Diff for /imach/src/imach.c between versions 1.8 and 1.100

version 1.8, 2001/05/02 17:54:31 version 1.100, 2004/07/12 18:29:06
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 1.100  2004/07/12 18:29:06  brouard
   individuals from different ages are interviewed on their health status    Add version for Mac OS X. Just define UNIX in Makefile
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.99  2004/06/05 08:57:40  brouard
   Health expectancies are computed from the transistions observed between    *** empty log message ***
   waves and are computed for each degree of severity of disability (number  
   of life states). More degrees you consider, more time is necessary to    Revision 1.98  2004/05/16 15:05:56  brouard
   reach the Maximum Likelihood of the parameters involved in the model.    New version 0.97 . First attempt to estimate force of mortality
   The simplest model is the multinomial logistic model where pij is    directly from the data i.e. without the need of knowing the health
   the probabibility to be observed in state j at the second wave conditional    state at each age, but using a Gompertz model: log u =a + b*age .
   to be observed in state i at the first wave. Therefore the model is:    This is the basic analysis of mortality and should be done before any
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    other analysis, in order to test if the mortality estimated from the
   is a covariate. If you want to have a more complex model than "constant and    cross-longitudinal survey is different from the mortality estimated
   age", you should modify the program where the markup    from other sources like vital statistic data.
     *Covariates have to be included here again* invites you to do it.  
   More covariates you add, less is the speed of the convergence.    The same imach parameter file can be used but the option for mle should be -3.
   
   The advantage that this computer programme claims, comes from that if the    Agnès, who wrote this part of the code, tried to keep most of the
   delay between waves is not identical for each individual, or if some    former routines in order to include the new code within the former code.
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    The output is very simple: only an estimate of the intercept and of
   hPijx is the probability to be    the slope with 95% confident intervals.
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Current limitations:
   unobserved intermediate  states. This elementary transition (by month or    A) Even if you enter covariates, i.e. with the
   quarter trimester, semester or year) is model as a multinomial logistic.    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    B) There is no computation of Life Expectancy nor Life Table.
   and the contribution of each individual to the likelihood is simply hPijx.  
     Revision 1.97  2004/02/20 13:25:42  lievre
   Also this programme outputs the covariance matrix of the parameters but also    Version 0.96d. Population forecasting command line is (temporarily)
   of the life expectancies. It also computes the prevalence limits.    suppressed.
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.96  2003/07/15 15:38:55  brouard
            Institut national d'études démographiques, Paris.    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   This software have been partly granted by Euro-REVES, a concerted action    rewritten within the same printf. Workaround: many printfs.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.95  2003/07/08 07:54:34  brouard
   software can be distributed freely for non commercial use. Latest version    * imach.c (Repository):
   can be accessed at http://euroreves.ined.fr/imach .    (Repository): Using imachwizard code to output a more meaningful covariance
   **********************************************************************/    matrix (cov(a12,c31) instead of numbers.
    
 #include <math.h>    Revision 1.94  2003/06/27 13:00:02  brouard
 #include <stdio.h>    Just cleaning
 #include <stdlib.h>  
 #include <unistd.h>    Revision 1.93  2003/06/25 16:33:55  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 #define MAXLINE 256    exist so I changed back to asctime which exists.
 #define FILENAMELENGTH 80    (Module): Version 0.96b
 /*#define DEBUG*/  
 #define windows    Revision 1.92  2003/06/25 16:30:45  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): On windows (cygwin) function asctime_r doesn't
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    exist so I changed back to asctime which exists.
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.91  2003/06/25 15:30:29  brouard
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    * imach.c (Repository): Duplicated warning errors corrected.
     (Repository): Elapsed time after each iteration is now output. It
 #define NINTERVMAX 8    helps to forecast when convergence will be reached. Elapsed time
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    is stamped in powell.  We created a new html file for the graphs
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    concerning matrix of covariance. It has extension -cov.htm.
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.90  2003/06/24 12:34:15  brouard
 #define YEARM 12. /* Number of months per year */    (Module): Some bugs corrected for windows. Also, when
 #define AGESUP 130    mle=-1 a template is output in file "or"mypar.txt with the design
 #define AGEBASE 40    of the covariance matrix to be input.
   
     Revision 1.89  2003/06/24 12:30:52  brouard
 int nvar;    (Module): Some bugs corrected for windows. Also, when
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    mle=-1 a template is output in file "or"mypar.txt with the design
 int npar=NPARMAX;    of the covariance matrix to be input.
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.88  2003/06/23 17:54:56  brouard
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    * 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 *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.87  2003/06/18 12:26:01  brouard
 int maxwav; /* Maxim number of waves */    Version 0.96
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.86  2003/06/17 20:04:08  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): Change position of html and gnuplot routines and added
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    routine fileappend.
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.85  2003/06/17 13:12:43  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    * imach.c (Repository): Check when date of death was earlier that
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    current date of interview. It may happen when the death was just
 FILE *ficgp, *fichtm;    prior to the death. In this case, dh was negative and likelihood
 FILE *ficreseij;    was wrong (infinity). We still send an "Error" but patch by
   char filerese[FILENAMELENGTH];    assuming that the date of death was just one stepm after the
  FILE  *ficresvij;    interview.
   char fileresv[FILENAMELENGTH];    (Repository): Because some people have very long ID (first column)
  FILE  *ficresvpl;    we changed int to long in num[] and we added a new lvector for
   char fileresvpl[FILENAMELENGTH];    memory allocation. But we also truncated to 8 characters (left
     truncation)
 #define NR_END 1    (Repository): No more line truncation errors.
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 #define NRANSI    place. It differs from routine "prevalence" which may be called
 #define ITMAX 200    many times. Probs is memory consuming and must be used with
     parcimony.
 #define TOL 2.0e-4    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   
 #define CGOLD 0.3819660    Revision 1.83  2003/06/10 13:39:11  lievre
 #define ZEPS 1.0e-10    *** empty log message ***
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     Revision 1.82  2003/06/05 15:57:20  brouard
 #define GOLD 1.618034    Add log in  imach.c and  fullversion number is now printed.
 #define GLIMIT 100.0  
 #define TINY 1.0e-20  */
   /*
 static double maxarg1,maxarg2;     Interpolated Markov Chain
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Short summary of the programme:
      
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    This program computes Healthy Life Expectancies from
 #define rint(a) floor(a+0.5)    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     first survey ("cross") where individuals from different ages are
 static double sqrarg;    interviewed on their health status or degree of disability (in the
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    case of a health survey which is our main interest) -2- at least a
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    second wave of interviews ("longitudinal") which measure each change
     (if any) in individual health status.  Health expectancies are
 int imx;    computed from the time spent in each health state according to a
 int stepm;    model. More health states you consider, more time is necessary to reach the
 /* Stepm, step in month: minimum step interpolation*/    Maximum Likelihood of the parameters involved in the model.  The
     simplest model is the multinomial logistic model where pij is the
 int m,nb;    probability to be observed in state j at the second wave
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    conditional to be observed in state i at the first wave. Therefore
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 double **pmmij;    'age' is age and 'sex' is a covariate. If you want to have a more
     complex model than "constant and age", you should modify the program
 double *weight;    where the markup *Covariates have to be included here again* invites
 int **s; /* Status */    you to do it.  More covariates you add, slower the
 double *agedc, **covar, idx;    convergence.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     The advantage of this computer programme, compared to a simple
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    multinomial logistic model, is clear when the delay between waves is not
 double ftolhess; /* Tolerance for computing hessian */    identical for each individual. Also, if a individual missed an
     intermediate interview, the information is lost, but taken into
 /**************** split *************************/    account using an interpolation or extrapolation.  
 static  int split( char *path, char *dirc, char *name )  
 {    hPijx is the probability to be observed in state i at age x+h
    char *s;                             /* pointer */    conditional to the observed state i at age x. The delay 'h' can be
    int  l1, l2;                         /* length counters */    split into an exact number (nh*stepm) of unobserved intermediate
     states. This elementary transition (by month, quarter,
    l1 = strlen( path );                 /* length of path */    semester or year) is modelled as a multinomial logistic.  The hPx
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    matrix is simply the matrix product of nh*stepm elementary matrices
    s = strrchr( path, '\\' );           /* find last / */    and the contribution of each individual to the likelihood is simply
    if ( s == NULL ) {                   /* no directory, so use current */    hPijx.
 #if     defined(__bsd__)                /* get current working directory */  
       extern char       *getwd( );    Also this programme outputs the covariance matrix of the parameters but also
     of the life expectancies. It also computes the stable prevalence. 
       if ( getwd( dirc ) == NULL ) {    
 #else    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
       extern char       *getcwd( );             Institut national d'études démographiques, Paris.
     This software have been partly granted by Euro-REVES, a concerted action
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    from the European Union.
 #endif    It is copyrighted identically to a GNU software product, ie programme and
          return( GLOCK_ERROR_GETCWD );    software can be distributed freely for non commercial use. Latest version
       }    can be accessed at http://euroreves.ined.fr/imach .
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
       s++;                              /* after this, the filename */    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
       l2 = strlen( s );                 /* length of filename */    
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    **********************************************************************/
       strcpy( name, s );                /* save file name */  /*
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    main
       dirc[l1-l2] = 0;                  /* add zero */    read parameterfile
    }    read datafile
    l1 = strlen( dirc );                 /* length of directory */    concatwav
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    freqsummary
    return( 0 );                         /* we're done */    if (mle >= 1)
 }      mlikeli
     print results files
     if mle==1 
 /******************************************/       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 void replace(char *s, char*t)        begin-prev-date,...
 {    open gnuplot file
   int i;    open html file
   int lg=20;    stable prevalence
   i=0;     for age prevalim()
   lg=strlen(t);    h Pij x
   for(i=0; i<= lg; i++) {    variance of p varprob
     (s[i] = t[i]);    forecasting if prevfcast==1 prevforecast call prevalence()
     if (t[i]== '\\') s[i]='/';    health expectancies
   }    Variance-covariance of DFLE
 }    prevalence()
      movingaverage()
 int nbocc(char *s, char occ)    varevsij() 
 {    if popbased==1 varevsij(,popbased)
   int i,j=0;    total life expectancies
   int lg=20;    Variance of stable prevalence
   i=0;   end
   lg=strlen(s);  */
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;  
   }  
   return j;   
 }  #include <math.h>
   #include <stdio.h>
 void cutv(char *u,char *v, char*t, char occ)  #include <stdlib.h>
 {  #include <unistd.h>
   int i,lg,j,p=0;  
   i=0;  /* #include <sys/time.h> */
   for(j=0; j<=strlen(t)-1; j++) {  #include <time.h>
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  #include "timeval.h"
   }  
   /* #include <libintl.h> */
   lg=strlen(t);  /* #define _(String) gettext (String) */
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);  #define MAXLINE 256
   }  #define GNUPLOTPROGRAM "gnuplot"
      u[p]='\0';  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
    for(j=0; j<= lg; j++) {  /*#define DEBUG*/
     if (j>=(p+1))(v[j-p-1] = t[j]);  /*#define windows*/
   }  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 }  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
 /********************** nrerror ********************/  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 void nrerror(char error_text[])  
 {  #define NINTERVMAX 8
   fprintf(stderr,"ERREUR ...\n");  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   fprintf(stderr,"%s\n",error_text);  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   exit(1);  #define NCOVMAX 8 /* Maximum number of covariates */
 }  #define MAXN 20000
 /*********************** vector *******************/  #define YEARM 12. /* Number of months per year */
 double *vector(int nl, int nh)  #define AGESUP 130
 {  #define AGEBASE 40
   double *v;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #ifdef UNIX
   if (!v) nrerror("allocation failure in vector");  #define DIRSEPARATOR '/'
   return v-nl+NR_END;  #define ODIRSEPARATOR '\\'
 }  #else
   #define DIRSEPARATOR '\\'
 /************************ free vector ******************/  #define ODIRSEPARATOR '/'
 void free_vector(double*v, int nl, int nh)  #endif
 {  
   free((FREE_ARG)(v+nl-NR_END));  /* $Id$ */
 }  /* $State$ */
   
 /************************ivector *******************************/  char version[]="Imach version 0.97b, May 2004, INED-EUROREVES ";
 int *ivector(long nl,long nh)  char fullversion[]="$Revision$ $Date$"; 
 {  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   int *v;  int nvar;
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   if (!v) nrerror("allocation failure in ivector");  int npar=NPARMAX;
   return v-nl+NR_END;  int nlstate=2; /* Number of live states */
 }  int ndeath=1; /* Number of dead states */
   int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 /******************free ivector **************************/  int popbased=0;
 void free_ivector(int *v, long nl, long nh)  
 {  int *wav; /* Number of waves for this individuual 0 is possible */
   free((FREE_ARG)(v+nl-NR_END));  int maxwav; /* Maxim number of waves */
 }  int jmin, jmax; /* min, max spacing between 2 waves */
   int gipmx, gsw; /* Global variables on the number of contributions 
 /******************* imatrix *******************************/                     to the likelihood and the sum of weights (done by funcone)*/
 int **imatrix(long nrl, long nrh, long ncl, long nch)  int mle, weightopt;
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 {  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   int **m;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
    double jmean; /* Mean space between 2 waves */
   /* allocate pointers to rows */  double **oldm, **newm, **savm; /* Working pointers to matrices */
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   if (!m) nrerror("allocation failure 1 in matrix()");  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   m += NR_END;  FILE *ficlog, *ficrespow;
   m -= nrl;  int globpr; /* Global variable for printing or not */
    double fretone; /* Only one call to likelihood */
    long ipmx; /* Number of contributions */
   /* allocate rows and set pointers to them */  double sw; /* Sum of weights */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  char filerespow[FILENAMELENGTH];
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   m[nrl] += NR_END;  FILE *ficresilk;
   m[nrl] -= ncl;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
    FILE *ficresprobmorprev;
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  FILE *fichtm, *fichtmcov; /* Html File */
    FILE *ficreseij;
   /* return pointer to array of pointers to rows */  char filerese[FILENAMELENGTH];
   return m;  FILE  *ficresvij;
 }  char fileresv[FILENAMELENGTH];
   FILE  *ficresvpl;
 /****************** free_imatrix *************************/  char fileresvpl[FILENAMELENGTH];
 void free_imatrix(m,nrl,nrh,ncl,nch)  char title[MAXLINE];
       int **m;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       long nch,ncl,nrh,nrl;  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
      /* free an int matrix allocated by imatrix() */  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
 {  char command[FILENAMELENGTH];
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  int  outcmd=0;
   free((FREE_ARG) (m+nrl-NR_END));  
 }  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   
 /******************* matrix *******************************/  char filelog[FILENAMELENGTH]; /* Log file */
 double **matrix(long nrl, long nrh, long ncl, long nch)  char filerest[FILENAMELENGTH];
 {  char fileregp[FILENAMELENGTH];
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  char popfile[FILENAMELENGTH];
   double **m;  
   char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   m += NR_END;  struct timezone tzp;
   m -= nrl;  extern int gettimeofday();
   struct tm tmg, tm, tmf, *gmtime(), *localtime();
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  long time_value;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  extern long time();
   m[nrl] += NR_END;  char strcurr[80], strfor[80];
   m[nrl] -= ncl;  
   #define NR_END 1
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define FREE_ARG char*
   return m;  #define FTOL 1.0e-10
 }  
   #define NRANSI 
 /*************************free matrix ************************/  #define ITMAX 200 
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  
 {  #define TOL 2.0e-4 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define CGOLD 0.3819660 
 }  #define ZEPS 1.0e-10 
   #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #define GOLD 1.618034 
 {  #define GLIMIT 100.0 
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define TINY 1.0e-20 
   double ***m;  
   static double maxarg1,maxarg2;
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   if (!m) nrerror("allocation failure 1 in matrix()");  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   m += NR_END;    
   m -= nrl;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   #define rint(a) floor(a+0.5)
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  static double sqrarg;
   m[nrl] += NR_END;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   m[nrl] -= ncl;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int agegomp= AGEGOMP;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   int imx; 
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  int stepm=1;
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  /* Stepm, step in month: minimum step interpolation*/
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  int estepm;
   for (j=ncl+1; j<=nch; j++)  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
     m[nrl][j]=m[nrl][j-1]+nlay;  
    int m,nb;
   for (i=nrl+1; i<=nrh; i++) {  long *num;
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     for (j=ncl+1; j<=nch; j++)  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
       m[i][j]=m[i][j-1]+nlay;  double **pmmij, ***probs;
   }  double *ageexmed,*agecens;
   return m;  double dateintmean=0;
 }  
   double *weight;
 /*************************free ma3x ************************/  int **s; /* Status */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  double *agedc, **covar, idx;
 {  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   free((FREE_ARG)(m+nrl-NR_END));  double ftolhess; /* Tolerance for computing hessian */
 }  
   /**************** split *************************/
 /***************** f1dim *************************/  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 extern int ncom;  {
 extern double *pcom,*xicom;    /* From a file name with full path (either Unix or Windows) we extract the directory (dirc)
 extern double (*nrfunc)(double []);       the name of the file (name), its extension only (ext) and its first part of the name (finame)
      */ 
 double f1dim(double x)    char  *ss;                            /* pointer */
 {    int   l1, l2;                         /* length counters */
   int j;  
   double f;    l1 = strlen(path );                   /* length of path */
   double *xt;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
      ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   xt=vector(1,ncom);    if ( ss == NULL ) {                   /* no directory, so use current */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   f=(*nrfunc)(xt);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   free_vector(xt,1,ncom);      /* get current working directory */
   return f;      /*    extern  char* getcwd ( char *buf , int len);*/
 }      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
         return( GLOCK_ERROR_GETCWD );
 /*****************brent *************************/      }
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)      strcpy( name, path );               /* we've got it */
 {    } else {                              /* strip direcotry from path */
   int iter;      ss++;                               /* after this, the filename */
   double a,b,d,etemp;      l2 = strlen( ss );                  /* length of filename */
   double fu,fv,fw,fx;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   double ftemp;      strcpy( name, ss );         /* save file name */
   double p,q,r,tol1,tol2,u,v,w,x,xm;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   double e=0.0;      dirc[l1-l2] = 0;                    /* add zero */
      }
   a=(ax < cx ? ax : cx);    l1 = strlen( dirc );                  /* length of directory */
   b=(ax > cx ? ax : cx);    /*#ifdef windows
   x=w=v=bx;    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
   fw=fv=fx=(*f)(x);  #else
   for (iter=1;iter<=ITMAX;iter++) {    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
     xm=0.5*(a+b);  #endif
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    ss = strrchr( name, '.' );            /* find last / */
     printf(".");fflush(stdout);    if (ss >0){
 #ifdef DEBUG      ss++;
     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);      strcpy(ext,ss);                     /* save extension */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */      l1= strlen( name);
 #endif      l2= strlen(ss)+1;
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){      strncpy( finame, name, l1-l2);
       *xmin=x;      finame[l1-l2]= 0;
       return fx;    }
     }    return( 0 );                          /* we're done */
     ftemp=fu;  }
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  
       q=(x-v)*(fx-fw);  /******************************************/
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  void replace_back_to_slash(char *s, char*t)
       if (q > 0.0) p = -p;  {
       q=fabs(q);    int i;
       etemp=e;    int lg=0;
       e=d;    i=0;
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    lg=strlen(t);
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    for(i=0; i<= lg; i++) {
       else {      (s[i] = t[i]);
         d=p/q;      if (t[i]== '\\') s[i]='/';
         u=x+d;    }
         if (u-a < tol2 || b-u < tol2)  }
           d=SIGN(tol1,xm-x);  
       }  int nbocc(char *s, char occ)
     } else {  {
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    int i,j=0;
     }    int lg=20;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    i=0;
     fu=(*f)(u);    lg=strlen(s);
     if (fu <= fx) {    for(i=0; i<= lg; i++) {
       if (u >= x) a=x; else b=x;    if  (s[i] == occ ) j++;
       SHFT(v,w,x,u)    }
         SHFT(fv,fw,fx,fu)    return j;
         } else {  }
           if (u < x) a=u; else b=u;  
           if (fu <= fw || w == x) {  void cutv(char *u,char *v, char*t, char occ)
             v=w;  {
             w=u;    /* cuts string t into u and v where u is ended by char occ excluding it
             fv=fw;       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
             fw=fu;       gives u="abcedf" and v="ghi2j" */
           } else if (fu <= fv || v == x || v == w) {    int i,lg,j,p=0;
             v=u;    i=0;
             fv=fu;    for(j=0; j<=strlen(t)-1; j++) {
           }      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
         }    }
   }  
   nrerror("Too many iterations in brent");    lg=strlen(t);
   *xmin=x;    for(j=0; j<p; j++) {
   return fx;      (u[j] = t[j]);
 }    }
        u[p]='\0';
 /****************** mnbrak ***********************/  
      for(j=0; j<= lg; j++) {
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,      if (j>=(p+1))(v[j-p-1] = t[j]);
             double (*func)(double))    }
 {  }
   double ulim,u,r,q, dum;  
   double fu;  /********************** nrerror ********************/
    
   *fa=(*func)(*ax);  void nrerror(char error_text[])
   *fb=(*func)(*bx);  {
   if (*fb > *fa) {    fprintf(stderr,"ERREUR ...\n");
     SHFT(dum,*ax,*bx,dum)    fprintf(stderr,"%s\n",error_text);
       SHFT(dum,*fb,*fa,dum)    exit(EXIT_FAILURE);
       }  }
   *cx=(*bx)+GOLD*(*bx-*ax);  /*********************** vector *******************/
   *fc=(*func)(*cx);  double *vector(int nl, int nh)
   while (*fb > *fc) {  {
     r=(*bx-*ax)*(*fb-*fc);    double *v;
     q=(*bx-*cx)*(*fb-*fa);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    if (!v) nrerror("allocation failure in vector");
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    return v-nl+NR_END;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  }
     if ((*bx-u)*(u-*cx) > 0.0) {  
       fu=(*func)(u);  /************************ free vector ******************/
     } else if ((*cx-u)*(u-ulim) > 0.0) {  void free_vector(double*v, int nl, int nh)
       fu=(*func)(u);  {
       if (fu < *fc) {    free((FREE_ARG)(v+nl-NR_END));
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  }
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  /************************ivector *******************************/
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  int *ivector(long nl,long nh)
       u=ulim;  {
       fu=(*func)(u);    int *v;
     } else {    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       u=(*cx)+GOLD*(*cx-*bx);    if (!v) nrerror("allocation failure in ivector");
       fu=(*func)(u);    return v-nl+NR_END;
     }  }
     SHFT(*ax,*bx,*cx,u)  
       SHFT(*fa,*fb,*fc,fu)  /******************free ivector **************************/
       }  void free_ivector(int *v, long nl, long nh)
 }  {
     free((FREE_ARG)(v+nl-NR_END));
 /*************** linmin ************************/  }
   
 int ncom;  /************************lvector *******************************/
 double *pcom,*xicom;  long *lvector(long nl,long nh)
 double (*nrfunc)(double []);  {
      long *v;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
 {    if (!v) nrerror("allocation failure in ivector");
   double brent(double ax, double bx, double cx,    return v-nl+NR_END;
                double (*f)(double), double tol, double *xmin);  }
   double f1dim(double x);  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  /******************free lvector **************************/
               double *fc, double (*func)(double));  void free_lvector(long *v, long nl, long nh)
   int j;  {
   double xx,xmin,bx,ax;    free((FREE_ARG)(v+nl-NR_END));
   double fx,fb,fa;  }
    
   ncom=n;  /******************* imatrix *******************************/
   pcom=vector(1,n);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   xicom=vector(1,n);       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   nrfunc=func;  { 
   for (j=1;j<=n;j++) {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     pcom[j]=p[j];    int **m; 
     xicom[j]=xi[j];    
   }    /* allocate pointers to rows */ 
   ax=0.0;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   xx=1.0;    if (!m) nrerror("allocation failure 1 in matrix()"); 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    m += NR_END; 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    m -= nrl; 
 #ifdef DEBUG    
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    
 #endif    /* allocate rows and set pointers to them */ 
   for (j=1;j<=n;j++) {    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     xi[j] *= xmin;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     p[j] += xi[j];    m[nrl] += NR_END; 
   }    m[nrl] -= ncl; 
   free_vector(xicom,1,n);    
   free_vector(pcom,1,n);    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
 }    
     /* return pointer to array of pointers to rows */ 
 /*************** powell ************************/    return m; 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  } 
             double (*func)(double []))  
 {  /****************** free_imatrix *************************/
   void linmin(double p[], double xi[], int n, double *fret,  void free_imatrix(m,nrl,nrh,ncl,nch)
               double (*func)(double []));        int **m;
   int i,ibig,j;        long nch,ncl,nrh,nrl; 
   double del,t,*pt,*ptt,*xit;       /* free an int matrix allocated by imatrix() */ 
   double fp,fptt;  { 
   double *xits;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   pt=vector(1,n);    free((FREE_ARG) (m+nrl-NR_END)); 
   ptt=vector(1,n);  } 
   xit=vector(1,n);  
   xits=vector(1,n);  /******************* matrix *******************************/
   *fret=(*func)(p);  double **matrix(long nrl, long nrh, long ncl, long nch)
   for (j=1;j<=n;j++) pt[j]=p[j];  {
   for (*iter=1;;++(*iter)) {    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     fp=(*fret);    double **m;
     ibig=0;  
     del=0.0;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    if (!m) nrerror("allocation failure 1 in matrix()");
     for (i=1;i<=n;i++)    m += NR_END;
       printf(" %d %.12f",i, p[i]);    m -= nrl;
     printf("\n");  
     for (i=1;i<=n;i++) {    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       fptt=(*fret);    m[nrl] += NR_END;
 #ifdef DEBUG    m[nrl] -= ncl;
       printf("fret=%lf \n",*fret);  
 #endif    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       printf("%d",i);fflush(stdout);    return m;
       linmin(p,xit,n,fret,func);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       if (fabs(fptt-(*fret)) > del) {     */
         del=fabs(fptt-(*fret));  }
         ibig=i;  
       }  /*************************free matrix ************************/
 #ifdef DEBUG  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       printf("%d %.12e",i,(*fret));  {
       for (j=1;j<=n;j++) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    free((FREE_ARG)(m+nrl-NR_END));
         printf(" x(%d)=%.12e",j,xit[j]);  }
       }  
       for(j=1;j<=n;j++)  /******************* ma3x *******************************/
         printf(" p=%.12e",p[j]);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       printf("\n");  {
 #endif    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     }    double ***m;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       int k[2],l;    if (!m) nrerror("allocation failure 1 in matrix()");
       k[0]=1;    m += NR_END;
       k[1]=-1;    m -= nrl;
       printf("Max: %.12e",(*func)(p));  
       for (j=1;j<=n;j++)    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         printf(" %.12e",p[j]);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       printf("\n");    m[nrl] += NR_END;
       for(l=0;l<=1;l++) {    m[nrl] -= ncl;
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
           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]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       }    m[nrl][ncl] += NR_END;
 #endif    m[nrl][ncl] -= nll;
     for (j=ncl+1; j<=nch; j++) 
       m[nrl][j]=m[nrl][j-1]+nlay;
       free_vector(xit,1,n);    
       free_vector(xits,1,n);    for (i=nrl+1; i<=nrh; i++) {
       free_vector(ptt,1,n);      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       free_vector(pt,1,n);      for (j=ncl+1; j<=nch; j++) 
       return;        m[i][j]=m[i][j-1]+nlay;
     }    }
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    return m; 
     for (j=1;j<=n;j++) {    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
       ptt[j]=2.0*p[j]-pt[j];             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       xit[j]=p[j]-pt[j];    */
       pt[j]=p[j];  }
     }  
     fptt=(*func)(ptt);  /*************************free ma3x ************************/
     if (fptt < fp) {  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  {
       if (t < 0.0) {    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
         linmin(p,xit,n,fret,func);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         for (j=1;j<=n;j++) {    free((FREE_ARG)(m+nrl-NR_END));
           xi[j][ibig]=xi[j][n];  }
           xi[j][n]=xit[j];  
         }  /*************** function subdirf ***********/
 #ifdef DEBUG  char *subdirf(char fileres[])
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  {
         for(j=1;j<=n;j++)    /* Caution optionfilefiname is hidden */
           printf(" %.12e",xit[j]);    strcpy(tmpout,optionfilefiname);
         printf("\n");    strcat(tmpout,"/"); /* Add to the right */
 #endif    strcat(tmpout,fileres);
       }    return tmpout;
     }  }
   }  
 }  /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
 /**** Prevalence limit ****************/  {
     
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    /* Caution optionfilefiname is hidden */
 {    strcpy(tmpout,optionfilefiname);
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    strcat(tmpout,"/");
      matrix by transitions matrix until convergence is reached */    strcat(tmpout,preop);
     strcat(tmpout,fileres);
   int i, ii,j,k;    return tmpout;
   double min, max, maxmin, maxmax,sumnew=0.;  }
   double **matprod2();  
   double **out, cov[NCOVMAX], **pmij();  /*************** function subdirf3 ***********/
   double **newm;  char *subdirf3(char fileres[], char *preop, char *preop2)
   double agefin, delaymax=50 ; /* Max number of years to converge */  {
     
   for (ii=1;ii<=nlstate+ndeath;ii++)    /* Caution optionfilefiname is hidden */
     for (j=1;j<=nlstate+ndeath;j++){    strcpy(tmpout,optionfilefiname);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    strcat(tmpout,"/");
     }    strcat(tmpout,preop);
     strcat(tmpout,preop2);
    cov[1]=1.;    strcat(tmpout,fileres);
      return tmpout;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  }
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  
     newm=savm;  /***************** f1dim *************************/
     /* Covariates have to be included here again */  extern int ncom; 
      cov[2]=agefin;  extern double *pcom,*xicom;
    extern double (*nrfunc)(double []); 
       for (k=1; k<=cptcovn;k++) {   
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  double f1dim(double x) 
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/  { 
       }    int j; 
       for (k=1; k<=cptcovage;k++)    double f;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    double *xt; 
       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]]];    xt=vector(1,ncom); 
     for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    f=(*nrfunc)(xt); 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    free_vector(xt,1,ncom); 
     return f; 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  } 
   
     savm=oldm;  /*****************brent *************************/
     oldm=newm;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     maxmax=0.;  { 
     for(j=1;j<=nlstate;j++){    int iter; 
       min=1.;    double a,b,d,etemp;
       max=0.;    double fu,fv,fw,fx;
       for(i=1; i<=nlstate; i++) {    double ftemp;
         sumnew=0;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    double e=0.0; 
         prlim[i][j]= newm[i][j]/(1-sumnew);   
         max=FMAX(max,prlim[i][j]);    a=(ax < cx ? ax : cx); 
         min=FMIN(min,prlim[i][j]);    b=(ax > cx ? ax : cx); 
       }    x=w=v=bx; 
       maxmin=max-min;    fw=fv=fx=(*f)(x); 
       maxmax=FMAX(maxmax,maxmin);    for (iter=1;iter<=ITMAX;iter++) { 
     }      xm=0.5*(a+b); 
     if(maxmax < ftolpl){      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       return prlim;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     }      printf(".");fflush(stdout);
   }      fprintf(ficlog,".");fflush(ficlog);
 }  #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);
 /*************** transition probabilities **********/      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)))) { */
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  #endif
 {      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   double s1, s2;        *xmin=x; 
   /*double t34;*/        return fx; 
   int i,j,j1, nc, ii, jj;      } 
       ftemp=fu;
     for(i=1; i<= nlstate; i++){      if (fabs(e) > tol1) { 
     for(j=1; j<i;j++){        r=(x-w)*(fx-fv); 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        q=(x-v)*(fx-fw); 
         /*s2 += param[i][j][nc]*cov[nc];*/        p=(x-v)*q-(x-w)*r; 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];        q=2.0*(q-r); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/        if (q > 0.0) p = -p; 
       }        q=fabs(q); 
       ps[i][j]=s2;        etemp=e; 
       /*printf("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)) 
     for(j=i+1; j<=nlstate+ndeath;j++){          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        else { 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];          d=p/q; 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/          u=x+d; 
       }          if (u-a < tol2 || b-u < tol2) 
       ps[i][j]=s2;            d=SIGN(tol1,xm-x); 
     }        } 
   }      } else { 
   for(i=1; i<= nlstate; i++){        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
      s1=0;      } 
     for(j=1; j<i; j++)      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       s1+=exp(ps[i][j]);      fu=(*f)(u); 
     for(j=i+1; j<=nlstate+ndeath; j++)      if (fu <= fx) { 
       s1+=exp(ps[i][j]);        if (u >= x) a=x; else b=x; 
     ps[i][i]=1./(s1+1.);        SHFT(v,w,x,u) 
     for(j=1; j<i; j++)          SHFT(fv,fw,fx,fu) 
       ps[i][j]= exp(ps[i][j])*ps[i][i];          } else { 
     for(j=i+1; j<=nlstate+ndeath; j++)            if (u < x) a=u; else b=u; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];            if (fu <= fw || w == x) { 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */              v=w; 
   } /* end i */              w=u; 
               fv=fw; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){              fw=fu; 
     for(jj=1; jj<= nlstate+ndeath; jj++){            } else if (fu <= fv || v == x || v == w) { 
       ps[ii][jj]=0;              v=u; 
       ps[ii][ii]=1;              fv=fu; 
     }            } 
   }          } 
     } 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    nrerror("Too many iterations in brent"); 
     for(jj=1; jj<= nlstate+ndeath; jj++){    *xmin=x; 
      printf("%lf ",ps[ii][jj]);    return fx; 
    }  } 
     printf("\n ");  
     }  /****************** mnbrak ***********************/
     printf("\n ");printf("%lf ",cov[2]);*/  
 /*  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);              double (*func)(double)) 
   goto end;*/  { 
     return ps;    double ulim,u,r,q, dum;
 }    double fu; 
    
 /**************** Product of 2 matrices ******************/    *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    if (*fb > *fa) { 
 {      SHFT(dum,*ax,*bx,dum) 
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        SHFT(dum,*fb,*fa,dum) 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */        } 
   /* in, b, out are matrice of pointers which should have been initialized    *cx=(*bx)+GOLD*(*bx-*ax); 
      before: only the contents of out is modified. The function returns    *fc=(*func)(*cx); 
      a pointer to pointers identical to out */    while (*fb > *fc) { 
   long i, j, k;      r=(*bx-*ax)*(*fb-*fc); 
   for(i=nrl; i<= nrh; i++)      q=(*bx-*cx)*(*fb-*fa); 
     for(k=ncolol; k<=ncoloh; k++)      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
         out[i][k] +=in[i][j]*b[j][k];      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if ((*bx-u)*(u-*cx) > 0.0) { 
   return out;        fu=(*func)(u); 
 }      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         fu=(*func)(u); 
         if (fu < *fc) { 
 /************* Higher Matrix Product ***************/          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )            } 
 {      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        u=ulim; 
      duration (i.e. until        fu=(*func)(u); 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.      } else { 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        u=(*cx)+GOLD*(*cx-*bx); 
      (typically every 2 years instead of every month which is too big).        fu=(*func)(u); 
      Model is determined by parameters x and covariates have to be      } 
      included manually here.      SHFT(*ax,*bx,*cx,u) 
         SHFT(*fa,*fb,*fc,fu) 
      */        } 
   } 
   int i, j, d, h, k;  
   double **out, cov[NCOVMAX];  /*************** linmin ************************/
   double **newm;  
   int ncom; 
   /* Hstepm could be zero and should return the unit matrix */  double *pcom,*xicom;
   for (i=1;i<=nlstate+ndeath;i++)  double (*nrfunc)(double []); 
     for (j=1;j<=nlstate+ndeath;j++){   
       oldm[i][j]=(i==j ? 1.0 : 0.0);  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       po[i][j][0]=(i==j ? 1.0 : 0.0);  { 
     }    double brent(double ax, double bx, double cx, 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */                 double (*f)(double), double tol, double *xmin); 
   for(h=1; h <=nhstepm; h++){    double f1dim(double x); 
     for(d=1; d <=hstepm; d++){    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       newm=savm;                double *fc, double (*func)(double)); 
       /* Covariates have to be included here again */    int j; 
       cov[1]=1.;    double xx,xmin,bx,ax; 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    double fx,fb,fa;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];   
 for (k=1; k<=cptcovage;k++)    ncom=n; 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    pcom=vector(1,n); 
    for (k=1; k<=cptcovprod;k++)    xicom=vector(1,n); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    nrfunc=func; 
     for (j=1;j<=n;j++) { 
       pcom[j]=p[j]; 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/      xicom[j]=xi[j]; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    } 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    ax=0.0; 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    xx=1.0; 
       savm=oldm;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       oldm=newm;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     }  #ifdef DEBUG
     for(i=1; i<=nlstate+ndeath; i++)    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       for(j=1;j<=nlstate+ndeath;j++) {    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         po[i][j][h]=newm[i][j];  #endif
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    for (j=1;j<=n;j++) { 
          */      xi[j] *= xmin; 
       }      p[j] += xi[j]; 
   } /* end h */    } 
   return po;    free_vector(xicom,1,n); 
 }    free_vector(pcom,1,n); 
   } 
   
 /*************** log-likelihood *************/  char *asc_diff_time(long time_sec, char ascdiff[])
 double func( double *x)  {
 {    long sec_left, days, hours, minutes;
   int i, ii, j, k, mi, d, kk;    days = (time_sec) / (60*60*24);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    sec_left = (time_sec) % (60*60*24);
   double **out;    hours = (sec_left) / (60*60) ;
   double sw; /* Sum of weights */    sec_left = (sec_left) %(60*60);
   double lli; /* Individual log likelihood */    minutes = (sec_left) /60;
   long ipmx;    sec_left = (sec_left) % (60);
   /*extern weight */    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   /* We are differentiating ll according to initial status */    return ascdiff;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  }
   /*for(i=1;i<imx;i++)  
     printf(" %d\n",s[4][i]);  /*************** powell ************************/
   */  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   cov[1]=1.;              double (*func)(double [])) 
   { 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    void linmin(double p[], double xi[], int n, double *fret, 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){                double (*func)(double [])); 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    int i,ibig,j; 
     for(mi=1; mi<= wav[i]-1; mi++){    double del,t,*pt,*ptt,*xit;
       for (ii=1;ii<=nlstate+ndeath;ii++)    double fp,fptt;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    double *xits;
       for(d=0; d<dh[mi][i]; d++){    int niterf, itmp;
         newm=savm;  
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    pt=vector(1,n); 
         for (kk=1; kk<=cptcovage;kk++) {    ptt=vector(1,n); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    xit=vector(1,n); 
         }    xits=vector(1,n); 
            *fret=(*func)(p); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    for (j=1;j<=n;j++) pt[j]=p[j]; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    for (*iter=1;;++(*iter)) { 
         savm=oldm;      fp=(*fret); 
         oldm=newm;      ibig=0; 
              del=0.0; 
              last_time=curr_time;
       } /* end mult */      (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);
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      /*    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);
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
       ipmx +=1;      */
       sw += weight[i];     for (i=1;i<=n;i++) {
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        printf(" %d %.12f",i, p[i]);
     } /* end of wave */        fprintf(ficlog," %d %.12lf",i, p[i]);
   } /* end of individual */        fprintf(ficrespow," %.12lf", p[i]);
       }
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      printf("\n");
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      fprintf(ficlog,"\n");
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */      fprintf(ficrespow,"\n");fflush(ficrespow);
   return -l;      if(*iter <=3){
 }        tm = *localtime(&curr_time.tv_sec);
         strcpy(strcurr,asctime(&tmf));
   /*       asctime_r(&tm,strcurr); */
 /*********** Maximum Likelihood Estimation ***************/        forecast_time=curr_time;
         itmp = strlen(strcurr);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        if(strcurr[itmp-1]=='\n')
 {          strcurr[itmp-1]='\0';
   int i,j, iter;        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   double **xi,*delti;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   double fret;        for(niterf=10;niterf<=30;niterf+=10){
   xi=matrix(1,npar,1,npar);          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   for (i=1;i<=npar;i++)          tmf = *localtime(&forecast_time.tv_sec);
     for (j=1;j<=npar;j++)  /*      asctime_r(&tmf,strfor); */
       xi[i][j]=(i==j ? 1.0 : 0.0);          strcpy(strfor,asctime(&tmf));
   printf("Powell\n");          itmp = strlen(strfor);
   powell(p,xi,npar,ftol,&iter,&fret,func);          if(strfor[itmp-1]=='\n')
           strfor[itmp-1]='\0';
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          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);
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));          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);
         }
 }      }
       for (i=1;i<=n;i++) { 
 /**** Computes Hessian and covariance matrix ***/        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))        fptt=(*fret); 
 {  #ifdef DEBUG
   double  **a,**y,*x,pd;        printf("fret=%lf \n",*fret);
   double **hess;        fprintf(ficlog,"fret=%lf \n",*fret);
   int i, j,jk;  #endif
   int *indx;        printf("%d",i);fflush(stdout);
         fprintf(ficlog,"%d",i);fflush(ficlog);
   double hessii(double p[], double delta, int theta, double delti[]);        linmin(p,xit,n,fret,func); 
   double hessij(double p[], double delti[], int i, int j);        if (fabs(fptt-(*fret)) > del) { 
   void lubksb(double **a, int npar, int *indx, double b[]) ;          del=fabs(fptt-(*fret)); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;          ibig=i; 
         } 
   #ifdef DEBUG
   hess=matrix(1,npar,1,npar);        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
   printf("\nCalculation of the hessian matrix. Wait...\n");        for (j=1;j<=n;j++) {
   for (i=1;i<=npar;i++){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     printf("%d",i);fflush(stdout);          printf(" x(%d)=%.12e",j,xit[j]);
     hess[i][i]=hessii(p,ftolhess,i,delti);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     /*printf(" %f ",p[i]);*/        }
   }        for(j=1;j<=n;j++) {
           printf(" p=%.12e",p[j]);
   for (i=1;i<=npar;i++) {          fprintf(ficlog," p=%.12e",p[j]);
     for (j=1;j<=npar;j++)  {        }
       if (j>i) {        printf("\n");
         printf(".%d%d",i,j);fflush(stdout);        fprintf(ficlog,"\n");
         hess[i][j]=hessij(p,delti,i,j);  #endif
         hess[j][i]=hess[i][j];      } 
       }      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     }  #ifdef DEBUG
   }        int k[2],l;
   printf("\n");        k[0]=1;
         k[1]=-1;
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        printf("Max: %.12e",(*func)(p));
          fprintf(ficlog,"Max: %.12e",(*func)(p));
   a=matrix(1,npar,1,npar);        for (j=1;j<=n;j++) {
   y=matrix(1,npar,1,npar);          printf(" %.12e",p[j]);
   x=vector(1,npar);          fprintf(ficlog," %.12e",p[j]);
   indx=ivector(1,npar);        }
   for (i=1;i<=npar;i++)        printf("\n");
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];        fprintf(ficlog,"\n");
   ludcmp(a,npar,indx,&pd);        for(l=0;l<=1;l++) {
           for (j=1;j<=n;j++) {
   for (j=1;j<=npar;j++) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     for (i=1;i<=npar;i++) x[i]=0;            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     x[j]=1;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     lubksb(a,npar,indx,x);          }
     for (i=1;i<=npar;i++){          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       matcov[i][j]=x[i];          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     }        }
   }  #endif
   
   printf("\n#Hessian matrix#\n");  
   for (i=1;i<=npar;i++) {        free_vector(xit,1,n); 
     for (j=1;j<=npar;j++) {        free_vector(xits,1,n); 
       printf("%.3e ",hess[i][j]);        free_vector(ptt,1,n); 
     }        free_vector(pt,1,n); 
     printf("\n");        return; 
   }      } 
       if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   /* Recompute Inverse */      for (j=1;j<=n;j++) { 
   for (i=1;i<=npar;i++)        ptt[j]=2.0*p[j]-pt[j]; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];        xit[j]=p[j]-pt[j]; 
   ludcmp(a,npar,indx,&pd);        pt[j]=p[j]; 
       } 
   /*  printf("\n#Hessian matrix recomputed#\n");      fptt=(*func)(ptt); 
       if (fptt < fp) { 
   for (j=1;j<=npar;j++) {        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     for (i=1;i<=npar;i++) x[i]=0;        if (t < 0.0) { 
     x[j]=1;          linmin(p,xit,n,fret,func); 
     lubksb(a,npar,indx,x);          for (j=1;j<=n;j++) { 
     for (i=1;i<=npar;i++){            xi[j][ibig]=xi[j][n]; 
       y[i][j]=x[i];            xi[j][n]=xit[j]; 
       printf("%.3e ",y[i][j]);          }
     }  #ifdef DEBUG
     printf("\n");          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   */          for(j=1;j<=n;j++){
             printf(" %.12e",xit[j]);
   free_matrix(a,1,npar,1,npar);            fprintf(ficlog," %.12e",xit[j]);
   free_matrix(y,1,npar,1,npar);          }
   free_vector(x,1,npar);          printf("\n");
   free_ivector(indx,1,npar);          fprintf(ficlog,"\n");
   free_matrix(hess,1,npar,1,npar);  #endif
         }
       } 
 }    } 
   } 
 /*************** hessian matrix ****************/  
 double hessii( double x[], double delta, int theta, double delti[])  /**** Prevalence limit (stable prevalence)  ****************/
 {  
   int i;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   int l=1, lmax=20;  {
   double k1,k2;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   double p2[NPARMAX+1];       matrix by transitions matrix until convergence is reached */
   double res;  
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    int i, ii,j,k;
   double fx;    double min, max, maxmin, maxmax,sumnew=0.;
   int k=0,kmax=10;    double **matprod2();
   double l1;    double **out, cov[NCOVMAX], **pmij();
     double **newm;
   fx=func(x);    double agefin, delaymax=50 ; /* Max number of years to converge */
   for (i=1;i<=npar;i++) p2[i]=x[i];  
   for(l=0 ; l <=lmax; l++){    for (ii=1;ii<=nlstate+ndeath;ii++)
     l1=pow(10,l);      for (j=1;j<=nlstate+ndeath;j++){
     delts=delt;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(k=1 ; k <kmax; k=k+1){      }
       delt = delta*(l1*k);  
       p2[theta]=x[theta] +delt;     cov[1]=1.;
       k1=func(p2)-fx;   
       p2[theta]=x[theta]-delt;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       k2=func(p2)-fx;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       /*res= (k1-2.0*fx+k2)/delt/delt; */      newm=savm;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      /* Covariates have to be included here again */
             cov[2]=agefin;
 #ifdef DEBUG    
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);        for (k=1; k<=cptcovn;k++) {
 #endif          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          /*      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]]);*/
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        }
         k=kmax;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       }        for (k=1; k<=cptcovprod;k++)
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         k=kmax; l=lmax*10.;  
       }        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         delts=delt;        /*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);
     }  
   }      savm=oldm;
   delti[theta]=delts;      oldm=newm;
   return res;      maxmax=0.;
        for(j=1;j<=nlstate;j++){
 }        min=1.;
         max=0.;
 double hessij( double x[], double delti[], int thetai,int thetaj)        for(i=1; i<=nlstate; i++) {
 {          sumnew=0;
   int i;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   int l=1, l1, lmax=20;          prlim[i][j]= newm[i][j]/(1-sumnew);
   double k1,k2,k3,k4,res,fx;          max=FMAX(max,prlim[i][j]);
   double p2[NPARMAX+1];          min=FMIN(min,prlim[i][j]);
   int k;        }
         maxmin=max-min;
   fx=func(x);        maxmax=FMAX(maxmax,maxmin);
   for (k=1; k<=2; k++) {      }
     for (i=1;i<=npar;i++) p2[i]=x[i];      if(maxmax < ftolpl){
     p2[thetai]=x[thetai]+delti[thetai]/k;        return prlim;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      }
     k1=func(p2)-fx;    }
    }
     p2[thetai]=x[thetai]+delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  /*************** transition probabilities ***************/ 
     k2=func(p2)-fx;  
    double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
     p2[thetai]=x[thetai]-delti[thetai]/k;  {
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    double s1, s2;
     k3=func(p2)-fx;    /*double t34;*/
      int i,j,j1, nc, ii, jj;
     p2[thetai]=x[thetai]-delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      for(i=1; i<= nlstate; i++){
     k4=func(p2)-fx;        for(j=1; j<i;j++){
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
 #ifdef DEBUG            /*s2 += param[i][j][nc]*cov[nc];*/
     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);            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 #endif  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
   }          }
   return res;          ps[i][j]=s2;
 }  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
         }
 /************** Inverse of matrix **************/        for(j=i+1; j<=nlstate+ndeath;j++){
 void ludcmp(double **a, int n, int *indx, double *d)          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];
   int i,imax,j,k;  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
   double big,dum,sum,temp;          }
   double *vv;          ps[i][j]=s2;
          }
   vv=vector(1,n);      }
   *d=1.0;      /*ps[3][2]=1;*/
   for (i=1;i<=n;i++) {      
     big=0.0;      for(i=1; i<= nlstate; i++){
     for (j=1;j<=n;j++)        s1=0;
       if ((temp=fabs(a[i][j])) > big) big=temp;        for(j=1; j<i; j++)
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          s1+=exp(ps[i][j]);
     vv[i]=1.0/big;        for(j=i+1; j<=nlstate+ndeath; j++)
   }          s1+=exp(ps[i][j]);
   for (j=1;j<=n;j++) {        ps[i][i]=1./(s1+1.);
     for (i=1;i<j;i++) {        for(j=1; j<i; j++)
       sum=a[i][j];          ps[i][j]= exp(ps[i][j])*ps[i][i];
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        for(j=i+1; j<=nlstate+ndeath; j++)
       a[i][j]=sum;          ps[i][j]= exp(ps[i][j])*ps[i][i];
     }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     big=0.0;      } /* end i */
     for (i=j;i<=n;i++) {      
       sum=a[i][j];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       for (k=1;k<j;k++)        for(jj=1; jj<= nlstate+ndeath; jj++){
         sum -= a[i][k]*a[k][j];          ps[ii][jj]=0;
       a[i][j]=sum;          ps[ii][ii]=1;
       if ( (dum=vv[i]*fabs(sum)) >= big) {        }
         big=dum;      }
         imax=i;      
       }  
     }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
     if (j != imax) {  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       for (k=1;k<=n;k++) {  /*         printf("ddd %lf ",ps[ii][jj]); */
         dum=a[imax][k];  /*       } */
         a[imax][k]=a[j][k];  /*       printf("\n "); */
         a[j][k]=dum;  /*        } */
       }  /*        printf("\n ");printf("%lf ",cov[2]); */
       *d = -(*d);         /*
       vv[imax]=vv[j];        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     }        goto end;*/
     indx[j]=imax;      return ps;
     if (a[j][j] == 0.0) a[j][j]=TINY;  }
     if (j != n) {  
       dum=1.0/(a[j][j]);  /**************** Product of 2 matrices ******************/
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  
     }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   }  {
   free_vector(vv,1,n);  /* Doesn't work */    /* 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 
        before: only the contents of out is modified. The function returns
 void lubksb(double **a, int n, int *indx, double b[])       a pointer to pointers identical to out */
 {    long i, j, k;
   int i,ii=0,ip,j;    for(i=nrl; i<= nrh; i++)
   double sum;      for(k=ncolol; k<=ncoloh; k++)
          for(j=ncl,out[i][k]=0.; j<=nch; j++)
   for (i=1;i<=n;i++) {          out[i][k] +=in[i][j]*b[j][k];
     ip=indx[i];  
     sum=b[ip];    return out;
     b[ip]=b[i];  }
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  
     else if (sum) ii=i;  /************* Higher Matrix Product ***************/
     b[i]=sum;  
   }  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   for (i=n;i>=1;i--) {  {
     sum=b[i];    /* Computes the transition matrix starting at age 'age' over 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];       'nhstepm*hstepm*stepm' months (i.e. until
     b[i]=sum/a[i][i];       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   }       nhstepm*hstepm matrices. 
 }       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
        (typically every 2 years instead of every month which is too big 
 /************ Frequencies ********************/       for the memory).
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)       Model is determined by parameters x and covariates have to be 
 {  /* Some frequencies */       included manually here. 
    
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;       */
   double ***freq; /* Frequencies */  
   double *pp;    int i, j, d, h, k;
   double pos;    double **out, cov[NCOVMAX];
   FILE *ficresp;    double **newm;
   char fileresp[FILENAMELENGTH];  
     /* Hstepm could be zero and should return the unit matrix */
   pp=vector(1,nlstate);    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
   strcpy(fileresp,"p");        oldm[i][j]=(i==j ? 1.0 : 0.0);
   strcat(fileresp,fileres);        po[i][j][0]=(i==j ? 1.0 : 0.0);
   if((ficresp=fopen(fileresp,"w"))==NULL) {      }
     printf("Problem with prevalence resultfile: %s\n", fileresp);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     exit(0);    for(h=1; h <=nhstepm; h++){
   }      for(d=1; d <=hstepm; d++){
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        newm=savm;
   j1=0;        /* Covariates have to be included here again */
         cov[1]=1.;
   j=cptcoveff;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         for (k=1; k<=cptcovage;k++)
   for(k1=1; k1<=j;k1++){          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
    for(i1=1; i1<=ncodemax[k1];i1++){        for (k=1; k<=cptcovprod;k++)
        j1++;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);  
          scanf("%d", i);*/  
         for (i=-1; i<=nlstate+ndeath; i++)          /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          for (jk=-1; jk<=nlstate+ndeath; jk++)          /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
            for(m=agemin; m <= agemax+3; m++)        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
              freq[i][jk][m]=0;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
                savm=oldm;
        for (i=1; i<=imx; i++) {        oldm=newm;
          bool=1;      }
          if  (cptcovn>0) {      for(i=1; i<=nlstate+ndeath; i++)
            for (z1=1; z1<=cptcoveff; z1++)        for(j=1;j<=nlstate+ndeath;j++) {
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          po[i][j][h]=newm[i][j];
                bool=0;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
          }           */
           if (bool==1) {        }
            for(m=firstpass; m<=lastpass-1; m++){    } /* end h */
              if(agev[m][i]==0) agev[m][i]=agemax+1;    return po;
              if(agev[m][i]==1) agev[m][i]=agemax+2;  }
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  
            }  /*************** log-likelihood *************/
          }  double func( double *x)
        }  {
         if  (cptcovn>0) {    int i, ii, j, k, mi, d, kk;
          fprintf(ficresp, "\n#********** Variable ");    double l, ll[NLSTATEMAX], cov[NCOVMAX];
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    double **out;
        fprintf(ficresp, "**********\n#");    double sw; /* Sum of weights */
         }    double lli; /* Individual log likelihood */
        for(i=1; i<=nlstate;i++)    int s1, s2;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    double bbh, survp;
        fprintf(ficresp, "\n");    long ipmx;
            /*extern weight */
   for(i=(int)agemin; i <= (int)agemax+3; i++){    /* We are differentiating ll according to initial status */
     if(i==(int)agemax+3)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       printf("Total");    /*for(i=1;i<imx;i++) 
     else      printf(" %d\n",s[4][i]);
       printf("Age %d", i);    */
     for(jk=1; jk <=nlstate ; jk++){    cov[1]=1.;
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  
         pp[jk] += freq[jk][m][i];    for(k=1; k<=nlstate; k++) ll[k]=0.;
     }  
     for(jk=1; jk <=nlstate ; jk++){    if(mle==1){
       for(m=-1, pos=0; m <=0 ; m++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         pos += freq[jk][m][i];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       if(pp[jk]>=1.e-10)        for(mi=1; mi<= wav[i]-1; mi++){
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          for (ii=1;ii<=nlstate+ndeath;ii++)
       else            for (j=1;j<=nlstate+ndeath;j++){
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(jk=1; jk <=nlstate ; jk++){            }
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)          for(d=0; d<dh[mi][i]; d++){
         pp[jk] += freq[jk][m][i];            newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(jk=1,pos=0; jk <=nlstate ; jk++)            for (kk=1; kk<=cptcovage;kk++) {
       pos += pp[jk];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(jk=1; jk <=nlstate ; jk++){            }
       if(pos>=1.e-5)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       else            savm=oldm;
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);            oldm=newm;
       if( i <= (int) agemax){          } /* end mult */
         if(pos>=1.e-5)        
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       else          /* But now since version 0.9 we anticipate for bias and large stepm.
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       }           * (in months) between two waves is not a multiple of stepm, we rounded to 
     }           * the nearest (and in case of equal distance, to the lowest) interval but now
     for(jk=-1; jk <=nlstate+ndeath; jk++)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       for(m=-1; m <=nlstate+ndeath; m++)           * (i.e to dh[mi][i]-1) saved in 'savm'. The we inter(extra)polate the
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);           * probability in order to take into account the bias as a fraction of the way
     if(i <= (int) agemax)           * from savm to out if bh is neagtive or even beyond if bh is positive. bh varies
       fprintf(ficresp,"\n");           * -stepm/2 to stepm/2 .
     printf("\n");           * For stepm=1 the results are the same as for previous versions of Imach.
     }           * For stepm > 1 the results are less biased than in previous versions. 
     }           */
  }          s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
   fclose(ficresp);          bbh=(double)bh[mi][i]/(double)stepm; 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /* bias is positive if real duration
   free_vector(pp,1,nlstate);           * is higher than the multiple of stepm and negative otherwise.
            */
 }  /* End of Freq */          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           if( s2 > nlstate){ 
 /************* Waves Concatenation ***************/            /* i.e. if s2 is a death state and if the date of death is known then the contribution
                to the likelihood is the probability to die between last step unit time and current 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)               step unit time, which is also the differences between probability to die before dh 
 {               and probability to die before dh-stepm . 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.               In version up to 0.92 likelihood was computed
      Death is a valid wave (if date is known).          as if date of death was unknown. Death was treated as any other
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          health state: the date of the interview describes the actual state
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          and not the date of a change in health state. The former idea was
      and mw[mi+1][i]. dh depends on stepm.          to consider that at each interview the state was recorded
      */          (healthy, disable or death) and IMaCh was corrected; but when we
           introduced the exact date of death then we should have modified
   int i, mi, m;          the contribution of an exact death to the likelihood. This new
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          contribution is smaller and very dependent of the step unit
      double sum=0., jmean=0.;*/          stepm. It is no more the probability to die between last interview
           and month of death but the probability to survive from last
 int j, k=0,jk, ju, jl;          interview up to one month before death multiplied by the
      double sum=0.;          probability to die within a month. Thanks to Chris
 jmin=1e+5;          Jackson for correcting this bug.  Former versions increased
  jmax=-1;          mortality artificially. The bad side is that we add another loop
 jmean=0.;          which slows down the processing. The difference can be up to 10%
   for(i=1; i<=imx; i++){          lower mortality.
     mi=0;            */
     m=firstpass;            lli=log(out[s1][s2] - savm[s1][s2]);
     while(s[m][i] <= nlstate){          }else{
       if(s[m][i]>=1)            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         mw[++mi][i]=m;            /*  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 */
       if(m >=lastpass)          } 
         break;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       else          /*if(lli ==000.0)*/
         m++;          /*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); */
     }/* end while */          ipmx +=1;
     if (s[m][i] > nlstate){          sw += weight[i];
       mi++;     /* Death is another wave */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       /* if(mi==0)  never been interviewed correctly before death */        } /* end of wave */
          /* Only death is a correct wave */      } /* end of individual */
       mw[mi][i]=m;    }  else if(mle==2){
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     wav[i]=mi;        for(mi=1; mi<= wav[i]-1; mi++){
     if(mi==0)          for (ii=1;ii<=nlstate+ndeath;ii++)
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);            for (j=1;j<=nlstate+ndeath;j++){
   }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(i=1; i<=imx; i++){            }
     for(mi=1; mi<wav[i];mi++){          for(d=0; d<=dh[mi][i]; d++){
       if (stepm <=0)            newm=savm;
         dh[mi][i]=1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       else{            for (kk=1; kk<=cptcovage;kk++) {
         if (s[mw[mi+1][i]][i] > nlstate) {              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            }
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           if(j==0) j=1;  /* Survives at least one month after exam */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           k=k+1;            savm=oldm;
           if (j >= jmax) jmax=j;            oldm=newm;
           else if (j <= jmin)jmin=j;          } /* end mult */
           sum=sum+j;        
         }          s1=s[mw[mi][i]][i];
         else{          s2=s[mw[mi+1][i]][i];
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          bbh=(double)bh[mi][i]/(double)stepm; 
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
           k=k+1;          ipmx +=1;
           if (j >= jmax) jmax=j;          sw += weight[i];
           else if (j <= jmin)jmin=j;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           sum=sum+j;        } /* end of wave */
         }      } /* end of individual */
         jk= j/stepm;    }  else if(mle==3){  /* exponential inter-extrapolation */
         jl= j -jk*stepm;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         ju= j -(jk+1)*stepm;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         if(jl <= -ju)        for(mi=1; mi<= wav[i]-1; mi++){
           dh[mi][i]=jk;          for (ii=1;ii<=nlstate+ndeath;ii++)
         else            for (j=1;j<=nlstate+ndeath;j++){
           dh[mi][i]=jk+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         if(dh[mi][i]==0)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           dh[mi][i]=1; /* At least one step */            }
       }          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
   }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   jmean=sum/k;            for (kk=1; kk<=cptcovage;kk++) {
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 }            }
 /*********** Tricode ****************************/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 void tricode(int *Tvar, int **nbcode, int imx)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 {            savm=oldm;
   int Ndum[20],ij=1, k, j, i;            oldm=newm;
   int cptcode=0;          } /* end mult */
   cptcoveff=0;        
            s1=s[mw[mi][i]][i];
   for (k=0; k<19; k++) Ndum[k]=0;          s2=s[mw[mi+1][i]][i];
   for (k=1; k<=7; k++) ncodemax[k]=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 (j=1; j<=(cptcovn+2*cptcovprod); j++) {          ipmx +=1;
     for (i=1; i<=imx; i++) {          sw += weight[i];
       ij=(int)(covar[Tvar[j]][i]);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       Ndum[ij]++;        } /* end of wave */
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/      } /* end of individual */
       if (ij > cptcode) cptcode=ij;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     for (i=0; i<=cptcode; i++) {        for(mi=1; mi<= wav[i]-1; mi++){
       if(Ndum[i]!=0) ncodemax[j]++;          for (ii=1;ii<=nlstate+ndeath;ii++)
     }            for (j=1;j<=nlstate+ndeath;j++){
     ij=1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
     for (i=1; i<=ncodemax[j]; i++) {          for(d=0; d<dh[mi][i]; d++){
       for (k=0; k<=19; k++) {            newm=savm;
         if (Ndum[k] != 0) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           nbcode[Tvar[j]][ij]=k;            for (kk=1; kk<=cptcovage;kk++) {
           ij++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         }            }
         if (ij > ncodemax[j]) break;          
       }              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   }              savm=oldm;
             oldm=newm;
  for (k=0; k<19; k++) Ndum[k]=0;          } /* end mult */
         
  for (i=1; i<=ncovmodel; i++) {          s1=s[mw[mi][i]][i];
       ij=Tvar[i];          s2=s[mw[mi+1][i]][i];
       Ndum[ij]++;          if( s2 > nlstate){ 
     }            lli=log(out[s1][s2] - savm[s1][s2]);
           }else{
  ij=1;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
  for (i=1; i<=10; i++) {          }
    if((Ndum[i]!=0) && (i<=ncov)){          ipmx +=1;
      Tvaraff[ij]=i;          sw += weight[i];
      ij++;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    }  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
  }        } /* end of wave */
        } /* end of individual */
     cptcoveff=ij-1;    }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];
 /*********** Health Expectancies ****************/        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)            for (j=1;j<=nlstate+ndeath;j++){
 {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* Health expectancies */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j, nhstepm, hstepm, h;            }
   double age, agelim,hf;          for(d=0; d<dh[mi][i]; d++){
   double ***p3mat;            newm=savm;
              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficreseij,"# Health expectancies\n");            for (kk=1; kk<=cptcovage;kk++) {
   fprintf(ficreseij,"# Age");              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   for(i=1; i<=nlstate;i++)            }
     for(j=1; j<=nlstate;j++)          
       fprintf(ficreseij," %1d-%1d",i,j);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   fprintf(ficreseij,"\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   hstepm=1*YEARM; /*  Every j years of age (in month) */            oldm=newm;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          } /* end mult */
         
   agelim=AGESUP;          s1=s[mw[mi][i]][i];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          s2=s[mw[mi+1][i]][i];
     /* nhstepm age range expressed in number of stepm */          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          ipmx +=1;
     /* Typically if 20 years = 20*12/6=40 stepm */          sw += weight[i];
     if (stepm >= YEARM) hstepm=1;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */          /*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]);*/
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        } /* end of wave */
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      } /* end of individual */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    } /* End of if */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      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(i=1; i<=nlstate;i++)    return -l;
       for(j=1; j<=nlstate;j++)  }
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){  
           eij[i][j][(int)age] +=p3mat[i][j][h];  /*************** log-likelihood *************/
         }  double funcone( double *x)
      {
     hf=1;    /* Same as likeli but slower because of a lot of printf and if */
     if (stepm >= YEARM) hf=stepm/YEARM;    int i, ii, j, k, mi, d, kk;
     fprintf(ficreseij,"%.0f",age );    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     for(i=1; i<=nlstate;i++)    double **out;
       for(j=1; j<=nlstate;j++){    double lli; /* Individual log likelihood */
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);    double llt;
       }    int s1, s2;
     fprintf(ficreseij,"\n");    double bbh, survp;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /*extern weight */
   }    /* We are differentiating ll according to initial status */
 }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     /*for(i=1;i<imx;i++) 
 /************ Variance ******************/      printf(" %d\n",s[4][i]);
 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)    */
 {    cov[1]=1.;
   /* Variance of health expectancies */  
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    for(k=1; k<=nlstate; k++) ll[k]=0.;
   double **newm;  
   double **dnewm,**doldm;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   int i, j, nhstepm, hstepm, h;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int k, cptcode;      for(mi=1; mi<= wav[i]-1; mi++){
    double *xp;        for (ii=1;ii<=nlstate+ndeath;ii++)
   double **gp, **gm;          for (j=1;j<=nlstate+ndeath;j++){
   double ***gradg, ***trgradg;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double ***p3mat;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double age,agelim;          }
   int theta;        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
    fprintf(ficresvij,"# Covariances of life expectancies\n");          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficresvij,"# Age");          for (kk=1; kk<=cptcovage;kk++) {
   for(i=1; i<=nlstate;i++)            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(j=1; j<=nlstate;j++)          }
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   fprintf(ficresvij,"\n");                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           savm=oldm;
   xp=vector(1,npar);          oldm=newm;
   dnewm=matrix(1,nlstate,1,npar);        } /* end mult */
   doldm=matrix(1,nlstate,1,nlstate);        
          s1=s[mw[mi][i]][i];
   hstepm=1*YEARM; /* Every year of age */        s2=s[mw[mi+1][i]][i];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        bbh=(double)bh[mi][i]/(double)stepm; 
   agelim = AGESUP;        /* bias is positive if real duration
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */         * is higher than the multiple of stepm and negative otherwise.
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */         */
     if (stepm >= YEARM) hstepm=1;        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          lli=log(out[s1][s2] - savm[s1][s2]);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        } else if (mle==1){
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     gp=matrix(0,nhstepm,1,nlstate);        } else if(mle==2){
     gm=matrix(0,nhstepm,1,nlstate);          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         } else if(mle==3){  /* exponential inter-extrapolation */
     for(theta=1; theta <=npar; theta++){          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 */
       for(i=1; i<=npar; i++){ /* Computes gradient */        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          lli=log(out[s1][s2]); /* Original formula */
       }        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            lli=log(out[s1][s2]); /* Original formula */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        } /* End of if */
       for(j=1; j<= nlstate; j++){        ipmx +=1;
         for(h=0; h<=nhstepm; h++){        sw += weight[i];
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         }        if(globpr){
       }          fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
       %10.6f %10.6f %10.6f ", \
       for(i=1; i<=npar; i++) /* Computes gradient */                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
         xp[i] = x[i] - (i==theta ?delti[theta]:0);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            llt +=ll[k]*gipmx/gsw;
       for(j=1; j<= nlstate; j++){            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         for(h=0; h<=nhstepm; h++){          }
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          fprintf(ficresilk," %10.6f\n", -llt);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        }
         }      } /* end of wave */
       }    } /* end of individual */
       for(j=1; j<= nlstate; j++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         for(h=0; h<=nhstepm; h++){    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
         }    if(globpr==0){ /* First time we count the contributions and weights */
     } /* End theta */      gipmx=ipmx;
       gsw=sw;
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    }
     return -l;
     for(h=0; h<=nhstepm; h++)  }
       for(j=1; j<=nlstate;j++)  
         for(theta=1; theta <=npar; theta++)  
           trgradg[h][j][theta]=gradg[h][theta][j];  /*************** function likelione ***********/
   void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
     for(i=1;i<=nlstate;i++)  {
       for(j=1;j<=nlstate;j++)    /* This routine should help understanding what is done with 
         vareij[i][j][(int)age] =0.;       the selection of individuals/waves and
     for(h=0;h<=nhstepm;h++){       to check the exact contribution to the likelihood.
       for(k=0;k<=nhstepm;k++){       Plotting could be done.
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);     */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    int k;
         for(i=1;i<=nlstate;i++)  
           for(j=1;j<=nlstate;j++)    if(*globpri !=0){ /* Just counts and sums, no printings */
             vareij[i][j][(int)age] += doldm[i][j];      strcpy(fileresilk,"ilk"); 
       }      strcat(fileresilk,fileres);
     }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
     h=1;        printf("Problem with resultfile: %s\n", fileresilk);
     if (stepm >= YEARM) h=stepm/YEARM;        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     fprintf(ficresvij,"%.0f ",age );      }
     for(i=1; i<=nlstate;i++)      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");
       for(j=1; j<=nlstate;j++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)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(k=1; k<=nlstate; k++) 
     fprintf(ficresvij,"\n");        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     free_matrix(gp,0,nhstepm,1,nlstate);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     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);    *fretone=(*funcone)(p);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if(*globpri !=0){
   } /* End age */      fclose(ficresilk);
        fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   free_vector(xp,1,npar);      fflush(fichtm); 
   free_matrix(doldm,1,nlstate,1,npar);    } 
   free_matrix(dnewm,1,nlstate,1,nlstate);    return;
   }
 }  
   
 /************ Variance of prevlim ******************/  /*********** Maximum Likelihood Estimation ***************/
 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)  
 {  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   /* Variance of prevalence limit */  {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    int i,j, iter;
   double **newm;    double **xi;
   double **dnewm,**doldm;    double fret;
   int i, j, nhstepm, hstepm;    double fretone; /* Only one call to likelihood */
   int k, cptcode;    /*  char filerespow[FILENAMELENGTH];*/
   double *xp;    xi=matrix(1,npar,1,npar);
   double *gp, *gm;    for (i=1;i<=npar;i++)
   double **gradg, **trgradg;      for (j=1;j<=npar;j++)
   double age,agelim;        xi[i][j]=(i==j ? 1.0 : 0.0);
   int theta;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
        strcpy(filerespow,"pow"); 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");    strcat(filerespow,fileres);
   fprintf(ficresvpl,"# Age");    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   for(i=1; i<=nlstate;i++)      printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficresvpl," %1d-%1d",i,i);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   fprintf(ficresvpl,"\n");    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
   xp=vector(1,npar);    for (i=1;i<=nlstate;i++)
   dnewm=matrix(1,nlstate,1,npar);      for(j=1;j<=nlstate+ndeath;j++)
   doldm=matrix(1,nlstate,1,nlstate);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
      fprintf(ficrespow,"\n");
   hstepm=1*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    powell(p,xi,npar,ftol,&iter,&fret,func);
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    fclose(ficrespow);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     if (stepm >= YEARM) hstepm=1;    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     gradg=matrix(1,npar,1,nlstate);  
     gp=vector(1,nlstate);  }
     gm=vector(1,nlstate);  
   /**** Computes Hessian and covariance matrix ***/
     for(theta=1; theta <=npar; theta++){  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       for(i=1; i<=npar; i++){ /* Computes gradient */  {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    double  **a,**y,*x,pd;
       }    double **hess;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    int i, j,jk;
       for(i=1;i<=nlstate;i++)    int *indx;
         gp[i] = prlim[i][i];  
        double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(i=1; i<=npar; i++) /* Computes gradient */    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    void lubksb(double **a, int npar, int *indx, double b[]) ;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    void ludcmp(double **a, int npar, int *indx, double *d) ;
       for(i=1;i<=nlstate;i++)    double gompertz(double p[]);
         gm[i] = prlim[i][i];    hess=matrix(1,npar,1,npar);
   
       for(i=1;i<=nlstate;i++)    printf("\nCalculation of the hessian matrix. Wait...\n");
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     } /* End theta */    for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
     trgradg =matrix(1,nlstate,1,npar);      fprintf(ficlog,"%d",i);fflush(ficlog);
      
     for(j=1; j<=nlstate;j++)       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
       for(theta=1; theta <=npar; theta++)      
         trgradg[j][theta]=gradg[theta][j];      /*  printf(" %f ",p[i]);
           printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     for(i=1;i<=nlstate;i++)    }
       varpl[i][(int)age] =0.;    
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    for (i=1;i<=npar;i++) {
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);      for (j=1;j<=npar;j++)  {
     for(i=1;i<=nlstate;i++)        if (j>i) { 
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          printf(".%d%d",i,j);fflush(stdout);
           fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     fprintf(ficresvpl,"%.0f ",age );          hess[i][j]=hessij(p,delti,i,j,func,npar);
     for(i=1; i<=nlstate;i++)          
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          hess[j][i]=hess[i][j];    
     fprintf(ficresvpl,"\n");          /*printf(" %lf ",hess[i][j]);*/
     free_vector(gp,1,nlstate);        }
     free_vector(gm,1,nlstate);      }
     free_matrix(gradg,1,npar,1,nlstate);    }
     free_matrix(trgradg,1,nlstate,1,npar);    printf("\n");
   } /* End age */    fprintf(ficlog,"\n");
   
   free_vector(xp,1,npar);    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   free_matrix(doldm,1,nlstate,1,npar);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   free_matrix(dnewm,1,nlstate,1,nlstate);    
     a=matrix(1,npar,1,npar);
 }    y=matrix(1,npar,1,npar);
     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];
 /**************** Main Program *****************/    ludcmp(a,npar,indx,&pd);
 /***********************************************/  
     for (j=1;j<=npar;j++) {
 /*int main(int argc, char *argv[])*/      for (i=1;i<=npar;i++) x[i]=0;
 int main()      x[j]=1;
 {      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;        matcov[i][j]=x[i];
   double agedeb, agefin,hf;      }
   double agemin=1.e20, agemax=-1.e20;    }
   
   double fret;    printf("\n#Hessian matrix#\n");
   double **xi,tmp,delta;    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
   double dum; /* Dummy variable */      for (j=1;j<=npar;j++) { 
   double ***p3mat;        printf("%.3e ",hess[i][j]);
   int *indx;        fprintf(ficlog,"%.3e ",hess[i][j]);
   char line[MAXLINE], linepar[MAXLINE];      }
   char title[MAXLINE];      printf("\n");
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];      fprintf(ficlog,"\n");
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];    }
   char filerest[FILENAMELENGTH];  
   char fileregp[FILENAMELENGTH];    /* Recompute Inverse */
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    for (i=1;i<=npar;i++)
   int firstobs=1, lastobs=10;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   int sdeb, sfin; /* Status at beginning and end */    ludcmp(a,npar,indx,&pd);
   int c,  h , cpt,l;  
   int ju,jl, mi;    /*  printf("\n#Hessian matrix recomputed#\n");
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;  
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    for (j=1;j<=npar;j++) {
        for (i=1;i<=npar;i++) x[i]=0;
   int hstepm, nhstepm;      x[j]=1;
   double bage, fage, age, agelim, agebase;      lubksb(a,npar,indx,x);
   double ftolpl=FTOL;      for (i=1;i<=npar;i++){ 
   double **prlim;        y[i][j]=x[i];
   double *severity;        printf("%.3e ",y[i][j]);
   double ***param; /* Matrix of parameters */        fprintf(ficlog,"%.3e ",y[i][j]);
   double  *p;      }
   double **matcov; /* Matrix of covariance */      printf("\n");
   double ***delti3; /* Scale */      fprintf(ficlog,"\n");
   double *delti; /* Scale */    }
   double ***eij, ***vareij;    */
   double **varpl; /* Variances of prevalence limits by age */  
   double *epj, vepp;    free_matrix(a,1,npar,1,npar);
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";    free_matrix(y,1,npar,1,npar);
   char *alph[]={"a","a","b","c","d","e"}, str[4];    free_vector(x,1,npar);
     free_ivector(indx,1,npar);
   char z[1]="c", occ;    free_matrix(hess,1,npar,1,npar);
 #include <sys/time.h>  
 #include <time.h>  
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  }
   /* long total_usecs;  
   struct timeval start_time, end_time;  /*************** hessian matrix ****************/
    double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  {
     int i;
     int l=1, lmax=20;
   printf("\nIMACH, Version 0.64a");    double k1,k2;
   printf("\nEnter the parameter file name: ");    double p2[NPARMAX+1];
     double res;
 #ifdef windows    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   scanf("%s",pathtot);    double fx;
   getcwd(pathcd, size);    int k=0,kmax=10;
   /*cygwin_split_path(pathtot,path,optionfile);    double l1;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/  
   /* cutv(path,optionfile,pathtot,'\\');*/    fx=func(x);
     for (i=1;i<=npar;i++) p2[i]=x[i];
 split(pathtot, path,optionfile);    for(l=0 ; l <=lmax; l++){
   chdir(path);      l1=pow(10,l);
   replace(pathc,path);      delts=delt;
 #endif      for(k=1 ; k <kmax; k=k+1){
 #ifdef unix        delt = delta*(l1*k);
   scanf("%s",optionfile);        p2[theta]=x[theta] +delt;
 #endif        k1=func(p2)-fx;
         p2[theta]=x[theta]-delt;
 /*-------- arguments in the command line --------*/        k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
   strcpy(fileres,"r");        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   strcat(fileres, optionfile);        
   #ifdef DEBUG
   /*---------arguments file --------*/        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);
         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);
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  #endif
     printf("Problem with optionfile %s\n",optionfile);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     goto end;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   }          k=kmax;
         }
   strcpy(filereso,"o");        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   strcat(filereso,fileres);          k=kmax; l=lmax*10.;
   if((ficparo=fopen(filereso,"w"))==NULL) {        }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   }          delts=delt;
         }
   /* Reads comments: lines beginning with '#' */      }
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    delti[theta]=delts;
     fgets(line, MAXLINE, ficpar);    return res; 
     puts(line);    
     fputs(line,ficparo);  }
   }  
   ungetc(c,ficpar);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   {
   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);    int i;
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);    int l=1, l1, lmax=20;
   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);    double k1,k2,k3,k4,res,fx;
     double p2[NPARMAX+1];
   covar=matrix(0,NCOVMAX,1,n);    int k;
   cptcovn=0;  
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    fx=func(x);
     for (k=1; k<=2; k++) {
   ncovmodel=2+cptcovn;      for (i=1;i<=npar;i++) p2[i]=x[i];
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      p2[thetai]=x[thetai]+delti[thetai]/k;
        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   /* Read guess parameters */      k1=func(p2)-fx;
   /* Reads comments: lines beginning with '#' */    
   while((c=getc(ficpar))=='#' && c!= EOF){      p2[thetai]=x[thetai]+delti[thetai]/k;
     ungetc(c,ficpar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     fgets(line, MAXLINE, ficpar);      k2=func(p2)-fx;
     puts(line);    
     fputs(line,ficparo);      p2[thetai]=x[thetai]-delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   ungetc(c,ficpar);      k3=func(p2)-fx;
      
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      p2[thetai]=x[thetai]-delti[thetai]/k;
     for(i=1; i <=nlstate; i++)      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     for(j=1; j <=nlstate+ndeath-1; j++){      k4=func(p2)-fx;
       fscanf(ficpar,"%1d%1d",&i1,&j1);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
       fprintf(ficparo,"%1d%1d",i1,j1);  #ifdef DEBUG
       printf("%1d%1d",i,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);
       for(k=1; k<=ncovmodel;k++){      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);
         fscanf(ficpar," %lf",&param[i][j][k]);  #endif
         printf(" %lf",param[i][j][k]);    }
         fprintf(ficparo," %lf",param[i][j][k]);    return res;
       }  }
       fscanf(ficpar,"\n");  
       printf("\n");  /************** Inverse of matrix **************/
       fprintf(ficparo,"\n");  void ludcmp(double **a, int n, int *indx, double *d) 
     }  { 
      int i,imax,j,k; 
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    double big,dum,sum,temp; 
   p=param[1][1];    double *vv; 
     
   /* Reads comments: lines beginning with '#' */    vv=vector(1,n); 
   while((c=getc(ficpar))=='#' && c!= EOF){    *d=1.0; 
     ungetc(c,ficpar);    for (i=1;i<=n;i++) { 
     fgets(line, MAXLINE, ficpar);      big=0.0; 
     puts(line);      for (j=1;j<=n;j++) 
     fputs(line,ficparo);        if ((temp=fabs(a[i][j])) > big) big=temp; 
   }      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   ungetc(c,ficpar);      vv[i]=1.0/big; 
     } 
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    for (j=1;j<=n;j++) { 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      for (i=1;i<j;i++) { 
   for(i=1; i <=nlstate; i++){        sum=a[i][j]; 
     for(j=1; j <=nlstate+ndeath-1; j++){        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);        a[i][j]=sum; 
       printf("%1d%1d",i,j);      } 
       fprintf(ficparo,"%1d%1d",i1,j1);      big=0.0; 
       for(k=1; k<=ncovmodel;k++){      for (i=j;i<=n;i++) { 
         fscanf(ficpar,"%le",&delti3[i][j][k]);        sum=a[i][j]; 
         printf(" %le",delti3[i][j][k]);        for (k=1;k<j;k++) 
         fprintf(ficparo," %le",delti3[i][j][k]);          sum -= a[i][k]*a[k][j]; 
       }        a[i][j]=sum; 
       fscanf(ficpar,"\n");        if ( (dum=vv[i]*fabs(sum)) >= big) { 
       printf("\n");          big=dum; 
       fprintf(ficparo,"\n");          imax=i; 
     }        } 
   }      } 
   delti=delti3[1][1];      if (j != imax) { 
          for (k=1;k<=n;k++) { 
   /* Reads comments: lines beginning with '#' */          dum=a[imax][k]; 
   while((c=getc(ficpar))=='#' && c!= EOF){          a[imax][k]=a[j][k]; 
     ungetc(c,ficpar);          a[j][k]=dum; 
     fgets(line, MAXLINE, ficpar);        } 
     puts(line);        *d = -(*d); 
     fputs(line,ficparo);        vv[imax]=vv[j]; 
   }      } 
   ungetc(c,ficpar);      indx[j]=imax; 
        if (a[j][j] == 0.0) a[j][j]=TINY; 
   matcov=matrix(1,npar,1,npar);      if (j != n) { 
   for(i=1; i <=npar; i++){        dum=1.0/(a[j][j]); 
     fscanf(ficpar,"%s",&str);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
     printf("%s",str);      } 
     fprintf(ficparo,"%s",str);    } 
     for(j=1; j <=i; j++){    free_vector(vv,1,n);  /* Doesn't work */
       fscanf(ficpar," %le",&matcov[i][j]);  ;
       printf(" %.5le",matcov[i][j]);  } 
       fprintf(ficparo," %.5le",matcov[i][j]);  
     }  void lubksb(double **a, int n, int *indx, double b[]) 
     fscanf(ficpar,"\n");  { 
     printf("\n");    int i,ii=0,ip,j; 
     fprintf(ficparo,"\n");    double sum; 
   }   
   for(i=1; i <=npar; i++)    for (i=1;i<=n;i++) { 
     for(j=i+1;j<=npar;j++)      ip=indx[i]; 
       matcov[i][j]=matcov[j][i];      sum=b[ip]; 
          b[ip]=b[i]; 
   printf("\n");      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       else if (sum) ii=i; 
     /*-------- data file ----------*/      b[i]=sum; 
     if((ficres =fopen(fileres,"w"))==NULL) {    } 
       printf("Problem with resultfile: %s\n", fileres);goto end;    for (i=n;i>=1;i--) { 
     }      sum=b[i]; 
     fprintf(ficres,"#%s\n",version);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
          b[i]=sum/a[i][i]; 
     if((fic=fopen(datafile,"r"))==NULL)    {    } 
       printf("Problem with datafile: %s\n", datafile);goto end;  } 
     }  
   /************ Frequencies ********************/
     n= lastobs;  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)
     severity = vector(1,maxwav);  {  /* Some frequencies */
     outcome=imatrix(1,maxwav+1,1,n);    
     num=ivector(1,n);    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     moisnais=vector(1,n);    int first;
     annais=vector(1,n);    double ***freq; /* Frequencies */
     moisdc=vector(1,n);    double *pp, **prop;
     andc=vector(1,n);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     agedc=vector(1,n);    FILE *ficresp;
     cod=ivector(1,n);    char fileresp[FILENAMELENGTH];
     weight=vector(1,n);    
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    pp=vector(1,nlstate);
     mint=matrix(1,maxwav,1,n);    prop=matrix(1,nlstate,iagemin,iagemax+3);
     anint=matrix(1,maxwav,1,n);    strcpy(fileresp,"p");
     s=imatrix(1,maxwav+1,1,n);    strcat(fileresp,fileres);
     adl=imatrix(1,maxwav+1,1,n);        if((ficresp=fopen(fileresp,"w"))==NULL) {
     tab=ivector(1,NCOVMAX);      printf("Problem with prevalence resultfile: %s\n", fileresp);
     ncodemax=ivector(1,8);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
       exit(0);
     i=1;    }
     while (fgets(line, MAXLINE, fic) != NULL)    {    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
       if ((i >= firstobs) && (i <=lastobs)) {    j1=0;
            
         for (j=maxwav;j>=1;j--){    j=cptcoveff;
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           strcpy(line,stra);  
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    first=1;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);  
         }    for(k1=1; k1<=j;k1++){
              for(i1=1; i1<=ncodemax[k1];i1++){
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        j1++;
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           scanf("%d", i);*/
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);        for (i=-1; i<=nlstate+ndeath; i++)  
         cutv(stra, strb,line,' '); moisnais[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,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);              freq[i][jk][m]=0;
         for (j=ncov;j>=1;j--){  
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      for (i=1; i<=nlstate; i++)  
         }        for(m=iagemin; m <= iagemax+3; m++)
         num[i]=atol(stra);          prop[i][m]=0;
         
         /*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]));*/        dateintsum=0;
         k2cpt=0;
         i=i+1;        for (i=1; i<=imx; i++) {
       }          bool=1;
     }          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
     /*scanf("%d",i);*/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   imx=i-1; /* Number of individuals */                bool=0;
           }
   /* Calculation of the number of parameter from char model*/          if (bool==1){
   Tvar=ivector(1,15);            for(m=firstpass; m<=lastpass; m++){
   Tprod=ivector(1,15);              k2=anint[m][i]+(mint[m][i]/12.);
   Tvaraff=ivector(1,15);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   Tvard=imatrix(1,15,1,2);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   Tage=ivector(1,15);                      if(agev[m][i]==1) agev[m][i]=iagemax+2;
                    if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   if (strlen(model) >1){                if (m<lastpass) {
     j=0, j1=0, k1=1, k2=1;                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     j=nbocc(model,'+');                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     j1=nbocc(model,'*');                }
     cptcovn=j+1;                
     cptcovprod=j1;                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                      dateintsum=dateintsum+k2;
                      k2cpt++;
     strcpy(modelsav,model);                }
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){                /*}*/
       printf("Error. Non available option model=%s ",model);            }
       goto end;          }
     }        }
             
     for(i=(j+1); i>=1;i--){        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       cutv(stra,strb,modelsav,'+');  
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);        if  (cptcovn>0) {
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          fprintf(ficresp, "\n#********** Variable "); 
       /*scanf("%d",i);*/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       if (strchr(strb,'*')) {          fprintf(ficresp, "**********\n#");
         cutv(strd,strc,strb,'*');        }
         if (strcmp(strc,"age")==0) {        for(i=1; i<=nlstate;i++) 
           cptcovprod--;          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
           cutv(strb,stre,strd,'V');        fprintf(ficresp, "\n");
           Tvar[i]=atoi(stre);        
           cptcovage++;        for(i=iagemin; i <= iagemax+3; i++){
             Tage[cptcovage]=i;          if(i==iagemax+3){
             /*printf("stre=%s ", stre);*/            fprintf(ficlog,"Total");
         }          }else{
         else if (strcmp(strd,"age")==0) {            if(first==1){
           cptcovprod--;              first=0;
           cutv(strb,stre,strc,'V');              printf("See log file for details...\n");
           Tvar[i]=atoi(stre);            }
           cptcovage++;            fprintf(ficlog,"Age %d", i);
           Tage[cptcovage]=i;          }
         }          for(jk=1; jk <=nlstate ; jk++){
         else {            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
           cutv(strb,stre,strc,'V');              pp[jk] += freq[jk][m][i]; 
           Tvar[i]=ncov+k1;          }
           cutv(strb,strc,strd,'V');          for(jk=1; jk <=nlstate ; jk++){
           Tprod[k1]=i;            for(m=-1, pos=0; m <=0 ; m++)
           Tvard[k1][1]=atoi(strc);              pos += freq[jk][m][i];
           Tvard[k1][2]=atoi(stre);            if(pp[jk]>=1.e-10){
           Tvar[cptcovn+k2]=Tvard[k1][1];              if(first==1){
           Tvar[cptcovn+k2+1]=Tvard[k1][2];              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           for (k=1; k<=lastobs;k++)              }
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           k1++;            }else{
           k2=k2+2;              if(first==1)
         }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       else {            }
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          }
        /*  scanf("%d",i);*/  
       cutv(strd,strc,strb,'V');          for(jk=1; jk <=nlstate ; jk++){
       Tvar[i]=atoi(strc);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
       }              pp[jk] += freq[jk][m][i];
       strcpy(modelsav,stra);            }       
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
         scanf("%d",i);*/            pos += pp[jk];
     }            posprop += prop[jk][i];
 }          }
            for(jk=1; jk <=nlstate ; jk++){
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);            if(pos>=1.e-5){
   printf("cptcovprod=%d ", cptcovprod);              if(first==1)
   scanf("%d ",i);*/                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     fclose(fic);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
     /*  if(mle==1){*/              if(first==1)
     if (weightopt != 1) { /* Maximisation without weights*/                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       for(i=1;i<=n;i++) weight[i]=1.0;              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     }            }
     /*-calculation of age at interview from date of interview and age at death -*/            if( i <= iagemax){
     agev=matrix(1,maxwav,1,imx);              if(pos>=1.e-5){
                    fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     for (i=1; i<=imx; i++)  {                /*probs[i][jk][j1]= pp[jk]/pos;*/
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);                /*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(m=1; (m<= maxwav); m++){              }
         if(s[m][i] >0){              else
           if (s[m][i] == nlstate+1) {                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             if(agedc[i]>0)            }
               if(moisdc[i]!=99 && andc[i]!=9999)          }
               agev[m][i]=agedc[i];          
             else {          for(jk=-1; jk <=nlstate+ndeath; jk++)
               if (andc[i]!=9999){            for(m=-1; m <=nlstate+ndeath; m++)
               printf("Warning negative age at death: %d line:%d\n",num[i],i);              if(freq[jk][m][i] !=0 ) {
               agev[m][i]=-1;              if(first==1)
               }                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
             }                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
           }              }
           else if(s[m][i] !=9){ /* Should no more exist */          if(i <= iagemax)
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);            fprintf(ficresp,"\n");
             if(mint[m][i]==99 || anint[m][i]==9999)          if(first==1)
               agev[m][i]=1;            printf("Others in log...\n");
             else if(agev[m][i] <agemin){          fprintf(ficlog,"\n");
               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){    dateintmean=dateintsum/k2cpt; 
               agemax=agev[m][i];   
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    fclose(ficresp);
             }    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
             /*agev[m][i]=anint[m][i]-annais[i];*/    free_vector(pp,1,nlstate);
             /*   agev[m][i] = age[i]+2*m;*/    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
           }    /* End of Freq */
           else { /* =9 */  }
             agev[m][i]=1;  
             s[m][i]=-1;  /************ Prevalence ********************/
           }  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
         }  {  
         else /*= 0 Unknown */    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
           agev[m][i]=1;       in each health status at the date of interview (if between dateprev1 and dateprev2).
       }       We still use firstpass and lastpass as another selection.
        */
     }   
     for (i=1; i<=imx; i++)  {    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
       for(m=1; (m<= maxwav); m++){    double ***freq; /* Frequencies */
         if (s[m][i] > (nlstate+ndeath)) {    double *pp, **prop;
           printf("Error: Wrong value in nlstate or ndeath\n");      double pos,posprop; 
           goto end;    double  y2; /* in fractional years */
         }    int iagemin, iagemax;
       }  
     }    iagemin= (int) agemin;
     iagemax= (int) agemax;
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    /*pp=vector(1,nlstate);*/
     prop=matrix(1,nlstate,iagemin,iagemax+3); 
     free_vector(severity,1,maxwav);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     free_imatrix(outcome,1,maxwav+1,1,n);    j1=0;
     free_vector(moisnais,1,n);    
     free_vector(annais,1,n);    j=cptcoveff;
     free_matrix(mint,1,maxwav,1,n);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_matrix(anint,1,maxwav,1,n);    
     free_vector(moisdc,1,n);    for(k1=1; k1<=j;k1++){
     free_vector(andc,1,n);      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
            
     wav=ivector(1,imx);        for (i=1; i<=nlstate; i++)  
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          for(m=iagemin; m <= iagemax+3; m++)
     mw=imatrix(1,lastpass-firstpass+1,1,imx);            prop[i][m]=0.0;
           
     /* Concatenates waves */        for (i=1; i<=imx; i++) { /* Each individual */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);          bool=1;
           if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
       Tcode=ivector(1,100);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);                bool=0;
       ncodemax[1]=1;          } 
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          if (bool==1) { 
                  for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
    codtab=imatrix(1,100,1,10);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
    h=0;              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
    m=pow(2,cptcoveff);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                  if(agev[m][i]==1) agev[m][i]=iagemax+2;
    for(k=1;k<=cptcoveff; k++){                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); 
      for(i=1; i <=(m/pow(2,k));i++){                if (s[m][i]>0 && s[m][i]<=nlstate) { 
        for(j=1; j <= ncodemax[k]; j++){                  /*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(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
            h++;                  prop[s[m][i]][iagemax+3] += weight[i]; 
            if (h>m) h=1;codtab[h][k]=j;                } 
          }              }
        }            } /* end selection of waves */
      }          }
    }        }
         for(i=iagemin; i <= iagemax+3; i++){  
           
    /*for(i=1; i <=m ;i++){          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
      for(k=1; k <=cptcovn; k++){            posprop += prop[jk][i]; 
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);          } 
      }  
      printf("\n");          for(jk=1; jk <=nlstate ; jk++){     
    }            if( i <=  iagemax){ 
    scanf("%d",i);*/              if(posprop>=1.e-5){ 
                    probs[i][jk][j1]= prop[jk][i]/posprop;
    /* Calculates basic frequencies. Computes observed prevalence at single age              } 
        and prints on file fileres'p'. */            } 
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);          }/* end jk */ 
         }/* end i */ 
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      } /* end i1 */
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    } /* end k1 */
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    /*free_vector(pp,1,nlstate);*/
        free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     /* For Powell, parameters are in a vector p[] starting at p[1]  }  /* End of prevalence */
        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) */  /************* Waves Concatenation ***************/
   
     if(mle==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)
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);  {
     }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           Death is a valid wave (if date is known).
     /*--------- results files --------------*/       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);       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.
    jk=1;       */
    fprintf(ficres,"# Parameters\n");  
    printf("# Parameters\n");    int i, mi, m;
    for(i=1,jk=1; i <=nlstate; i++){    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
      for(k=1; k <=(nlstate+ndeath); k++){       double sum=0., jmean=0.;*/
        if (k != i)    int first;
          {    int j, k=0,jk, ju, jl;
            printf("%d%d ",i,k);    double sum=0.;
            fprintf(ficres,"%1d%1d ",i,k);    first=0;
            for(j=1; j <=ncovmodel; j++){    jmin=1e+5;
              printf("%f ",p[jk]);    jmax=-1;
              fprintf(ficres,"%f ",p[jk]);    jmean=0.;
              jk++;    for(i=1; i<=imx; i++){
            }      mi=0;
            printf("\n");      m=firstpass;
            fprintf(ficres,"\n");      while(s[m][i] <= nlstate){
          }        if(s[m][i]>=1)
      }          mw[++mi][i]=m;
    }        if(m >=lastpass)
  if(mle==1){          break;
     /* Computing hessian and covariance matrix */        else
     ftolhess=ftol; /* Usually correct */          m++;
     hesscov(matcov, p, npar, delti, ftolhess, func);      }/* end while */
  }      if (s[m][i] > nlstate){
     fprintf(ficres,"# Scales\n");        mi++;     /* Death is another wave */
     printf("# Scales\n");        /* if(mi==0)  never been interviewed correctly before death */
      for(i=1,jk=1; i <=nlstate; i++){           /* Only death is a correct wave */
       for(j=1; j <=nlstate+ndeath; j++){        mw[mi][i]=m;
         if (j!=i) {      }
           fprintf(ficres,"%1d%1d",i,j);  
           printf("%1d%1d",i,j);      wav[i]=mi;
           for(k=1; k<=ncovmodel;k++){      if(mi==0){
             printf(" %.5e",delti[jk]);        nbwarn++;
             fprintf(ficres," %.5e",delti[jk]);        if(first==0){
             jk++;          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
           }          first=1;
           printf("\n");        }
           fprintf(ficres,"\n");        if(first==1){
         }          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
       }        }
       }      } /* end mi==0 */
        } /* End individuals */
     k=1;  
     fprintf(ficres,"# Covariance\n");    for(i=1; i<=imx; i++){
     printf("# Covariance\n");      for(mi=1; mi<wav[i];mi++){
     for(i=1;i<=npar;i++){        if (stepm <=0)
       /*  if (k>nlstate) k=1;          dh[mi][i]=1;
       i1=(i-1)/(ncovmodel*nlstate)+1;        else{
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       printf("%s%d%d",alph[k],i1,tab[i]);*/            if (agedc[i] < 2*AGESUP) {
       fprintf(ficres,"%3d",i);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       printf("%3d",i);              if(j==0) j=1;  /* Survives at least one month after exam */
       for(j=1; j<=i;j++){              else if(j<0){
         fprintf(ficres," %.5e",matcov[i][j]);                nberr++;
         printf(" %.5e",matcov[i][j]);                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       }                j=1; /* Temporary Dangerous patch */
       fprintf(ficres,"\n");                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("\n");                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]);
       k++;                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
     }              }
                  k=k+1;
     while((c=getc(ficpar))=='#' && c!= EOF){              if (j >= jmax) jmax=j;
       ungetc(c,ficpar);              if (j <= jmin) jmin=j;
       fgets(line, MAXLINE, ficpar);              sum=sum+j;
       puts(line);              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       fputs(line,ficparo);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     }            }
     ungetc(c,ficpar);          }
            else{
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
                /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     if (fage <= 2) {            k=k+1;
       bage = agemin;            if (j >= jmax) jmax=j;
       fage = agemax;            else if (j <= jmin)jmin=j;
     }            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");            if(j<0){
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);              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(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]);
 /*------------ gnuplot -------------*/            }
 chdir(pathcd);            sum=sum+j;
   if((ficgp=fopen("graph.plt","w"))==NULL) {          }
     printf("Problem with file graph.gp");goto end;          jk= j/stepm;
   }          jl= j -jk*stepm;
 #ifdef windows          ju= j -(jk+1)*stepm;
   fprintf(ficgp,"cd \"%s\" \n",pathc);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
 #endif            if(jl==0){
 m=pow(2,cptcoveff);              dh[mi][i]=jk;
                bh[mi][i]=0;
  /* 1eme*/            }else{ /* We want a negative bias in order to only have interpolation ie
   for (cpt=1; cpt<= nlstate ; cpt ++) {                    * at the price of an extra matrix product in likelihood */
    for (k1=1; k1<= m ; k1 ++) {              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
 #ifdef windows            }
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);          }else{
 #endif            if(jl <= -ju){
 #ifdef unix              dh[mi][i]=jk;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);              bh[mi][i]=jl;       /* bias is positive if real duration
 #endif                                   * is higher than the multiple of stepm and negative otherwise.
                                    */
 for (i=1; i<= nlstate ; i ++) {            }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            else{
   else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=jk+1;
 }              bh[mi][i]=ju;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            }
     for (i=1; i<= nlstate ; i ++) {            if(dh[mi][i]==0){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              dh[mi][i]=1; /* At least one step */
   else fprintf(ficgp," \%%*lf (\%%*lf)");              bh[mi][i]=ju; /* At least one step */
 }              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            }
      for (i=1; i<= nlstate ; i ++) {          } /* end if mle */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        }
   else fprintf(ficgp," \%%*lf (\%%*lf)");      } /* end wave */
 }      }
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    jmean=sum/k;
 #ifdef unix    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
 fprintf(ficgp,"\nset ter gif small size 400,300");    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
 #endif   }
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  
    }  /*********** Tricode ****************************/
   }  void tricode(int *Tvar, int **nbcode, int imx)
   /*2 eme*/  {
     
   for (k1=1; k1<= m ; k1 ++) {    int Ndum[20],ij=1, k, j, i, maxncov=19;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    int cptcode=0;
        cptcoveff=0; 
     for (i=1; i<= nlstate+1 ; i ++) {   
       k=2*i;    for (k=0; k<maxncov; k++) Ndum[k]=0;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    for (k=1; k<=7; k++) ncodemax[k]=0;
       for (j=1; j<= nlstate+1 ; j ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
 }                                   modality*/ 
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);        Ndum[ij]++; /*store the modality */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
       for (j=1; j<= nlstate+1 ; j ++) {        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                                         Tvar[j]. If V=sex and male is 0 and 
         else fprintf(ficgp," \%%*lf (\%%*lf)");                                         female is 1, then  cptcode=1.*/
 }        }
       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 (i=0; i<=cptcode; i++) {
       for (j=1; j<= nlstate+1 ; j ++) {        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 */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }        ij=1; 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");      for (i=1; i<=ncodemax[j]; i++) {
       else fprintf(ficgp,"\" t\"\" w l 0,");        for (k=0; k<= maxncov; k++) {
     }          if (Ndum[k] != 0) {
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);            nbcode[Tvar[j]][ij]=k; 
   }            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
              
   /*3eme*/            ij++;
           }
   for (k1=1; k1<= m ; k1 ++) {          if (ij > ncodemax[j]) break; 
     for (cpt=1; cpt<= nlstate ; cpt ++) {        }  
       k=2+nlstate*(cpt-1);      } 
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);    }  
       for (i=1; i< nlstate ; i ++) {  
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);   for (k=0; k< maxncov; k++) Ndum[k]=0;
       }  
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);   for (i=1; i<=ncovmodel-2; i++) { 
     }     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   }     ij=Tvar[i];
       Ndum[ij]++;
   /* CV preval stat */   }
   for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {   ij=1;
       k=3;   for (i=1; i<= maxncov; i++) {
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);     if((Ndum[i]!=0) && (i<=ncovcol)){
       for (i=1; i< nlstate ; i ++)       Tvaraff[ij]=i; /*For printing */
         fprintf(ficgp,"+$%d",k+i+1);       ij++;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);     }
         }
       l=3+(nlstate+ndeath)*cpt;   
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);   cptcoveff=ij-1; /*Number of simple covariates*/
       for (i=1; i< nlstate ; i ++) {  }
         l=3+(nlstate+ndeath)*cpt;  
         fprintf(ficgp,"+$%d",l+i+1);  /*********** Health Expectancies ****************/
       }  
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);    void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  
     }  {
   }    /* Health expectancies */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
   /* proba elementaires */    double age, agelim, hf;
    for(i=1,jk=1; i <=nlstate; i++){    double ***p3mat,***varhe;
     for(k=1; k <=(nlstate+ndeath); k++){    double **dnewm,**doldm;
       if (k != i) {    double *xp;
         for(j=1; j <=ncovmodel; j++){    double **gp, **gm;
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    double ***gradg, ***trgradg;
           /*fprintf(ficgp,"%s",alph[1]);*/    int theta;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);  
           jk++;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
           fprintf(ficgp,"\n");    xp=vector(1,npar);
         }    dnewm=matrix(1,nlstate*nlstate,1,npar);
       }    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     }    
     }    fprintf(ficreseij,"# Health expectancies\n");
     fprintf(ficreseij,"# Age");
   for(jk=1; jk <=m; jk++) {    for(i=1; i<=nlstate;i++)
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);      for(j=1; j<=nlstate;j++)
    i=1;        fprintf(ficreseij," %1d-%1d (SE)",i,j);
    for(k2=1; k2<=nlstate; k2++) {    fprintf(ficreseij,"\n");
      k3=i;  
      for(k=1; k<=(nlstate+ndeath); k++) {    if(estepm < stepm){
        if (k != k2){      printf ("Problem %d lower than %d\n",estepm, stepm);
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    }
 ij=1;    else  hstepm=estepm;   
         for(j=3; j <=ncovmodel; j++) {    /* We compute the life expectancy from trapezoids spaced every estepm months
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {     * This is mainly to measure the difference between two models: for example
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);     * if stepm=24 months pijx are given only every 2 years and by summing them
             ij++;     * we are calculating an estimate of the Life Expectancy assuming a linear 
           }     * progression in between and thus overestimating or underestimating according
           else     * to the curvature of the survival function. If, for the same date, we 
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);     * 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 
           fprintf(ficgp,")/(1");     * hypothesis. A more precise result, taking into account a more precise
             * curvature will be obtained if estepm is as small as stepm. */
         for(k1=1; k1 <=nlstate; k1++){    
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    /* For example we decided to compute the life expectancy with the smallest unit */
 ij=1;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           for(j=3; j <=ncovmodel; j++){       nhstepm is the number of hstepm from age to agelim 
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {       nstepm is the number of stepm from age to agelin. 
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);       Look at hpijx to understand the reason of that which relies in memory size
             ij++;       and note for a fixed period like estepm months */
           }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           else       survival function given by stepm (the optimization length). Unfortunately it
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);       means that if the survival funtion is printed only each two years of age and if
           }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           fprintf(ficgp,")");       results. So we changed our mind and took the option of the best precision.
         }    */
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");  
         i=i+ncovmodel;    agelim=AGESUP;
        }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      }      /* nhstepm age range expressed in number of stepm */
    }      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      /* 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 */
   fclose(ficgp);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
          gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
 chdir(path);      gp=matrix(0,nhstepm,1,nlstate*nlstate);
     free_matrix(agev,1,maxwav,1,imx);      gm=matrix(0,nhstepm,1,nlstate*nlstate);
     free_ivector(wav,1,imx);  
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
          hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
     free_imatrix(s,1,maxwav+1,1,n);   
      
          hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     free_ivector(num,1,n);  
     free_vector(agedc,1,n);      /* Computing  Variances of health expectancies */
     free_vector(weight,1,n);  
     /*free_matrix(covar,1,NCOVMAX,1,n);*/       for(theta=1; theta <=npar; theta++){
     fclose(ficparo);        for(i=1; i<=npar; i++){ 
     fclose(ficres);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     /*  }*/        }
            hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
    /*________fin mle=1_________*/    
            cptj=0;
         for(j=1; j<= nlstate; j++){
            for(i=1; i<=nlstate; i++){
     /* No more information from the sample is required now */            cptj=cptj+1;
   /* Reads comments: lines beginning with '#' */            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
   while((c=getc(ficpar))=='#' && c!= EOF){              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
     ungetc(c,ficpar);            }
     fgets(line, MAXLINE, ficpar);          }
     puts(line);        }
     fputs(line,ficparo);       
   }       
   ungetc(c,ficpar);        for(i=1; i<=npar; i++) 
            xp[i] = x[i] - (i==theta ?delti[theta]:0);
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);        
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        cptj=0;
 /*--------- index.htm --------*/        for(j=1; j<= nlstate; j++){
           for(i=1;i<=nlstate;i++){
   if((fichtm=fopen("index.htm","w"))==NULL)    {            cptj=cptj+1;
     printf("Problem with index.htm \n");goto end;            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
   }  
               gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.64a </font> <hr size=\"2\" color=\"#EC5E5E\">            }
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>          }
 Total number of observations=%d <br>        }
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>        for(j=1; j<= nlstate*nlstate; j++)
 <hr  size=\"2\" color=\"#EC5E5E\">          for(h=0; h<=nhstepm-1; h++){
 <li>Outputs files<br><br>\n            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n          }
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>       } 
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>     
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>  /* End theta */
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>  
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>       for(h=0; h<=nhstepm-1; h++)
         - 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);        for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
  fprintf(fichtm," <li>Graphs</li><p>");            trgradg[h][j][theta]=gradg[h][theta][j];
        
  m=cptcoveff;  
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}       for(i=1;i<=nlstate*nlstate;i++)
         for(j=1;j<=nlstate*nlstate;j++)
  j1=0;          varhe[i][j][(int)age] =0.;
  for(k1=1; k1<=m;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){       printf("%d|",(int)age);fflush(stdout);
        j1++;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        if (cptcovn > 0) {       for(h=0;h<=nhstepm-1;h++){
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");        for(k=0;k<=nhstepm-1;k++){
          for (cpt=1; cpt<=cptcoveff;cpt++)          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");          for(i=1;i<=nlstate*nlstate;i++)
        }            for(j=1;j<=nlstate*nlstate;j++)
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);            }
        for(cpt=1; cpt<nlstate;cpt++){      }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>      /* Computing expectancies */
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      for(i=1; i<=nlstate;i++)
        }        for(j=1; j<=nlstate;j++)
     for(cpt=1; cpt<=nlstate;cpt++) {          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
 interval) in state (%d): v%s%d%d.gif <br>            
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
      }  
      for(cpt=1; cpt<=nlstate;cpt++) {          }
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>  
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      fprintf(ficreseij,"%3.0f",age );
      }      cptj=0;
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      for(i=1; i<=nlstate;i++)
 health expectancies in states (1) and (2): e%s%d.gif<br>        for(j=1; j<=nlstate;j++){
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          cptj++;
 fprintf(fichtm,"\n</body>");          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
    }        }
  }      fprintf(ficreseij,"\n");
 fclose(fichtm);     
       free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   /*--------------- Prevalence limit --------------*/      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
        free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   strcpy(filerespl,"pl");      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   strcat(filerespl,fileres);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    printf("\n");
   }    fprintf(ficlog,"\n");
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);  
   fprintf(ficrespl,"#Prevalence limit\n");    free_vector(xp,1,npar);
   fprintf(ficrespl,"#Age ");    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   fprintf(ficrespl,"\n");    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
    }
   prlim=matrix(1,nlstate,1,nlstate);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  /************ Variance ******************/
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  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)
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  {
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* Variance of health expectancies */
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   k=0;    /* double **newm;*/
   agebase=agemin;    double **dnewm,**doldm;
   agelim=agemax;    double **dnewmp,**doldmp;
   ftolpl=1.e-10;    int i, j, nhstepm, hstepm, h, nstepm ;
   i1=cptcoveff;    int k, cptcode;
   if (cptcovn < 1){i1=1;}    double *xp;
     double **gp, **gm;  /* for var eij */
   for(cptcov=1;cptcov<=i1;cptcov++){    double ***gradg, ***trgradg; /*for var eij */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double **gradgp, **trgradgp; /* for var p point j */
         k=k+1;    double *gpp, *gmp; /* for var p point j */
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
         fprintf(ficrespl,"\n#******");    double ***p3mat;
         for(j=1;j<=cptcoveff;j++)    double age,agelim, hf;
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    double ***mobaverage;
         fprintf(ficrespl,"******\n");    int theta;
            char digit[4];
         for (age=agebase; age<=agelim; age++){    char digitp[25];
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  
           fprintf(ficrespl,"%.0f",age );    char fileresprobmorprev[FILENAMELENGTH];
           for(i=1; i<=nlstate;i++)  
           fprintf(ficrespl," %.5f", prlim[i][i]);    if(popbased==1){
           fprintf(ficrespl,"\n");      if(mobilav!=0)
         }        strcpy(digitp,"-populbased-mobilav-");
       }      else strcpy(digitp,"-populbased-nomobil-");
     }    }
   fclose(ficrespl);    else 
   /*------------- h Pij x at various ages ------------*/      strcpy(digitp,"-stablbased-");
    
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    if (mobilav!=0) {
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   }        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   printf("Computing pij: result on file '%s' \n", filerespij);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
        }
   stepsize=(int) (stepm+YEARM-1)/YEARM;    }
   if (stepm<=24) stepsize=2;  
     strcpy(fileresprobmorprev,"prmorprev"); 
   agelim=AGESUP;    sprintf(digit,"%-d",ij);
   hstepm=stepsize*YEARM; /* Every year of age */    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    strcat(fileresprobmorprev,digit); /* Tvar to be done */
      strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   k=0;    strcat(fileresprobmorprev,fileres);
   for(cptcov=1;cptcov<=i1;cptcov++){    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       k=k+1;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
         fprintf(ficrespij,"\n#****** ");    }
         for(j=1;j<=cptcoveff;j++)    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    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);
            fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      fprintf(ficresprobmorprev," p.%-d SE",j);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for(i=1; i<=nlstate;i++)
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           oldm=oldms;savm=savms;    }  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      fprintf(ficresprobmorprev,"\n");
           fprintf(ficrespij,"# Age");    fprintf(ficgp,"\n# Routine varevsij");
           for(i=1; i<=nlstate;i++)    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
             for(j=1; j<=nlstate+ndeath;j++)    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
               fprintf(ficrespij," %1d-%1d",i,j);  /*   } */
           fprintf(ficrespij,"\n");    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           for (h=0; h<=nhstepm; h++){  
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    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");
             for(i=1; i<=nlstate;i++)    fprintf(ficresvij,"# Age");
               for(j=1; j<=nlstate+ndeath;j++)    for(i=1; i<=nlstate;i++)
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);      for(j=1; j<=nlstate;j++)
             fprintf(ficrespij,"\n");        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
           }    fprintf(ficresvij,"\n");
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           fprintf(ficrespij,"\n");    xp=vector(1,npar);
         }    dnewm=matrix(1,nlstate,1,npar);
     }    doldm=matrix(1,nlstate,1,nlstate);
   }    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   fclose(ficrespij);  
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   /*---------- Health expectancies and variances ------------*/    gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
   strcpy(filerest,"t");    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   strcat(filerest,fileres);    
   if((ficrest=fopen(filerest,"w"))==NULL) {    if(estepm < stepm){
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    else  hstepm=estepm;   
     /* 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. 
   strcpy(filerese,"e");       nhstepm is the number of hstepm from age to agelim 
   strcat(filerese,fileres);       nstepm is the number of stepm from age to agelin. 
   if((ficreseij=fopen(filerese,"w"))==NULL) {       Look at hpijx to understand the reason of that which relies in memory size
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);       and note for a fixed period like k years */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);       survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
  strcpy(fileresv,"v");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   strcat(fileresv,fileres);       results. So we changed our mind and took the option of the best precision.
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   }    agelim = AGESUP;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   k=0;      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   for(cptcov=1;cptcov<=i1;cptcov++){      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       k=k+1;      gp=matrix(0,nhstepm,1,nlstate);
       fprintf(ficrest,"\n#****** ");      gm=matrix(0,nhstepm,1,nlstate);
       for(j=1;j<=cptcoveff;j++)  
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficrest,"******\n");      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
       fprintf(ficreseij,"\n#****** ");          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       for(j=1;j<=cptcoveff;j++)        }
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       fprintf(ficreseij,"******\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   
       fprintf(ficresvij,"\n#****** ");        if (popbased==1) {
       for(j=1;j<=cptcoveff;j++)          if(mobilav ==0){
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);            for(i=1; i<=nlstate;i++)
       fprintf(ficresvij,"******\n");              prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            for(i=1; i<=nlstate;i++)
       oldm=oldms;savm=savms;              prlim[i][i]=mobaverage[(int)age][i][ij];
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);            }
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        }
       oldm=oldms;savm=savms;    
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);        for(j=1; j<= nlstate; j++){
                for(h=0; h<=nhstepm; h++){
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       fprintf(ficrest,"\n");          }
                }
       hf=1;        /* This for computing probability of death (h=1 means
       if (stepm >= YEARM) hf=stepm/YEARM;           computed over hstepm matrices product = hstepm*stepm months) 
       epj=vector(1,nlstate+1);           as a weighted average of prlim.
       for(age=bage; age <=fage ;age++){        */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         fprintf(ficrest," %.0f",age);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){            gpp[j] += prlim[i][i]*p3mat[i][j][1];
           for(i=1, epj[j]=0.;i <=nlstate;i++) {        }    
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];        /* end probability of death */
           }  
           epj[nlstate+1] +=epj[j];        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
         }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         for(i=1, vepp=0.;i <=nlstate;i++)        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           for(j=1;j <=nlstate;j++)        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
             vepp += vareij[i][j][(int)age];   
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));        if (popbased==1) {
         for(j=1;j <=nlstate;j++){          if(mobilav ==0){
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));            for(i=1; i<=nlstate;i++)
         }              prlim[i][i]=probs[(int)age][i][ij];
         fprintf(ficrest,"\n");          }else{ /* mobilav */ 
       }            for(i=1; i<=nlstate;i++)
     }              prlim[i][i]=mobaverage[(int)age][i][ij];
   }          }
                }
  fclose(ficreseij);  
  fclose(ficresvij);        for(j=1; j<= nlstate; j++){
   fclose(ficrest);          for(h=0; h<=nhstepm; h++){
   fclose(ficpar);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   free_vector(epj,1,nlstate+1);              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   /*  scanf("%d ",i); */          }
         }
   /*------- Variance limit prevalence------*/          /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
 strcpy(fileresvpl,"vpl");           as a weighted average of prlim.
   strcat(fileresvpl,fileres);        */
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     exit(0);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
   }        }    
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);        /* end probability of death */
   
  k=0;        for(j=1; j<= nlstate; j++) /* vareij */
  for(cptcov=1;cptcov<=i1;cptcov++){          for(h=0; h<=nhstepm; h++){
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
      k=k+1;          }
      fprintf(ficresvpl,"\n#****** ");  
      for(j=1;j<=cptcoveff;j++)        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
      fprintf(ficresvpl,"******\n");        }
        
      varpl=matrix(1,nlstate,(int) bage, (int) fage);      } /* End theta */
      oldm=oldms;savm=savms;  
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
    }  
  }      for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
   fclose(ficresvpl);          for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   /*---------- End : free ----------------*/  
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
          for(theta=1; theta <=npar; theta++)
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);          trgradgp[j][theta]=gradgp[theta][j];
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    
    
        hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);      for(i=1;i<=nlstate;i++)
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(j=1;j<=nlstate;j++)
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          vareij[i][j][(int)age] =0.;
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);  
        for(h=0;h<=nhstepm;h++){
   free_matrix(matcov,1,npar,1,npar);        for(k=0;k<=nhstepm;k++){
   free_vector(delti,1,npar);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
            matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
   printf("End of Imach\n");              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        }
        }
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/    
   /*printf("Total time was %d uSec.\n", total_usecs);*/      /* pptj */
   /*------ End -----------*/      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
  end:      for(j=nlstate+1;j<=nlstate+ndeath;j++)
 #ifdef windows        for(i=nlstate+1;i<=nlstate+ndeath;i++)
  chdir(pathcd);          varppt[j][i]=doldmp[j][i];
 #endif      /* end ppptj */
  /*system("wgnuplot graph.plt");*/      /*  x centered again */
  system("../gp37mgw/wgnuplot graph.plt");      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
 #ifdef windows   
   while (z[0] != 'q') {      if (popbased==1) {
     chdir(pathcd);        if(mobilav ==0){
     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]=probs[(int)age][i][ij];
     if (z[0] == 'c') system("./imach");        }else{ /* mobilav */ 
     else if (z[0] == 'e') {          for(i=1; i<=nlstate;i++)
       chdir(path);            prlim[i][i]=mobaverage[(int)age][i][ij];
       system("index.htm");        }
     }      }
     else if (z[0] == 'q') exit(0);               
   }      /* This for computing probability of death (h=1 means
 #endif         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
 }         as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",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.1.100


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