
   double p,q,r,tol1,tol2,u,v,w,x,xm;    l1 = strlen( dirc );                  /* length of directory */
   double e=0.0;    /*#ifdef windows
      if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   a=(ax < cx ? ax : cx);  #else
   b=(ax > cx ? ax : cx);    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
   x=w=v=bx;  #endif
   fw=fv=fx=(*f)(x);    */
   for (iter=1;iter<=ITMAX;iter++) {    ss = strrchr( name, '.' );            /* find last / */
     xm=0.5*(a+b);    if (ss >0){
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);      ss++;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/      strcpy(ext,ss);                     /* save extension */
     printf(".");fflush(stdout);      l1= strlen( name);
 #ifdef DEBUG      l2= strlen(ss)+1;
     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);      strncpy( finame, name, l1-l2);
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */      finame[l1-l2]= 0;
 #endif    }
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    return( 0 );                          /* we're done */
       *xmin=x;  }
       return fx;  
     }  
     ftemp=fu;  /******************************************/
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  void replace_back_to_slash(char *s, char*t)
       q=(x-v)*(fx-fw);  {
       p=(x-v)*q-(x-w)*r;    int i;
       q=2.0*(q-r);    int lg=0;
       if (q > 0.0) p = -p;    i=0;
       q=fabs(q);    lg=strlen(t);
       etemp=e;    for(i=0; i<= lg; i++) {
       e=d;      (s[i] = t[i]);
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))      if (t[i]== '\\') s[i]='/';
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    }
       else {  }
         d=p/q;  
         u=x+d;  int nbocc(char *s, char occ)
         if (u-a < tol2 || b-u < tol2)  {
           d=SIGN(tol1,xm-x);    int i,j=0;
       }    int lg=20;
     } else {    i=0;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    lg=strlen(s);
     }    for(i=0; i<= lg; i++) {
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    if  (s[i] == occ ) j++;
     fu=(*f)(u);    }
     if (fu <= fx) {    return j;
       if (u >= x) a=x; else b=x;  }
       SHFT(v,w,x,u)  
         SHFT(fv,fw,fx,fu)  void cutv(char *u,char *v, char*t, char occ)
         } else {  {
           if (u < x) a=u; else b=u;    /* cuts string t into u and v where u is ended by char occ excluding it
           if (fu <= fw || w == x) {       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
             v=w;       gives u="abcedf" and v="ghi2j" */
             w=u;    int i,lg,j,p=0;
             fv=fw;    i=0;
             fw=fu;    for(j=0; j<=strlen(t)-1; j++) {
           } else if (fu <= fv || v == x || v == w) {      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
             v=u;    }
             fv=fu;  
           }    lg=strlen(t);
         }    for(j=0; j<p; j++) {
   }      (u[j] = t[j]);
   nrerror("Too many iterations in brent");    }
   *xmin=x;       u[p]='\0';
   return fx;  
 }     for(j=0; j<= lg; j++) {
       if (j>=(p+1))(v[j-p-1] = t[j]);
 /****************** mnbrak ***********************/    }
   }
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  /********************** nrerror ********************/
 {  
   double ulim,u,r,q, dum;  void nrerror(char error_text[])
   double fu;  {
      fprintf(stderr,"ERREUR ...\n");
   *fa=(*func)(*ax);    fprintf(stderr,"%s\n",error_text);
   *fb=(*func)(*bx);    exit(EXIT_FAILURE);
   if (*fb > *fa) {  }
     SHFT(dum,*ax,*bx,dum)  /*********************** vector *******************/
       SHFT(dum,*fb,*fa,dum)  double *vector(int nl, int nh)
       }  {
   *cx=(*bx)+GOLD*(*bx-*ax);    double *v;
   *fc=(*func)(*cx);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   while (*fb > *fc) {    if (!v) nrerror("allocation failure in vector");
     r=(*bx-*ax)*(*fb-*fc);    return v-nl+NR_END;
     q=(*bx-*cx)*(*fb-*fa);  }
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  /************************ free vector ******************/
     ulim=(*bx)+GLIMIT*(*cx-*bx);  void free_vector(double*v, int nl, int nh)
     if ((*bx-u)*(u-*cx) > 0.0) {  {
       fu=(*func)(u);    free((FREE_ARG)(v+nl-NR_END));
     } else if ((*cx-u)*(u-ulim) > 0.0) {  }
       fu=(*func)(u);  
       if (fu < *fc) {  /************************ivector *******************************/
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  int *ivector(long nl,long nh)
           SHFT(*fb,*fc,fu,(*func)(u))  {
           }    int *v;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       u=ulim;    if (!v) nrerror("allocation failure in ivector");
       fu=(*func)(u);    return v-nl+NR_END;
     } else {  }
       u=(*cx)+GOLD*(*cx-*bx);  
       fu=(*func)(u);  /******************free ivector **************************/
     }  void free_ivector(int *v, long nl, long nh)
     SHFT(*ax,*bx,*cx,u)  {
       SHFT(*fa,*fb,*fc,fu)    free((FREE_ARG)(v+nl-NR_END));
       }  }
 }  
   /************************lvector *******************************/
 /*************** linmin ************************/  long *lvector(long nl,long nh)
   {
 int ncom;    long *v;
 double *pcom,*xicom;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
 double (*nrfunc)(double []);    if (!v) nrerror("allocation failure in ivector");
      return v-nl+NR_END;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  }
 {  
   double brent(double ax, double bx, double cx,  /******************free lvector **************************/
                double (*f)(double), double tol, double *xmin);  void free_lvector(long *v, long nl, long nh)
   double f1dim(double x);  {
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    free((FREE_ARG)(v+nl-NR_END));
               double *fc, double (*func)(double));  }
   int j;  
   double xx,xmin,bx,ax;  /******************* imatrix *******************************/
   double fx,fb,fa;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   ncom=n;  { 
   pcom=vector(1,n);    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   xicom=vector(1,n);    int **m; 
   nrfunc=func;    
   for (j=1;j<=n;j++) {    /* allocate pointers to rows */ 
     pcom[j]=p[j];    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     xicom[j]=xi[j];    if (!m) nrerror("allocation failure 1 in matrix()"); 
   }    m += NR_END; 
   ax=0.0;    m -= nrl; 
   xx=1.0;    
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    /* allocate rows and set pointers to them */ 
 #ifdef DEBUG    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 #endif    m[nrl] += NR_END; 
   for (j=1;j<=n;j++) {    m[nrl] -= ncl; 
     xi[j] *= xmin;    
     p[j] += xi[j];    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   }    
   free_vector(xicom,1,n);    /* return pointer to array of pointers to rows */ 
   free_vector(pcom,1,n);    return m; 
 }  } 
   
 /*************** powell ************************/  /****************** free_imatrix *************************/
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  void free_imatrix(m,nrl,nrh,ncl,nch)
             double (*func)(double []))        int **m;
 {        long nch,ncl,nrh,nrl; 
   void linmin(double p[], double xi[], int n, double *fret,       /* free an int matrix allocated by imatrix() */ 
               double (*func)(double []));  { 
   int i,ibig,j;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   double del,t,*pt,*ptt,*xit;    free((FREE_ARG) (m+nrl-NR_END)); 
   double fp,fptt;  } 
   double *xits;  
   pt=vector(1,n);  /******************* matrix *******************************/
   ptt=vector(1,n);  double **matrix(long nrl, long nrh, long ncl, long nch)
   xit=vector(1,n);  {
   xits=vector(1,n);    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   *fret=(*func)(p);    double **m;
   for (j=1;j<=n;j++) pt[j]=p[j];  
   for (*iter=1;;++(*iter)) {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     fp=(*fret);    if (!m) nrerror("allocation failure 1 in matrix()");
     ibig=0;    m += NR_END;
     del=0.0;    m -= nrl;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       printf(" %d %.12f",i, p[i]);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     printf("\n");    m[nrl] += NR_END;
     for (i=1;i<=n;i++) {    m[nrl] -= ncl;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 #ifdef DEBUG    return m;
       printf("fret=%lf \n",*fret);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
 #endif     */
       printf("%d",i);fflush(stdout);  }
       linmin(p,xit,n,fret,func);  
       if (fabs(fptt-(*fret)) > del) {  /*************************free matrix ************************/
         del=fabs(fptt-(*fret));  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         ibig=i;  {
       }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 #ifdef DEBUG    free((FREE_ARG)(m+nrl-NR_END));
       printf("%d %.12e",i,(*fret));  }
       for (j=1;j<=n;j++) {  
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  /******************* ma3x *******************************/
         printf(" x(%d)=%.12e",j,xit[j]);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       }  {
       for(j=1;j<=n;j++)    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
         printf(" p=%.12e",p[j]);    double ***m;
       printf("\n");  
 #endif    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     }    if (!m) nrerror("allocation failure 1 in matrix()");
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    m += NR_END;
 #ifdef DEBUG    m -= nrl;
       int k[2],l;  
       k[0]=1;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       k[1]=-1;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       printf("Max: %.12e",(*func)(p));    m[nrl] += NR_END;
       for (j=1;j<=n;j++)    m[nrl] -= ncl;
         printf(" %.12e",p[j]);  
       printf("\n");    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       for(l=0;l<=1;l++) {  
         for (j=1;j<=n;j++) {    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    m[nrl][ncl] += NR_END;
         }    m[nrl][ncl] -= nll;
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    for (j=ncl+1; j<=nch; j++) 
       }      m[nrl][j]=m[nrl][j-1]+nlay;
 #endif    
     for (i=nrl+1; i<=nrh; i++) {
       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       free_vector(xit,1,n);      for (j=ncl+1; j<=nch; j++) 
       free_vector(xits,1,n);        m[i][j]=m[i][j-1]+nlay;
       free_vector(ptt,1,n);    }
       free_vector(pt,1,n);    return m; 
       return;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     }             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    */
     for (j=1;j<=n;j++) {  }
       ptt[j]=2.0*p[j]-pt[j];  
       xit[j]=p[j]-pt[j];  /*************************free ma3x ************************/
       pt[j]=p[j];  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     }  {
     fptt=(*func)(ptt);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     if (fptt < fp) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    free((FREE_ARG)(m+nrl-NR_END));
       if (t < 0.0) {  }
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {  /*************** function subdirf ***********/
           xi[j][ibig]=xi[j][n];  char *subdirf(char fileres[])
           xi[j][n]=xit[j];  {
         }    /* Caution optionfilefiname is hidden */
 #ifdef DEBUG    strcpy(tmpout,optionfilefiname);
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    strcat(tmpout,"/"); /* Add to the right */
         for(j=1;j<=n;j++)    strcat(tmpout,fileres);
           printf(" %.12e",xit[j]);    return tmpout;
         printf("\n");  }
 #endif  
       }  /*************** function subdirf2 ***********/
     }  char *subdirf2(char fileres[], char *preop)
   }  {
 }    
     /* Caution optionfilefiname is hidden */
 /**** Prevalence limit ****************/    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    strcat(tmpout,preop);
 {    strcat(tmpout,fileres);
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    return tmpout;
      matrix by transitions matrix until convergence is reached */  }
   
   int i, ii,j,k;  /*************** function subdirf3 ***********/
   double min, max, maxmin, maxmax,sumnew=0.;  char *subdirf3(char fileres[], char *preop, char *preop2)
   double **matprod2();  {
   double **out, cov[NCOVMAX], **pmij();    
   double **newm;    /* Caution optionfilefiname is hidden */
   double agefin, delaymax=50 ; /* Max number of years to converge */    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
   for (ii=1;ii<=nlstate+ndeath;ii++)    strcat(tmpout,preop);
     for (j=1;j<=nlstate+ndeath;j++){    strcat(tmpout,preop2);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    strcat(tmpout,fileres);
     }    return tmpout;
   }
    cov[1]=1.;  
    /***************** f1dim *************************/
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  extern int ncom; 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  extern double *pcom,*xicom;
     newm=savm;  extern double (*nrfunc)(double []); 
     /* Covariates have to be included here again */   
      cov[2]=agefin;  double f1dim(double x) 
    { 
       for (k=1; k<=cptcovn;k++) {    int j; 
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    double f;
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    double *xt; 
       }   
       for (k=1; k<=cptcovage;k++)    xt=vector(1,ncom); 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       for (k=1; k<=cptcovprod;k++)    f=(*nrfunc)(xt); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    free_vector(xt,1,ncom); 
     return f; 
       /*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]);*/  
   /*****************brent *************************/
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   { 
     savm=oldm;    int iter; 
     oldm=newm;    double a,b,d,etemp;
     maxmax=0.;    double fu,fv,fw,fx;
     for(j=1;j<=nlstate;j++){    double ftemp;
       min=1.;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       max=0.;    double e=0.0; 
       for(i=1; i<=nlstate; i++) {   
         sumnew=0;    a=(ax < cx ? ax : cx); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    b=(ax > cx ? ax : cx); 
         prlim[i][j]= newm[i][j]/(1-sumnew);    x=w=v=bx; 
         max=FMAX(max,prlim[i][j]);    fw=fv=fx=(*f)(x); 
         min=FMIN(min,prlim[i][j]);    for (iter=1;iter<=ITMAX;iter++) { 
       }      xm=0.5*(a+b); 
       maxmin=max-min;      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       maxmax=FMAX(maxmax,maxmin);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     }      printf(".");fflush(stdout);
     if(maxmax < ftolpl){      fprintf(ficlog,".");fflush(ficlog);
       return prlim;  #ifdef DEBUG
     }      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   }      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
 }      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   #endif
 /*************** transition probabilities **********/      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
         *xmin=x; 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )        return fx; 
 {      } 
   double s1, s2;      ftemp=fu;
   /*double t34;*/      if (fabs(e) > tol1) { 
   int i,j,j1, nc, ii, jj;        r=(x-w)*(fx-fv); 
         q=(x-v)*(fx-fw); 
     for(i=1; i<= nlstate; i++){        p=(x-v)*q-(x-w)*r; 
     for(j=1; j<i;j++){        q=2.0*(q-r); 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        if (q > 0.0) p = -p; 
         /*s2 += param[i][j][nc]*cov[nc];*/        q=fabs(q); 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];        etemp=e; 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/        e=d; 
       }        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
       ps[i][j]=s2;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/        else { 
     }          d=p/q; 
     for(j=i+1; j<=nlstate+ndeath;j++){          u=x+d; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){          if (u-a < tol2 || b-u < tol2) 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];            d=SIGN(tol1,xm-x); 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/        } 
       }      } else { 
       ps[i][j]=s2;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     }      } 
   }      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   for(i=1; i<= nlstate; i++){      fu=(*f)(u); 
      s1=0;      if (fu <= fx) { 
     for(j=1; j<i; j++)        if (u >= x) a=x; else b=x; 
       s1+=exp(ps[i][j]);        SHFT(v,w,x,u) 
     for(j=i+1; j<=nlstate+ndeath; j++)          SHFT(fv,fw,fx,fu) 
       s1+=exp(ps[i][j]);          } else { 
     ps[i][i]=1./(s1+1.);            if (u < x) a=u; else b=u; 
     for(j=1; j<i; j++)            if (fu <= fw || w == x) { 
       ps[i][j]= exp(ps[i][j])*ps[i][i];              v=w; 
     for(j=i+1; j<=nlstate+ndeath; j++)              w=u; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];              fv=fw; 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */              fw=fu; 
   } /* end i */            } else if (fu <= fv || v == x || v == w) { 
               v=u; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){              fv=fu; 
     for(jj=1; jj<= nlstate+ndeath; jj++){            } 
       ps[ii][jj]=0;          } 
       ps[ii][ii]=1;    } 
     }    nrerror("Too many iterations in brent"); 
   }    *xmin=x; 
     return fx; 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  } 
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /****************** mnbrak ***********************/
    }  
     printf("\n ");  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
     }              double (*func)(double)) 
     printf("\n ");printf("%lf ",cov[2]);*/  { 
 /*    double ulim,u,r,q, dum;
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    double fu; 
   goto end;*/   
     return ps;    *fa=(*func)(*ax); 
 }    *fb=(*func)(*bx); 
     if (*fb > *fa) { 
 /**************** Product of 2 matrices ******************/      SHFT(dum,*ax,*bx,dum) 
         SHFT(dum,*fb,*fa,dum) 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)        } 
 {    *cx=(*bx)+GOLD*(*bx-*ax); 
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    *fc=(*func)(*cx); 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    while (*fb > *fc) { 
   /* in, b, out are matrice of pointers which should have been initialized      r=(*bx-*ax)*(*fb-*fc); 
      before: only the contents of out is modified. The function returns      q=(*bx-*cx)*(*fb-*fa); 
      a pointer to pointers identical to out */      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   long i, j, k;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   for(i=nrl; i<= nrh; i++)      ulim=(*bx)+GLIMIT*(*cx-*bx); 
     for(k=ncolol; k<=ncoloh; k++)      if ((*bx-u)*(u-*cx) > 0.0) { 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        fu=(*func)(u); 
         out[i][k] +=in[i][j]*b[j][k];      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         fu=(*func)(u); 
   return out;        if (fu < *fc) { 
 }          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
             } 
 /************* Higher Matrix Product ***************/      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
         u=ulim; 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )        fu=(*func)(u); 
 {      } else { 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        u=(*cx)+GOLD*(*cx-*bx); 
      duration (i.e. until        fu=(*func)(u); 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.      } 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step      SHFT(*ax,*bx,*cx,u) 
      (typically every 2 years instead of every month which is too big).        SHFT(*fa,*fb,*fc,fu) 
      Model is determined by parameters x and covariates have to be        } 
      included manually here.  } 
   
      */  /*************** linmin ************************/
   
   int i, j, d, h, k;  int ncom; 
   double **out, cov[NCOVMAX];  double *pcom,*xicom;
   double **newm;  double (*nrfunc)(double []); 
    
   /* Hstepm could be zero and should return the unit matrix */  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for (i=1;i<=nlstate+ndeath;i++)  { 
     for (j=1;j<=nlstate+ndeath;j++){    double brent(double ax, double bx, double cx, 
       oldm[i][j]=(i==j ? 1.0 : 0.0);                 double (*f)(double), double tol, double *xmin); 
       po[i][j][0]=(i==j ? 1.0 : 0.0);    double f1dim(double x); 
     }    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */                double *fc, double (*func)(double)); 
   for(h=1; h <=nhstepm; h++){    int j; 
     for(d=1; d <=hstepm; d++){    double xx,xmin,bx,ax; 
       newm=savm;    double fx,fb,fa;
       /* Covariates have to be included here again */   
       cov[1]=1.;    ncom=n; 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    pcom=vector(1,n); 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    xicom=vector(1,n); 
 for (k=1; k<=cptcovage;k++)    nrfunc=func; 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    for (j=1;j<=n;j++) { 
    for (k=1; k<=cptcovprod;k++)      pcom[j]=p[j]; 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      xicom[j]=xi[j]; 
     } 
     ax=0.0; 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    xx=1.0; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  #ifdef DEBUG
       savm=oldm;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       oldm=newm;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     }  #endif
     for(i=1; i<=nlstate+ndeath; i++)    for (j=1;j<=n;j++) { 
       for(j=1;j<=nlstate+ndeath;j++) {      xi[j] *= xmin; 
         po[i][j][h]=newm[i][j];      p[j] += xi[j]; 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    } 
          */    free_vector(xicom,1,n); 
       }    free_vector(pcom,1,n); 
   } /* end h */  } 
   return po;  
 }  char *asc_diff_time(long time_sec, char ascdiff[])
   {
     long sec_left, days, hours, minutes;
 /*************** log-likelihood *************/    days = (time_sec) / (60*60*24);
 double func( double *x)    sec_left = (time_sec) % (60*60*24);
 {    hours = (sec_left) / (60*60) ;
   int i, ii, j, k, mi, d, kk;    sec_left = (sec_left) %(60*60);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    minutes = (sec_left) /60;
   double **out;    sec_left = (sec_left) % (60);
   double sw; /* Sum of weights */    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   double lli; /* Individual log likelihood */    return ascdiff;
   long ipmx;  }
   /*extern weight */  
   /* We are differentiating ll according to initial status */  /*************** powell ************************/
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   /*for(i=1;i<imx;i++)              double (*func)(double [])) 
     printf(" %d\n",s[4][i]);  { 
   */    void linmin(double p[], double xi[], int n, double *fret, 
   cov[1]=1.;                double (*func)(double [])); 
     int i,ibig,j; 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    double del,t,*pt,*ptt,*xit;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    double fp,fptt;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    double *xits;
     for(mi=1; mi<= wav[i]-1; mi++){    int niterf, itmp;
       for (ii=1;ii<=nlstate+ndeath;ii++)  
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    pt=vector(1,n); 
       for(d=0; d<dh[mi][i]; d++){    ptt=vector(1,n); 
         newm=savm;    xit=vector(1,n); 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    xits=vector(1,n); 
         for (kk=1; kk<=cptcovage;kk++) {    *fret=(*func)(p); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    for (j=1;j<=n;j++) pt[j]=p[j]; 
         }    for (*iter=1;;++(*iter)) { 
              fp=(*fret); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      ibig=0; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));      del=0.0; 
         savm=oldm;      last_time=curr_time;
         oldm=newm;      (void) gettimeofday(&curr_time,&tzp);
              printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
              /*    fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);
       } /* end mult */      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
            */
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);     for (i=1;i<=n;i++) {
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        printf(" %d %.12f",i, p[i]);
       ipmx +=1;        fprintf(ficlog," %d %.12lf",i, p[i]);
       sw += weight[i];        fprintf(ficrespow," %.12lf", p[i]);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;      }
     } /* end of wave */      printf("\n");
   } /* end of individual */      fprintf(ficlog,"\n");
       fprintf(ficrespow,"\n");fflush(ficrespow);
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      if(*iter <=3){
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */        tm = *localtime(&curr_time.tv_sec);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */        strcpy(strcurr,asctime(&tmf));
   return -l;  /*       asctime_r(&tm,strcurr); */
 }        forecast_time=curr_time;
         itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')
 /*********** Maximum Likelihood Estimation ***************/          strcurr[itmp-1]='\0';
         printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 {        for(niterf=10;niterf<=30;niterf+=10){
   int i,j, iter;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   double **xi,*delti;          tmf = *localtime(&forecast_time.tv_sec);
   double fret;  /*      asctime_r(&tmf,strfor); */
   xi=matrix(1,npar,1,npar);          strcpy(strfor,asctime(&tmf));
   for (i=1;i<=npar;i++)          itmp = strlen(strfor);
     for (j=1;j<=npar;j++)          if(strfor[itmp-1]=='\n')
       xi[i][j]=(i==j ? 1.0 : 0.0);          strfor[itmp-1]='\0';
   printf("Powell\n");          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s or\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   powell(p,xi,npar,ftol,&iter,&fret,func);          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s or\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
         }
    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));      for (i=1;i<=n;i++) { 
         for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 }        fptt=(*fret); 
   #ifdef DEBUG
 /**** Computes Hessian and covariance matrix ***/        printf("fret=%lf \n",*fret);
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))        fprintf(ficlog,"fret=%lf \n",*fret);
 {  #endif
   double  **a,**y,*x,pd;        printf("%d",i);fflush(stdout);
   double **hess;        fprintf(ficlog,"%d",i);fflush(ficlog);
   int i, j,jk;        linmin(p,xit,n,fret,func); 
   int *indx;        if (fabs(fptt-(*fret)) > del) { 
           del=fabs(fptt-(*fret)); 
   double hessii(double p[], double delta, int theta, double delti[]);          ibig=i; 
   double hessij(double p[], double delti[], int i, int j);        } 
   void lubksb(double **a, int npar, int *indx, double b[]) ;  #ifdef DEBUG
   void ludcmp(double **a, int npar, int *indx, double *d) ;        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
         for (j=1;j<=n;j++) {
   hess=matrix(1,npar,1,npar);          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           printf(" x(%d)=%.12e",j,xit[j]);
   printf("\nCalculation of the hessian matrix. Wait...\n");          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   for (i=1;i<=npar;i++){        }
     printf("%d",i);fflush(stdout);        for(j=1;j<=n;j++) {
     hess[i][i]=hessii(p,ftolhess,i,delti);          printf(" p=%.12e",p[j]);
     /*printf(" %f ",p[i]);*/          fprintf(ficlog," p=%.12e",p[j]);
   }        }
         printf("\n");
   for (i=1;i<=npar;i++) {        fprintf(ficlog,"\n");
     for (j=1;j<=npar;j++)  {  #endif
       if (j>i) {      } 
         printf(".%d%d",i,j);fflush(stdout);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
         hess[i][j]=hessij(p,delti,i,j);  #ifdef DEBUG
         hess[j][i]=hess[i][j];        int k[2],l;
       }        k[0]=1;
     }        k[1]=-1;
   }        printf("Max: %.12e",(*func)(p));
   printf("\n");        fprintf(ficlog,"Max: %.12e",(*func)(p));
         for (j=1;j<=n;j++) {
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");          printf(" %.12e",p[j]);
            fprintf(ficlog," %.12e",p[j]);
   a=matrix(1,npar,1,npar);        }
   y=matrix(1,npar,1,npar);        printf("\n");
   x=vector(1,npar);        fprintf(ficlog,"\n");
   indx=ivector(1,npar);        for(l=0;l<=1;l++) {
   for (i=1;i<=npar;i++)          for (j=1;j<=n;j++) {
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   ludcmp(a,npar,indx,&pd);            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   for (j=1;j<=npar;j++) {          }
     for (i=1;i<=npar;i++) x[i]=0;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     x[j]=1;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     lubksb(a,npar,indx,x);        }
     for (i=1;i<=npar;i++){  #endif
       matcov[i][j]=x[i];  
     }  
   }        free_vector(xit,1,n); 
         free_vector(xits,1,n); 
   printf("\n#Hessian matrix#\n");        free_vector(ptt,1,n); 
   for (i=1;i<=npar;i++) {        free_vector(pt,1,n); 
     for (j=1;j<=npar;j++) {        return; 
       printf("%.3e ",hess[i][j]);      } 
     }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     printf("\n");      for (j=1;j<=n;j++) { 
   }        ptt[j]=2.0*p[j]-pt[j]; 
         xit[j]=p[j]-pt[j]; 
   /* Recompute Inverse */        pt[j]=p[j]; 
   for (i=1;i<=npar;i++)      } 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      fptt=(*func)(ptt); 
   ludcmp(a,npar,indx,&pd);      if (fptt < fp) { 
         t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
   /*  printf("\n#Hessian matrix recomputed#\n");        if (t < 0.0) { 
           linmin(p,xit,n,fret,func); 
   for (j=1;j<=npar;j++) {          for (j=1;j<=n;j++) { 
     for (i=1;i<=npar;i++) x[i]=0;            xi[j][ibig]=xi[j][n]; 
     x[j]=1;            xi[j][n]=xit[j]; 
     lubksb(a,npar,indx,x);          }
     for (i=1;i<=npar;i++){  #ifdef DEBUG
       y[i][j]=x[i];          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       printf("%.3e ",y[i][j]);          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     }          for(j=1;j<=n;j++){
     printf("\n");            printf(" %.12e",xit[j]);
   }            fprintf(ficlog," %.12e",xit[j]);
   */          }
           printf("\n");
   free_matrix(a,1,npar,1,npar);          fprintf(ficlog,"\n");
   free_matrix(y,1,npar,1,npar);  #endif
   free_vector(x,1,npar);        }
   free_ivector(indx,1,npar);      } 
   free_matrix(hess,1,npar,1,npar);    } 
   } 
   
 }  /**** Prevalence limit (stable prevalence)  ****************/
   
 /*************** hessian matrix ****************/  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
 double hessii( double x[], double delta, int theta, double delti[])  {
 {    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   int i;       matrix by transitions matrix until convergence is reached */
   int l=1, lmax=20;  
   double k1,k2;    int i, ii,j,k;
   double p2[NPARMAX+1];    double min, max, maxmin, maxmax,sumnew=0.;
   double res;    double **matprod2();
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    double **out, cov[NCOVMAX], **pmij();
   double fx;    double **newm;
   int k=0,kmax=10;    double agefin, delaymax=50 ; /* Max number of years to converge */
   double l1;  
     for (ii=1;ii<=nlstate+ndeath;ii++)
   fx=func(x);      for (j=1;j<=nlstate+ndeath;j++){
   for (i=1;i<=npar;i++) p2[i]=x[i];        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(l=0 ; l <=lmax; l++){      }
     l1=pow(10,l);  
     delts=delt;     cov[1]=1.;
     for(k=1 ; k <kmax; k=k+1){   
       delt = delta*(l1*k);   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       p2[theta]=x[theta] +delt;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       k1=func(p2)-fx;      newm=savm;
       p2[theta]=x[theta]-delt;      /* Covariates have to be included here again */
       k2=func(p2)-fx;       cov[2]=agefin;
       /*res= (k1-2.0*fx+k2)/delt/delt; */    
       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]]];
 #ifdef DEBUG          /*      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("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);        }
 #endif        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        for (k=1; k<=cptcovprod;k++)
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         k=kmax;  
       }        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         k=kmax; l=lmax*10.;        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       }      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  
         delts=delt;      savm=oldm;
       }      oldm=newm;
     }      maxmax=0.;
   }      for(j=1;j<=nlstate;j++){
   delti[theta]=delts;        min=1.;
   return res;        max=0.;
          for(i=1; i<=nlstate; i++) {
 }          sumnew=0;
           for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
 double hessij( double x[], double delti[], int thetai,int thetaj)          prlim[i][j]= newm[i][j]/(1-sumnew);
 {          max=FMAX(max,prlim[i][j]);
   int i;          min=FMIN(min,prlim[i][j]);
   int l=1, l1, lmax=20;        }
   double k1,k2,k3,k4,res,fx;        maxmin=max-min;
   double p2[NPARMAX+1];        maxmax=FMAX(maxmax,maxmin);
   int k;      }
       if(maxmax < ftolpl){
   fx=func(x);        return prlim;
   for (k=1; k<=2; k++) {      }
     for (i=1;i<=npar;i++) p2[i]=x[i];    }
     p2[thetai]=x[thetai]+delti[thetai]/k;  }
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k1=func(p2)-fx;  /*************** transition probabilities ***************/ 
    
     p2[thetai]=x[thetai]+delti[thetai]/k;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  {
     k2=func(p2)-fx;    double s1, s2;
      /*double t34;*/
     p2[thetai]=x[thetai]-delti[thetai]/k;    int i,j,j1, nc, ii, jj;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k3=func(p2)-fx;      for(i=1; i<= nlstate; i++){
          for(j=1; j<i;j++){
     p2[thetai]=x[thetai]-delti[thetai]/k;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            /*s2 += param[i][j][nc]*cov[nc];*/
     k4=func(p2)-fx;            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
 #ifdef DEBUG          }
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);          ps[i][j]=s2;
 #endif  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
   }        }
   return res;        for(j=i+1; j<=nlstate+ndeath;j++){
 }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
             s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 /************** Inverse of matrix **************/  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
 void ludcmp(double **a, int n, int *indx, double *d)          }
 {          ps[i][j]=s2;
   int i,imax,j,k;        }
   double big,dum,sum,temp;      }
   double *vv;      /*ps[3][2]=1;*/
        
   vv=vector(1,n);      for(i=1; i<= nlstate; i++){
   *d=1.0;        s1=0;
   for (i=1;i<=n;i++) {        for(j=1; j<i; j++)
     big=0.0;          s1+=exp(ps[i][j]);
     for (j=1;j<=n;j++)        for(j=i+1; j<=nlstate+ndeath; j++)
       if ((temp=fabs(a[i][j])) > big) big=temp;          s1+=exp(ps[i][j]);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");        ps[i][i]=1./(s1+1.);
     vv[i]=1.0/big;        for(j=1; j<i; j++)
   }          ps[i][j]= exp(ps[i][j])*ps[i][i];
   for (j=1;j<=n;j++) {        for(j=i+1; j<=nlstate+ndeath; j++)
     for (i=1;i<j;i++) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
       sum=a[i][j];        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];      } /* end i */
       a[i][j]=sum;      
     }      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     big=0.0;        for(jj=1; jj<= nlstate+ndeath; jj++){
     for (i=j;i<=n;i++) {          ps[ii][jj]=0;
       sum=a[i][j];          ps[ii][ii]=1;
       for (k=1;k<j;k++)        }
         sum -= a[i][k]*a[k][j];      }
       a[i][j]=sum;      
       if ( (dum=vv[i]*fabs(sum)) >= big) {  
         big=dum;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
         imax=i;  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       }  /*         printf("ddd %lf ",ps[ii][jj]); */
     }  /*       } */
     if (j != imax) {  /*       printf("\n "); */
       for (k=1;k<=n;k++) {  /*        } */
         dum=a[imax][k];  /*        printf("\n ");printf("%lf ",cov[2]); */
         a[imax][k]=a[j][k];         /*
         a[j][k]=dum;        for(i=1; i<= npar; i++) printf("%f ",x[i]);
       }        goto end;*/
       *d = -(*d);      return ps;
       vv[imax]=vv[j];  }
     }  
     indx[j]=imax;  /**************** Product of 2 matrices ******************/
     if (a[j][j] == 0.0) a[j][j]=TINY;  
     if (j != n) {  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       dum=1.0/(a[j][j]);  {
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    /* 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(...) */
   }    /* in, b, out are matrice of pointers which should have been initialized 
   free_vector(vv,1,n);  /* Doesn't work */       before: only the contents of out is modified. The function returns
 ;       a pointer to pointers identical to out */
 }    long i, j, k;
     for(i=nrl; i<= nrh; i++)
 void lubksb(double **a, int n, int *indx, double b[])      for(k=ncolol; k<=ncoloh; k++)
 {        for(j=ncl,out[i][k]=0.; j<=nch; j++)
   int i,ii=0,ip,j;          out[i][k] +=in[i][j]*b[j][k];
   double sum;  
      return out;
   for (i=1;i<=n;i++) {  }
     ip=indx[i];  
     sum=b[ip];  
     b[ip]=b[i];  /************* Higher Matrix Product ***************/
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     else if (sum) ii=i;  {
     b[i]=sum;    /* Computes the transition matrix starting at age 'age' over 
   }       'nhstepm*hstepm*stepm' months (i.e. until
   for (i=n;i>=1;i--) {       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     sum=b[i];       nhstepm*hstepm matrices. 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     b[i]=sum/a[i][i];       (typically every 2 years instead of every month which is too big 
   }       for the memory).
 }       Model is determined by parameters x and covariates have to be 
        included manually here. 
 /************ Frequencies ********************/  
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)       */
 {  /* Some frequencies */  
      int i, j, d, h, k;
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    double **out, cov[NCOVMAX];
   double ***freq; /* Frequencies */    double **newm;
   double *pp;  
   double pos;    /* Hstepm could be zero and should return the unit matrix */
   FILE *ficresp;    for (i=1;i<=nlstate+ndeath;i++)
   char fileresp[FILENAMELENGTH];      for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
   pp=vector(1,nlstate);        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }
   strcpy(fileresp,"p");    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   strcat(fileresp,fileres);    for(h=1; h <=nhstepm; h++){
   if((ficresp=fopen(fileresp,"w"))==NULL) {      for(d=1; d <=hstepm; d++){
     printf("Problem with prevalence resultfile: %s\n", fileresp);        newm=savm;
     exit(0);        /* Covariates have to be included here again */
   }        cov[1]=1.;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   j1=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         for (k=1; k<=cptcovage;k++)
   j=cptcoveff;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        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]]];
   for(k1=1; k1<=j;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){  
        j1++;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
          scanf("%d", i);*/        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         for (i=-1; i<=nlstate+ndeath; i++)                       pmij(pmmij,cov,ncovmodel,x,nlstate));
          for (jk=-1; jk<=nlstate+ndeath; jk++)          savm=oldm;
            for(m=agemin; m <= agemax+3; m++)        oldm=newm;
              freq[i][jk][m]=0;      }
              for(i=1; i<=nlstate+ndeath; i++)
        for (i=1; i<=imx; i++) {        for(j=1;j<=nlstate+ndeath;j++) {
          bool=1;          po[i][j][h]=newm[i][j];
          if  (cptcovn>0) {          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
            for (z1=1; z1<=cptcoveff; z1++)           */
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        }
                bool=0;    } /* end h */
          }    return po;
           if (bool==1) {  }
            for(m=firstpass; m<=lastpass-1; m++){  
              if(agev[m][i]==0) agev[m][i]=agemax+1;  
              if(agev[m][i]==1) agev[m][i]=agemax+2;  /*************** log-likelihood *************/
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  double func( double *x)
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  {
            }    int i, ii, j, k, mi, d, kk;
          }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
        }    double **out;
         if  (cptcovn>0) {    double sw; /* Sum of weights */
          fprintf(ficresp, "\n#********** Variable ");    double lli; /* Individual log likelihood */
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    int s1, s2;
        fprintf(ficresp, "**********\n#");    double bbh, survp;
         }    long ipmx;
        for(i=1; i<=nlstate;i++)    /*extern weight */
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    /* We are differentiating ll according to initial status */
        fprintf(ficresp, "\n");    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
            /*for(i=1;i<imx;i++) 
   for(i=(int)agemin; i <= (int)agemax+3; i++){      printf(" %d\n",s[4][i]);
     if(i==(int)agemax+3)    */
       printf("Total");    cov[1]=1.;
     else  
       printf("Age %d", i);    for(k=1; k<=nlstate; k++) ll[k]=0.;
     for(jk=1; jk <=nlstate ; jk++){  
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    if(mle==1){
         pp[jk] += freq[jk][m][i];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     for(jk=1; jk <=nlstate ; jk++){        for(mi=1; mi<= wav[i]-1; mi++){
       for(m=-1, pos=0; m <=0 ; m++)          for (ii=1;ii<=nlstate+ndeath;ii++)
         pos += freq[jk][m][i];            for (j=1;j<=nlstate+ndeath;j++){
       if(pp[jk]>=1.e-10)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       else            }
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
     for(jk=1; jk <=nlstate ; jk++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)            for (kk=1; kk<=cptcovage;kk++) {
         pp[jk] += freq[jk][m][i];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
     for(jk=1,pos=0; jk <=nlstate ; jk++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       pos += pp[jk];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(jk=1; jk <=nlstate ; jk++){            savm=oldm;
       if(pos>=1.e-5)            oldm=newm;
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          } /* end mult */
       else        
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       if( i <= (int) agemax){          /* But now since version 0.9 we anticipate for bias and large stepm.
         if(pos>=1.e-5)           * If stepm is larger than one month (smallest stepm) and if the exact delay 
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);           * (in months) between two waves is not a multiple of stepm, we rounded to 
       else           * the nearest (and in case of equal distance, to the lowest) interval but now
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       }           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
     }           * probability in order to take into account the bias as a fraction of the way
     for(jk=-1; jk <=nlstate+ndeath; jk++)           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
       for(m=-1; m <=nlstate+ndeath; m++)           * -stepm/2 to stepm/2 .
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);           * For stepm=1 the results are the same as for previous versions of Imach.
     if(i <= (int) agemax)           * For stepm > 1 the results are less biased than in previous versions. 
       fprintf(ficresp,"\n");           */
     printf("\n");          s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
  }          /* bias is positive if real duration
             * is higher than the multiple of stepm and negative otherwise.
   fclose(ficresp);           */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   free_vector(pp,1,nlstate);          if( s2 > nlstate){ 
             /* i.e. if s2 is a death state and if the date of death is known then the contribution
 }  /* End of Freq */               to the likelihood is the probability to die between last step unit time and current 
                step unit time, which is also the differences between probability to die before dh 
 /************* Waves Concatenation ***************/               and probability to die before dh-stepm . 
                In version up to 0.92 likelihood was computed
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          as if date of death was unknown. Death was treated as any other
 {          health state: the date of the interview describes the actual state
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          and not the date of a change in health state. The former idea was
      Death is a valid wave (if date is known).          to consider that at each interview the state was recorded
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          (healthy, disable or death) and IMaCh was corrected; but when we
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          introduced the exact date of death then we should have modified
      and mw[mi+1][i]. dh depends on stepm.          the contribution of an exact death to the likelihood. This new
      */          contribution is smaller and very dependent of the step unit
           stepm. It is no more the probability to die between last interview
   int i, mi, m;          and month of death but the probability to survive from last
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          interview up to one month before death multiplied by the
      double sum=0., jmean=0.;*/          probability to die within a month. Thanks to Chris
           Jackson for correcting this bug.  Former versions increased
 int j, k=0,jk, ju, jl;          mortality artificially. The bad side is that we add another loop
      double sum=0.;          which slows down the processing. The difference can be up to 10%
 jmin=1e+5;          lower mortality.
  jmax=-1;            */
 jmean=0.;            lli=log(out[s1][s2] - savm[s1][s2]);
   for(i=1; i<=imx; i++){          }else{
     mi=0;            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     m=firstpass;            /*  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 */
     while(s[m][i] <= nlstate){          } 
       if(s[m][i]>=1)          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         mw[++mi][i]=m;          /*if(lli ==000.0)*/
       if(m >=lastpass)          /*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); */
         break;          ipmx +=1;
       else          sw += weight[i];
         m++;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }/* end while */        } /* end of wave */
     if (s[m][i] > nlstate){      } /* end of individual */
       mi++;     /* Death is another wave */    }  else if(mle==2){
       /* if(mi==0)  never been interviewed correctly before death */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          /* Only death is a correct wave */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       mw[mi][i]=m;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     wav[i]=mi;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     if(mi==0)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);            }
   }          for(d=0; d<=dh[mi][i]; d++){
             newm=savm;
   for(i=1; i<=imx; i++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(mi=1; mi<wav[i];mi++){            for (kk=1; kk<=cptcovage;kk++) {
       if (stepm <=0)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         dh[mi][i]=1;            }
       else{            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         if (s[mw[mi+1][i]][i] > nlstate) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            savm=oldm;
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/            oldm=newm;
           if(j==0) j=1;  /* Survives at least one month after exam */          } /* end mult */
           k=k+1;        
           if (j >= jmax) jmax=j;          s1=s[mw[mi][i]][i];
           else if (j <= jmin)jmin=j;          s2=s[mw[mi+1][i]][i];
           sum=sum+j;          bbh=(double)bh[mi][i]/(double)stepm; 
         }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         else{          ipmx +=1;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          sw += weight[i];
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           k=k+1;        } /* end of wave */
           if (j >= jmax) jmax=j;      } /* end of individual */
           else if (j <= jmin)jmin=j;    }  else if(mle==3){  /* exponential inter-extrapolation */
           sum=sum+j;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         jk= j/stepm;        for(mi=1; mi<= wav[i]-1; mi++){
         jl= j -jk*stepm;          for (ii=1;ii<=nlstate+ndeath;ii++)
         ju= j -(jk+1)*stepm;            for (j=1;j<=nlstate+ndeath;j++){
         if(jl <= -ju)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           dh[mi][i]=jk;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         else            }
           dh[mi][i]=jk+1;          for(d=0; d<dh[mi][i]; d++){
         if(dh[mi][i]==0)            newm=savm;
           dh[mi][i]=1; /* At least one step */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
     }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   }            }
   jmean=sum/k;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 }            savm=oldm;
 /*********** Tricode ****************************/            oldm=newm;
 void tricode(int *Tvar, int **nbcode, int imx)          } /* end mult */
 {        
   int Ndum[20],ij=1, k, j, i;          s1=s[mw[mi][i]][i];
   int cptcode=0;          s2=s[mw[mi+1][i]][i];
   cptcoveff=0;          bbh=(double)bh[mi][i]/(double)stepm; 
            lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
   for (k=0; k<19; k++) Ndum[k]=0;          ipmx +=1;
   for (k=1; k<=7; k++) ncodemax[k]=0;          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {        } /* end of wave */
     for (i=1; i<=imx; i++) {      } /* end of individual */
       ij=(int)(covar[Tvar[j]][i]);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
       Ndum[ij]++;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       if (ij > cptcode) cptcode=ij;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     for (i=0; i<=cptcode; i++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       if(Ndum[i]!=0) ncodemax[j]++;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     }            }
     ij=1;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for (i=1; i<=ncodemax[j]; i++) {            for (kk=1; kk<=cptcovage;kk++) {
       for (k=0; k<=19; k++) {              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         if (Ndum[k] != 0) {            }
           nbcode[Tvar[j]][ij]=k;          
           ij++;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         if (ij > ncodemax[j]) break;            savm=oldm;
       }              oldm=newm;
     }          } /* end mult */
   }          
           s1=s[mw[mi][i]][i];
  for (k=0; k<19; k++) Ndum[k]=0;          s2=s[mw[mi+1][i]][i];
           if( s2 > nlstate){ 
  for (i=1; i<=ncovmodel; i++) {            lli=log(out[s1][s2] - savm[s1][s2]);
       ij=Tvar[i];          }else{
       Ndum[ij]++;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     }          }
           ipmx +=1;
  ij=1;          sw += weight[i];
  for (i=1; i<=10; i++) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    if((Ndum[i]!=0) && (i<=ncov)){  /*      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]); */
      Tvaraff[ij]=i;        } /* end of wave */
      ij++;      } /* end of individual */
    }    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
  }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     cptcoveff=ij-1;        for(mi=1; mi<= wav[i]-1; mi++){
 }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
 /*********** Health Expectancies ****************/              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)            }
 {          for(d=0; d<dh[mi][i]; d++){
   /* Health expectancies */            newm=savm;
   int i, j, nhstepm, hstepm, h;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double age, agelim,hf;            for (kk=1; kk<=cptcovage;kk++) {
   double ***p3mat;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              }
   fprintf(ficreseij,"# Health expectancies\n");          
   fprintf(ficreseij,"# Age");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(j=1; j<=nlstate;j++)            savm=oldm;
       fprintf(ficreseij," %1d-%1d",i,j);            oldm=newm;
   fprintf(ficreseij,"\n");          } /* end mult */
         
   hstepm=1*YEARM; /*  Every j years of age (in month) */          s1=s[mw[mi][i]][i];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          s2=s[mw[mi+1][i]][i];
           lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   agelim=AGESUP;          ipmx +=1;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          sw += weight[i];
     /* nhstepm age range expressed in number of stepm */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          /*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]);*/
     /* Typically if 20 years = 20*12/6=40 stepm */        } /* end of wave */
     if (stepm >= YEARM) hstepm=1;      } /* end of individual */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */    } /* End of if */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      return -l;
   }
   
     for(i=1; i<=nlstate;i++)  /*************** log-likelihood *************/
       for(j=1; j<=nlstate;j++)  double funcone( double *x)
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){  {
           eij[i][j][(int)age] +=p3mat[i][j][h];    /* Same as likeli but slower because of a lot of printf and if */
         }    int i, ii, j, k, mi, d, kk;
        double l, ll[NLSTATEMAX], cov[NCOVMAX];
     hf=1;    double **out;
     if (stepm >= YEARM) hf=stepm/YEARM;    double lli; /* Individual log likelihood */
     fprintf(ficreseij,"%.0f",age );    double llt;
     for(i=1; i<=nlstate;i++)    int s1, s2;
       for(j=1; j<=nlstate;j++){    double bbh, survp;
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);    /*extern weight */
       }    /* We are differentiating ll according to initial status */
     fprintf(ficreseij,"\n");    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /*for(i=1;i<imx;i++) 
   }      printf(" %d\n",s[4][i]);
 }    */
     cov[1]=1.;
 /************ 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)    for(k=1; k<=nlstate; k++) ll[k]=0.;
 {  
   /* Variance of health expectancies */    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double **newm;      for(mi=1; mi<= wav[i]-1; mi++){
   double **dnewm,**doldm;        for (ii=1;ii<=nlstate+ndeath;ii++)
   int i, j, nhstepm, hstepm, h;          for (j=1;j<=nlstate+ndeath;j++){
   int k, cptcode;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
    double *xp;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **gp, **gm;          }
   double ***gradg, ***trgradg;        for(d=0; d<dh[mi][i]; d++){
   double ***p3mat;          newm=savm;
   double age,agelim;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   int theta;          for (kk=1; kk<=cptcovage;kk++) {
             cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
    fprintf(ficresvij,"# Covariances of life expectancies\n");          }
   fprintf(ficresvij,"# Age");          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for(i=1; i<=nlstate;i++)                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(j=1; j<=nlstate;j++)          savm=oldm;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          oldm=newm;
   fprintf(ficresvij,"\n");        } /* end mult */
         
   xp=vector(1,npar);        s1=s[mw[mi][i]][i];
   dnewm=matrix(1,nlstate,1,npar);        s2=s[mw[mi+1][i]][i];
   doldm=matrix(1,nlstate,1,nlstate);        bbh=(double)bh[mi][i]/(double)stepm; 
          /* bias is positive if real duration
   hstepm=1*YEARM; /* Every year of age */         * is higher than the multiple of stepm and negative otherwise.
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */         */
   agelim = AGESUP;        if( s2 > nlstate && (mle <5) ){  /* Jackson */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          lli=log(out[s1][s2] - savm[s1][s2]);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        } else if (mle==1){
     if (stepm >= YEARM) hstepm=1;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        } else if(mle==2){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          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 */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        } else if(mle==3){  /* exponential inter-extrapolation */
     gp=matrix(0,nhstepm,1,nlstate);          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
     gm=matrix(0,nhstepm,1,nlstate);        } else if (mle==4){  /* mle=4 no inter-extrapolation */
           lli=log(out[s1][s2]); /* Original formula */
     for(theta=1; theta <=npar; theta++){        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       for(i=1; i<=npar; i++){ /* Computes gradient */          lli=log(out[s1][s2]); /* Original formula */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        } /* End of if */
       }        ipmx +=1;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          sw += weight[i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(j=1; j<= nlstate; j++){  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         for(h=0; h<=nhstepm; h++){        if(globpr){
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];   %10.6f %10.6f %10.6f ", \
         }                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
       }                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
              for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       for(i=1; i<=npar; i++) /* Computes gradient */            llt +=ll[k]*gipmx/gsw;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          fprintf(ficresilk," %10.6f\n", -llt);
       for(j=1; j<= nlstate; j++){        }
         for(h=0; h<=nhstepm; h++){      } /* end of wave */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    } /* end of individual */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       for(j=1; j<= nlstate; j++)    if(globpr==0){ /* First time we count the contributions and weights */
         for(h=0; h<=nhstepm; h++){      gipmx=ipmx;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      gsw=sw;
         }    }
     } /* End theta */    return -l;
   }
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);  
   
     for(h=0; h<=nhstepm; h++)  /*************** function likelione ***********/
       for(j=1; j<=nlstate;j++)  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
         for(theta=1; theta <=npar; theta++)  {
           trgradg[h][j][theta]=gradg[h][theta][j];    /* This routine should help understanding what is done with 
        the selection of individuals/waves and
     for(i=1;i<=nlstate;i++)       to check the exact contribution to the likelihood.
       for(j=1;j<=nlstate;j++)       Plotting could be done.
         vareij[i][j][(int)age] =0.;     */
     for(h=0;h<=nhstepm;h++){    int k;
       for(k=0;k<=nhstepm;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    if(*globpri !=0){ /* Just counts and sums, no printings */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      strcpy(fileresilk,"ilk"); 
         for(i=1;i<=nlstate;i++)      strcat(fileresilk,fileres);
           for(j=1;j<=nlstate;j++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
             vareij[i][j][(int)age] += doldm[i][j];        printf("Problem with resultfile: %s\n", fileresilk);
       }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     }      }
     h=1;      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
     if (stepm >= YEARM) h=stepm/YEARM;      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
     fprintf(ficresvij,"%.0f ",age );      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     for(i=1; i<=nlstate;i++)      for(k=1; k<=nlstate; k++) 
       for(j=1; j<=nlstate;j++){        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       }    }
     fprintf(ficresvij,"\n");  
     free_matrix(gp,0,nhstepm,1,nlstate);    *fretone=(*funcone)(p);
     free_matrix(gm,0,nhstepm,1,nlstate);    if(*globpri !=0){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      fclose(ficresilk);
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fflush(fichtm); 
   } /* End age */    } 
      return;
   free_vector(xp,1,npar);  }
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);  
   /*********** Maximum Likelihood Estimation ***************/
 }  
   void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
 /************ 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)    int i,j, iter;
 {    double **xi;
   /* Variance of prevalence limit */    double fret;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    double fretone; /* Only one call to likelihood */
   double **newm;    /*  char filerespow[FILENAMELENGTH];*/
   double **dnewm,**doldm;    xi=matrix(1,npar,1,npar);
   int i, j, nhstepm, hstepm;    for (i=1;i<=npar;i++)
   int k, cptcode;      for (j=1;j<=npar;j++)
   double *xp;        xi[i][j]=(i==j ? 1.0 : 0.0);
   double *gp, *gm;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   double **gradg, **trgradg;    strcpy(filerespow,"pow"); 
   double age,agelim;    strcat(filerespow,fileres);
   int theta;    if((ficrespow=fopen(filerespow,"w"))==NULL) {
          printf("Problem with resultfile: %s\n", filerespow);
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   fprintf(ficresvpl,"# Age");    }
   for(i=1; i<=nlstate;i++)    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       fprintf(ficresvpl," %1d-%1d",i,i);    for (i=1;i<=nlstate;i++)
   fprintf(ficresvpl,"\n");      for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   xp=vector(1,npar);    fprintf(ficrespow,"\n");
   dnewm=matrix(1,nlstate,1,npar);  
   doldm=matrix(1,nlstate,1,nlstate);    powell(p,xi,npar,ftol,&iter,&fret,func);
    
   hstepm=1*YEARM; /* Every year of age */    fclose(ficrespow);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
   agelim = AGESUP;    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     if (stepm >= YEARM) hstepm=1;  }
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
     gradg=matrix(1,npar,1,nlstate);  /**** Computes Hessian and covariance matrix ***/
     gp=vector(1,nlstate);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     gm=vector(1,nlstate);  {
     double  **a,**y,*x,pd;
     for(theta=1; theta <=npar; theta++){    double **hess;
       for(i=1; i<=npar; i++){ /* Computes gradient */    int i, j,jk;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    int *indx;
       }  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(i=1;i<=nlstate;i++)    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         gp[i] = prlim[i][i];    void lubksb(double **a, int npar, int *indx, double b[]) ;
        void ludcmp(double **a, int npar, int *indx, double *d) ;
       for(i=1; i<=npar; i++) /* Computes gradient */    double gompertz(double p[]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    hess=matrix(1,npar,1,npar);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)    printf("\nCalculation of the hessian matrix. Wait...\n");
         gm[i] = prlim[i][i];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     for (i=1;i<=npar;i++){
       for(i=1;i<=nlstate;i++)      printf("%d",i);fflush(stdout);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];      fprintf(ficlog,"%d",i);fflush(ficlog);
     } /* End theta */     
        hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     trgradg =matrix(1,nlstate,1,npar);      
       /*  printf(" %f ",p[i]);
     for(j=1; j<=nlstate;j++)          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
       for(theta=1; theta <=npar; theta++)    }
         trgradg[j][theta]=gradg[theta][j];    
     for (i=1;i<=npar;i++) {
     for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++)  {
       varpl[i][(int)age] =0.;        if (j>i) { 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);          printf(".%d%d",i,j);fflush(stdout);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     for(i=1;i<=nlstate;i++)          hess[i][j]=hessij(p,delti,i,j,func,npar);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          
           hess[j][i]=hess[i][j];    
     fprintf(ficresvpl,"%.0f ",age );          /*printf(" %lf ",hess[i][j]);*/
     for(i=1; i<=nlstate;i++)        }
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      }
     fprintf(ficresvpl,"\n");    }
     free_vector(gp,1,nlstate);    printf("\n");
     free_vector(gm,1,nlstate);    fprintf(ficlog,"\n");
     free_matrix(gradg,1,npar,1,nlstate);  
     free_matrix(trgradg,1,nlstate,1,npar);    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   } /* End age */    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     
   free_vector(xp,1,npar);    a=matrix(1,npar,1,npar);
   free_matrix(doldm,1,nlstate,1,npar);    y=matrix(1,npar,1,npar);
   free_matrix(dnewm,1,nlstate,1,nlstate);    x=vector(1,npar);
     indx=ivector(1,npar);
 }    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     ludcmp(a,npar,indx,&pd);
   
 /***********************************************/    for (j=1;j<=npar;j++) {
 /**************** Main Program *****************/      for (i=1;i<=npar;i++) x[i]=0;
 /***********************************************/      x[j]=1;
       lubksb(a,npar,indx,x);
 /*int main(int argc, char *argv[])*/      for (i=1;i<=npar;i++){ 
 int main()        matcov[i][j]=x[i];
 {      }
     }
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;  
   double agedeb, agefin,hf;    printf("\n#Hessian matrix#\n");
   double agemin=1.e20, agemax=-1.e20;    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
   double fret;      for (j=1;j<=npar;j++) { 
   double **xi,tmp,delta;        printf("%.3e ",hess[i][j]);
         fprintf(ficlog,"%.3e ",hess[i][j]);
   double dum; /* Dummy variable */      }
   double ***p3mat;      printf("\n");
   int *indx;      fprintf(ficlog,"\n");
   char line[MAXLINE], linepar[MAXLINE];    }
   char title[MAXLINE];  
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    /* Recompute Inverse */
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];    for (i=1;i<=npar;i++)
   char filerest[FILENAMELENGTH];      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   char fileregp[FILENAMELENGTH];    ludcmp(a,npar,indx,&pd);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];  
   int firstobs=1, lastobs=10;    /*  printf("\n#Hessian matrix recomputed#\n");
   int sdeb, sfin; /* Status at beginning and end */  
   int c,  h , cpt,l;    for (j=1;j<=npar;j++) {
   int ju,jl, mi;      for (i=1;i<=npar;i++) x[i]=0;
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      x[j]=1;
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      lubksb(a,npar,indx,x);
        for (i=1;i<=npar;i++){ 
   int hstepm, nhstepm;        y[i][j]=x[i];
   double bage, fage, age, agelim, agebase;        printf("%.3e ",y[i][j]);
   double ftolpl=FTOL;        fprintf(ficlog,"%.3e ",y[i][j]);
   double **prlim;      }
   double *severity;      printf("\n");
   double ***param; /* Matrix of parameters */      fprintf(ficlog,"\n");
   double  *p;    }
   double **matcov; /* Matrix of covariance */    */
   double ***delti3; /* Scale */  
   double *delti; /* Scale */    free_matrix(a,1,npar,1,npar);
   double ***eij, ***vareij;    free_matrix(y,1,npar,1,npar);
   double **varpl; /* Variances of prevalence limits by age */    free_vector(x,1,npar);
   double *epj, vepp;    free_ivector(indx,1,npar);
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";    free_matrix(hess,1,npar,1,npar);
   char *alph[]={"a","a","b","c","d","e"}, str[4];  
   
   char z[1]="c", occ;  }
 #include <sys/time.h>  
 #include <time.h>  /*************** hessian matrix ****************/
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   /* long total_usecs;  {
   struct timeval start_time, end_time;    int i;
      int l=1, lmax=20;
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    double k1,k2;
     double p2[NPARMAX+1];
     double res;
   printf("\nIMACH, Version 0.64a");    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   printf("\nEnter the parameter file name: ");    double fx;
     int k=0,kmax=10;
 #ifdef windows    double l1;
   scanf("%s",pathtot);  
   getcwd(pathcd, size);    fx=func(x);
   /*cygwin_split_path(pathtot,path,optionfile);    for (i=1;i<=npar;i++) p2[i]=x[i];
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    for(l=0 ; l <=lmax; l++){
   /* cutv(path,optionfile,pathtot,'\\');*/      l1=pow(10,l);
       delts=delt;
 split(pathtot, path,optionfile);      for(k=1 ; k <kmax; k=k+1){
   chdir(path);        delt = delta*(l1*k);
   replace(pathc,path);        p2[theta]=x[theta] +delt;
 #endif        k1=func(p2)-fx;
 #ifdef unix        p2[theta]=x[theta]-delt;
   scanf("%s",optionfile);        k2=func(p2)-fx;
 #endif        /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
 /*-------- arguments in the command line --------*/        
   #ifdef DEBUG
   strcpy(fileres,"r");        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);
   strcat(fileres, optionfile);        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   #endif
   /*---------arguments file --------*/        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   if((ficpar=fopen(optionfile,"r"))==NULL)    {          k=kmax;
     printf("Problem with optionfile %s\n",optionfile);        }
     goto end;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   }          k=kmax; l=lmax*10.;
         }
   strcpy(filereso,"o");        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   strcat(filereso,fileres);          delts=delt;
   if((ficparo=fopen(filereso,"w"))==NULL) {        }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;      }
   }    }
     delti[theta]=delts;
   /* Reads comments: lines beginning with '#' */    return res; 
   while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);  }
     fgets(line, MAXLINE, ficpar);  
     puts(line);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
     fputs(line,ficparo);  {
   }    int i;
   ungetc(c,ficpar);    int l=1, l1, lmax=20;
     double k1,k2,k3,k4,res,fx;
   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);    double p2[NPARMAX+1];
   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);    int k;
   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);  
     fx=func(x);
   covar=matrix(0,NCOVMAX,1,n);    for (k=1; k<=2; k++) {
   cptcovn=0;      for (i=1;i<=npar;i++) p2[i]=x[i];
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   ncovmodel=2+cptcovn;      k1=func(p2)-fx;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    
        p2[thetai]=x[thetai]+delti[thetai]/k;
   /* Read guess parameters */      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   /* Reads comments: lines beginning with '#' */      k2=func(p2)-fx;
   while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);      p2[thetai]=x[thetai]-delti[thetai]/k;
     fgets(line, MAXLINE, ficpar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     puts(line);      k3=func(p2)-fx;
     fputs(line,ficparo);    
   }      p2[thetai]=x[thetai]-delti[thetai]/k;
   ungetc(c,ficpar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
        k4=func(p2)-fx;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     for(i=1; i <=nlstate; i++)  #ifdef DEBUG
     for(j=1; j <=nlstate+ndeath-1; j++){      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);
       fscanf(ficpar,"%1d%1d",&i1,&j1);      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);
       fprintf(ficparo,"%1d%1d",i1,j1);  #endif
       printf("%1d%1d",i,j);    }
       for(k=1; k<=ncovmodel;k++){    return res;
         fscanf(ficpar," %lf",&param[i][j][k]);  }
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);  /************** Inverse of matrix **************/
       }  void ludcmp(double **a, int n, int *indx, double *d) 
       fscanf(ficpar,"\n");  { 
       printf("\n");    int i,imax,j,k; 
       fprintf(ficparo,"\n");    double big,dum,sum,temp; 
     }    double *vv; 
     
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    vv=vector(1,n); 
   p=param[1][1];    *d=1.0; 
      for (i=1;i<=n;i++) { 
   /* Reads comments: lines beginning with '#' */      big=0.0; 
   while((c=getc(ficpar))=='#' && c!= EOF){      for (j=1;j<=n;j++) 
     ungetc(c,ficpar);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     fgets(line, MAXLINE, ficpar);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     puts(line);      vv[i]=1.0/big; 
     fputs(line,ficparo);    } 
   }    for (j=1;j<=n;j++) { 
   ungetc(c,ficpar);      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        a[i][j]=sum; 
   for(i=1; i <=nlstate; i++){      } 
     for(j=1; j <=nlstate+ndeath-1; j++){      big=0.0; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);      for (i=j;i<=n;i++) { 
       printf("%1d%1d",i,j);        sum=a[i][j]; 
       fprintf(ficparo,"%1d%1d",i1,j1);        for (k=1;k<j;k++) 
       for(k=1; k<=ncovmodel;k++){          sum -= a[i][k]*a[k][j]; 
         fscanf(ficpar,"%le",&delti3[i][j][k]);        a[i][j]=sum; 
         printf(" %le",delti3[i][j][k]);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
         fprintf(ficparo," %le",delti3[i][j][k]);          big=dum; 
       }          imax=i; 
       fscanf(ficpar,"\n");        } 
       printf("\n");      } 
       fprintf(ficparo,"\n");      if (j != imax) { 
     }        for (k=1;k<=n;k++) { 
   }          dum=a[imax][k]; 
   delti=delti3[1][1];          a[imax][k]=a[j][k]; 
            a[j][k]=dum; 
   /* Reads comments: lines beginning with '#' */        } 
   while((c=getc(ficpar))=='#' && c!= EOF){        *d = -(*d); 
     ungetc(c,ficpar);        vv[imax]=vv[j]; 
     fgets(line, MAXLINE, ficpar);      } 
     puts(line);      indx[j]=imax; 
     fputs(line,ficparo);      if (a[j][j] == 0.0) a[j][j]=TINY; 
   }      if (j != n) { 
   ungetc(c,ficpar);        dum=1.0/(a[j][j]); 
          for (i=j+1;i<=n;i++) a[i][j] *= dum; 
   matcov=matrix(1,npar,1,npar);      } 
   for(i=1; i <=npar; i++){    } 
     fscanf(ficpar,"%s",&str);    free_vector(vv,1,n);  /* Doesn't work */
     printf("%s",str);  ;
     fprintf(ficparo,"%s",str);  } 
     for(j=1; j <=i; j++){  
       fscanf(ficpar," %le",&matcov[i][j]);  void lubksb(double **a, int n, int *indx, double b[]) 
       printf(" %.5le",matcov[i][j]);  { 
       fprintf(ficparo," %.5le",matcov[i][j]);    int i,ii=0,ip,j; 
     }    double sum; 
     fscanf(ficpar,"\n");   
     printf("\n");    for (i=1;i<=n;i++) { 
     fprintf(ficparo,"\n");      ip=indx[i]; 
   }      sum=b[ip]; 
   for(i=1; i <=npar; i++)      b[ip]=b[i]; 
     for(j=i+1;j<=npar;j++)      if (ii) 
       matcov[i][j]=matcov[j][i];        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
          else if (sum) ii=i; 
   printf("\n");      b[i]=sum; 
     } 
     for (i=n;i>=1;i--) { 
     /*-------- data file ----------*/      sum=b[i]; 
     if((ficres =fopen(fileres,"w"))==NULL) {      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       printf("Problem with resultfile: %s\n", fileres);goto end;      b[i]=sum/a[i][i]; 
     }    } 
     fprintf(ficres,"#%s\n",version);  } 
      
     if((fic=fopen(datafile,"r"))==NULL)    {  /************ Frequencies ********************/
       printf("Problem with datafile: %s\n", datafile);goto end;  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)
     }  {  /* Some frequencies */
     
     n= lastobs;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     severity = vector(1,maxwav);    int first;
     outcome=imatrix(1,maxwav+1,1,n);    double ***freq; /* Frequencies */
     num=ivector(1,n);    double *pp, **prop;
     moisnais=vector(1,n);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     annais=vector(1,n);    FILE *ficresp;
     moisdc=vector(1,n);    char fileresp[FILENAMELENGTH];
     andc=vector(1,n);    
     agedc=vector(1,n);    pp=vector(1,nlstate);
     cod=ivector(1,n);    prop=matrix(1,nlstate,iagemin,iagemax+3);
     weight=vector(1,n);    strcpy(fileresp,"p");
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    strcat(fileresp,fileres);
     mint=matrix(1,maxwav,1,n);    if((ficresp=fopen(fileresp,"w"))==NULL) {
     anint=matrix(1,maxwav,1,n);      printf("Problem with prevalence resultfile: %s\n", fileresp);
     s=imatrix(1,maxwav+1,1,n);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     adl=imatrix(1,maxwav+1,1,n);          exit(0);
     tab=ivector(1,NCOVMAX);    }
     ncodemax=ivector(1,8);    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
     j1=0;
     i=1;    
     while (fgets(line, MAXLINE, fic) != NULL)    {    j=cptcoveff;
       if ((i >= firstobs) && (i <=lastobs)) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
          
         for (j=maxwav;j>=1;j--){    first=1;
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  
           strcpy(line,stra);    for(k1=1; k1<=j;k1++){
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      for(i1=1; i1<=ncodemax[k1];i1++){
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        j1++;
         }        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
                  scanf("%d", i);*/
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        for (i=-1; i<=nlstate+ndeath; i++)  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          for (jk=-1; jk<=nlstate+ndeath; jk++)  
             for(m=iagemin; m <= iagemax+3; m++)
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);              freq[i][jk][m]=0;
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);  
       for (i=1; i<=nlstate; i++)  
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        for(m=iagemin; m <= iagemax+3; m++)
         for (j=ncov;j>=1;j--){          prop[i][m]=0;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        
         }        dateintsum=0;
         num[i]=atol(stra);        k2cpt=0;
         for (i=1; i<=imx; i++) {
         /*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]));*/          bool=1;
           if  (cptcovn>0) {
         i=i+1;            for (z1=1; z1<=cptcoveff; z1++) 
       }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     }                bool=0;
           }
     /*scanf("%d",i);*/          if (bool==1){
   imx=i-1; /* Number of individuals */            for(m=firstpass; m<=lastpass; m++){
               k2=anint[m][i]+(mint[m][i]/12.);
   /* Calculation of the number of parameter from char model*/              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   Tvar=ivector(1,15);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   Tprod=ivector(1,15);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   Tvaraff=ivector(1,15);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   Tvard=imatrix(1,15,1,2);                if (m<lastpass) {
   Tage=ivector(1,15);                        freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                      freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
   if (strlen(model) >1){                }
     j=0, j1=0, k1=1, k2=1;                
     j=nbocc(model,'+');                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     j1=nbocc(model,'*');                  dateintsum=dateintsum+k2;
     cptcovn=j+1;                  k2cpt++;
     cptcovprod=j1;                }
                    /*}*/
                }
     strcpy(modelsav,model);          }
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){        }
       printf("Error. Non available option model=%s ",model);         
       goto end;        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
     }  
            if  (cptcovn>0) {
     for(i=(j+1); i>=1;i--){          fprintf(ficresp, "\n#********** Variable "); 
       cutv(stra,strb,modelsav,'+');          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          fprintf(ficresp, "**********\n#");
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        }
       /*scanf("%d",i);*/        for(i=1; i<=nlstate;i++) 
       if (strchr(strb,'*')) {          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         cutv(strd,strc,strb,'*');        fprintf(ficresp, "\n");
         if (strcmp(strc,"age")==0) {        
           cptcovprod--;        for(i=iagemin; i <= iagemax+3; i++){
           cutv(strb,stre,strd,'V');          if(i==iagemax+3){
           Tvar[i]=atoi(stre);            fprintf(ficlog,"Total");
           cptcovage++;          }else{
             Tage[cptcovage]=i;            if(first==1){
             /*printf("stre=%s ", stre);*/              first=0;
         }              printf("See log file for details...\n");
         else if (strcmp(strd,"age")==0) {            }
           cptcovprod--;            fprintf(ficlog,"Age %d", i);
           cutv(strb,stre,strc,'V');          }
           Tvar[i]=atoi(stre);          for(jk=1; jk <=nlstate ; jk++){
           cptcovage++;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
           Tage[cptcovage]=i;              pp[jk] += freq[jk][m][i]; 
         }          }
         else {          for(jk=1; jk <=nlstate ; jk++){
           cutv(strb,stre,strc,'V');            for(m=-1, pos=0; m <=0 ; m++)
           Tvar[i]=ncov+k1;              pos += freq[jk][m][i];
           cutv(strb,strc,strd,'V');            if(pp[jk]>=1.e-10){
           Tprod[k1]=i;              if(first==1){
           Tvard[k1][1]=atoi(strc);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           Tvard[k1][2]=atoi(stre);              }
           Tvar[cptcovn+k2]=Tvard[k1][1];              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           Tvar[cptcovn+k2+1]=Tvard[k1][2];            }else{
           for (k=1; k<=lastobs;k++)              if(first==1)
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           k1++;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           k2=k2+2;            }
         }          }
       }  
       else {          for(jk=1; jk <=nlstate ; jk++){
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
        /*  scanf("%d",i);*/              pp[jk] += freq[jk][m][i];
       cutv(strd,strc,strb,'V');          }       
       Tvar[i]=atoi(strc);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
       }            pos += pp[jk];
       strcpy(modelsav,stra);              posprop += prop[jk][i];
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);          }
         scanf("%d",i);*/          for(jk=1; jk <=nlstate ; jk++){
     }            if(pos>=1.e-5){
 }              if(first==1)
                  printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   printf("cptcovprod=%d ", cptcovprod);            }else{
   scanf("%d ",i);*/              if(first==1)
     fclose(fic);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     /*  if(mle==1){*/            }
     if (weightopt != 1) { /* Maximisation without weights*/            if( i <= iagemax){
       for(i=1;i<=n;i++) weight[i]=1.0;              if(pos>=1.e-5){
     }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     /*-calculation of age at interview from date of interview and age at death -*/                /*probs[i][jk][j1]= pp[jk]/pos;*/
     agev=matrix(1,maxwav,1,imx);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
                  }
     for (i=1; i<=imx; i++)  {              else
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
       for(m=1; (m<= maxwav); m++){            }
         if(s[m][i] >0){          }
           if (s[m][i] == nlstate+1) {          
             if(agedc[i]>0)          for(jk=-1; jk <=nlstate+ndeath; jk++)
               if(moisdc[i]!=99 && andc[i]!=9999)            for(m=-1; m <=nlstate+ndeath; m++)
               agev[m][i]=agedc[i];              if(freq[jk][m][i] !=0 ) {
             else {              if(first==1)
               if (andc[i]!=9999){                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
               printf("Warning negative age at death: %d line:%d\n",num[i],i);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               agev[m][i]=-1;              }
               }          if(i <= iagemax)
             }            fprintf(ficresp,"\n");
           }          if(first==1)
           else if(s[m][i] !=9){ /* Should no more exist */            printf("Others in log...\n");
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          fprintf(ficlog,"\n");
             if(mint[m][i]==99 || anint[m][i]==9999)        }
               agev[m][i]=1;      }
             else if(agev[m][i] <agemin){    }
               agemin=agev[m][i];    dateintmean=dateintsum/k2cpt; 
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/   
             }    fclose(ficresp);
             else if(agev[m][i] >agemax){    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
               agemax=agev[m][i];    free_vector(pp,1,nlstate);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
             }    /* End of Freq */
             /*agev[m][i]=anint[m][i]-annais[i];*/  }
             /*   agev[m][i] = age[i]+2*m;*/  
           }  /************ Prevalence ********************/
           else { /* =9 */  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)
             agev[m][i]=1;  {  
             s[m][i]=-1;    /* 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).
         }       We still use firstpass and lastpass as another selection.
         else /*= 0 Unknown */    */
           agev[m][i]=1;   
       }    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
        double ***freq; /* Frequencies */
     }    double *pp, **prop;
     for (i=1; i<=imx; i++)  {    double pos,posprop; 
       for(m=1; (m<= maxwav); m++){    double  y2; /* in fractional years */
         if (s[m][i] > (nlstate+ndeath)) {    int iagemin, iagemax;
           printf("Error: Wrong value in nlstate or ndeath\n");    
           goto end;    iagemin= (int) agemin;
         }    iagemax= (int) agemax;
       }    /*pp=vector(1,nlstate);*/
     }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    j1=0;
     
     free_vector(severity,1,maxwav);    j=cptcoveff;
     free_imatrix(outcome,1,maxwav+1,1,n);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_vector(moisnais,1,n);    
     free_vector(annais,1,n);    for(k1=1; k1<=j;k1++){
     free_matrix(mint,1,maxwav,1,n);      for(i1=1; i1<=ncodemax[k1];i1++){
     free_matrix(anint,1,maxwav,1,n);        j1++;
     free_vector(moisdc,1,n);        
     free_vector(andc,1,n);        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
                prop[i][m]=0.0;
     wav=ivector(1,imx);       
     dh=imatrix(1,lastpass-firstpass+1,1,imx);        for (i=1; i<=imx; i++) { /* Each individual */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);          bool=1;
              if  (cptcovn>0) {
     /* Concatenates waves */            for (z1=1; z1<=cptcoveff; z1++) 
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
           } 
       Tcode=ivector(1,100);          if (bool==1) { 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
       ncodemax[1]=1;              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                      if(agev[m][i]==0) agev[m][i]=iagemax+1;
    codtab=imatrix(1,100,1,10);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
    h=0;                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); 
    m=pow(2,cptcoveff);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                    /*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]]);*/
    for(k=1;k<=cptcoveff; k++){                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
      for(i=1; i <=(m/pow(2,k));i++){                  prop[s[m][i]][iagemax+3] += weight[i]; 
        for(j=1; j <= ncodemax[k]; j++){                } 
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){              }
            h++;            } /* end selection of waves */
            if (h>m) h=1;codtab[h][k]=j;          }
          }        }
        }        for(i=iagemin; i <= iagemax+3; i++){  
      }          
    }          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             posprop += prop[jk][i]; 
           } 
    /*for(i=1; i <=m ;i++){  
      for(k=1; k <=cptcovn; k++){          for(jk=1; jk <=nlstate ; jk++){     
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);            if( i <=  iagemax){ 
      }              if(posprop>=1.e-5){ 
      printf("\n");                probs[i][jk][j1]= prop[jk][i]/posprop;
    }              } 
    scanf("%d",i);*/            } 
              }/* end jk */ 
    /* Calculates basic frequencies. Computes observed prevalence at single age        }/* end i */ 
        and prints on file fileres'p'. */      } /* end i1 */
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);    } /* end k1 */
     
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*free_vector(pp,1,nlstate);*/
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  }  /* End of prevalence */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  
      /************* Waves Concatenation ***************/
     /* 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] */  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)
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
     if(mle==1){       Death is a valid wave (if date is known).
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);       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.
     /*--------- results files --------------*/       */
     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);  
        int i, mi, m;
    jk=1;    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
    fprintf(ficres,"# Parameters\n");       double sum=0., jmean=0.;*/
    printf("# Parameters\n");    int first;
    for(i=1,jk=1; i <=nlstate; i++){    int j, k=0,jk, ju, jl;
      for(k=1; k <=(nlstate+ndeath); k++){    double sum=0.;
        if (k != i)    first=0;
          {    jmin=1e+5;
            printf("%d%d ",i,k);    jmax=-1;
            fprintf(ficres,"%1d%1d ",i,k);    jmean=0.;
            for(j=1; j <=ncovmodel; j++){    for(i=1; i<=imx; i++){
              printf("%f ",p[jk]);      mi=0;
              fprintf(ficres,"%f ",p[jk]);      m=firstpass;
              jk++;      while(s[m][i] <= nlstate){
            }        if(s[m][i]>=1)
            printf("\n");          mw[++mi][i]=m;
            fprintf(ficres,"\n");        if(m >=lastpass)
          }          break;
      }        else
    }          m++;
  if(mle==1){      }/* end while */
     /* Computing hessian and covariance matrix */      if (s[m][i] > nlstate){
     ftolhess=ftol; /* Usually correct */        mi++;     /* Death is another wave */
     hesscov(matcov, p, npar, delti, ftolhess, func);        /* if(mi==0)  never been interviewed correctly before death */
  }           /* Only death is a correct wave */
     fprintf(ficres,"# Scales\n");        mw[mi][i]=m;
     printf("# Scales\n");      }
      for(i=1,jk=1; i <=nlstate; i++){  
       for(j=1; j <=nlstate+ndeath; j++){      wav[i]=mi;
         if (j!=i) {      if(mi==0){
           fprintf(ficres,"%1d%1d",i,j);        nbwarn++;
           printf("%1d%1d",i,j);        if(first==0){
           for(k=1; k<=ncovmodel;k++){          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
             printf(" %.5e",delti[jk]);          first=1;
             fprintf(ficres," %.5e",delti[jk]);        }
             jk++;        if(first==1){
           }          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
           printf("\n");        }
           fprintf(ficres,"\n");      } /* end mi==0 */
         }    } /* End individuals */
       }  
       }    for(i=1; i<=imx; i++){
          for(mi=1; mi<wav[i];mi++){
     k=1;        if (stepm <=0)
     fprintf(ficres,"# Covariance\n");          dh[mi][i]=1;
     printf("# Covariance\n");        else{
     for(i=1;i<=npar;i++){          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       /*  if (k>nlstate) k=1;            if (agedc[i] < 2*AGESUP) {
       i1=(i-1)/(ncovmodel*nlstate)+1;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);              if(j==0) j=1;  /* Survives at least one month after exam */
       printf("%s%d%d",alph[k],i1,tab[i]);*/              else if(j<0){
       fprintf(ficres,"%3d",i);                nberr++;
       printf("%3d",i);                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       for(j=1; j<=i;j++){                j=1; /* Temporary Dangerous patch */
         fprintf(ficres," %.5e",matcov[i][j]);                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
         printf(" %.5e",matcov[i][j]);                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       }                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
       fprintf(ficres,"\n");              }
       printf("\n");              k=k+1;
       k++;              if (j >= jmax) jmax=j;
     }              if (j <= jmin) jmin=j;
                  sum=sum+j;
     while((c=getc(ficpar))=='#' && c!= EOF){              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       ungetc(c,ficpar);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       fgets(line, MAXLINE, ficpar);            }
       puts(line);          }
       fputs(line,ficparo);          else{
     }            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     ungetc(c,ficpar);            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
              k=k+1;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);            if (j >= jmax) jmax=j;
                else if (j <= jmin)jmin=j;
     if (fage <= 2) {            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       bage = agemin;            /*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]);*/
       fage = agemax;            if(j<0){
     }              nberr++;
               printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);            }
             sum=sum+j;
              }
 /*------------ gnuplot -------------*/          jk= j/stepm;
 chdir(pathcd);          jl= j -jk*stepm;
   if((ficgp=fopen("graph.plt","w"))==NULL) {          ju= j -(jk+1)*stepm;
     printf("Problem with file graph.gp");goto end;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   }            if(jl==0){
 #ifdef windows              dh[mi][i]=jk;
   fprintf(ficgp,"cd \"%s\" \n",pathc);              bh[mi][i]=0;
 #endif            }else{ /* We want a negative bias in order to only have interpolation ie
 m=pow(2,cptcoveff);                    * at the price of an extra matrix product in likelihood */
                dh[mi][i]=jk+1;
  /* 1eme*/              bh[mi][i]=ju;
   for (cpt=1; cpt<= nlstate ; cpt ++) {            }
    for (k1=1; k1<= m ; k1 ++) {          }else{
             if(jl <= -ju){
 #ifdef windows              dh[mi][i]=jk;
     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);              bh[mi][i]=jl;       /* bias is positive if real duration
 #endif                                   * is higher than the multiple of stepm and negative otherwise.
 #ifdef unix                                   */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);            }
 #endif            else{
               dh[mi][i]=jk+1;
 for (i=1; i<= nlstate ; i ++) {              bh[mi][i]=ju;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            if(dh[mi][i]==0){
 }              dh[mi][i]=1; /* At least one step */
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);              bh[mi][i]=ju; /* At least one step */
     for (i=1; i<= nlstate ; i ++) {              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          } /* end if mle */
 }        }
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);      } /* end wave */
      for (i=1; i<= nlstate ; i ++) {    }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    jmean=sum/k;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
 }      fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));   }
 #ifdef unix  
 fprintf(ficgp,"\nset ter gif small size 400,300");  /*********** Tricode ****************************/
 #endif  void tricode(int *Tvar, int **nbcode, int imx)
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  {
    }    
   }    int Ndum[20],ij=1, k, j, i, maxncov=19;
   /*2 eme*/    int cptcode=0;
     cptcoveff=0; 
   for (k1=1; k1<= m ; k1 ++) {   
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    for (k=0; k<maxncov; k++) Ndum[k]=0;
        for (k=1; k<=7; k++) ncodemax[k]=0;
     for (i=1; i<= nlstate+1 ; i ++) {  
       k=2*i;    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
       for (j=1; j<= nlstate+1 ; j ++) {                                 modality*/ 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");        Ndum[ij]++; /*store the modality */
 }          /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);                                         Tvar[j]. If V=sex and male is 0 and 
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);                                         female is 1, then  cptcode=1.*/
       for (j=1; j<= nlstate+1 ; j ++) {      }
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
         else fprintf(ficgp," \%%*lf (\%%*lf)");      for (i=0; i<=cptcode; i++) {
 }          if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
       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 ++) {      ij=1; 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      for (i=1; i<=ncodemax[j]; i++) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");        for (k=0; k<= maxncov; k++) {
 }            if (Ndum[k] != 0) {
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");            nbcode[Tvar[j]][ij]=k; 
       else fprintf(ficgp,"\" t\"\" w l 0,");            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
     }            
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);            ij++;
   }          }
            if (ij > ncodemax[j]) break; 
   /*3eme*/        }  
       } 
   for (k1=1; k1<= m ; k1 ++) {    }  
     for (cpt=1; cpt<= nlstate ; cpt ++) {  
       k=2+nlstate*(cpt-1);   for (k=0; k< maxncov; k++) Ndum[k]=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<=ncovmodel-2; i++) { 
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);     /* 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];
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);     Ndum[ij]++;
     }   }
   }  
     ij=1;
   /* CV preval stat */   for (i=1; i<= maxncov; i++) {
   for (k1=1; k1<= m ; k1 ++) {     if((Ndum[i]!=0) && (i<=ncovcol)){
     for (cpt=1; cpt<nlstate ; cpt ++) {       Tvaraff[ij]=i; /*For printing */
       k=3;       ij++;
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);     }
       for (i=1; i< nlstate ; i ++)   }
         fprintf(ficgp,"+$%d",k+i+1);   
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);   cptcoveff=ij-1; /*Number of simple covariates*/
        }
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  /*********** Health Expectancies ****************/
       for (i=1; i< nlstate ; i ++) {  
         l=3+(nlstate+ndeath)*cpt;  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )
         fprintf(ficgp,"+$%d",l+i+1);  
       }  {
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      /* Health expectancies */
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
     }    double age, agelim, hf;
   }    double ***p3mat,***varhe;
     double **dnewm,**doldm;
   /* proba elementaires */    double *xp;
    for(i=1,jk=1; i <=nlstate; i++){    double **gp, **gm;
     for(k=1; k <=(nlstate+ndeath); k++){    double ***gradg, ***trgradg;
       if (k != i) {    int theta;
         for(j=1; j <=ncovmodel; j++){  
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
           /*fprintf(ficgp,"%s",alph[1]);*/    xp=vector(1,npar);
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    dnewm=matrix(1,nlstate*nlstate,1,npar);
           jk++;    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
           fprintf(ficgp,"\n");    
         }    fprintf(ficreseij,"# Health expectancies\n");
       }    fprintf(ficreseij,"# Age");
     }    for(i=1; i<=nlstate;i++)
     }      for(j=1; j<=nlstate;j++)
         fprintf(ficreseij," %1d-%1d (SE)",i,j);
   for(jk=1; jk <=m; jk++) {    fprintf(ficreseij,"\n");
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);  
    i=1;    if(estepm < stepm){
    for(k2=1; k2<=nlstate; k2++) {      printf ("Problem %d lower than %d\n",estepm, stepm);
      k3=i;    }
      for(k=1; k<=(nlstate+ndeath); k++) {    else  hstepm=estepm;   
        if (k != k2){    /* We compute the life expectancy from trapezoids spaced every estepm months
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);     * This is mainly to measure the difference between two models: for example
 ij=1;     * if stepm=24 months pijx are given only every 2 years and by summing them
         for(j=3; j <=ncovmodel; j++) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {     * progression in between and thus overestimating or underestimating according
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);     * to the curvature of the survival function. If, for the same date, we 
             ij++;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
           }     * to compare the new estimate of Life expectancy with the same linear 
           else     * hypothesis. A more precise result, taking into account a more precise
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);     * curvature will be obtained if estepm is as small as stepm. */
         }  
           fprintf(ficgp,")/(1");    /* For example we decided to compute the life expectancy with the smallest unit */
            /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         for(k1=1; k1 <=nlstate; k1++){         nhstepm is the number of hstepm from age to agelim 
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);       nstepm is the number of stepm from age to agelin. 
 ij=1;       Look at hpijx to understand the reason of that which relies in memory size
           for(j=3; j <=ncovmodel; j++){       and note for a fixed period like estepm months */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);       survival function given by stepm (the optimization length). Unfortunately it
             ij++;       means that if the survival funtion is printed only each two years of age and if
           }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           else       results. So we changed our mind and took the option of the best precision.
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    */
           }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           fprintf(ficgp,")");  
         }    agelim=AGESUP;
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      /* nhstepm age range expressed in number of stepm */
         i=i+ncovmodel;      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
        }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      }      /* if (stepm >= YEARM) hstepm=1;*/
    }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
          gp=matrix(0,nhstepm,1,nlstate*nlstate);
   fclose(ficgp);      gm=matrix(0,nhstepm,1,nlstate*nlstate);
      
 chdir(path);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     free_matrix(agev,1,maxwav,1,imx);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
     free_ivector(wav,1,imx);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);   
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);  
          hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     free_imatrix(s,1,maxwav+1,1,n);  
          /* Computing  Variances of health expectancies */
      
     free_ivector(num,1,n);       for(theta=1; theta <=npar; theta++){
     free_vector(agedc,1,n);        for(i=1; i<=npar; i++){ 
     free_vector(weight,1,n);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     /*free_matrix(covar,1,NCOVMAX,1,n);*/        }
     fclose(ficparo);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     fclose(ficres);    
     /*  }*/        cptj=0;
            for(j=1; j<= nlstate; j++){
    /*________fin mle=1_________*/          for(i=1; i<=nlstate; i++){
                cptj=cptj+1;
             for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
                gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
     /* No more information from the sample is required now */            }
   /* Reads comments: lines beginning with '#' */          }
   while((c=getc(ficpar))=='#' && c!= EOF){        }
     ungetc(c,ficpar);       
     fgets(line, MAXLINE, ficpar);       
     puts(line);        for(i=1; i<=npar; i++) 
     fputs(line,ficparo);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   ungetc(c,ficpar);        
          cptj=0;
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        for(j=1; j<= nlstate; j++){
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);          for(i=1;i<=nlstate;i++){
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);            cptj=cptj+1;
 /*--------- index.htm --------*/            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
   
   if((fichtm=fopen("index.htm","w"))==NULL)    {              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
     printf("Problem with index.htm \n");goto end;            }
   }          }
         }
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.64a </font> <hr size=\"2\" color=\"#EC5E5E\">        for(j=1; j<= nlstate*nlstate; j++)
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>          for(h=0; h<=nhstepm-1; h++){
 Total number of observations=%d <br>            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>          }
 <hr  size=\"2\" color=\"#EC5E5E\">       } 
 <li>Outputs files<br><br>\n     
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n  /* End theta */
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>  
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>  
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>       for(h=0; h<=nhstepm-1; h++)
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>        for(j=1; j<=nlstate*nlstate;j++)
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>          for(theta=1; theta <=npar; theta++)
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>            trgradg[h][j][theta]=gradg[h][theta][j];
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);       
   
  fprintf(fichtm," <li>Graphs</li><p>");       for(i=1;i<=nlstate*nlstate;i++)
         for(j=1;j<=nlstate*nlstate;j++)
  m=cptcoveff;          varhe[i][j][(int)age] =0.;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  
        printf("%d|",(int)age);fflush(stdout);
  j1=0;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
  for(k1=1; k1<=m;k1++){       for(h=0;h<=nhstepm-1;h++){
    for(i1=1; i1<=ncodemax[k1];i1++){        for(k=0;k<=nhstepm-1;k++){
        j1++;          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
        if (cptcovn > 0) {          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");          for(i=1;i<=nlstate*nlstate;i++)
          for (cpt=1; cpt<=cptcoveff;cpt++)            for(j=1;j<=nlstate*nlstate;j++)
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");        }
        }      }
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      /* Computing expectancies */
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          for(i=1; i<=nlstate;i++)
        for(cpt=1; cpt<nlstate;cpt++){        for(j=1; j<=nlstate;j++)
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
        }            
     for(cpt=1; cpt<=nlstate;cpt++) {  /* 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]);*/
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  
 interval) in state (%d): v%s%d%d.gif <br>          }
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    
      }      fprintf(ficreseij,"%3.0f",age );
      for(cpt=1; cpt<=nlstate;cpt++) {      cptj=0;
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>      for(i=1; i<=nlstate;i++)
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        for(j=1; j<=nlstate;j++){
      }          cptj++;
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
 health expectancies in states (1) and (2): e%s%d.gif<br>        }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);      fprintf(ficreseij,"\n");
 fprintf(fichtm,"\n</body>");     
    }      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
  }      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
 fclose(fichtm);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   /*--------------- Prevalence limit --------------*/      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      }
   strcpy(filerespl,"pl");    printf("\n");
   strcat(filerespl,fileres);    fprintf(ficlog,"\n");
   if((ficrespl=fopen(filerespl,"w"))==NULL) {  
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    free_vector(xp,1,npar);
   }    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   fprintf(ficrespl,"#Prevalence limit\n");    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   fprintf(ficrespl,"#Age ");  }
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");  /************ Variance ******************/
    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)
   prlim=matrix(1,nlstate,1,nlstate);  {
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* Variance of health expectancies */
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* double **newm;*/
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **dnewm,**doldm;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    double **dnewmp,**doldmp;
   k=0;    int i, j, nhstepm, hstepm, h, nstepm ;
   agebase=agemin;    int k, cptcode;
   agelim=agemax;    double *xp;
   ftolpl=1.e-10;    double **gp, **gm;  /* for var eij */
   i1=cptcoveff;    double ***gradg, ***trgradg; /*for var eij */
   if (cptcovn < 1){i1=1;}    double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
   for(cptcov=1;cptcov<=i1;cptcov++){    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double ***p3mat;
         k=k+1;    double age,agelim, hf;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    double ***mobaverage;
         fprintf(ficrespl,"\n#******");    int theta;
         for(j=1;j<=cptcoveff;j++)    char digit[4];
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    char digitp[25];
         fprintf(ficrespl,"******\n");  
            char fileresprobmorprev[FILENAMELENGTH];
         for (age=agebase; age<=agelim; age++){  
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    if(popbased==1){
           fprintf(ficrespl,"%.0f",age );      if(mobilav!=0)
           for(i=1; i<=nlstate;i++)        strcpy(digitp,"-populbased-mobilav-");
           fprintf(ficrespl," %.5f", prlim[i][i]);      else strcpy(digitp,"-populbased-nomobil-");
           fprintf(ficrespl,"\n");    }
         }    else 
       }      strcpy(digitp,"-stablbased-");
     }  
   fclose(ficrespl);    if (mobilav!=0) {
   /*------------- h Pij x at various ages ------------*/      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
        if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;      }
   }    }
   printf("Computing pij: result on file '%s' \n", filerespij);  
      strcpy(fileresprobmorprev,"prmorprev"); 
   stepsize=(int) (stepm+YEARM-1)/YEARM;    sprintf(digit,"%-d",ij);
   if (stepm<=24) stepsize=2;    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
   agelim=AGESUP;    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   hstepm=stepsize*YEARM; /* Every year of age */    strcat(fileresprobmorprev,fileres);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprobmorprev);
   k=0;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   for(cptcov=1;cptcov<=i1;cptcov++){    }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       k=k+1;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
         fprintf(ficrespij,"\n#****** ");    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
         for(j=1;j<=cptcoveff;j++)    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficrespij,"******\n");      fprintf(ficresprobmorprev," p.%-d SE",j);
              for(i=1; i<=nlstate;i++)
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    }  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    fprintf(ficresprobmorprev,"\n");
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficgp,"\n# Routine varevsij");
           oldm=oldms;savm=savms;    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");
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           fprintf(ficrespij,"# Age");  /*   } */
           for(i=1; i<=nlstate;i++)    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);    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(ficrespij,"\n");    fprintf(ficresvij,"# Age");
           for (h=0; h<=nhstepm; h++){    for(i=1; i<=nlstate;i++)
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      for(j=1; j<=nlstate;j++)
             for(i=1; i<=nlstate;i++)        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
               for(j=1; j<=nlstate+ndeath;j++)    fprintf(ficresvij,"\n");
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);  
             fprintf(ficrespij,"\n");    xp=vector(1,npar);
           }    dnewm=matrix(1,nlstate,1,npar);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    doldm=matrix(1,nlstate,1,nlstate);
           fprintf(ficrespij,"\n");    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
         }    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     }  
   }    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     gpp=vector(nlstate+1,nlstate+ndeath);
   fclose(ficrespij);    gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   /*---------- Health expectancies and variances ------------*/    
     if(estepm < stepm){
   strcpy(filerest,"t");      printf ("Problem %d lower than %d\n",estepm, stepm);
   strcat(filerest,fileres);    }
   if((ficrest=fopen(filerest,"w"))==NULL) {    else  hstepm=estepm;   
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    /* For example we decided to compute the life expectancy with the smallest unit */
   }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);       nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   strcpy(filerese,"e");       and note for a fixed period like k years */
   strcat(filerese,fileres);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   if((ficreseij=fopen(filerese,"w"))==NULL) {       survival function given by stepm (the optimization length). Unfortunately it
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);       means that if the survival funtion is printed every two years of age and if
   }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);       results. So we changed our mind and took the option of the best precision.
     */
  strcpy(fileresv,"v");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   strcat(fileresv,fileres);    agelim = AGESUP;
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   k=0;      gp=matrix(0,nhstepm,1,nlstate);
   for(cptcov=1;cptcov<=i1;cptcov++){      gm=matrix(0,nhstepm,1,nlstate);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;  
       fprintf(ficrest,"\n#****** ");      for(theta=1; theta <=npar; theta++){
       for(j=1;j<=cptcoveff;j++)        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       fprintf(ficrest,"******\n");        }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       fprintf(ficreseij,"\n#****** ");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       for(j=1;j<=cptcoveff;j++)  
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);        if (popbased==1) {
       fprintf(ficreseij,"******\n");          if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
       fprintf(ficresvij,"\n#****** ");              prlim[i][i]=probs[(int)age][i][ij];
       for(j=1;j<=cptcoveff;j++)          }else{ /* mobilav */ 
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);            for(i=1; i<=nlstate;i++)
       fprintf(ficresvij,"******\n");              prlim[i][i]=mobaverage[(int)age][i][ij];
           }
       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);          for(j=1; j<= nlstate; j++){
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          for(h=0; h<=nhstepm; h++){
       oldm=oldms;savm=savms;            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
                }
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");        }
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);        /* This for computing probability of death (h=1 means
       fprintf(ficrest,"\n");           computed over hstepm matrices product = hstepm*stepm months) 
                   as a weighted average of prlim.
       hf=1;        */
       if (stepm >= YEARM) hf=stepm/YEARM;        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       epj=vector(1,nlstate+1);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
       for(age=bage; age <=fage ;age++){            gpp[j] += prlim[i][i]*p3mat[i][j][1];
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        }    
         fprintf(ficrest," %.0f",age);        /* end probability of death */
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){  
           for(i=1, epj[j]=0.;i <=nlstate;i++) {        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           epj[nlstate+1] +=epj[j];        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         }   
         for(i=1, vepp=0.;i <=nlstate;i++)        if (popbased==1) {
           for(j=1;j <=nlstate;j++)          if(mobilav ==0){
             vepp += vareij[i][j][(int)age];            for(i=1; i<=nlstate;i++)
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));              prlim[i][i]=probs[(int)age][i][ij];
         for(j=1;j <=nlstate;j++){          }else{ /* mobilav */ 
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));            for(i=1; i<=nlstate;i++)
         }              prlim[i][i]=mobaverage[(int)age][i][ij];
         fprintf(ficrest,"\n");          }
       }        }
     }  
   }        for(j=1; j<= nlstate; j++){
                  for(h=0; h<=nhstepm; h++){
  fclose(ficreseij);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
  fclose(ficresvij);              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   fclose(ficrest);          }
   fclose(ficpar);        }
   free_vector(epj,1,nlstate+1);        /* This for computing probability of death (h=1 means
   /*  scanf("%d ",i); */           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
   /*------- Variance limit prevalence------*/          */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
 strcpy(fileresvpl,"vpl");          for(i=1,gmp[j]=0.; i<= nlstate; i++)
   strcat(fileresvpl,fileres);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        }    
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);        /* end probability of death */
     exit(0);  
   }        for(j=1; j<= nlstate; j++) /* vareij */
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
  k=0;          }
  for(cptcov=1;cptcov<=i1;cptcov++){  
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
      k=k+1;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
      fprintf(ficresvpl,"\n#****** ");        }
      for(j=1;j<=cptcoveff;j++)  
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      } /* End theta */
      fprintf(ficresvpl,"******\n");  
            trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
      varpl=matrix(1,nlstate,(int) bage, (int) fage);  
      oldm=oldms;savm=savms;      for(h=0; h<=nhstepm; h++) /* veij */
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);        for(j=1; j<=nlstate;j++)
    }          for(theta=1; theta <=npar; theta++)
  }            trgradg[h][j][theta]=gradg[h][theta][j];
   
   fclose(ficresvpl);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
   /*---------- End : free ----------------*/          trgradgp[j][theta]=gradgp[theta][j];
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    
    
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      for(i=1;i<=nlstate;i++)
          for(j=1;j<=nlstate;j++)
            vareij[i][j][(int)age] =0.;
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);      for(h=0;h<=nhstepm;h++){
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(k=0;k<=nhstepm;k++){
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
            matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   free_matrix(matcov,1,npar,1,npar);          for(i=1;i<=nlstate;i++)
   free_vector(delti,1,npar);            for(j=1;j<=nlstate;j++)
                vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        }
       }
   printf("End of Imach\n");    
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */      /* pptj */
        matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
   /* 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);*/      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
   /*printf("Total time was %d uSec.\n", total_usecs);*/      for(j=nlstate+1;j<=nlstate+ndeath;j++)
   /*------ End -----------*/        for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
  end:      /* end ppptj */
 #ifdef windows      /*  x centered again */
  chdir(pathcd);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
 #endif      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
  /*system("wgnuplot graph.plt");*/   
  system("../gp37mgw/wgnuplot graph.plt");      if (popbased==1) {
         if(mobilav ==0){
 #ifdef windows          for(i=1; i<=nlstate;i++)
   while (z[0] != 'q') {            prlim[i][i]=probs[(int)age][i][ij];
     chdir(pathcd);        }else{ /* mobilav */ 
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          for(i=1; i<=nlstate;i++)
     scanf("%s",z);            prlim[i][i]=mobaverage[(int)age][i][ij];
     if (z[0] == 'c') system("./imach");        }
     else if (z[0] == 'e') {      }
       chdir(path);               
       system("index.htm");      /* This for computing probability of death (h=1 means
     }         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
     else if (z[0] == 'q') exit(0);         as a weighted average of prlim.
   }      */
 #endif      for(j=nlstate+1;j<=nlstate+ndeath;j++){
 }        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
      
     fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcov,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     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> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   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>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<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(fichtmcov, "\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(fichtmcov, "**********\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(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), 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(fichtmcov," %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 \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), 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);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* 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;
   
      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=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Stable prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - Life expectancies by age and initial health status (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   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: %s%d1.png<br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),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: %s%d2.png<br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),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=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): %s%d%d.png <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,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", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Health expectancies with their variances (no covariance): <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of stable prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  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); */
    fflush(fichtm);
    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 (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     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);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),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,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),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,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),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,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),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,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),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,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),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 \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),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," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),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 \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),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,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%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 \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),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 */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# 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(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       sump=sump+1;
       num=num+1;
     }
    
    
     /* for (i=1; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=0;i<=imx-1 ; i++)
       {
         if (cens[i]==1 & wav[i]>1)
           A=-x[1]/(x[2])*
             (exp(x[2]/YEARM*(agecens[i]*12-agegomp*12))-exp(x[2]/YEARM*(ageexmed[i]*12-agegomp*12)));
         
         if (cens[i]==0 & wav[i]>1)
           A=-x[1]/(x[2])*
                (exp(x[2]/YEARM*(agedc[i]*12-agegomp*12))-exp(x[2]/YEARM*(ageexmed[i]*12-agegomp*12)))
             +log(x[1]/YEARM)+x[2]/YEARM*(agedc[i]*12-agegomp*12)+log(YEARM);      
         
         if (wav[i]>1 & agecens[i]>15) {
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov){
     int i;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     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;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char strstart[80], *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     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, MAXLINE)!= 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(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("pathimach=%s, pathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter 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);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     while (fgets(line, MAXLINE, fic) != NULL)    {
       if ((i >= firstobs) && (i <=lastobs)) {
           
         for (j=maxwav;j>=1;j--){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb); 
           strcpy(line,stra);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         }
           
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);
         for (j=ncovcol;j>=1;j--){
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         } 
         lstra=strlen(stra);
         if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
           stratrunc = &(stra[lstra-9]);
           num[i]=atol(stratrunc);
         }
         else
           num[i]=atol(stra);
           
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
           printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
   
         i=i+1;
       }
     }
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
    for (i=1; i<=imx; i++)
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameter from char model*/
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);
     fclose(fic);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a
                                    month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<body>\n<title>IMaCh Cov %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<body>\n<title>IMaCh %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* 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);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (j=1; j<=lastpass; j++)
           if (s[j][i]>nlstate) {
             dcwave[i]=j;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];agecens[i]=1.; 
           if (ageexmed[i]>1 & wav[i]>0) agecens[i]=agev[mw[j][i]][i];
           cens[i]=1;
           
           if (ageexmed[i]<1) cens[i]=-1;
           if (agedc[i]< AGESUP & agedc[i]>1 & dcwave[i]>firstpass & dcwave[i]<=lastpass) cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
   
       p[1]=0.1; p[2]=0.1;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow-mort"); 
     strcat(filerespow,fileres);
     if((ficrespow=fopen(filerespow,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
     /*  for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     */
     fprintf(ficrespow,"\n");
   
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM,delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov);
     } /* Endof if mle==-3 */
   
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       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");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       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.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficrespl,"#Stable prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
   
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- 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 ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
       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);
   
       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);
   
   
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocaltime at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>",strstart, strtend);
     fclose(fichtm);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
     chdir(path);
     strcpy(plotcmd,"\"");
     strcat(plotcmd,pathimach);
     strcat(plotcmd,GNUPLOTPROGRAM);
     strcat(plotcmd,"\"");
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting graphs with: %s",plotcmd);fflush(stdout);
     if((outcmd=system(plotcmd)) != 0){
       printf(" Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

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  Added in v.1.99


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