Diff for /imach/src/imach.c between versions 1.15 and 1.110

version 1.15, 2002/02/20 17:08:52 version 1.110, 2006/01/25 00:51:50
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 1.110  2006/01/25 00:51:50  brouard
   individuals from different ages are interviewed on their health status    (Module): Lots of cleaning and bugs added (Gompertz)
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.109  2006/01/24 19:37:15  brouard
   Health expectancies are computed from the transistions observed between    (Module): Comments (lines starting with a #) are allowed in data.
   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 1.108  2006/01/19 18:05:42  lievre
   reach the Maximum Likelihood of the parameters involved in the model.    Gnuplot problem appeared...
   The simplest model is the multinomial logistic model where pij is    To be fixed
   the probabibility to be observed in state j at the second wave conditional  
   to be observed in state i at the first wave. Therefore the model is:    Revision 1.107  2006/01/19 16:20:37  brouard
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Test existence of gnuplot in imach path
   is a covariate. If you want to have a more complex model than "constant and  
   age", you should modify the program where the markup    Revision 1.106  2006/01/19 13:24:36  brouard
     *Covariates have to be included here again* invites you to do it.    Some cleaning and links added in html output
   More covariates you add, less is the speed of the convergence.  
     Revision 1.105  2006/01/05 20:23:19  lievre
   The advantage that this computer programme claims, comes from that if the    *** empty log message ***
   delay between waves is not identical for each individual, or if some  
   individual missed an interview, the information is not rounded or lost, but    Revision 1.104  2005/09/30 16:11:43  lievre
   taken into account using an interpolation or extrapolation.    (Module): sump fixed, loop imx fixed, and simplifications.
   hPijx is the probability to be    (Module): If the status is missing at the last wave but we know
   observed in state i at age x+h conditional to the observed state i at age    that the person is alive, then we can code his/her status as -2
   x. The delay 'h' can be split into an exact number (nh*stepm) of    (instead of missing=-1 in earlier versions) and his/her
   unobserved intermediate  states. This elementary transition (by month or    contributions to the likelihood is 1 - Prob of dying from last
   quarter trimester, semester or year) is model as a multinomial logistic.    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    the healthy state at last known wave). Version is 0.98
   and the contribution of each individual to the likelihood is simply hPijx.  
     Revision 1.103  2005/09/30 15:54:49  lievre
   Also this programme outputs the covariance matrix of the parameters but also    (Module): sump fixed, loop imx fixed, and simplifications.
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.102  2004/09/15 17:31:30  brouard
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Add the possibility to read data file including tab characters.
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.101  2004/09/15 10:38:38  brouard
   from the European Union.    Fix on curr_time
   It is copyrighted identically to a GNU software product, ie programme and  
   software can be distributed freely for non commercial use. Latest version    Revision 1.100  2004/07/12 18:29:06  brouard
   can be accessed at http://euroreves.ined.fr/imach .    Add version for Mac OS X. Just define UNIX in Makefile
   **********************************************************************/  
      Revision 1.99  2004/06/05 08:57:40  brouard
 #include <math.h>    *** empty log message ***
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.98  2004/05/16 15:05:56  brouard
 #include <unistd.h>    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 #define MAXLINE 256    state at each age, but using a Gompertz model: log u =a + b*age .
 #define FILENAMELENGTH 80    This is the basic analysis of mortality and should be done before any
 /*#define DEBUG*/    other analysis, in order to test if the mortality estimated from the
 #define windows    cross-longitudinal survey is different from the mortality estimated
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    from other sources like vital statistic data.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     The same imach parameter file can be used but the option for mle should be -3.
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Agnès, who wrote this part of the code, tried to keep most of the
     former routines in order to include the new code within the former code.
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    The output is very simple: only an estimate of the intercept and of
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    the slope with 95% confident intervals.
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Current limitations:
 #define YEARM 12. /* Number of months per year */    A) Even if you enter covariates, i.e. with the
 #define AGESUP 130    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 #define AGEBASE 40    B) There is no computation of Life Expectancy nor Life Table.
   
     Revision 1.97  2004/02/20 13:25:42  lievre
 int nvar;    Version 0.96d. Population forecasting command line is (temporarily)
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    suppressed.
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.96  2003/07/15 15:38:55  brouard
 int ndeath=1; /* Number of dead states */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    rewritten within the same printf. Workaround: many printfs.
 int popbased=0;  
     Revision 1.95  2003/07/08 07:54:34  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    * imach.c (Repository):
 int maxwav; /* Maxim number of waves */    (Repository): Using imachwizard code to output a more meaningful covariance
 int jmin, jmax; /* min, max spacing between 2 waves */    matrix (cov(a12,c31) instead of numbers.
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.94  2003/06/27 13:00:02  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Just cleaning
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.93  2003/06/25 16:33:55  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    (Module): On windows (cygwin) function asctime_r doesn't
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    exist so I changed back to asctime which exists.
 FILE *ficgp, *fichtm,*ficresprob;    (Module): Version 0.96b
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Revision 1.92  2003/06/25 16:30:45  brouard
  FILE  *ficresvij;    (Module): On windows (cygwin) function asctime_r doesn't
   char fileresv[FILENAMELENGTH];    exist so I changed back to asctime which exists.
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.91  2003/06/25 15:30:29  brouard
     * imach.c (Repository): Duplicated warning errors corrected.
 #define NR_END 1    (Repository): Elapsed time after each iteration is now output. It
 #define FREE_ARG char*    helps to forecast when convergence will be reached. Elapsed time
 #define FTOL 1.0e-10    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
 #define NRANSI  
 #define ITMAX 200    Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
 #define TOL 2.0e-4    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10    Revision 1.89  2003/06/24 12:30:52  brouard
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
 #define GOLD 1.618034    of the covariance matrix to be input.
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.88  2003/06/23 17:54:56  brouard
     * 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.
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.87  2003/06/18 12:26:01  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Version 0.96
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.86  2003/06/17 20:04:08  brouard
 #define rint(a) floor(a+0.5)    (Module): Change position of html and gnuplot routines and added
     routine fileappend.
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.85  2003/06/17 13:12:43  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    * imach.c (Repository): Check when date of death was earlier that
     current date of interview. It may happen when the death was just
 int imx;    prior to the death. In this case, dh was negative and likelihood
 int stepm;    was wrong (infinity). We still send an "Error" but patch by
 /* Stepm, step in month: minimum step interpolation*/    assuming that the date of death was just one stepm after the
     interview.
 int m,nb;    (Repository): Because some people have very long ID (first column)
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    we changed int to long in num[] and we added a new lvector for
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    memory allocation. But we also truncated to 8 characters (left
 double **pmmij, ***probs, ***mobaverage;    truncation)
     (Repository): No more line truncation errors.
 double *weight;  
 int **s; /* Status */    Revision 1.84  2003/06/13 21:44:43  brouard
 double *agedc, **covar, idx;    * imach.c (Repository): Replace "freqsummary" at a correct
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    place. It differs from routine "prevalence" which may be called
     many times. Probs is memory consuming and must be used with
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    parcimony.
 double ftolhess; /* Tolerance for computing hessian */    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   
 /**************** split *************************/    Revision 1.83  2003/06/10 13:39:11  lievre
 static  int split( char *path, char *dirc, char *name )    *** empty log message ***
 {  
    char *s;                             /* pointer */    Revision 1.82  2003/06/05 15:57:20  brouard
    int  l1, l2;                         /* length counters */    Add log in  imach.c and  fullversion number is now printed.
   
    l1 = strlen( path );                 /* length of path */  */
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  /*
    s = strrchr( path, '\\' );           /* find last / */     Interpolated Markov Chain
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Short summary of the programme:
       extern char       *getwd( );    
     This program computes Healthy Life Expectancies from
       if ( getwd( dirc ) == NULL ) {    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 #else    first survey ("cross") where individuals from different ages are
       extern char       *getcwd( );    interviewed on their health status or degree of disability (in the
     case of a health survey which is our main interest) -2- at least a
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    second wave of interviews ("longitudinal") which measure each change
 #endif    (if any) in individual health status.  Health expectancies are
          return( GLOCK_ERROR_GETCWD );    computed from the time spent in each health state according to a
       }    model. More health states you consider, more time is necessary to reach the
       strcpy( name, path );             /* we've got it */    Maximum Likelihood of the parameters involved in the model.  The
    } else {                             /* strip direcotry from path */    simplest model is the multinomial logistic model where pij is the
       s++;                              /* after this, the filename */    probability to be observed in state j at the second wave
       l2 = strlen( s );                 /* length of filename */    conditional to be observed in state i at the first wave. Therefore
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
       strcpy( name, s );                /* save file name */    'age' is age and 'sex' is a covariate. If you want to have a more
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    complex model than "constant and age", you should modify the program
       dirc[l1-l2] = 0;                  /* add zero */    where the markup *Covariates have to be included here again* invites
    }    you to do it.  More covariates you add, slower the
    l1 = strlen( dirc );                 /* length of directory */    convergence.
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
    return( 0 );                         /* we're done */    The advantage of this computer programme, compared to a simple
 }    multinomial logistic model, is clear when the delay between waves is not
     identical for each individual. Also, if a individual missed an
     intermediate interview, the information is lost, but taken into
 /******************************************/    account using an interpolation or extrapolation.  
   
 void replace(char *s, char*t)    hPijx is the probability to be observed in state i at age x+h
 {    conditional to the observed state i at age x. The delay 'h' can be
   int i;    split into an exact number (nh*stepm) of unobserved intermediate
   int lg=20;    states. This elementary transition (by month, quarter,
   i=0;    semester or year) is modelled as a multinomial logistic.  The hPx
   lg=strlen(t);    matrix is simply the matrix product of nh*stepm elementary matrices
   for(i=0; i<= lg; i++) {    and the contribution of each individual to the likelihood is simply
     (s[i] = t[i]);    hPijx.
     if (t[i]== '\\') s[i]='/';  
   }    Also this programme outputs the covariance matrix of the parameters but also
 }    of the life expectancies. It also computes the stable prevalence. 
     
 int nbocc(char *s, char occ)    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 {             Institut national d'études démographiques, Paris.
   int i,j=0;    This software have been partly granted by Euro-REVES, a concerted action
   int lg=20;    from the European Union.
   i=0;    It is copyrighted identically to a GNU software product, ie programme and
   lg=strlen(s);    software can be distributed freely for non commercial use. Latest version
   for(i=0; i<= lg; i++) {    can be accessed at http://euroreves.ined.fr/imach .
   if  (s[i] == occ ) j++;  
   }    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   return j;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 }    
     **********************************************************************/
 void cutv(char *u,char *v, char*t, char occ)  /*
 {    main
   int i,lg,j,p=0;    read parameterfile
   i=0;    read datafile
   for(j=0; j<=strlen(t)-1; j++) {    concatwav
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    freqsummary
   }    if (mle >= 1)
       mlikeli
   lg=strlen(t);    print results files
   for(j=0; j<p; j++) {    if mle==1 
     (u[j] = t[j]);       computes hessian
   }    read end of parameter file: agemin, agemax, bage, fage, estepm
      u[p]='\0';        begin-prev-date,...
     open gnuplot file
    for(j=0; j<= lg; j++) {    open html file
     if (j>=(p+1))(v[j-p-1] = t[j]);    stable prevalence
   }     for age prevalim()
 }    h Pij x
     variance of p varprob
 /********************** nrerror ********************/    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
 void nrerror(char error_text[])    Variance-covariance of DFLE
 {    prevalence()
   fprintf(stderr,"ERREUR ...\n");     movingaverage()
   fprintf(stderr,"%s\n",error_text);    varevsij() 
   exit(1);    if popbased==1 varevsij(,popbased)
 }    total life expectancies
 /*********************** vector *******************/    Variance of stable prevalence
 double *vector(int nl, int nh)   end
 {  */
   double *v;  
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;   
 }  #include <math.h>
   #include <stdio.h>
 /************************ free vector ******************/  #include <stdlib.h>
 void free_vector(double*v, int nl, int nh)  #include <string.h>
 {  #include <unistd.h>
   free((FREE_ARG)(v+nl-NR_END));  
 }  #include <limits.h>
   #include <sys/types.h>
 /************************ivector *******************************/  #include <sys/stat.h>
 int *ivector(long nl,long nh)  #include <errno.h>
 {  extern int errno;
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  /* #include <sys/time.h> */
   if (!v) nrerror("allocation failure in ivector");  #include <time.h>
   return v-nl+NR_END;  #include "timeval.h"
 }  
   /* #include <libintl.h> */
 /******************free ivector **************************/  /* #define _(String) gettext (String) */
 void free_ivector(int *v, long nl, long nh)  
 {  #define MAXLINE 256
   free((FREE_ARG)(v+nl-NR_END));  
 }  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 /******************* imatrix *******************************/  #define FILENAMELENGTH 132
 int **imatrix(long nrl, long nrh, long ncl, long nch)  
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 {  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  
   int **m;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
    #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   /* allocate pointers to rows */  
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  #define NINTERVMAX 8
   if (!m) nrerror("allocation failure 1 in matrix()");  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   m += NR_END;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   m -= nrl;  #define NCOVMAX 8 /* Maximum number of covariates */
    #define MAXN 20000
    #define YEARM 12. /* Number of months per year */
   /* allocate rows and set pointers to them */  #define AGESUP 130
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  #define AGEBASE 40
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   m[nrl] += NR_END;  #ifdef UNIX
   m[nrl] -= ncl;  #define DIRSEPARATOR '/'
    #define CHARSEPARATOR "/"
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  #define ODIRSEPARATOR '\\'
    #else
   /* return pointer to array of pointers to rows */  #define DIRSEPARATOR '\\'
   return m;  #define CHARSEPARATOR "\\"
 }  #define ODIRSEPARATOR '/'
   #endif
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)  /* $Id$ */
       int **m;  /* $State$ */
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */  char version[]="Imach version 0.98a, January 2006, INED-EUROREVES ";
 {  char fullversion[]="$Revision$ $Date$"; 
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   free((FREE_ARG) (m+nrl-NR_END));  int nvar;
 }  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int npar=NPARMAX;
 /******************* matrix *******************************/  int nlstate=2; /* Number of live states */
 double **matrix(long nrl, long nrh, long ncl, long nch)  int ndeath=1; /* Number of dead states */
 {  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  int popbased=0;
   double **m;  
   int *wav; /* Number of waves for this individuual 0 is possible */
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  int maxwav; /* Maxim number of waves */
   if (!m) nrerror("allocation failure 1 in matrix()");  int jmin, jmax; /* min, max spacing between 2 waves */
   m += NR_END;  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
   m -= nrl;  int gipmx, gsw; /* Global variables on the number of contributions 
                      to the likelihood and the sum of weights (done by funcone)*/
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  int mle, weightopt;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   m[nrl] += NR_END;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   m[nrl] -= ncl;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
              * wave mi and wave mi+1 is not an exact multiple of stepm. */
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  double jmean; /* Mean space between 2 waves */
   return m;  double **oldm, **newm, **savm; /* Working pointers to matrices */
 }  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 /*************************free matrix ************************/  FILE *ficlog, *ficrespow;
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  int globpr; /* Global variable for printing or not */
 {  double fretone; /* Only one call to likelihood */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  long ipmx; /* Number of contributions */
   free((FREE_ARG)(m+nrl-NR_END));  double sw; /* Sum of weights */
 }  char filerespow[FILENAMELENGTH];
   char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
 /******************* ma3x *******************************/  FILE *ficresilk;
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 {  FILE *ficresprobmorprev;
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  FILE *fichtm, *fichtmcov; /* Html File */
   double ***m;  FILE *ficreseij;
   char filerese[FILENAMELENGTH];
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  FILE  *ficresvij;
   if (!m) nrerror("allocation failure 1 in matrix()");  char fileresv[FILENAMELENGTH];
   m += NR_END;  FILE  *ficresvpl;
   m -= nrl;  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   m[nrl] += NR_END;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   m[nrl] -= ncl;  char command[FILENAMELENGTH];
   int  outcmd=0;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  char filelog[FILENAMELENGTH]; /* Log file */
   m[nrl][ncl] += NR_END;  char filerest[FILENAMELENGTH];
   m[nrl][ncl] -= nll;  char fileregp[FILENAMELENGTH];
   for (j=ncl+1; j<=nch; j++)  char popfile[FILENAMELENGTH];
     m[nrl][j]=m[nrl][j-1]+nlay;  
    char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   for (i=nrl+1; i<=nrh; i++) {  
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     for (j=ncl+1; j<=nch; j++)  struct timezone tzp;
       m[i][j]=m[i][j-1]+nlay;  extern int gettimeofday();
   }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   return m;  long time_value;
 }  extern long time();
   char strcurr[80], strfor[80];
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  char *endptr;
 {  long lval;
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define NR_END 1
   free((FREE_ARG)(m+nrl-NR_END));  #define FREE_ARG char*
 }  #define FTOL 1.0e-10
   
 /***************** f1dim *************************/  #define NRANSI 
 extern int ncom;  #define ITMAX 200 
 extern double *pcom,*xicom;  
 extern double (*nrfunc)(double []);  #define TOL 2.0e-4 
    
 double f1dim(double x)  #define CGOLD 0.3819660 
 {  #define ZEPS 1.0e-10 
   int j;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   double f;  
   double *xt;  #define GOLD 1.618034 
    #define GLIMIT 100.0 
   xt=vector(1,ncom);  #define TINY 1.0e-20 
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);  static double maxarg1,maxarg2;
   free_vector(xt,1,ncom);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   return f;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 }    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 /*****************brent *************************/  #define rint(a) floor(a+0.5)
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {  static double sqrarg;
   int iter;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   double a,b,d,etemp;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   double fu,fv,fw,fx;  int agegomp= AGEGOMP;
   double ftemp;  
   double p,q,r,tol1,tol2,u,v,w,x,xm;  int imx; 
   double e=0.0;  int stepm=1;
    /* Stepm, step in month: minimum step interpolation*/
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  int estepm;
   x=w=v=bx;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {  int m,nb;
     xm=0.5*(a+b);  long *num;
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     printf(".");fflush(stdout);  double **pmmij, ***probs;
 #ifdef DEBUG  double *ageexmed,*agecens;
     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);  double dateintmean=0;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif  double *weight;
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int **s; /* Status */
       *xmin=x;  double *agedc, **covar, idx;
       return fx;  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
     }  double *lsurv, *lpop, *tpop;
     ftemp=fu;  
     if (fabs(e) > tol1) {  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
       r=(x-w)*(fx-fv);  double ftolhess; /* Tolerance for computing hessian */
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;  /**************** split *************************/
       q=2.0*(q-r);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
       if (q > 0.0) p = -p;  {
       q=fabs(q);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       etemp=e;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       e=d;    */ 
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    char  *ss;                            /* pointer */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    int   l1, l2;                         /* length counters */
       else {  
         d=p/q;    l1 = strlen(path );                   /* length of path */
         u=x+d;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
         if (u-a < tol2 || b-u < tol2)    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
           d=SIGN(tol1,xm-x);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       }      strcpy( name, path );               /* we got the fullname name because no directory */
     } else {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
       d=CGOLD*(e=(x >= xm ? a-x : b-x));        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     }      /* get current working directory */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));      /*    extern  char* getcwd ( char *buf , int len);*/
     fu=(*f)(u);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     if (fu <= fx) {        return( GLOCK_ERROR_GETCWD );
       if (u >= x) a=x; else b=x;      }
       SHFT(v,w,x,u)      /* got dirc from getcwd*/
         SHFT(fv,fw,fx,fu)      printf(" DIRC = %s \n",dirc);
         } else {    } else {                              /* strip direcotry from path */
           if (u < x) a=u; else b=u;      ss++;                               /* after this, the filename */
           if (fu <= fw || w == x) {      l2 = strlen( ss );                  /* length of filename */
             v=w;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
             w=u;      strcpy( name, ss );         /* save file name */
             fv=fw;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
             fw=fu;      dirc[l1-l2] = 0;                    /* add zero */
           } else if (fu <= fv || v == x || v == w) {      printf(" DIRC2 = %s \n",dirc);
             v=u;    }
             fv=fu;    /* We add a separator at the end of dirc if not exists */
           }    l1 = strlen( dirc );                  /* length of directory */
         }    if( dirc[l1-1] != DIRSEPARATOR ){
   }      dirc[l1] =  DIRSEPARATOR;
   nrerror("Too many iterations in brent");      dirc[l1+1] = 0; 
   *xmin=x;      printf(" DIRC3 = %s \n",dirc);
   return fx;    }
 }    ss = strrchr( name, '.' );            /* find last / */
     if (ss >0){
 /****************** mnbrak ***********************/      ss++;
       strcpy(ext,ss);                     /* save extension */
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,      l1= strlen( name);
             double (*func)(double))      l2= strlen(ss)+1;
 {      strncpy( finame, name, l1-l2);
   double ulim,u,r,q, dum;      finame[l1-l2]= 0;
   double fu;    }
    
   *fa=(*func)(*ax);    return( 0 );                          /* we're done */
   *fb=(*func)(*bx);  }
   if (*fb > *fa) {  
     SHFT(dum,*ax,*bx,dum)  
       SHFT(dum,*fb,*fa,dum)  /******************************************/
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);  void replace_back_to_slash(char *s, char*t)
   *fc=(*func)(*cx);  {
   while (*fb > *fc) {    int i;
     r=(*bx-*ax)*(*fb-*fc);    int lg=0;
     q=(*bx-*cx)*(*fb-*fa);    i=0;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    lg=strlen(t);
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    for(i=0; i<= lg; i++) {
     ulim=(*bx)+GLIMIT*(*cx-*bx);      (s[i] = t[i]);
     if ((*bx-u)*(u-*cx) > 0.0) {      if (t[i]== '\\') s[i]='/';
       fu=(*func)(u);    }
     } else if ((*cx-u)*(u-ulim) > 0.0) {  }
       fu=(*func)(u);  
       if (fu < *fc) {  int nbocc(char *s, char occ)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  {
           SHFT(*fb,*fc,fu,(*func)(u))    int i,j=0;
           }    int lg=20;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    i=0;
       u=ulim;    lg=strlen(s);
       fu=(*func)(u);    for(i=0; i<= lg; i++) {
     } else {    if  (s[i] == occ ) j++;
       u=(*cx)+GOLD*(*cx-*bx);    }
       fu=(*func)(u);    return j;
     }  }
     SHFT(*ax,*bx,*cx,u)  
       SHFT(*fa,*fb,*fc,fu)  void cutv(char *u,char *v, char*t, char occ)
       }  {
 }    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
        and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
 /*************** linmin ************************/       gives u="abcedf" and v="ghi2j" */
     int i,lg,j,p=0;
 int ncom;    i=0;
 double *pcom,*xicom;    for(j=0; j<=strlen(t)-1; j++) {
 double (*nrfunc)(double []);      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
      }
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {    lg=strlen(t);
   double brent(double ax, double bx, double cx,    for(j=0; j<p; j++) {
                double (*f)(double), double tol, double *xmin);      (u[j] = t[j]);
   double f1dim(double x);    }
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,       u[p]='\0';
               double *fc, double (*func)(double));  
   int j;     for(j=0; j<= lg; j++) {
   double xx,xmin,bx,ax;      if (j>=(p+1))(v[j-p-1] = t[j]);
   double fx,fb,fa;    }
    }
   ncom=n;  
   pcom=vector(1,n);  /********************** nrerror ********************/
   xicom=vector(1,n);  
   nrfunc=func;  void nrerror(char error_text[])
   for (j=1;j<=n;j++) {  {
     pcom[j]=p[j];    fprintf(stderr,"ERREUR ...\n");
     xicom[j]=xi[j];    fprintf(stderr,"%s\n",error_text);
   }    exit(EXIT_FAILURE);
   ax=0.0;  }
   xx=1.0;  /*********************** vector *******************/
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  double *vector(int nl, int nh)
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  {
 #ifdef DEBUG    double *v;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 #endif    if (!v) nrerror("allocation failure in vector");
   for (j=1;j<=n;j++) {    return v-nl+NR_END;
     xi[j] *= xmin;  }
     p[j] += xi[j];  
   }  /************************ free vector ******************/
   free_vector(xicom,1,n);  void free_vector(double*v, int nl, int nh)
   free_vector(pcom,1,n);  {
 }    free((FREE_ARG)(v+nl-NR_END));
   }
 /*************** powell ************************/  
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  /************************ivector *******************************/
             double (*func)(double []))  int *ivector(long nl,long nh)
 {  {
   void linmin(double p[], double xi[], int n, double *fret,    int *v;
               double (*func)(double []));    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   int i,ibig,j;    if (!v) nrerror("allocation failure in ivector");
   double del,t,*pt,*ptt,*xit;    return v-nl+NR_END;
   double fp,fptt;  }
   double *xits;  
   pt=vector(1,n);  /******************free ivector **************************/
   ptt=vector(1,n);  void free_ivector(int *v, long nl, long nh)
   xit=vector(1,n);  {
   xits=vector(1,n);    free((FREE_ARG)(v+nl-NR_END));
   *fret=(*func)(p);  }
   for (j=1;j<=n;j++) pt[j]=p[j];  
   for (*iter=1;;++(*iter)) {  /************************lvector *******************************/
     fp=(*fret);  long *lvector(long nl,long nh)
     ibig=0;  {
     del=0.0;    long *v;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     for (i=1;i<=n;i++)    if (!v) nrerror("allocation failure in ivector");
       printf(" %d %.12f",i, p[i]);    return v-nl+NR_END;
     printf("\n");  }
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  /******************free lvector **************************/
       fptt=(*fret);  void free_lvector(long *v, long nl, long nh)
 #ifdef DEBUG  {
       printf("fret=%lf \n",*fret);    free((FREE_ARG)(v+nl-NR_END));
 #endif  }
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);  /******************* imatrix *******************************/
       if (fabs(fptt-(*fret)) > del) {  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         del=fabs(fptt-(*fret));       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
         ibig=i;  { 
       }    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
 #ifdef DEBUG    int **m; 
       printf("%d %.12e",i,(*fret));    
       for (j=1;j<=n;j++) {    /* allocate pointers to rows */ 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
         printf(" x(%d)=%.12e",j,xit[j]);    if (!m) nrerror("allocation failure 1 in matrix()"); 
       }    m += NR_END; 
       for(j=1;j<=n;j++)    m -= nrl; 
         printf(" p=%.12e",p[j]);    
       printf("\n");    
 #endif    /* allocate rows and set pointers to them */ 
     }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 #ifdef DEBUG    m[nrl] += NR_END; 
       int k[2],l;    m[nrl] -= ncl; 
       k[0]=1;    
       k[1]=-1;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
       printf("Max: %.12e",(*func)(p));    
       for (j=1;j<=n;j++)    /* return pointer to array of pointers to rows */ 
         printf(" %.12e",p[j]);    return m; 
       printf("\n");  } 
       for(l=0;l<=1;l++) {  
         for (j=1;j<=n;j++) {  /****************** free_imatrix *************************/
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  void free_imatrix(m,nrl,nrh,ncl,nch)
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);        int **m;
         }        long nch,ncl,nrh,nrl; 
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));       /* free an int matrix allocated by imatrix() */ 
       }  { 
 #endif    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     free((FREE_ARG) (m+nrl-NR_END)); 
   } 
       free_vector(xit,1,n);  
       free_vector(xits,1,n);  /******************* matrix *******************************/
       free_vector(ptt,1,n);  double **matrix(long nrl, long nrh, long ncl, long nch)
       free_vector(pt,1,n);  {
       return;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     }    double **m;
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  
     for (j=1;j<=n;j++) {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       ptt[j]=2.0*p[j]-pt[j];    if (!m) nrerror("allocation failure 1 in matrix()");
       xit[j]=p[j]-pt[j];    m += NR_END;
       pt[j]=p[j];    m -= nrl;
     }  
     fptt=(*func)(ptt);    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (fptt < fp) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    m[nrl] += NR_END;
       if (t < 0.0) {    m[nrl] -= ncl;
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
           xi[j][ibig]=xi[j][n];    return m;
           xi[j][n]=xit[j];    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
         }     */
 #ifdef DEBUG  }
         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++)  /*************************free matrix ************************/
           printf(" %.12e",xit[j]);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         printf("\n");  {
 #endif    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       }    free((FREE_ARG)(m+nrl-NR_END));
     }  }
   }  
 }  /******************* ma3x *******************************/
   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
 /**** Prevalence limit ****************/  {
     long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    double ***m;
 {  
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      matrix by transitions matrix until convergence is reached */    if (!m) nrerror("allocation failure 1 in matrix()");
     m += NR_END;
   int i, ii,j,k;    m -= nrl;
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   double **out, cov[NCOVMAX], **pmij();    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double **newm;    m[nrl] += NR_END;
   double agefin, delaymax=50 ; /* Max number of years to converge */    m[nrl] -= ncl;
   
   for (ii=1;ii<=nlstate+ndeath;ii++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     for (j=1;j<=nlstate+ndeath;j++){  
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     }    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     m[nrl][ncl] += NR_END;
    cov[1]=1.;    m[nrl][ncl] -= nll;
      for (j=ncl+1; j<=nch; j++) 
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */      m[nrl][j]=m[nrl][j-1]+nlay;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    
     newm=savm;    for (i=nrl+1; i<=nrh; i++) {
     /* Covariates have to be included here again */      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
      cov[2]=agefin;      for (j=ncl+1; j<=nch; j++) 
          m[i][j]=m[i][j-1]+nlay;
       for (k=1; k<=cptcovn;k++) {    }
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    return m; 
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
       }             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       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]]];  /*************************free ma3x ************************/
   void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  {
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     free((FREE_ARG)(m[nrl]+ncl-NR_END));
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    free((FREE_ARG)(m+nrl-NR_END));
   }
     savm=oldm;  
     oldm=newm;  /*************** function subdirf ***********/
     maxmax=0.;  char *subdirf(char fileres[])
     for(j=1;j<=nlstate;j++){  {
       min=1.;    /* Caution optionfilefiname is hidden */
       max=0.;    strcpy(tmpout,optionfilefiname);
       for(i=1; i<=nlstate; i++) {    strcat(tmpout,"/"); /* Add to the right */
         sumnew=0;    strcat(tmpout,fileres);
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    return tmpout;
         prlim[i][j]= newm[i][j]/(1-sumnew);  }
         max=FMAX(max,prlim[i][j]);  
         min=FMIN(min,prlim[i][j]);  /*************** function subdirf2 ***********/
       }  char *subdirf2(char fileres[], char *preop)
       maxmin=max-min;  {
       maxmax=FMAX(maxmax,maxmin);    
     }    /* Caution optionfilefiname is hidden */
     if(maxmax < ftolpl){    strcpy(tmpout,optionfilefiname);
       return prlim;    strcat(tmpout,"/");
     }    strcat(tmpout,preop);
   }    strcat(tmpout,fileres);
 }    return tmpout;
   }
 /*************** transition probabilities ***************/  
   /*************** function subdirf3 ***********/
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  char *subdirf3(char fileres[], char *preop, char *preop2)
 {  {
   double s1, s2;    
   /*double t34;*/    /* Caution optionfilefiname is hidden */
   int i,j,j1, nc, ii, jj;    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
     for(i=1; i<= nlstate; i++){    strcat(tmpout,preop);
     for(j=1; j<i;j++){    strcat(tmpout,preop2);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    strcat(tmpout,fileres);
         /*s2 += param[i][j][nc]*cov[nc];*/    return tmpout;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  }
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  
       }  /***************** f1dim *************************/
       ps[i][j]=s2;  extern int ncom; 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  extern double *pcom,*xicom;
     }  extern double (*nrfunc)(double []); 
     for(j=i+1; j<=nlstate+ndeath;j++){   
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  double f1dim(double x) 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  { 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    int j; 
       }    double f;
       ps[i][j]=(s2);    double *xt; 
     }   
   }    xt=vector(1,ncom); 
     /*ps[3][2]=1;*/    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
   for(i=1; i<= nlstate; i++){    free_vector(xt,1,ncom); 
      s1=0;    return f; 
     for(j=1; j<i; j++)  } 
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)  /*****************brent *************************/
       s1+=exp(ps[i][j]);  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     ps[i][i]=1./(s1+1.);  { 
     for(j=1; j<i; j++)    int iter; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    double a,b,d,etemp;
     for(j=i+1; j<=nlstate+ndeath; j++)    double fu,fv,fw,fx;
       ps[i][j]= exp(ps[i][j])*ps[i][i];    double ftemp;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   } /* end i */    double e=0.0; 
    
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    a=(ax < cx ? ax : cx); 
     for(jj=1; jj<= nlstate+ndeath; jj++){    b=(ax > cx ? ax : cx); 
       ps[ii][jj]=0;    x=w=v=bx; 
       ps[ii][ii]=1;    fw=fv=fx=(*f)(x); 
     }    for (iter=1;iter<=ITMAX;iter++) { 
   }      xm=0.5*(a+b); 
       tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      printf(".");fflush(stdout);
     for(jj=1; jj<= nlstate+ndeath; jj++){      fprintf(ficlog,".");fflush(ficlog);
      printf("%lf ",ps[ii][jj]);  #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);
     printf("\n ");      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
     }      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     printf("\n ");printf("%lf ",cov[2]);*/  #endif
 /*      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        *xmin=x; 
   goto end;*/        return fx; 
     return ps;      } 
 }      ftemp=fu;
       if (fabs(e) > tol1) { 
 /**************** Product of 2 matrices ******************/        r=(x-w)*(fx-fv); 
         q=(x-v)*(fx-fw); 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)        p=(x-v)*q-(x-w)*r; 
 {        q=2.0*(q-r); 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        if (q > 0.0) p = -p; 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */        q=fabs(q); 
   /* in, b, out are matrice of pointers which should have been initialized        etemp=e; 
      before: only the contents of out is modified. The function returns        e=d; 
      a pointer to pointers identical to out */        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   long i, j, k;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   for(i=nrl; i<= nrh; i++)        else { 
     for(k=ncolol; k<=ncoloh; k++)          d=p/q; 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)          u=x+d; 
         out[i][k] +=in[i][j]*b[j][k];          if (u-a < tol2 || b-u < tol2) 
             d=SIGN(tol1,xm-x); 
   return out;        } 
 }      } else { 
         d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
 /************* Higher Matrix Product ***************/      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*f)(u); 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )      if (fu <= fx) { 
 {        if (u >= x) a=x; else b=x; 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        SHFT(v,w,x,u) 
      duration (i.e. until          SHFT(fv,fw,fx,fu) 
      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            if (u < x) a=u; else b=u; 
      (typically every 2 years instead of every month which is too big).            if (fu <= fw || w == x) { 
      Model is determined by parameters x and covariates have to be              v=w; 
      included manually here.              w=u; 
               fv=fw; 
      */              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
   int i, j, d, h, k;              v=u; 
   double **out, cov[NCOVMAX];              fv=fu; 
   double **newm;            } 
           } 
   /* Hstepm could be zero and should return the unit matrix */    } 
   for (i=1;i<=nlstate+ndeath;i++)    nrerror("Too many iterations in brent"); 
     for (j=1;j<=nlstate+ndeath;j++){    *xmin=x; 
       oldm[i][j]=(i==j ? 1.0 : 0.0);    return fx; 
       po[i][j][0]=(i==j ? 1.0 : 0.0);  } 
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /****************** mnbrak ***********************/
   for(h=1; h <=nhstepm; h++){  
     for(d=1; d <=hstepm; d++){  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       newm=savm;              double (*func)(double)) 
       /* Covariates have to be included here again */  { 
       cov[1]=1.;    double ulim,u,r,q, dum;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    double fu; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];   
       for (k=1; k<=cptcovage;k++)    *fa=(*func)(*ax); 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    *fb=(*func)(*bx); 
       for (k=1; k<=cptcovprod;k++)    if (*fb > *fa) { 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      SHFT(dum,*ax,*bx,dum) 
         SHFT(dum,*fb,*fa,dum) 
         } 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    *cx=(*bx)+GOLD*(*bx-*ax); 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    *fc=(*func)(*cx); 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    while (*fb > *fc) { 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      r=(*bx-*ax)*(*fb-*fc); 
       savm=oldm;      q=(*bx-*cx)*(*fb-*fa); 
       oldm=newm;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     }        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     for(i=1; i<=nlstate+ndeath; i++)      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       for(j=1;j<=nlstate+ndeath;j++) {      if ((*bx-u)*(u-*cx) > 0.0) { 
         po[i][j][h]=newm[i][j];        fu=(*func)(u); 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      } else if ((*cx-u)*(u-ulim) > 0.0) { 
          */        fu=(*func)(u); 
       }        if (fu < *fc) { 
   } /* end h */          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   return po;            SHFT(*fb,*fc,fu,(*func)(u)) 
 }            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
         u=ulim; 
 /*************** log-likelihood *************/        fu=(*func)(u); 
 double func( double *x)      } else { 
 {        u=(*cx)+GOLD*(*cx-*bx); 
   int i, ii, j, k, mi, d, kk;        fu=(*func)(u); 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      } 
   double **out;      SHFT(*ax,*bx,*cx,u) 
   double sw; /* Sum of weights */        SHFT(*fa,*fb,*fc,fu) 
   double lli; /* Individual log likelihood */        } 
   long ipmx;  } 
   /*extern weight */  
   /* We are differentiating ll according to initial status */  /*************** linmin ************************/
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  
   /*for(i=1;i<imx;i++)  int ncom; 
     printf(" %d\n",s[4][i]);  double *pcom,*xicom;
   */  double (*nrfunc)(double []); 
   cov[1]=1.;   
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for(k=1; k<=nlstate; k++) ll[k]=0.;  { 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    double brent(double ax, double bx, double cx, 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];                 double (*f)(double), double tol, double *xmin); 
     for(mi=1; mi<= wav[i]-1; mi++){    double f1dim(double x); 
       for (ii=1;ii<=nlstate+ndeath;ii++)    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);                double *fc, double (*func)(double)); 
       for(d=0; d<dh[mi][i]; d++){    int j; 
         newm=savm;    double xx,xmin,bx,ax; 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    double fx,fb,fa;
         for (kk=1; kk<=cptcovage;kk++) {   
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    ncom=n; 
         }    pcom=vector(1,n); 
            xicom=vector(1,n); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    nrfunc=func; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    for (j=1;j<=n;j++) { 
         savm=oldm;      pcom[j]=p[j]; 
         oldm=newm;      xicom[j]=xi[j]; 
            } 
            ax=0.0; 
       } /* end mult */    xx=1.0; 
          mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  #ifdef DEBUG
       ipmx +=1;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       sw += weight[i];    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  #endif
     } /* end of wave */    for (j=1;j<=n;j++) { 
   } /* end of individual */      xi[j] *= xmin; 
       p[j] += xi[j]; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    } 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    free_vector(xicom,1,n); 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    free_vector(pcom,1,n); 
   return -l;  } 
 }  
   char *asc_diff_time(long time_sec, char ascdiff[])
   {
 /*********** Maximum Likelihood Estimation ***************/    long sec_left, days, hours, minutes;
     days = (time_sec) / (60*60*24);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    sec_left = (time_sec) % (60*60*24);
 {    hours = (sec_left) / (60*60) ;
   int i,j, iter;    sec_left = (sec_left) %(60*60);
   double **xi,*delti;    minutes = (sec_left) /60;
   double fret;    sec_left = (sec_left) % (60);
   xi=matrix(1,npar,1,npar);    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   for (i=1;i<=npar;i++)    return ascdiff;
     for (j=1;j<=npar;j++)  }
       xi[i][j]=(i==j ? 1.0 : 0.0);  
   printf("Powell\n");  /*************** powell ************************/
   powell(p,xi,npar,ftol,&iter,&fret,func);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
               double (*func)(double [])) 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  { 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    void linmin(double p[], double xi[], int n, double *fret, 
                 double (*func)(double [])); 
 }    int i,ibig,j; 
     double del,t,*pt,*ptt,*xit;
 /**** Computes Hessian and covariance matrix ***/    double fp,fptt;
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    double *xits;
 {    int niterf, itmp;
   double  **a,**y,*x,pd;  
   double **hess;    pt=vector(1,n); 
   int i, j,jk;    ptt=vector(1,n); 
   int *indx;    xit=vector(1,n); 
     xits=vector(1,n); 
   double hessii(double p[], double delta, int theta, double delti[]);    *fret=(*func)(p); 
   double hessij(double p[], double delti[], int i, int j);    for (j=1;j<=n;j++) pt[j]=p[j]; 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    for (*iter=1;;++(*iter)) { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;      fp=(*fret); 
       ibig=0; 
   hess=matrix(1,npar,1,npar);      del=0.0; 
       last_time=curr_time;
   printf("\nCalculation of the hessian matrix. Wait...\n");      (void) gettimeofday(&curr_time,&tzp);
   for (i=1;i<=npar;i++){      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);
     printf("%d",i);fflush(stdout);      /*    fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);
     hess[i][i]=hessii(p,ftolhess,i,delti);      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
     /*printf(" %f ",p[i]);*/      */
     /*printf(" %lf ",hess[i][i]);*/     for (i=1;i<=n;i++) {
   }        printf(" %d %.12f",i, p[i]);
          fprintf(ficlog," %d %.12lf",i, p[i]);
   for (i=1;i<=npar;i++) {        fprintf(ficrespow," %.12lf", p[i]);
     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);      fprintf(ficrespow,"\n");fflush(ficrespow);
         hess[j][i]=hess[i][j];          if(*iter <=3){
         /*printf(" %lf ",hess[i][j]);*/        tm = *localtime(&curr_time.tv_sec);
       }        strcpy(strcurr,asctime(&tm));
     }  /*       asctime_r(&tm,strcurr); */
   }        forecast_time=curr_time; 
   printf("\n");        itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");          strcurr[itmp-1]='\0';
          printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   a=matrix(1,npar,1,npar);        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   y=matrix(1,npar,1,npar);        for(niterf=10;niterf<=30;niterf+=10){
   x=vector(1,npar);          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   indx=ivector(1,npar);          tmf = *localtime(&forecast_time.tv_sec);
   for (i=1;i<=npar;i++)  /*      asctime_r(&tmf,strfor); */
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          strcpy(strfor,asctime(&tmf));
   ludcmp(a,npar,indx,&pd);          itmp = strlen(strfor);
           if(strfor[itmp-1]=='\n')
   for (j=1;j<=npar;j++) {          strfor[itmp-1]='\0';
     for (i=1;i<=npar;i++) x[i]=0;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
     x[j]=1;          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
     lubksb(a,npar,indx,x);        }
     for (i=1;i<=npar;i++){      }
       matcov[i][j]=x[i];      for (i=1;i<=n;i++) { 
     }        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   }        fptt=(*fret); 
   #ifdef DEBUG
   printf("\n#Hessian matrix#\n");        printf("fret=%lf \n",*fret);
   for (i=1;i<=npar;i++) {        fprintf(ficlog,"fret=%lf \n",*fret);
     for (j=1;j<=npar;j++) {  #endif
       printf("%.3e ",hess[i][j]);        printf("%d",i);fflush(stdout);
     }        fprintf(ficlog,"%d",i);fflush(ficlog);
     printf("\n");        linmin(p,xit,n,fret,func); 
   }        if (fabs(fptt-(*fret)) > del) { 
           del=fabs(fptt-(*fret)); 
   /* Recompute Inverse */          ibig=i; 
   for (i=1;i<=npar;i++)        } 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  #ifdef DEBUG
   ludcmp(a,npar,indx,&pd);        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
   /*  printf("\n#Hessian matrix recomputed#\n");        for (j=1;j<=n;j++) {
           xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   for (j=1;j<=npar;j++) {          printf(" x(%d)=%.12e",j,xit[j]);
     for (i=1;i<=npar;i++) x[i]=0;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     x[j]=1;        }
     lubksb(a,npar,indx,x);        for(j=1;j<=n;j++) {
     for (i=1;i<=npar;i++){          printf(" p=%.12e",p[j]);
       y[i][j]=x[i];          fprintf(ficlog," p=%.12e",p[j]);
       printf("%.3e ",y[i][j]);        }
     }        printf("\n");
     printf("\n");        fprintf(ficlog,"\n");
   }  #endif
   */      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   free_matrix(a,1,npar,1,npar);  #ifdef DEBUG
   free_matrix(y,1,npar,1,npar);        int k[2],l;
   free_vector(x,1,npar);        k[0]=1;
   free_ivector(indx,1,npar);        k[1]=-1;
   free_matrix(hess,1,npar,1,npar);        printf("Max: %.12e",(*func)(p));
         fprintf(ficlog,"Max: %.12e",(*func)(p));
         for (j=1;j<=n;j++) {
 }          printf(" %.12e",p[j]);
           fprintf(ficlog," %.12e",p[j]);
 /*************** hessian matrix ****************/        }
 double hessii( double x[], double delta, int theta, double delti[])        printf("\n");
 {        fprintf(ficlog,"\n");
   int i;        for(l=0;l<=1;l++) {
   int l=1, lmax=20;          for (j=1;j<=n;j++) {
   double k1,k2;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   double p2[NPARMAX+1];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   double res;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;          }
   double fx;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   int k=0,kmax=10;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   double l1;        }
   #endif
   fx=func(x);  
   for (i=1;i<=npar;i++) p2[i]=x[i];  
   for(l=0 ; l <=lmax; l++){        free_vector(xit,1,n); 
     l1=pow(10,l);        free_vector(xits,1,n); 
     delts=delt;        free_vector(ptt,1,n); 
     for(k=1 ; k <kmax; k=k+1){        free_vector(pt,1,n); 
       delt = delta*(l1*k);        return; 
       p2[theta]=x[theta] +delt;      } 
       k1=func(p2)-fx;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       p2[theta]=x[theta]-delt;      for (j=1;j<=n;j++) { 
       k2=func(p2)-fx;        ptt[j]=2.0*p[j]-pt[j]; 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        xit[j]=p[j]-pt[j]; 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        pt[j]=p[j]; 
            } 
 #ifdef DEBUG      fptt=(*func)(ptt); 
       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);      if (fptt < fp) { 
 #endif        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        if (t < 0.0) { 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          linmin(p,xit,n,fret,func); 
         k=kmax;          for (j=1;j<=n;j++) { 
       }            xi[j][ibig]=xi[j][n]; 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */            xi[j][n]=xit[j]; 
         k=kmax; l=lmax*10.;          }
       }  #ifdef DEBUG
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         delts=delt;          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]);
   }            fprintf(ficlog," %.12e",xit[j]);
   delti[theta]=delts;          }
   return res;          printf("\n");
            fprintf(ficlog,"\n");
 }  #endif
         }
 double hessij( double x[], double delti[], int thetai,int thetaj)      } 
 {    } 
   int i;  } 
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;  /**** Prevalence limit (stable prevalence)  ****************/
   double p2[NPARMAX+1];  
   int k;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   {
   fx=func(x);    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   for (k=1; k<=2; k++) {       matrix by transitions matrix until convergence is reached */
     for (i=1;i<=npar;i++) p2[i]=x[i];  
     p2[thetai]=x[thetai]+delti[thetai]/k;    int i, ii,j,k;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    double min, max, maxmin, maxmax,sumnew=0.;
     k1=func(p2)-fx;    double **matprod2();
      double **out, cov[NCOVMAX], **pmij();
     p2[thetai]=x[thetai]+delti[thetai]/k;    double **newm;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    double agefin, delaymax=50 ; /* Max number of years to converge */
     k2=func(p2)-fx;  
      for (ii=1;ii<=nlstate+ndeath;ii++)
     p2[thetai]=x[thetai]-delti[thetai]/k;      for (j=1;j<=nlstate+ndeath;j++){
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     k3=func(p2)-fx;      }
    
     p2[thetai]=x[thetai]-delti[thetai]/k;     cov[1]=1.;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;   
     k4=func(p2)-fx;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
 #ifdef DEBUG      newm=savm;
     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);      /* Covariates have to be included here again */
 #endif       cov[2]=agefin;
   }    
   return res;        for (k=1; k<=cptcovn;k++) {
 }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           /*      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]]);*/
 /************** Inverse of matrix **************/        }
 void ludcmp(double **a, int n, int *indx, double *d)        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 {        for (k=1; k<=cptcovprod;k++)
   int i,imax,j,k;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   double big,dum,sum,temp;  
   double *vv;        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
          /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   vv=vector(1,n);        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   *d=1.0;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   for (i=1;i<=n;i++) {  
     big=0.0;      savm=oldm;
     for (j=1;j<=n;j++)      oldm=newm;
       if ((temp=fabs(a[i][j])) > big) big=temp;      maxmax=0.;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");      for(j=1;j<=nlstate;j++){
     vv[i]=1.0/big;        min=1.;
   }        max=0.;
   for (j=1;j<=n;j++) {        for(i=1; i<=nlstate; i++) {
     for (i=1;i<j;i++) {          sumnew=0;
       sum=a[i][j];          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          prlim[i][j]= newm[i][j]/(1-sumnew);
       a[i][j]=sum;          max=FMAX(max,prlim[i][j]);
     }          min=FMIN(min,prlim[i][j]);
     big=0.0;        }
     for (i=j;i<=n;i++) {        maxmin=max-min;
       sum=a[i][j];        maxmax=FMAX(maxmax,maxmin);
       for (k=1;k<j;k++)      }
         sum -= a[i][k]*a[k][j];      if(maxmax < ftolpl){
       a[i][j]=sum;        return prlim;
       if ( (dum=vv[i]*fabs(sum)) >= big) {      }
         big=dum;    }
         imax=i;  }
       }  
     }  /*************** transition probabilities ***************/ 
     if (j != imax) {  
       for (k=1;k<=n;k++) {  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         dum=a[imax][k];  {
         a[imax][k]=a[j][k];    double s1, s2;
         a[j][k]=dum;    /*double t34;*/
       }    int i,j,j1, nc, ii, jj;
       *d = -(*d);  
       vv[imax]=vv[j];      for(i=1; i<= nlstate; i++){
     }        for(j=1; j<i;j++){
     indx[j]=imax;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     if (a[j][j] == 0.0) a[j][j]=TINY;            /*s2 += param[i][j][nc]*cov[nc];*/
     if (j != n) {            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
       dum=1.0/(a[j][j]);  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          }
     }          ps[i][j]=s2;
   }  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
   free_vector(vv,1,n);  /* Doesn't work */        }
 ;        for(j=i+1; j<=nlstate+ndeath;j++){
 }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
             s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 void lubksb(double **a, int n, int *indx, double b[])  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
 {          }
   int i,ii=0,ip,j;          ps[i][j]=s2;
   double sum;        }
        }
   for (i=1;i<=n;i++) {      /*ps[3][2]=1;*/
     ip=indx[i];      
     sum=b[ip];      for(i=1; i<= nlstate; i++){
     b[ip]=b[i];        s1=0;
     if (ii)        for(j=1; j<i; j++)
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          s1+=exp(ps[i][j]);
     else if (sum) ii=i;        for(j=i+1; j<=nlstate+ndeath; j++)
     b[i]=sum;          s1+=exp(ps[i][j]);
   }        ps[i][i]=1./(s1+1.);
   for (i=n;i>=1;i--) {        for(j=1; j<i; j++)
     sum=b[i];          ps[i][j]= exp(ps[i][j])*ps[i][i];
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        for(j=i+1; j<=nlstate+ndeath; j++)
     b[i]=sum/a[i][i];          ps[i][j]= exp(ps[i][j])*ps[i][i];
   }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
 }      } /* end i */
       
 /************ Frequencies ********************/      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax, int fprev1,int lprev1)        for(jj=1; jj<= nlstate+ndeath; jj++){
 {  /* Some frequencies */          ps[ii][jj]=0;
            ps[ii][ii]=1;
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;        }
   double ***freq; /* Frequencies */      }
   double *pp;      
   double pos;  
   FILE *ficresp;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   char fileresp[FILENAMELENGTH];  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   /*         printf("ddd %lf ",ps[ii][jj]); */
   pp=vector(1,nlstate);  /*       } */
  probs= ma3x(1,130 ,1,8, 1,8);  /*       printf("\n "); */
   strcpy(fileresp,"p");  /*        } */
   strcat(fileresp,fileres);  /*        printf("\n ");printf("%lf ",cov[2]); */
   if((ficresp=fopen(fileresp,"w"))==NULL) {         /*
     printf("Problem with prevalence resultfile: %s\n", fileresp);        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     exit(0);        goto end;*/
   }      return ps;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  }
   j1=0;  
   /**************** Product of 2 matrices ******************/
   j=cptcoveff;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   {
   for(k1=1; k1<=j;k1++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
    for(i1=1; i1<=ncodemax[k1];i1++){       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
        j1++;    /* in, b, out are matrice of pointers which should have been initialized 
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);       before: only the contents of out is modified. The function returns
          scanf("%d", i);*/       a pointer to pointers identical to out */
         for (i=-1; i<=nlstate+ndeath; i++)      long i, j, k;
          for (jk=-1; jk<=nlstate+ndeath; jk++)      for(i=nrl; i<= nrh; i++)
            for(m=agemin; m <= agemax+3; m++)      for(k=ncolol; k<=ncoloh; k++)
              freq[i][jk][m]=0;        for(j=ncl,out[i][k]=0.; j<=nch; j++)
                  out[i][k] +=in[i][j]*b[j][k];
        for (i=1; i<=imx; i++) {  
          bool=1;    return out;
          if  (cptcovn>0) {  }
            for (z1=1; z1<=cptcoveff; z1++)  
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  
                bool=0;  /************* Higher Matrix Product ***************/
          }  
           if (bool==1) {  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
            for(m=fprev1; m<=lprev1; m++){  {
              if(agev[m][i]==0) agev[m][i]=agemax+1;    /* Computes the transition matrix starting at age 'age' over 
              if(agev[m][i]==1) agev[m][i]=agemax+2;       'nhstepm*hstepm*stepm' months (i.e. until
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];       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 
        }       for the memory).
         if  (cptcovn>0) {       Model is determined by parameters x and covariates have to be 
          fprintf(ficresp, "\n#********** Variable ");       included manually here. 
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  
        fprintf(ficresp, "**********\n#");       */
         }  
        for(i=1; i<=nlstate;i++)    int i, j, d, h, k;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    double **out, cov[NCOVMAX];
        fprintf(ficresp, "\n");    double **newm;
          
   for(i=(int)agemin; i <= (int)agemax+3; i++){    /* Hstepm could be zero and should return the unit matrix */
     if(i==(int)agemax+3)    for (i=1;i<=nlstate+ndeath;i++)
       printf("Total");      for (j=1;j<=nlstate+ndeath;j++){
     else        oldm[i][j]=(i==j ? 1.0 : 0.0);
       printf("Age %d", i);        po[i][j][0]=(i==j ? 1.0 : 0.0);
     for(jk=1; jk <=nlstate ; jk++){      }
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         pp[jk] += freq[jk][m][i];    for(h=1; h <=nhstepm; h++){
     }      for(d=1; d <=hstepm; d++){
     for(jk=1; jk <=nlstate ; jk++){        newm=savm;
       for(m=-1, pos=0; m <=0 ; m++)        /* Covariates have to be included here again */
         pos += freq[jk][m][i];        cov[1]=1.;
       if(pp[jk]>=1.e-10)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       else        for (k=1; k<=cptcovage;k++)
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          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]]];
      for(jk=1; jk <=nlstate ; jk++){  
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  
         pp[jk] += freq[jk][m][i];        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
      }        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     for(jk=1,pos=0; jk <=nlstate ; jk++)                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       pos += pp[jk];        savm=oldm;
     for(jk=1; jk <=nlstate ; jk++){        oldm=newm;
       if(pos>=1.e-5)      }
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);      for(i=1; i<=nlstate+ndeath; i++)
       else        for(j=1;j<=nlstate+ndeath;j++) {
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          po[i][j][h]=newm[i][j];
       if( i <= (int) agemax){          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
         if(pos>=1.e-5){           */
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        }
           probs[i][jk][j1]= pp[jk]/pos;    } /* end h */
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/    return po;
         }  }
       else  
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  
       }  /*************** log-likelihood *************/
     }  double func( double *x)
     for(jk=-1; jk <=nlstate+ndeath; jk++)  {
       for(m=-1; m <=nlstate+ndeath; m++)    int i, ii, j, k, mi, d, kk;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     if(i <= (int) agemax)    double **out;
       fprintf(ficresp,"\n");    double sw; /* Sum of weights */
     printf("\n");    double lli; /* Individual log likelihood */
     }    int s1, s2;
     }    double bbh, survp;
  }    long ipmx;
      /*extern weight */
   fclose(ficresp);    /* We are differentiating ll according to initial status */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   free_vector(pp,1,nlstate);    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
 }  /* End of Freq */    */
     cov[1]=1.;
 /************ Prevalence ********************/  
 void prevalence(int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax, int fprev1,int lprev1)    for(k=1; k<=nlstate; k++) ll[k]=0.;
 {  /* Some frequencies */  
      if(mle==1){
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***freq; /* Frequencies */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double *pp;        for(mi=1; mi<= wav[i]-1; mi++){
   double pos;          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
   pp=vector(1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   probs= ma3x(1,130 ,1,8, 1,8);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          for(d=0; d<dh[mi][i]; d++){
   j1=0;            newm=savm;
              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   j=cptcoveff;            for (kk=1; kk<=cptcovage;kk++) {
   if (cptcovn<1) {j=1;ncodemax[1]=1;}              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              }
  for(k1=1; k1<=j;k1++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(i1=1; i1<=ncodemax[k1];i1++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       j1++;            savm=oldm;
              oldm=newm;
       for (i=-1; i<=nlstate+ndeath; i++)            } /* end mult */
         for (jk=-1; jk<=nlstate+ndeath; jk++)          
           for(m=agemin; m <= agemax+3; m++)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           freq[i][jk][m]=0;          /* But now since version 0.9 we anticipate for bias at large stepm.
                 * If stepm is larger than one month (smallest stepm) and if the exact delay 
       for (i=1; i<=imx; i++) {           * (in months) between two waves is not a multiple of stepm, we rounded to 
         bool=1;           * the nearest (and in case of equal distance, to the lowest) interval but now
         if  (cptcovn>0) {           * we keep into memory the bias bh[mi][i] and also the previous matrix product
           for (z1=1; z1<=cptcoveff; z1++)           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])           * probability in order to take into account the bias as a fraction of the way
               bool=0;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
               }           * -stepm/2 to stepm/2 .
         if (bool==1) {           * For stepm=1 the results are the same as for previous versions of Imach.
           for(m=fprev1; m<=lprev1; m++){           * For stepm > 1 the results are less biased than in previous versions. 
             if(agev[m][i]==0) agev[m][i]=agemax+1;           */
             if(agev[m][i]==1) agev[m][i]=agemax+2;          s1=s[mw[mi][i]][i];
             freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          s2=s[mw[mi+1][i]][i];
             freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          bbh=(double)bh[mi][i]/(double)stepm; 
           }          /* bias bh is positive if real duration
         }           * is higher than the multiple of stepm and negative otherwise.
       }           */
        for(i=(int)agemin; i <= (int)agemax+3; i++){          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
         for(jk=1; jk <=nlstate ; jk++){          if( s2 > nlstate){ 
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)            /* i.e. if s2 is a death state and if the date of death is known 
             pp[jk] += freq[jk][m][i];               then the contribution to the likelihood is the probability to 
         }               die between last step unit time and current  step unit time, 
         for(jk=1; jk <=nlstate ; jk++){               which is also equal to probability to die before dh 
           for(m=-1, pos=0; m <=0 ; m++)               minus probability to die before dh-stepm . 
             pos += freq[jk][m][i];               In version up to 0.92 likelihood was computed
         }          as if date of death was unknown. Death was treated as any other
                  health state: the date of the interview describes the actual state
          for(jk=1; jk <=nlstate ; jk++){          and not the date of a change in health state. The former idea was
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          to consider that at each interview the state was recorded
              pp[jk] += freq[jk][m][i];          (healthy, disable or death) and IMaCh was corrected; but when we
          }          introduced the exact date of death then we should have modified
                    the contribution of an exact death to the likelihood. This new
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];          contribution is smaller and very dependent of the step unit
           stepm. It is no more the probability to die between last interview
          for(jk=1; jk <=nlstate ; jk++){                    and month of death but the probability to survive from last
            if( i <= (int) agemax){          interview up to one month before death multiplied by the
              if(pos>=1.e-5){          probability to die within a month. Thanks to Chris
                probs[i][jk][j1]= pp[jk]/pos;          Jackson for correcting this bug.  Former versions increased
              }          mortality artificially. The bad side is that we add another loop
            }          which slows down the processing. The difference can be up to 10%
          }          lower mortality.
                      */
          }            lli=log(out[s1][s2] - savm[s1][s2]);
     }  
   }  
            } else if  (s2==-2) {
              for (j=1,survp=0. ; j<=nlstate; j++) 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);              survp += out[s1][j];
   free_vector(pp,1,nlstate);            lli= survp;
            }
 }  /* End of Freq */          
 /************* Waves Concatenation ***************/          else if  (s2==-4) {
             for (j=3,survp=0. ; j<=nlstate; j++) 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)              survp += out[s1][j];
 {            lli= survp;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          }
      Death is a valid wave (if date is known).          
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          else if  (s2==-5) {
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]            for (j=1,survp=0. ; j<=2; j++) 
      and mw[mi+1][i]. dh depends on stepm.              survp += out[s1][j];
      */            lli= survp;
           }
   int i, mi, m;  
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  
      double sum=0., jmean=0.;*/          else{
             lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   int j, k=0,jk, ju, jl;            /*  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 */
   double sum=0.;          } 
   jmin=1e+5;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   jmax=-1;          /*if(lli ==000.0)*/
   jmean=0.;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
   for(i=1; i<=imx; i++){          ipmx +=1;
     mi=0;          sw += weight[i];
     m=firstpass;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     while(s[m][i] <= nlstate){        } /* end of wave */
       if(s[m][i]>=1)      } /* end of individual */
         mw[++mi][i]=m;    }  else if(mle==2){
       if(m >=lastpass)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         break;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       else        for(mi=1; mi<= wav[i]-1; mi++){
         m++;          for (ii=1;ii<=nlstate+ndeath;ii++)
     }/* end while */            for (j=1;j<=nlstate+ndeath;j++){
     if (s[m][i] > nlstate){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       mi++;     /* Death is another wave */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       /* if(mi==0)  never been interviewed correctly before death */            }
          /* Only death is a correct wave */          for(d=0; d<=dh[mi][i]; d++){
       mw[mi][i]=m;            newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
     wav[i]=mi;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     if(mi==0)            }
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   for(i=1; i<=imx; i++){            oldm=newm;
     for(mi=1; mi<wav[i];mi++){          } /* end mult */
       if (stepm <=0)        
         dh[mi][i]=1;          s1=s[mw[mi][i]][i];
       else{          s2=s[mw[mi+1][i]][i];
         if (s[mw[mi+1][i]][i] > nlstate) {          bbh=(double)bh[mi][i]/(double)stepm; 
           if (agedc[i] < 2*AGESUP) {          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 */
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          ipmx +=1;
           if(j==0) j=1;  /* Survives at least one month after exam */          sw += weight[i];
           k=k+1;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           if (j >= jmax) jmax=j;        } /* end of wave */
           if (j <= jmin) jmin=j;      } /* end of individual */
           sum=sum+j;    }  else if(mle==3){  /* exponential inter-extrapolation */
           /* if (j<10) printf("j=%d num=%d ",j,i); */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
         else{          for (ii=1;ii<=nlstate+ndeath;ii++)
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));            for (j=1;j<=nlstate+ndeath;j++){
           k=k+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           if (j >= jmax) jmax=j;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           else if (j <= jmin)jmin=j;            }
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */          for(d=0; d<dh[mi][i]; d++){
           sum=sum+j;            newm=savm;
         }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         jk= j/stepm;            for (kk=1; kk<=cptcovage;kk++) {
         jl= j -jk*stepm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         ju= j -(jk+1)*stepm;            }
         if(jl <= -ju)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           dh[mi][i]=jk;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         else            savm=oldm;
           dh[mi][i]=jk+1;            oldm=newm;
         if(dh[mi][i]==0)          } /* end mult */
           dh[mi][i]=1; /* At least one step */        
       }          s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
   }          bbh=(double)bh[mi][i]/(double)stepm; 
   jmean=sum/k;          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 */
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          ipmx +=1;
  }          sw += weight[i];
 /*********** Tricode ****************************/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 void tricode(int *Tvar, int **nbcode, int imx)        } /* end of wave */
 {      } /* end of individual */
   int Ndum[20],ij=1, k, j, i;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
   int cptcode=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   cptcoveff=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          for(mi=1; mi<= wav[i]-1; mi++){
   for (k=0; k<19; k++) Ndum[k]=0;          for (ii=1;ii<=nlstate+ndeath;ii++)
   for (k=1; k<=7; k++) ncodemax[k]=0;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=1; i<=imx; i++) {            }
       ij=(int)(covar[Tvar[j]][i]);          for(d=0; d<dh[mi][i]; d++){
       Ndum[ij]++;            newm=savm;
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       if (ij > cptcode) cptcode=ij;            for (kk=1; kk<=cptcovage;kk++) {
     }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
     for (i=0; i<=cptcode; i++) {          
       if(Ndum[i]!=0) ncodemax[j]++;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     ij=1;            savm=oldm;
             oldm=newm;
           } /* end mult */
     for (i=1; i<=ncodemax[j]; i++) {        
       for (k=0; k<=19; k++) {          s1=s[mw[mi][i]][i];
         if (Ndum[k] != 0) {          s2=s[mw[mi+1][i]][i];
           nbcode[Tvar[j]][ij]=k;          if( s2 > nlstate){ 
           ij++;            lli=log(out[s1][s2] - savm[s1][s2]);
         }          }else{
         if (ij > ncodemax[j]) break;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       }            }
     }          ipmx +=1;
   }            sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
  for (k=0; k<19; k++) Ndum[k]=0;  /*      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 */
  for (i=1; i<=ncovmodel-2; i++) {      } /* end of individual */
       ij=Tvar[i];    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
       Ndum[ij]++;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
  ij=1;          for (ii=1;ii<=nlstate+ndeath;ii++)
  for (i=1; i<=10; i++) {            for (j=1;j<=nlstate+ndeath;j++){
    if((Ndum[i]!=0) && (i<=ncov)){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      Tvaraff[ij]=i;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
      ij++;            }
    }          for(d=0; d<dh[mi][i]; d++){
  }            newm=savm;
              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     cptcoveff=ij-1;            for (kk=1; kk<=cptcovage;kk++) {
 }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
 /*********** Health Expectancies ****************/          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 {            savm=oldm;
   /* Health expectancies */            oldm=newm;
   int i, j, nhstepm, hstepm, h;          } /* end mult */
   double age, agelim,hf;        
   double ***p3mat;          s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
   fprintf(ficreseij,"# Health expectancies\n");          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   fprintf(ficreseij,"# Age");          ipmx +=1;
   for(i=1; i<=nlstate;i++)          sw += weight[i];
     for(j=1; j<=nlstate;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficreseij," %1d-%1d",i,j);          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
   fprintf(ficreseij,"\n");        } /* end of wave */
       } /* end of individual */
   hstepm=1*YEARM; /*  Every j years of age (in month) */    } /* End of if */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   agelim=AGESUP;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    return -l;
     /* nhstepm age range expressed in number of stepm */  }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);  
     /* Typically if 20 years = 20*12/6=40 stepm */  /*************** log-likelihood *************/
     if (stepm >= YEARM) hstepm=1;  double funcone( double *x)
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */  {
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* Same as likeli but slower because of a lot of printf and if */
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    int i, ii, j, k, mi, d, kk;
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      double **out;
     double lli; /* Individual log likelihood */
     double llt;
     for(i=1; i<=nlstate;i++)    int s1, s2;
       for(j=1; j<=nlstate;j++)    double bbh, survp;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){    /*extern weight */
           eij[i][j][(int)age] +=p3mat[i][j][h];    /* We are differentiating ll according to initial status */
         }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
        /*for(i=1;i<imx;i++) 
     hf=1;      printf(" %d\n",s[4][i]);
     if (stepm >= YEARM) hf=stepm/YEARM;    */
     fprintf(ficreseij,"%.0f",age );    cov[1]=1.;
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++){    for(k=1; k<=nlstate; k++) ll[k]=0.;
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);  
       }    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     fprintf(ficreseij,"\n");      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(mi=1; mi<= wav[i]-1; mi++){
   }        for (ii=1;ii<=nlstate+ndeath;ii++)
 }          for (j=1;j<=nlstate+ndeath;j++){
             oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /************ Variance ******************/            savm[ii][j]=(ii==j ? 1.0 : 0.0);
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)          }
 {        for(d=0; d<dh[mi][i]; d++){
   /* Variance of health expectancies */          newm=savm;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double **newm;          for (kk=1; kk<=cptcovage;kk++) {
   double **dnewm,**doldm;            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int i, j, nhstepm, hstepm, h;          }
   int k, cptcode;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double *xp;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double **gp, **gm;          savm=oldm;
   double ***gradg, ***trgradg;          oldm=newm;
   double ***p3mat;        } /* end mult */
   double age,agelim;        
   int theta;        s1=s[mw[mi][i]][i];
         s2=s[mw[mi+1][i]][i];
    fprintf(ficresvij,"# Covariances of life expectancies\n");        bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficresvij,"# Age");        /* bias is positive if real duration
   for(i=1; i<=nlstate;i++)         * is higher than the multiple of stepm and negative otherwise.
     for(j=1; j<=nlstate;j++)         */
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
   fprintf(ficresvij,"\n");          lli=log(out[s1][s2] - savm[s1][s2]);
         } else if (mle==1){
   xp=vector(1,npar);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   dnewm=matrix(1,nlstate,1,npar);        } else if(mle==2){
   doldm=matrix(1,nlstate,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 */
   hstepm=1*YEARM; /* Every year of age */          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 */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   agelim = AGESUP;          lli=log(out[s1][s2]); /* Original formula */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          lli=log(out[s1][s2]); /* Original formula */
     if (stepm >= YEARM) hstepm=1;        } /* End of if */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        ipmx +=1;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        sw += weight[i];
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     gp=matrix(0,nhstepm,1,nlstate);  /*       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]); */
     gm=matrix(0,nhstepm,1,nlstate);        if(globpr){
           fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
     for(theta=1; theta <=npar; theta++){   %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]);
       }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              llt +=ll[k]*gipmx/gsw;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           }
       if (popbased==1) {          fprintf(ficresilk," %10.6f\n", -llt);
         for(i=1; i<=nlstate;i++)        }
           prlim[i][i]=probs[(int)age][i][ij];      } /* end of wave */
       }    } /* end of individual */
          for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       for(j=1; j<= nlstate; j++){    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         for(h=0; h<=nhstepm; h++){    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    if(globpr==0){ /* First time we count the contributions and weights */
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      gipmx=ipmx;
         }      gsw=sw;
       }    }
        return -l;
       for(i=1; i<=npar; i++) /* Computes gradient */  }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  /*************** function likelione ***********/
   void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       if (popbased==1) {  {
         for(i=1; i<=nlstate;i++)    /* This routine should help understanding what is done with 
           prlim[i][i]=probs[(int)age][i][ij];       the selection of individuals/waves and
       }       to check the exact contribution to the likelihood.
        Plotting could be done.
       for(j=1; j<= nlstate; j++){     */
         for(h=0; h<=nhstepm; h++){    int k;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    if(*globpri !=0){ /* Just counts and sums, no printings */
         }      strcpy(fileresilk,"ilk"); 
       }      strcat(fileresilk,fileres);
       if((ficresilk=fopen(fileresilk,"w"))==NULL) {
       for(j=1; j<= nlstate; j++)        printf("Problem with resultfile: %s\n", fileresilk);
         for(h=0; h<=nhstepm; h++){        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      }
         }      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");
     } /* End theta */      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);      for(k=1; k<=nlstate; k++) 
         fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     for(h=0; h<=nhstepm; h++)      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       for(j=1; j<=nlstate;j++)    }
         for(theta=1; theta <=npar; theta++)  
           trgradg[h][j][theta]=gradg[h][theta][j];    *fretone=(*funcone)(p);
     if(*globpri !=0){
     for(i=1;i<=nlstate;i++)      fclose(ficresilk);
       for(j=1;j<=nlstate;j++)      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
         vareij[i][j][(int)age] =0.;      fflush(fichtm); 
     for(h=0;h<=nhstepm;h++){    } 
       for(k=0;k<=nhstepm;k++){    return;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);  }
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  
         for(i=1;i<=nlstate;i++)  
           for(j=1;j<=nlstate;j++)  /*********** Maximum Likelihood Estimation ***************/
             vareij[i][j][(int)age] += doldm[i][j];  
       }  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     }  {
     h=1;    int i,j, iter;
     if (stepm >= YEARM) h=stepm/YEARM;    double **xi;
     fprintf(ficresvij,"%.0f ",age );    double fret;
     for(i=1; i<=nlstate;i++)    double fretone; /* Only one call to likelihood */
       for(j=1; j<=nlstate;j++){    /*  char filerespow[FILENAMELENGTH];*/
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);    xi=matrix(1,npar,1,npar);
       }    for (i=1;i<=npar;i++)
     fprintf(ficresvij,"\n");      for (j=1;j<=npar;j++)
     free_matrix(gp,0,nhstepm,1,nlstate);        xi[i][j]=(i==j ? 1.0 : 0.0);
     free_matrix(gm,0,nhstepm,1,nlstate);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    strcpy(filerespow,"pow"); 
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    strcat(filerespow,fileres);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   } /* End age */      printf("Problem with resultfile: %s\n", filerespow);
        fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   free_vector(xp,1,npar);    }
   free_matrix(doldm,1,nlstate,1,npar);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   free_matrix(dnewm,1,nlstate,1,nlstate);    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");
 /************ 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)    powell(p,xi,npar,ftol,&iter,&fret,func);
 {  
   /* Variance of prevalence limit */    fclose(ficrespow);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
   double **newm;    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   double **dnewm,**doldm;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   int i, j, nhstepm, hstepm;  
   int k, cptcode;  }
   double *xp;  
   double *gp, *gm;  /**** Computes Hessian and covariance matrix ***/
   double **gradg, **trgradg;  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   double age,agelim;  {
   int theta;    double  **a,**y,*x,pd;
        double **hess;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");    int i, j,jk;
   fprintf(ficresvpl,"# Age");    int *indx;
   for(i=1; i<=nlstate;i++)  
       fprintf(ficresvpl," %1d-%1d",i,i);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   fprintf(ficresvpl,"\n");    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     void lubksb(double **a, int npar, int *indx, double b[]) ;
   xp=vector(1,npar);    void ludcmp(double **a, int npar, int *indx, double *d) ;
   dnewm=matrix(1,nlstate,1,npar);    double gompertz(double p[]);
   doldm=matrix(1,nlstate,1,nlstate);    hess=matrix(1,npar,1,npar);
    
   hstepm=1*YEARM; /* Every year of age */    printf("\nCalculation of the hessian matrix. Wait...\n");
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   agelim = AGESUP;    for (i=1;i<=npar;i++){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      printf("%d",i);fflush(stdout);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      fprintf(ficlog,"%d",i);fflush(ficlog);
     if (stepm >= YEARM) hstepm=1;     
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     gradg=matrix(1,npar,1,nlstate);      
     gp=vector(1,nlstate);      /*  printf(" %f ",p[i]);
     gm=vector(1,nlstate);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
     for(theta=1; theta <=npar; theta++){    
       for(i=1; i<=npar; i++){ /* Computes gradient */    for (i=1;i<=npar;i++) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for (j=1;j<=npar;j++)  {
       }        if (j>i) { 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          printf(".%d%d",i,j);fflush(stdout);
       for(i=1;i<=nlstate;i++)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
         gp[i] = prlim[i][i];          hess[i][j]=hessij(p,delti,i,j,func,npar);
              
       for(i=1; i<=npar; i++) /* Computes gradient */          hess[j][i]=hess[i][j];    
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          /*printf(" %lf ",hess[i][j]);*/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        }
       for(i=1;i<=nlstate;i++)      }
         gm[i] = prlim[i][i];    }
     printf("\n");
       for(i=1;i<=nlstate;i++)    fprintf(ficlog,"\n");
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     trgradg =matrix(1,nlstate,1,npar);    
     a=matrix(1,npar,1,npar);
     for(j=1; j<=nlstate;j++)    y=matrix(1,npar,1,npar);
       for(theta=1; theta <=npar; theta++)    x=vector(1,npar);
         trgradg[j][theta]=gradg[theta][j];    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
     for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
       varpl[i][(int)age] =0.;    ludcmp(a,npar,indx,&pd);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);  
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    for (j=1;j<=npar;j++) {
     for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++) x[i]=0;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */      x[j]=1;
       lubksb(a,npar,indx,x);
     fprintf(ficresvpl,"%.0f ",age );      for (i=1;i<=npar;i++){ 
     for(i=1; i<=nlstate;i++)        matcov[i][j]=x[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);    printf("\n#Hessian matrix#\n");
     free_matrix(gradg,1,npar,1,nlstate);    fprintf(ficlog,"\n#Hessian matrix#\n");
     free_matrix(trgradg,1,nlstate,1,npar);    for (i=1;i<=npar;i++) { 
   } /* End age */      for (j=1;j<=npar;j++) { 
         printf("%.3e ",hess[i][j]);
   free_vector(xp,1,npar);        fprintf(ficlog,"%.3e ",hess[i][j]);
   free_matrix(doldm,1,nlstate,1,npar);      }
   free_matrix(dnewm,1,nlstate,1,nlstate);      printf("\n");
       fprintf(ficlog,"\n");
 }    }
   
 /************ Variance of one-step probabilities  ******************/    /* Recompute Inverse */
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)    for (i=1;i<=npar;i++)
 {      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   int i, j;    ludcmp(a,npar,indx,&pd);
   int k=0, cptcode;  
   double **dnewm,**doldm;    /*  printf("\n#Hessian matrix recomputed#\n");
   double *xp;  
   double *gp, *gm;    for (j=1;j<=npar;j++) {
   double **gradg, **trgradg;      for (i=1;i<=npar;i++) x[i]=0;
   double age,agelim, cov[NCOVMAX];      x[j]=1;
   int theta;      lubksb(a,npar,indx,x);
   char fileresprob[FILENAMELENGTH];      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
   strcpy(fileresprob,"prob");        printf("%.3e ",y[i][j]);
   strcat(fileresprob,fileres);        fprintf(ficlog,"%.3e ",y[i][j]);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {      }
     printf("Problem with resultfile: %s\n", fileresprob);      printf("\n");
   }      fprintf(ficlog,"\n");
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);    }
      */
   
   xp=vector(1,npar);    free_matrix(a,1,npar,1,npar);
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    free_matrix(y,1,npar,1,npar);
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
   cov[1]=1;    free_matrix(hess,1,npar,1,npar);
   for (age=bage; age<=fage; age ++){  
     cov[2]=age;  
     gradg=matrix(1,npar,1,9);  }
     trgradg=matrix(1,9,1,npar);  
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));  /*************** hessian matrix ****************/
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
      {
     for(theta=1; theta <=npar; theta++){    int i;
       for(i=1; i<=npar; i++)    int l=1, lmax=20;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    double k1,k2;
          double p2[NPARMAX+1];
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    double res;
        double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       k=0;    double fx;
       for(i=1; i<= (nlstate+ndeath); i++){    int k=0,kmax=10;
         for(j=1; j<=(nlstate+ndeath);j++){    double l1;
            k=k+1;  
           gp[k]=pmmij[i][j];    fx=func(x);
         }    for (i=1;i<=npar;i++) p2[i]=x[i];
       }    for(l=0 ; l <=lmax; l++){
       l1=pow(10,l);
       for(i=1; i<=npar; i++)      delts=delt;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      for(k=1 ; k <kmax; k=k+1){
            delt = delta*(l1*k);
         p2[theta]=x[theta] +delt;
       pmij(pmmij,cov,ncovmodel,xp,nlstate);        k1=func(p2)-fx;
       k=0;        p2[theta]=x[theta]-delt;
       for(i=1; i<=(nlstate+ndeath); i++){        k2=func(p2)-fx;
         for(j=1; j<=(nlstate+ndeath);j++){        /*res= (k1-2.0*fx+k2)/delt/delt; */
           k=k+1;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
           gm[k]=pmmij[i][j];        
         }  #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);
              fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)  #endif
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];          /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)        }
       for(theta=1; theta <=npar; theta++)        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       trgradg[j][theta]=gradg[theta][j];          k=kmax; l=lmax*10.;
          }
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);          delts=delt;
         }
      pmij(pmmij,cov,ncovmodel,x,nlstate);      }
     }
      k=0;    delti[theta]=delts;
      for(i=1; i<=(nlstate+ndeath); i++){    return res; 
        for(j=1; j<=(nlstate+ndeath);j++){    
          k=k+1;  }
          gm[k]=pmmij[i][j];  
         }  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
      }  {
          int i;
      /*printf("\n%d ",(int)age);    int l=1, l1, lmax=20;
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    double k1,k2,k3,k4,res,fx;
            double p2[NPARMAX+1];
     int k;
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));  
      }*/    fx=func(x);
     for (k=1; k<=2; k++) {
   fprintf(ficresprob,"\n%d ",(int)age);      for (i=1;i<=npar;i++) p2[i]=x[i];
       p2[thetai]=x[thetai]+delti[thetai]/k;
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      k1=func(p2)-fx;
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);    
   }      p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));      k2=func(p2)-fx;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      p2[thetai]=x[thetai]-delti[thetai]/k;
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
 }      k3=func(p2)-fx;
  free_vector(xp,1,npar);    
 fclose(ficresprob);      p2[thetai]=x[thetai]-delti[thetai]/k;
  exit(0);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
 }      k4=func(p2)-fx;
       res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
 /***********************************************/  #ifdef DEBUG
 /**************** Main Program *****************/      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
 /***********************************************/      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   #endif
 /*int main(int argc, char *argv[])*/    }
 int main()    return res;
 {  }
   
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;  /************** Inverse of matrix **************/
   double agedeb, agefin,hf;  void ludcmp(double **a, int n, int *indx, double *d) 
   double agemin=1.e20, agemax=-1.e20;  { 
     int i,imax,j,k; 
   double fret;    double big,dum,sum,temp; 
   double **xi,tmp,delta;    double *vv; 
    
   double dum; /* Dummy variable */    vv=vector(1,n); 
   double ***p3mat;    *d=1.0; 
   int *indx;    for (i=1;i<=n;i++) { 
   char line[MAXLINE], linepar[MAXLINE];      big=0.0; 
   char title[MAXLINE];      for (j=1;j<=n;j++) 
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];        if ((temp=fabs(a[i][j])) > big) big=temp; 
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   char filerest[FILENAMELENGTH];      vv[i]=1.0/big; 
   char fileregp[FILENAMELENGTH];    } 
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    for (j=1;j<=n;j++) { 
   int firstobs=1, lastobs=10;      for (i=1;i<j;i++) { 
   int sdeb, sfin; /* Status at beginning and end */        sum=a[i][j]; 
   int c,  h , cpt,l;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   int ju,jl, mi;        a[i][j]=sum; 
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      } 
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      big=0.0; 
   int mobilav=0, fprev, lprev ,fprevfore=1, lprevfore=1,nforecast;      for (i=j;i<=n;i++) { 
   int hstepm, nhstepm;        sum=a[i][j]; 
         for (k=1;k<j;k++) 
   double bage, fage, age, agelim, agebase;          sum -= a[i][k]*a[k][j]; 
   double ftolpl=FTOL;        a[i][j]=sum; 
   double **prlim;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   double *severity;          big=dum; 
   double ***param; /* Matrix of parameters */          imax=i; 
   double  *p;        } 
   double **matcov; /* Matrix of covariance */      } 
   double ***delti3; /* Scale */      if (j != imax) { 
   double *delti; /* Scale */        for (k=1;k<=n;k++) { 
   double ***eij, ***vareij;          dum=a[imax][k]; 
   double **varpl; /* Variances of prevalence limits by age */          a[imax][k]=a[j][k]; 
   double *epj, vepp;          a[j][k]=dum; 
   double kk1;        } 
         *d = -(*d); 
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";        vv[imax]=vv[j]; 
   char *alph[]={"a","a","b","c","d","e"}, str[4];      } 
       indx[j]=imax; 
       if (a[j][j] == 0.0) a[j][j]=TINY; 
   char z[1]="c", occ;      if (j != n) { 
 #include <sys/time.h>        dum=1.0/(a[j][j]); 
 #include <time.h>        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];      } 
   /* long total_usecs;    } 
   struct timeval start_time, end_time;    free_vector(vv,1,n);  /* Doesn't work */
    ;
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  } 
   
   void lubksb(double **a, int n, int *indx, double b[]) 
   printf("\nIMACH, Version 0.64b");  { 
   printf("\nEnter the parameter file name: ");    int i,ii=0,ip,j; 
     double sum; 
 #ifdef windows   
   scanf("%s",pathtot);    for (i=1;i<=n;i++) { 
   getcwd(pathcd, size);      ip=indx[i]; 
   /*cygwin_split_path(pathtot,path,optionfile);      sum=b[ip]; 
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      b[ip]=b[i]; 
   /* cutv(path,optionfile,pathtot,'\\');*/      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
 split(pathtot, path,optionfile);      else if (sum) ii=i; 
   chdir(path);      b[i]=sum; 
   replace(pathc,path);    } 
 #endif    for (i=n;i>=1;i--) { 
 #ifdef unix      sum=b[i]; 
   scanf("%s",optionfile);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
 #endif      b[i]=sum/a[i][i]; 
     } 
 /*-------- arguments in the command line --------*/  } 
   
   strcpy(fileres,"r");  /************ Frequencies ********************/
   strcat(fileres, optionfile);  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, char strstart[])
   {  /* Some frequencies */
   /*---------arguments file --------*/    
     int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    int first;
     printf("Problem with optionfile %s\n",optionfile);    double ***freq; /* Frequencies */
     goto end;    double *pp, **prop;
   }    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     FILE *ficresp;
   strcpy(filereso,"o");    char fileresp[FILENAMELENGTH];
   strcat(filereso,fileres);    
   if((ficparo=fopen(filereso,"w"))==NULL) {    pp=vector(1,nlstate);
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    prop=matrix(1,nlstate,iagemin,iagemax+3);
   }    strcpy(fileresp,"p");
     strcat(fileresp,fileres);
   /* Reads comments: lines beginning with '#' */    if((ficresp=fopen(fileresp,"w"))==NULL) {
   while((c=getc(ficpar))=='#' && c!= EOF){      printf("Problem with prevalence resultfile: %s\n", fileresp);
     ungetc(c,ficpar);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     fgets(line, MAXLINE, ficpar);      exit(0);
     puts(line);    }
     fputs(line,ficparo);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
   }    j1=0;
   ungetc(c,ficpar);    
     j=cptcoveff;
   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);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);  
   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);    first=1;
 while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    for(k1=1; k1<=j;k1++){
     fgets(line, MAXLINE, ficpar);      for(i1=1; i1<=ncodemax[k1];i1++){
     puts(line);        j1++;
     fputs(line,ficparo);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   }          scanf("%d", i);*/
   ungetc(c,ficpar);        for (i=-5; i<=nlstate+ndeath; i++)  
            for (jk=-5; jk<=nlstate+ndeath; jk++)  
   fscanf(ficpar,"fprevalence=%d lprevalence=%d pop_based=%d\n",&fprev,&lprev,&popbased);            for(m=iagemin; m <= iagemax+3; m++)
  while((c=getc(ficpar))=='#' && c!= EOF){              freq[i][jk][m]=0;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);      for (i=1; i<=nlstate; i++)  
     puts(line);        for(m=iagemin; m <= iagemax+3; m++)
     fputs(line,ficparo);          prop[i][m]=0;
   }        
   ungetc(c,ficpar);        dateintsum=0;
          k2cpt=0;
   fscanf(ficpar,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",&fprevfore,&lprevfore,&nforecast,&mobilav);        for (i=1; i<=imx; i++) {
            bool=1;
   covar=matrix(0,NCOVMAX,1,n);          if  (cptcovn>0) {
   cptcovn=0;            for (z1=1; z1<=cptcoveff; z1++) 
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
   ncovmodel=2+cptcovn;          }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */          if (bool==1){
              for(m=firstpass; m<=lastpass; m++){
   /* Read guess parameters */              k2=anint[m][i]+(mint[m][i]/12.);
   /* Reads comments: lines beginning with '#' */              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   while((c=getc(ficpar))=='#' && c!= EOF){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     ungetc(c,ficpar);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     fgets(line, MAXLINE, ficpar);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     puts(line);                if (m<lastpass) {
     fputs(line,ficparo);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   }                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
   ungetc(c,ficpar);                }
                  
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     for(i=1; i <=nlstate; i++)                  dateintsum=dateintsum+k2;
     for(j=1; j <=nlstate+ndeath-1; j++){                  k2cpt++;
       fscanf(ficpar,"%1d%1d",&i1,&j1);                }
       fprintf(ficparo,"%1d%1d",i1,j1);                /*}*/
       printf("%1d%1d",i,j);            }
       for(k=1; k<=ncovmodel;k++){          }
         fscanf(ficpar," %lf",&param[i][j][k]);        }
         printf(" %lf",param[i][j][k]);         
         fprintf(ficparo," %lf",param[i][j][k]);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       }  fprintf(ficresp, "#Local time at start: %s", strstart);
       fscanf(ficpar,"\n");        if  (cptcovn>0) {
       printf("\n");          fprintf(ficresp, "\n#********** Variable "); 
       fprintf(ficparo,"\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     }          fprintf(ficresp, "**********\n#");
          }
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   p=param[1][1];        fprintf(ficresp, "\n");
          
   /* Reads comments: lines beginning with '#' */        for(i=iagemin; i <= iagemax+3; i++){
   while((c=getc(ficpar))=='#' && c!= EOF){          if(i==iagemax+3){
     ungetc(c,ficpar);            fprintf(ficlog,"Total");
     fgets(line, MAXLINE, ficpar);          }else{
     puts(line);            if(first==1){
     fputs(line,ficparo);              first=0;
   }              printf("See log file for details...\n");
   ungetc(c,ficpar);            }
             fprintf(ficlog,"Age %d", i);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          }
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */          for(jk=1; jk <=nlstate ; jk++){
   for(i=1; i <=nlstate; i++){            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     for(j=1; j <=nlstate+ndeath-1; j++){              pp[jk] += freq[jk][m][i]; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);          }
       printf("%1d%1d",i,j);          for(jk=1; jk <=nlstate ; jk++){
       fprintf(ficparo,"%1d%1d",i1,j1);            for(m=-1, pos=0; m <=0 ; m++)
       for(k=1; k<=ncovmodel;k++){              pos += freq[jk][m][i];
         fscanf(ficpar,"%le",&delti3[i][j][k]);            if(pp[jk]>=1.e-10){
         printf(" %le",delti3[i][j][k]);              if(first==1){
         fprintf(ficparo," %le",delti3[i][j][k]);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       }              }
       fscanf(ficpar,"\n");              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       printf("\n");            }else{
       fprintf(ficparo,"\n");              if(first==1)
     }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   delti=delti3[1][1];            }
            }
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){          for(jk=1; jk <=nlstate ; jk++){
     ungetc(c,ficpar);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     fgets(line, MAXLINE, ficpar);              pp[jk] += freq[jk][m][i];
     puts(line);          }       
     fputs(line,ficparo);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
   }            pos += pp[jk];
   ungetc(c,ficpar);            posprop += prop[jk][i];
            }
   matcov=matrix(1,npar,1,npar);          for(jk=1; jk <=nlstate ; jk++){
   for(i=1; i <=npar; i++){            if(pos>=1.e-5){
     fscanf(ficpar,"%s",&str);              if(first==1)
     printf("%s",str);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     fprintf(ficparo,"%s",str);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     for(j=1; j <=i; j++){            }else{
       fscanf(ficpar," %le",&matcov[i][j]);              if(first==1)
       printf(" %.5le",matcov[i][j]);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficparo," %.5le",matcov[i][j]);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     }            }
     fscanf(ficpar,"\n");            if( i <= iagemax){
     printf("\n");              if(pos>=1.e-5){
     fprintf(ficparo,"\n");                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   }                /*probs[i][jk][j1]= pp[jk]/pos;*/
   for(i=1; i <=npar; i++)                /*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(j=i+1;j<=npar;j++)              }
       matcov[i][j]=matcov[j][i];              else
                    fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   printf("\n");            }
           }
           
     /*-------- data file ----------*/          for(jk=-1; jk <=nlstate+ndeath; jk++)
     if((ficres =fopen(fileres,"w"))==NULL) {            for(m=-1; m <=nlstate+ndeath; m++)
       printf("Problem with resultfile: %s\n", fileres);goto end;              if(freq[jk][m][i] !=0 ) {
     }              if(first==1)
     fprintf(ficres,"#%s\n",version);                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                    fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     if((fic=fopen(datafile,"r"))==NULL)    {              }
       printf("Problem with datafile: %s\n", datafile);goto end;          if(i <= iagemax)
     }            fprintf(ficresp,"\n");
           if(first==1)
     n= lastobs;            printf("Others in log...\n");
     severity = vector(1,maxwav);          fprintf(ficlog,"\n");
     outcome=imatrix(1,maxwav+1,1,n);        }
     num=ivector(1,n);      }
     moisnais=vector(1,n);    }
     annais=vector(1,n);    dateintmean=dateintsum/k2cpt; 
     moisdc=vector(1,n);   
     andc=vector(1,n);    fclose(ficresp);
     agedc=vector(1,n);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     cod=ivector(1,n);    free_vector(pp,1,nlstate);
     weight=vector(1,n);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    /* End of Freq */
     mint=matrix(1,maxwav,1,n);  }
     anint=matrix(1,maxwav,1,n);  
     s=imatrix(1,maxwav+1,1,n);  /************ Prevalence ********************/
     adl=imatrix(1,maxwav+1,1,n);      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)
     tab=ivector(1,NCOVMAX);  {  
     ncodemax=ivector(1,8);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
        in each health status at the date of interview (if between dateprev1 and dateprev2).
     i=1;       We still use firstpass and lastpass as another selection.
     while (fgets(line, MAXLINE, fic) != NULL)    {    */
       if ((i >= firstobs) && (i <=lastobs)) {   
            int i, m, jk, k1, i1, j1, bool, z1,z2,j;
         for (j=maxwav;j>=1;j--){    double ***freq; /* Frequencies */
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    double *pp, **prop;
           strcpy(line,stra);    double pos,posprop; 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    double  y2; /* in fractional years */
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int iagemin, iagemax;
         }  
            iagemin= (int) agemin;
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    iagemax= (int) agemax;
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    /*pp=vector(1,nlstate);*/
     prop=matrix(1,nlstate,iagemin,iagemax+3); 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    j1=0;
     
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    j=cptcoveff;
         for (j=ncov;j>=1;j--){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    
         }    for(k1=1; k1<=j;k1++){
         num[i]=atol(stra);      for(i1=1; i1<=ncodemax[k1];i1++){
                j1++;
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){        
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
         i=i+1;            prop[i][m]=0.0;
       }       
     }        for (i=1; i<=imx; i++) { /* Each individual */
     /* printf("ii=%d", ij);          bool=1;
        scanf("%d",i);*/          if  (cptcovn>0) {
   imx=i-1; /* Number of individuals */            for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   /* for (i=1; i<=imx; i++){                bool=0;
     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 (bool==1) { 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     }              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     for (i=1; i<=imx; i++) printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
   /* Calculation of the number of parameter from char model*/                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   Tvar=ivector(1,15);                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); 
   Tprod=ivector(1,15);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
   Tvaraff=ivector(1,15);                  /*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]]);*/
   Tvard=imatrix(1,15,1,2);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   Tage=ivector(1,15);                        prop[s[m][i]][iagemax+3] += weight[i]; 
                    } 
   if (strlen(model) >1){              }
     j=0, j1=0, k1=1, k2=1;            } /* end selection of waves */
     j=nbocc(model,'+');          }
     j1=nbocc(model,'*');        }
     cptcovn=j+1;        for(i=iagemin; i <= iagemax+3; i++){  
     cptcovprod=j1;          
              for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
                posprop += prop[jk][i]; 
     strcpy(modelsav,model);          } 
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);          for(jk=1; jk <=nlstate ; jk++){     
       goto end;            if( i <=  iagemax){ 
     }              if(posprop>=1.e-5){ 
                    probs[i][jk][j1]= prop[jk][i]/posprop;
     for(i=(j+1); i>=1;i--){              } 
       cutv(stra,strb,modelsav,'+');            } 
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          }/* end jk */ 
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        }/* end i */ 
       /*scanf("%d",i);*/      } /* end i1 */
       if (strchr(strb,'*')) {    } /* end k1 */
         cutv(strd,strc,strb,'*');    
         if (strcmp(strc,"age")==0) {    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
           cptcovprod--;    /*free_vector(pp,1,nlstate);*/
           cutv(strb,stre,strd,'V');    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
           Tvar[i]=atoi(stre);  }  /* End of prevalence */
           cptcovage++;  
             Tage[cptcovage]=i;  /************* Waves Concatenation ***************/
             /*printf("stre=%s ", stre);*/  
         }  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
         else if (strcmp(strd,"age")==0) {  {
           cptcovprod--;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           cutv(strb,stre,strc,'V');       Death is a valid wave (if date is known).
           Tvar[i]=atoi(stre);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
           cptcovage++;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
           Tage[cptcovage]=i;       and mw[mi+1][i]. dh depends on stepm.
         }       */
         else {  
           cutv(strb,stre,strc,'V');    int i, mi, m;
           Tvar[i]=ncov+k1;    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
           cutv(strb,strc,strd,'V');       double sum=0., jmean=0.;*/
           Tprod[k1]=i;    int first;
           Tvard[k1][1]=atoi(strc);    int j, k=0,jk, ju, jl;
           Tvard[k1][2]=atoi(stre);    double sum=0.;
           Tvar[cptcovn+k2]=Tvard[k1][1];    first=0;
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    jmin=1e+5;
           for (k=1; k<=lastobs;k++)    jmax=-1;
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    jmean=0.;
           k1++;    for(i=1; i<=imx; i++){
           k2=k2+2;      mi=0;
         }      m=firstpass;
       }      while(s[m][i] <= nlstate){
       else {        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          mw[++mi][i]=m;
        /*  scanf("%d",i);*/        if(m >=lastpass)
       cutv(strd,strc,strb,'V');          break;
       Tvar[i]=atoi(strc);        else
       }          m++;
       strcpy(modelsav,stra);        }/* end while */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);      if (s[m][i] > nlstate){
         scanf("%d",i);*/        mi++;     /* Death is another wave */
     }        /* if(mi==0)  never been interviewed correctly before death */
 }           /* Only death is a correct wave */
          mw[mi][i]=m;
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);      }
   printf("cptcovprod=%d ", cptcovprod);  
   scanf("%d ",i);*/      wav[i]=mi;
     fclose(fic);      if(mi==0){
         nbwarn++;
     /*  if(mle==1){*/        if(first==0){
     if (weightopt != 1) { /* Maximisation without weights*/          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
       for(i=1;i<=n;i++) weight[i]=1.0;          first=1;
     }        }
     /*-calculation of age at interview from date of interview and age at death -*/        if(first==1){
     agev=matrix(1,maxwav,1,imx);          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
         }
    for (i=1; i<=imx; i++)      } /* end mi==0 */
      for(m=2; (m<= maxwav); m++)    } /* End individuals */
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){  
          anint[m][i]=9999;    for(i=1; i<=imx; i++){
          s[m][i]=-1;      for(mi=1; mi<wav[i];mi++){
        }        if (stepm <=0)
              dh[mi][i]=1;
     for (i=1; i<=imx; i++)  {        else{
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       for(m=1; (m<= maxwav); m++){            if (agedc[i] < 2*AGESUP) {
         if(s[m][i] >0){              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
           if (s[m][i] == nlstate+1) {              if(j==0) j=1;  /* Survives at least one month after exam */
             if(agedc[i]>0)              else if(j<0){
               if(moisdc[i]!=99 && andc[i]!=9999)                nberr++;
               agev[m][i]=agedc[i];                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
             else {                j=1; /* Temporary Dangerous patch */
               if (andc[i]!=9999){                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. You MUST fix the contradiction between dates.\n",stepm);
               printf("Warning negative age at death: %d line:%d\n",num[i],i);                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]);
               agev[m][i]=-1;                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. You MUST fix the contradiction between dates.\n",stepm);
               }              }
             }              k=k+1;
           }              if (j >= jmax){
           else if(s[m][i] !=9){ /* Should no more exist */                jmax=j;
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);                ijmax=i;
             if(mint[m][i]==99 || anint[m][i]==9999)              }
               agev[m][i]=1;              if (j <= jmin){
             else if(agev[m][i] <agemin){                jmin=j;
               agemin=agev[m][i];                ijmin=i;
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/              }
             }              sum=sum+j;
             else if(agev[m][i] >agemax){              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
               agemax=agev[m][i];              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,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];*/          else{
             /*   agev[m][i] = age[i]+2*m;*/            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
           }  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
           else { /* =9 */  
             agev[m][i]=1;            k=k+1;
             s[m][i]=-1;            if (j >= jmax) {
           }              jmax=j;
         }              ijmax=i;
         else /*= 0 Unknown */            }
           agev[m][i]=1;            else if (j <= jmin){
       }              jmin=j;
                  ijmin=i;
     }            }
     for (i=1; i<=imx; i++)  {            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       for(m=1; (m<= maxwav); m++){            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
         if (s[m][i] > (nlstate+ndeath)) {            if(j<0){
           printf("Error: Wrong value in nlstate or ndeath\n");                nberr++;
           goto end;              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]);
       }            }
     }            sum=sum+j;
           }
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);          jk= j/stepm;
           jl= j -jk*stepm;
     free_vector(severity,1,maxwav);          ju= j -(jk+1)*stepm;
     free_imatrix(outcome,1,maxwav+1,1,n);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
     free_vector(moisnais,1,n);            if(jl==0){
     free_vector(annais,1,n);              dh[mi][i]=jk;
     free_matrix(mint,1,maxwav,1,n);              bh[mi][i]=0;
     free_matrix(anint,1,maxwav,1,n);            }else{ /* We want a negative bias in order to only have interpolation ie
     free_vector(moisdc,1,n);                    * at the price of an extra matrix product in likelihood */
     free_vector(andc,1,n);              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
                }
     wav=ivector(1,imx);          }else{
     dh=imatrix(1,lastpass-firstpass+1,1,imx);            if(jl <= -ju){
     mw=imatrix(1,lastpass-firstpass+1,1,imx);              dh[mi][i]=jk;
                  bh[mi][i]=jl;       /* bias is positive if real duration
     /* Concatenates waves */                                   * is higher than the multiple of stepm and negative otherwise.
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);                                   */
             }
             else{
       Tcode=ivector(1,100);              dh[mi][i]=jk+1;
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);              bh[mi][i]=ju;
       ncodemax[1]=1;            }
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);            if(dh[mi][i]==0){
                    dh[mi][i]=1; /* At least one step */
    codtab=imatrix(1,100,1,10);              bh[mi][i]=ju; /* At least one step */
    h=0;              /*  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);*/
    m=pow(2,cptcoveff);            }
            } /* end if mle */
    for(k=1;k<=cptcoveff; k++){        }
      for(i=1; i <=(m/pow(2,k));i++){      } /* end wave */
        for(j=1; j <= ncodemax[k]; j++){    }
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    jmean=sum/k;
            h++;    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
            if (h>m) h=1;codtab[h][k]=j;    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
          }   }
        }  
      }  /*********** Tricode ****************************/
    }  void tricode(int *Tvar, int **nbcode, int imx)
   {
     
    /*for(i=1; i <=m ;i++){    int Ndum[20],ij=1, k, j, i, maxncov=19;
      for(k=1; k <=cptcovn; k++){    int cptcode=0;
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);    cptcoveff=0; 
      }   
      printf("\n");    for (k=0; k<maxncov; k++) Ndum[k]=0;
    }    for (k=1; k<=7; k++) ncodemax[k]=0;
    scanf("%d",i);*/  
        for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
    /* Calculates basic frequencies. Computes observed prevalence at single age      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
        and prints on file fileres'p'. */                                 modality*/ 
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprev, lprev);        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
         Ndum[ij]++; /*store the modality */
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                                         Tvar[j]. If V=sex and male is 0 and 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                                         female is 1, then  cptcode=1.*/
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      }
        
     /* For Powell, parameters are in a vector p[] starting at p[1]      for (i=0; i<=cptcode; i++) {
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */        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 */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */      }
   
     if(mle==1){      ij=1; 
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      for (i=1; i<=ncodemax[j]; i++) {
     }        for (k=0; k<= maxncov; k++) {
              if (Ndum[k] != 0) {
     /*--------- results files --------------*/            nbcode[Tvar[j]][ij]=k; 
     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);            /* 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; */
                
    jk=1;            ij++;
    fprintf(ficres,"# Parameters\n");          }
    printf("# Parameters\n");          if (ij > ncodemax[j]) break; 
    for(i=1,jk=1; i <=nlstate; i++){        }  
      for(k=1; k <=(nlstate+ndeath); k++){      } 
        if (k != i)    }  
          {  
            printf("%d%d ",i,k);   for (k=0; k< maxncov; k++) Ndum[k]=0;
            fprintf(ficres,"%1d%1d ",i,k);  
            for(j=1; j <=ncovmodel; j++){   for (i=1; i<=ncovmodel-2; i++) { 
              printf("%f ",p[jk]);     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
              fprintf(ficres,"%f ",p[jk]);     ij=Tvar[i];
              jk++;     Ndum[ij]++;
            }   }
            printf("\n");  
            fprintf(ficres,"\n");   ij=1;
          }   for (i=1; i<= maxncov; i++) {
      }     if((Ndum[i]!=0) && (i<=ncovcol)){
    }       Tvaraff[ij]=i; /*For printing */
  if(mle==1){       ij++;
     /* Computing hessian and covariance matrix */     }
     ftolhess=ftol; /* Usually correct */   }
     hesscov(matcov, p, npar, delti, ftolhess, func);   
  }   cptcoveff=ij-1; /*Number of simple covariates*/
     fprintf(ficres,"# Scales\n");  }
     printf("# Scales\n");  
      for(i=1,jk=1; i <=nlstate; i++){  /*********** Health Expectancies ****************/
       for(j=1; j <=nlstate+ndeath; j++){  
         if (j!=i) {  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov,char strstart[] )
           fprintf(ficres,"%1d%1d",i,j);  
           printf("%1d%1d",i,j);  {
           for(k=1; k<=ncovmodel;k++){    /* Health expectancies */
             printf(" %.5e",delti[jk]);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
             fprintf(ficres," %.5e",delti[jk]);    double age, agelim, hf;
             jk++;    double ***p3mat,***varhe;
           }    double **dnewm,**doldm;
           printf("\n");    double *xp;
           fprintf(ficres,"\n");    double **gp, **gm;
         }    double ***gradg, ***trgradg;
       }    int theta;
       }  
        varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     k=1;    xp=vector(1,npar);
     fprintf(ficres,"# Covariance\n");    dnewm=matrix(1,nlstate*nlstate,1,npar);
     printf("# Covariance\n");    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     for(i=1;i<=npar;i++){    
       /*  if (k>nlstate) k=1;    fprintf(ficreseij,"# Local time at start: %s", strstart);
       i1=(i-1)/(ncovmodel*nlstate)+1;    fprintf(ficreseij,"# Health expectancies\n");
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    fprintf(ficreseij,"# Age");
       printf("%s%d%d",alph[k],i1,tab[i]);*/    for(i=1; i<=nlstate;i++)
       fprintf(ficres,"%3d",i);      for(j=1; j<=nlstate;j++)
       printf("%3d",i);        fprintf(ficreseij," %1d-%1d (SE)",i,j);
       for(j=1; j<=i;j++){    fprintf(ficreseij,"\n");
         fprintf(ficres," %.5e",matcov[i][j]);  
         printf(" %.5e",matcov[i][j]);    if(estepm < stepm){
       }      printf ("Problem %d lower than %d\n",estepm, stepm);
       fprintf(ficres,"\n");    }
       printf("\n");    else  hstepm=estepm;   
       k++;    /* We compute the life expectancy from trapezoids spaced every estepm months
     }     * This is mainly to measure the difference between two models: for example
         * if stepm=24 months pijx are given only every 2 years and by summing them
     while((c=getc(ficpar))=='#' && c!= EOF){     * we are calculating an estimate of the Life Expectancy assuming a linear 
       ungetc(c,ficpar);     * progression in between and thus overestimating or underestimating according
       fgets(line, MAXLINE, ficpar);     * to the curvature of the survival function. If, for the same date, we 
       puts(line);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       fputs(line,ficparo);     * to compare the new estimate of Life expectancy with the same linear 
     }     * hypothesis. A more precise result, taking into account a more precise
     ungetc(c,ficpar);     * curvature will be obtained if estepm is as small as stepm. */
    
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    /* For example we decided to compute the life expectancy with the smallest unit */
        /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     if (fage <= 2) {       nhstepm is the number of hstepm from age to agelim 
       bage = agemin;       nstepm is the number of stepm from age to agelin. 
       fage = agemax;       Look at hpijx to understand the reason of that which relies in memory size
     }       and note for a fixed period like estepm months */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");       survival function given by stepm (the optimization length). Unfortunately it
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);       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 
           results. So we changed our mind and took the option of the best precision.
 /*------------ gnuplot -------------*/    */
 chdir(pathcd);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   if((ficgp=fopen("graph.plt","w"))==NULL) {  
     printf("Problem with file graph.gp");goto end;    agelim=AGESUP;
   }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
 #ifdef windows      /* nhstepm age range expressed in number of stepm */
   fprintf(ficgp,"cd \"%s\" \n",pathc);      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
 #endif      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
 m=pow(2,cptcoveff);      /* if (stepm >= YEARM) hstepm=1;*/
        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
  /* 1eme*/      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   for (cpt=1; cpt<= nlstate ; cpt ++) {      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
    for (k1=1; k1<= m ; k1 ++) {      gp=matrix(0,nhstepm,1,nlstate*nlstate);
       gm=matrix(0,nhstepm,1,nlstate*nlstate);
 #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);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
 #endif         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
 #ifdef unix      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);   
 #endif  
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      /* Computing  Variances of health expectancies */
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }       for(theta=1; theta <=npar; theta++){
     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<=npar; i++){ 
     for (i=1; i<= nlstate ; i ++) {          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        }
   else fprintf(ficgp," \%%*lf (\%%*lf)");        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 }    
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        cptj=0;
      for (i=1; i<= nlstate ; i ++) {        for(j=1; j<= nlstate; j++){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          for(i=1; i<=nlstate; i++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");            cptj=cptj+1;
 }              for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
 #ifdef unix            }
 fprintf(ficgp,"\nset ter gif small size 400,300");          }
 #endif        }
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);       
    }       
   }        for(i=1; i<=npar; i++) 
   /*2 eme*/          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   for (k1=1; k1<= m ; k1 ++) {        
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);        cptj=0;
            for(j=1; j<= nlstate; j++){
     for (i=1; i<= nlstate+1 ; i ++) {          for(i=1;i<=nlstate;i++){
       k=2*i;            cptj=cptj+1;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
       for (j=1; j<= nlstate+1 ; j ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
   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);        for(j=1; j<= nlstate*nlstate; j++)
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);          for(h=0; h<=nhstepm-1; h++){
       for (j=1; j<= nlstate+1 ; j ++) {            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          }
         else fprintf(ficgp," \%%*lf (\%%*lf)");       } 
 }       
       fprintf(ficgp,"\" t\"\" w l 0,");  /* End theta */
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");       for(h=0; h<=nhstepm-1; h++)
 }          for(j=1; j<=nlstate*nlstate;j++)
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");          for(theta=1; theta <=npar; theta++)
       else fprintf(ficgp,"\" t\"\" w l 0,");            trgradg[h][j][theta]=gradg[h][theta][j];
     }       
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);  
   }       for(i=1;i<=nlstate*nlstate;i++)
          for(j=1;j<=nlstate*nlstate;j++)
   /*3eme*/          varhe[i][j][(int)age] =0.;
   
   for (k1=1; k1<= m ; k1 ++) {       printf("%d|",(int)age);fflush(stdout);
     for (cpt=1; cpt<= nlstate ; cpt ++) {       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       k=2+nlstate*(cpt-1);       for(h=0;h<=nhstepm-1;h++){
       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(k=0;k<=nhstepm-1;k++){
       for (i=1; i< nlstate ; i ++) {          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
         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);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       }          for(i=1;i<=nlstate*nlstate;i++)
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            for(j=1;j<=nlstate*nlstate;j++)
     }              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
   }        }
        }
   /* CV preval stat */      /* Computing expectancies */
   for (k1=1; k1<= m ; k1 ++) {      for(i=1; i<=nlstate;i++)
     for (cpt=1; cpt<nlstate ; cpt ++) {        for(j=1; j<=nlstate;j++)
       k=3;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
       for (i=1; i< nlstate ; i ++)            
         fprintf(ficgp,"+$%d",k+i+1);  /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
       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/($%d",fileres,k1,l+cpt+1,l+1);      fprintf(ficreseij,"%3.0f",age );
       for (i=1; i< nlstate ; i ++) {      cptj=0;
         l=3+(nlstate+ndeath)*cpt;      for(i=1; i<=nlstate;i++)
         fprintf(ficgp,"+$%d",l+i+1);        for(j=1; j<=nlstate;j++){
       }          cptj++;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);            fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        }
     }      fprintf(ficreseij,"\n");
   }       
       free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   /* proba elementaires */      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
    for(i=1,jk=1; i <=nlstate; i++){      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     for(k=1; k <=(nlstate+ndeath); k++){      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       if (k != i) {      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for(j=1; j <=ncovmodel; j++){    }
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    printf("\n");
           /*fprintf(ficgp,"%s",alph[1]);*/    fprintf(ficlog,"\n");
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);  
           jk++;    free_vector(xp,1,npar);
           fprintf(ficgp,"\n");    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
         }    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       }    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     }  }
     }  
   /************ Variance ******************/
   for(jk=1; jk <=m; jk++) {  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, char strstart[])
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);  {
    i=1;    /* Variance of health expectancies */
    for(k2=1; k2<=nlstate; k2++) {    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
      k3=i;    /* double **newm;*/
      for(k=1; k<=(nlstate+ndeath); k++) {    double **dnewm,**doldm;
        if (k != k2){    double **dnewmp,**doldmp;
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    int i, j, nhstepm, hstepm, h, nstepm ;
 ij=1;    int k, cptcode;
         for(j=3; j <=ncovmodel; j++) {    double *xp;
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    double **gp, **gm;  /* for var eij */
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    double ***gradg, ***trgradg; /*for var eij */
             ij++;    double **gradgp, **trgradgp; /* for var p point j */
           }    double *gpp, *gmp; /* for var p point j */
           else    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    double ***p3mat;
         }    double age,agelim, hf;
           fprintf(ficgp,")/(1");    double ***mobaverage;
            int theta;
         for(k1=1; k1 <=nlstate; k1++){      char digit[4];
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    char digitp[25];
 ij=1;  
           for(j=3; j <=ncovmodel; j++){    char fileresprobmorprev[FILENAMELENGTH];
           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]]]);    if(popbased==1){
             ij++;      if(mobilav!=0)
           }        strcpy(digitp,"-populbased-mobilav-");
           else      else strcpy(digitp,"-populbased-nomobil-");
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    }
           }    else 
           fprintf(ficgp,")");      strcpy(digitp,"-stablbased-");
         }  
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    if (mobilav!=0) {
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         i=i+ncovmodel;      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);
    }      }
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    }
   }  
        strcpy(fileresprobmorprev,"prmorprev"); 
   fclose(ficgp);    sprintf(digit,"%-d",ij);
        /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
 chdir(path);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
        strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     free_ivector(wav,1,imx);    strcat(fileresprobmorprev,fileres);
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);        printf("Problem with resultfile: %s\n", fileresprobmorprev);
     free_ivector(num,1,n);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     free_vector(agedc,1,n);    }
     /*free_matrix(covar,1,NCOVMAX,1,n);*/    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     fclose(ficparo);   
     fclose(ficres);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     /*  }*/    fprintf(ficresprobmorprev, "#Local time at start: %s", strstart);
        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);
    /*________fin mle=1_________*/    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
        for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
        for(i=1; i<=nlstate;i++)
     /* No more information from the sample is required now */        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   /* Reads comments: lines beginning with '#' */    }  
   while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficresprobmorprev,"\n");
     ungetc(c,ficpar);    fprintf(ficgp,"\n# Routine varevsij");
     fgets(line, MAXLINE, ficpar);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     puts(line);    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");
     fputs(line,ficparo);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   }  /*   } */
   ungetc(c,ficpar);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     fprintf(ficresvij, "#Local time at start: %s", strstart);
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    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");
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    fprintf(ficresvij,"# Age");
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    for(i=1; i<=nlstate;i++)
 /*--------- index.htm --------*/      for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
   strcpy(optionfilehtm,optionfile);    fprintf(ficresvij,"\n");
   strcat(optionfilehtm,".htm");  
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    xp=vector(1,npar);
     printf("Problem with %s \n",optionfilehtm);goto end;    dnewm=matrix(1,nlstate,1,npar);
   }    doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.64b </font> <hr size=\"2\" color=\"#EC5E5E\">    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>  
 Total number of observations=%d <br>    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>    gpp=vector(nlstate+1,nlstate+ndeath);
 <hr  size=\"2\" color=\"#EC5E5E\">    gmp=vector(nlstate+1,nlstate+ndeath);
 <li>Outputs files<br><br>\n    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
         - 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>    if(estepm < stepm){
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      printf ("Problem %d lower than %d\n",estepm, stepm);
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    }
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    else  hstepm=estepm;   
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    /* For example we decided to compute the life expectancy with the smallest unit */
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>       nhstepm is the number of hstepm from age to agelim 
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>       nstepm is the number of stepm from age to agelin. 
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>       Look at hpijx to understand the reason of that which relies in memory size
 <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,fileres,fileres);       and note for a fixed period like k years */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
  fprintf(fichtm," <li>Graphs</li><p>");       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
  m=cptcoveff;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}       results. So we changed our mind and took the option of the best precision.
     */
  j1=0;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
  for(k1=1; k1<=m;k1++){    agelim = AGESUP;
    for(i1=1; i1<=ncodemax[k1];i1++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
        j1++;      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
        if (cptcovn > 0) {      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
          for (cpt=1; cpt<=cptcoveff;cpt++)      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);      gp=matrix(0,nhstepm,1,nlstate);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      gm=matrix(0,nhstepm,1,nlstate);
        }  
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>  
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          for(theta=1; theta <=npar; theta++){
        for(cpt=1; cpt<nlstate;cpt++){        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        }
        }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     for(cpt=1; cpt<=nlstate;cpt++) {        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  
 interval) in state (%d): v%s%d%d.gif <br>        if (popbased==1) {
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            if(mobilav ==0){
      }            for(i=1; i<=nlstate;i++)
      for(cpt=1; cpt<=nlstate;cpt++) {              prlim[i][i]=probs[(int)age][i][ij];
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>          }else{ /* mobilav */ 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            for(i=1; i<=nlstate;i++)
      }              prlim[i][i]=mobaverage[(int)age][i][ij];
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          }
 health expectancies in states (1) and (2): e%s%d.gif<br>        }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);    
 fprintf(fichtm,"\n</body>");        for(j=1; j<= nlstate; j++){
    }          for(h=0; h<=nhstepm; h++){
  }            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
 fclose(fichtm);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
   /*--------------- Prevalence limit --------------*/        }
          /* This for computing probability of death (h=1 means
   strcpy(filerespl,"pl");           computed over hstepm matrices product = hstepm*stepm months) 
   strcat(filerespl,fileres);           as a weighted average of prlim.
   if((ficrespl=fopen(filerespl,"w"))==NULL) {        */
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   fprintf(ficrespl,"#Prevalence limit\n");        }    
   fprintf(ficrespl,"#Age ");        /* end probability of death */
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
            xp[i] = x[i] - (i==theta ?delti[theta]:0);
   prlim=matrix(1,nlstate,1,nlstate);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        if (popbased==1) {
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          if(mobilav ==0){
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            for(i=1; i<=nlstate;i++)
   k=0;              prlim[i][i]=probs[(int)age][i][ij];
   agebase=agemin;          }else{ /* mobilav */ 
   agelim=agemax;            for(i=1; i<=nlstate;i++)
   ftolpl=1.e-10;              prlim[i][i]=mobaverage[(int)age][i][ij];
   i1=cptcoveff;          }
   if (cptcovn < 1){i1=1;}        }
   
   for(cptcov=1;cptcov<=i1;cptcov++){        for(j=1; j<= nlstate; j++){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for(h=0; h<=nhstepm; h++){
         k=k+1;            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
         fprintf(ficrespl,"\n#******");          }
         for(j=1;j<=cptcoveff;j++)        }
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        /* This for computing probability of death (h=1 means
         fprintf(ficrespl,"******\n");           computed over hstepm matrices product = hstepm*stepm months) 
                   as a weighted average of prlim.
         for (age=agebase; age<=agelim; age++){        */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           fprintf(ficrespl,"%.0f",age );          for(i=1,gmp[j]=0.; i<= nlstate; i++)
           for(i=1; i<=nlstate;i++)           gmp[j] += prlim[i][i]*p3mat[i][j][1];
           fprintf(ficrespl," %.5f", prlim[i][i]);        }    
           fprintf(ficrespl,"\n");        /* end probability of death */
         }  
       }        for(j=1; j<= nlstate; j++) /* vareij */
     }          for(h=0; h<=nhstepm; h++){
   fclose(ficrespl);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   /*------------- h Pij x at various ages ------------*/  
          for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        }
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  
   }      } /* End theta */
   printf("Computing pij: result on file '%s' \n", filerespij);  
        trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   /*if (stepm<=24) stepsize=2;*/      for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
   agelim=AGESUP;          for(theta=1; theta <=npar; theta++)
   hstepm=stepsize*YEARM; /* Every year of age */            trgradg[h][j][theta]=gradg[h][theta][j];
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
        for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   k=0;        for(theta=1; theta <=npar; theta++)
   for(cptcov=1;cptcov<=i1;cptcov++){          trgradgp[j][theta]=gradgp[theta][j];
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    
       k=k+1;  
         fprintf(ficrespij,"\n#****** ");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         for(j=1;j<=cptcoveff;j++)      for(i=1;i<=nlstate;i++)
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(j=1;j<=nlstate;j++)
         fprintf(ficrespij,"******\n");          vareij[i][j][(int)age] =0.;
          
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      for(h=0;h<=nhstepm;h++){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        for(k=0;k<=nhstepm;k++){
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           oldm=oldms;savm=savms;          for(i=1;i<=nlstate;i++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              for(j=1;j<=nlstate;j++)
           fprintf(ficrespij,"# Age");              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
           for(i=1; i<=nlstate;i++)        }
             for(j=1; j<=nlstate+ndeath;j++)      }
               fprintf(ficrespij," %1d-%1d",i,j);    
           fprintf(ficrespij,"\n");      /* pptj */
           for (h=0; h<=nhstepm; h++){      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
             for(i=1; i<=nlstate;i++)      for(j=nlstate+1;j<=nlstate+ndeath;j++)
               for(j=1; j<=nlstate+ndeath;j++)        for(i=nlstate+1;i<=nlstate+ndeath;i++)
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          varppt[j][i]=doldmp[j][i];
             fprintf(ficrespij,"\n");      /* end ppptj */
           }      /*  x centered again */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
           fprintf(ficrespij,"\n");      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
         }   
     }      if (popbased==1) {
   }        if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/            prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
   fclose(ficrespij);          for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
   /*---------- Forecasting ------------------*/        }
       }
   strcpy(fileresf,"f");               
   strcat(fileresf,fileres);      /* This for computing probability of death (h=1 means
   if((ficresf=fopen(fileresf,"w"))==NULL) {         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;         as a weighted average of prlim.
   }      */
   printf("Computing forecasting: result on file '%s' \n", fileresf);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprevfore, lprevfore);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
  free_matrix(agev,1,maxwav,1,imx);      /* end probability of death */
   /* Mobile average */  
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
   if (mobilav==1) {        for(i=1; i<=nlstate;i++){
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)        }
       for (i=1; i<=nlstate;i++)      } 
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)      fprintf(ficresprobmorprev,"\n");
           mobaverage[(int)agedeb][i][cptcod]=0.;  
          fprintf(ficresvij,"%.0f ",age );
     for (agedeb=bage+4; agedeb<=fage; agedeb++){      for(i=1; i<=nlstate;i++)
       for (i=1; i<=nlstate;i++){        for(j=1; j<=nlstate;j++){
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
           for (cpt=0;cpt<=4;cpt++){        }
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];      fprintf(ficresvij,"\n");
           }      free_matrix(gp,0,nhstepm,1,nlstate);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      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);
   stepsize=(int) (stepm+YEARM-1)/YEARM;    free_vector(gmp,nlstate+1,nlstate+ndeath);
   if (stepm<=12) stepsize=1;    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   agelim=AGESUP;    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
   hstepm=stepsize*YEARM; /* Every year of age */    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */    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); */
    k=0;  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   for(cptcov=1;cptcov<=i1;cptcov++){  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
       k=k+1;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
       fprintf(ficresf,"\n#****** ");    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
       for(j=1;j<=cptcoveff;j++) {    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
         fprintf(ficresf,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    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(ficresf,"******\n");  */
       fprintf(ficresf,"# StartingAge FinalAge Horizon(in years)");  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
       for (agedeb=fage; agedeb>=bage; agedeb--){    free_vector(xp,1,npar);
         fprintf(ficresf,"\n%d %.f %.f 0 ",k,agedeb, agedeb);    free_matrix(doldm,1,nlstate,1,nlstate);
        if (mobilav==1) {    free_matrix(dnewm,1,nlstate,1,npar);
         for(j=1; j<=nlstate;j++)    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           fprintf(ficresf," %.5f ",mobaverage[(int)agedeb][j][cptcod]);    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
         }    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         else {    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           for(j=1; j<=nlstate;j++)    fclose(ficresprobmorprev);
           fprintf(ficresf," %.5f ",probs[(int)agedeb][j][cptcod]);    fflush(ficgp);
         }      fflush(fichtm); 
       for(j=1; j<=ndeath;j++) fprintf(ficresf," 0.00000");  }  /* end varevsij */
       }  
       for (cpt=1; cpt<=nforecast;cpt++)    /************ Variance of prevlim ******************/
       for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  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, char strstart[])
          {
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    /* Variance of prevalence limit */
         nhstepm = nhstepm/hstepm;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/    double **newm;
     double **dnewm,**doldm;
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int i, j, nhstepm, hstepm;
         oldm=oldms;savm=savms;    int k, cptcode;
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double *xp;
                    double *gp, *gm;
         for (h=0; h<=nhstepm; h++){    double **gradg, **trgradg;
            double age,agelim;
          if (h*hstepm/YEARM*stepm==cpt)    int theta;
             fprintf(ficresf,"\n%d %.f %.f %.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm, h*hstepm/YEARM*stepm);    fprintf(ficresvpl, "#Local time at start: %s", strstart); 
              fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
              fprintf(ficresvpl,"# Age");
           for(j=1; j<=nlstate+ndeath;j++) {    for(i=1; i<=nlstate;i++)
             kk1=0.;        fprintf(ficresvpl," %1d-%1d",i,i);
             for(i=1; i<=nlstate;i++) {            fprintf(ficresvpl,"\n");
               if (mobilav==1)  
               kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb][i][cptcod];    xp=vector(1,npar);
               else kk1=kk1+p3mat[i][j][h]*probs[(int)agedeb][i][cptcod];    dnewm=matrix(1,nlstate,1,npar);
             }        doldm=matrix(1,nlstate,1,nlstate);
           if (h*hstepm/YEARM*stepm==cpt) fprintf(ficresf," %.5f ", kk1);    
           }    hstepm=1*YEARM; /* Every year of age */
         }    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    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;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   free_imatrix(s,1,maxwav+1,1,n);      gradg=matrix(1,npar,1,nlstate);
   free_vector(weight,1,n);      gp=vector(1,nlstate);
   fclose(ficresf);      gm=vector(1,nlstate);
   /*---------- Health expectancies and variances ------------*/  
       for(theta=1; theta <=npar; theta++){
   strcpy(filerest,"t");        for(i=1; i<=npar; i++){ /* Computes gradient */
   strcat(filerest,fileres);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   if((ficrest=fopen(filerest,"w"))==NULL) {        }
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   }        for(i=1;i<=nlstate;i++)
   printf("Computing Total LEs with variances: file '%s' \n", filerest);          gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
   strcpy(filerese,"e");          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   strcat(filerese,fileres);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   if((ficreseij=fopen(filerese,"w"))==NULL) {        for(i=1;i<=nlstate;i++)
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          gm[i] = prlim[i][i];
   }  
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);        for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
  strcpy(fileresv,"v");      } /* End theta */
   strcat(fileresv,fileres);  
   if((ficresvij=fopen(fileresv,"w"))==NULL) {      trgradg =matrix(1,nlstate,1,npar);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);  
   }      for(j=1; j<=nlstate;j++)
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);        for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){      for(i=1;i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        varpl[i][(int)age] =0.;
       k=k+1;      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       fprintf(ficrest,"\n#****** ");      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(j=1;j<=cptcoveff;j++)      for(i=1;i<=nlstate;i++)
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
       fprintf(ficrest,"******\n");  
       fprintf(ficresvpl,"%.0f ",age );
       fprintf(ficreseij,"\n#****** ");      for(i=1; i<=nlstate;i++)
       for(j=1;j<=cptcoveff;j++)        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      fprintf(ficresvpl,"\n");
       fprintf(ficreseij,"******\n");      free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       fprintf(ficresvij,"\n#****** ");      free_matrix(gradg,1,npar,1,nlstate);
       for(j=1;j<=cptcoveff;j++)      free_matrix(trgradg,1,nlstate,1,npar);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    } /* End age */
       fprintf(ficresvij,"******\n");  
     free_vector(xp,1,npar);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    free_matrix(doldm,1,nlstate,1,npar);
       oldm=oldms;savm=savms;    free_matrix(dnewm,1,nlstate,1,nlstate);
       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);  /************ 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, char strstart[])
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");  {
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    int i, j=0,  i1, k1, l1, t, tj;
       fprintf(ficrest,"\n");    int k2, l2, j1,  z1;
            int k=0,l, cptcode;
       hf=1;    int first=1, first1;
       if (stepm >= YEARM) hf=stepm/YEARM;    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
       epj=vector(1,nlstate+1);    double **dnewm,**doldm;
       for(age=bage; age <=fage ;age++){    double *xp;
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    double *gp, *gm;
         if (popbased==1) {    double **gradg, **trgradg;
           for(i=1; i<=nlstate;i++)    double **mu;
             prlim[i][i]=probs[(int)age][i][k];    double age,agelim, cov[NCOVMAX];
         }    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
            int theta;
         fprintf(ficrest," %.0f",age);    char fileresprob[FILENAMELENGTH];
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    char fileresprobcov[FILENAMELENGTH];
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    char fileresprobcor[FILENAMELENGTH];
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];  
           }    double ***varpij;
           epj[nlstate+1] +=epj[j];  
         }    strcpy(fileresprob,"prob"); 
         for(i=1, vepp=0.;i <=nlstate;i++)    strcat(fileresprob,fileres);
           for(j=1;j <=nlstate;j++)    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
             vepp += vareij[i][j][(int)age];      printf("Problem with resultfile: %s\n", fileresprob);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
         for(j=1;j <=nlstate;j++){    }
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    strcpy(fileresprobcov,"probcov"); 
         }    strcat(fileresprobcov,fileres);
         fprintf(ficrest,"\n");    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);
  fclose(ficreseij);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
  fclose(ficresvij);    }
   fclose(ficrest);    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   fclose(ficpar);    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   free_vector(epj,1,nlstate+1);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   /*  scanf("%d ",i); */    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);
   /*------- Variance limit prevalence------*/      fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficresprob, "#Local time at start: %s", strstart);
 strcpy(fileresvpl,"vpl");    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   strcat(fileresvpl,fileres);    fprintf(ficresprob,"# Age");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    fprintf(ficresprobcov, "#Local time at start: %s", strstart);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     exit(0);    fprintf(ficresprobcov,"# Age");
   }    fprintf(ficresprobcor, "#Local time at start: %s", strstart);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcov,"# Age");
  k=0;  
  for(cptcov=1;cptcov<=i1;cptcov++){  
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    for(i=1; i<=nlstate;i++)
      k=k+1;      for(j=1; j<=(nlstate+ndeath);j++){
      fprintf(ficresvpl,"\n#****** ");        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
      for(j=1;j<=cptcoveff;j++)        fprintf(ficresprobcov," p%1d-%1d ",i,j);
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
      fprintf(ficresvpl,"******\n");      }  
         /* fprintf(ficresprob,"\n");
      varpl=matrix(1,nlstate,(int) bage, (int) fage);    fprintf(ficresprobcov,"\n");
      oldm=oldms;savm=savms;    fprintf(ficresprobcor,"\n");
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);   */
    }   xp=vector(1,npar);
  }    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   fclose(ficresvpl);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
   /*---------- End : free ----------------*/    first=1;
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    fprintf(ficgp,"\n# Routine varprob");
      fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    fprintf(fichtm,"\n");
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
      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\
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);    file %s<br>\n",optionfilehtmcov);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);  and drawn. It helps understanding how is the covariance between two incidences.\
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);   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. \
   free_matrix(matcov,1,npar,1,npar);  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   free_vector(delti,1,npar);  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>\
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);   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>\
   printf("End of Imach\n");  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  
      cov[1]=1;
   /* 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);*/    tj=cptcoveff;
   /*printf("Total time was %d uSec.\n", total_usecs);*/    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   /*------ End -----------*/    j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
  end:        j1++;
 #ifdef windows        if  (cptcovn>0) {
  chdir(pathcd);          fprintf(ficresprob, "\n#********** Variable "); 
 #endif          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprob, "**********\n#\n");
  system("..\\gp37mgw\\wgnuplot graph.plt");          fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 #ifdef windows          fprintf(ficresprobcov, "**********\n#\n");
   while (z[0] != 'q') {          
     chdir(pathcd);          fprintf(ficgp, "\n#********** Variable "); 
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     scanf("%s",z);          fprintf(ficgp, "**********\n#\n");
     if (z[0] == 'c') system("./imach");          
     else if (z[0] == 'e') {          
       chdir(path);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
       system(optionfilehtm);          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\">");
     else if (z[0] == 'q') exit(0);          
   }          fprintf(ficresprobcor, "\n#********** Variable ");    
 #endif          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><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></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> <a name='secondorder'>Result files (second order: variances)</a></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=0; 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=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           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,double agemortsup){
     int i,k;
   
     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>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     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 linei, month, year,iout;
     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 */
     struct stat info;
     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;
     int agemortsup;
     float  sumlpop=0.;
     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], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",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;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs)))    {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
           if(line[j] == '\t')
             line[j] = ' ';
         }
         for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
           ;
         };
         line[j+1]=0;  /* Trims blanks at end of line */
         if(line[0]=='#'){
           fprintf(ficlog,"Comment line\n%s\n",line);
           printf("Comment line\n%s\n",line);
           continue;
         }
         for (j=maxwav;j>=1;j--){
           cutv(stra, strb,line,' '); 
           errno=0;
           lval=strtol(strb,&endptr,10); 
           /*      if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %d %s for individual %d\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n",lval, i,line,linei,j,maxwav);
             exit(1);
           }
           s[j][i]=lval;
   
           strcpy(line,stra);
           cutv(stra, strb,line,' ');
           if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
           }
           else  if(iout=sscanf(strb,".") != 0){
             month=99;
             year=9999;
           }else{
             printf("Error reading data around '%s'.at line number %ld %s for individual %d\nShould be a year of exam at wave %d.  Exiting.\n",strb, i,line,linei,j);
             exit(1);
           }
           anint[j][i]= (double) year; 
           mint[j][i]= (double)month; 
           strcpy(line,stra);
         } /* ENd Waves */
           
         cutv(stra, strb,line,' '); 
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,".") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s'.at line number %ld %s for individual %d\nShould be a year of exam at wave %d.  Exiting.\n",strb, i,line,linei,j);
           exit(1);
         }
         andc[i]=(double) year; 
         moisdc[i]=(double) month; 
         strcpy(line,stra);
   
         cutv(stra, strb,line,' '); 
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,".") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s'.at line number %ld %s for individual %d\nShould be a year of exam at wave %d.  Exiting.\n",strb, i,line,linei,j);
           exit(1);
         }
         annais[i]=(double)(year);
         moisnais[i]=(double)(month); 
         strcpy(line,stra);
   
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d\nShould be a weight.  Exiting.\n",lval, i,line,linei);
           exit(1);
         }
         weight[i]=(double)(lval); 
         strcpy(line,stra);
   
         for (j=ncovcol;j>=1;j--){
           cutv(stra, strb,line,' '); 
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %ld %s for individual %d\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, i,line,linei);
             exit(1);
           }
           if(lval <-1 || lval >1){
             printf("Error reading data around '%d' at line number %ld %s for individual %d\nShould be a value of the %d covar (meaning 0 for the reference or 1. IMaCh does not build design variables, do it your self).  Exiting.\n",lval,i,line,linei,j);
             exit(1);
           }
           covar[j][i]=(double)(lval);
           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;
     } /* End loop reading  data */
     /* 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 parameters 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 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           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,strstart);
   
     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 (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    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;
           }else 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[NDIM]=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]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       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,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* 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, "#Local time at start: %s", strstart);
       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, "#Local time at start: %s", strstart);
       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,strstart);
   
       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, strstart);  
    
           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, strstart);
           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, strstart);
           }
   
           fprintf(ficrest, "#Local time at start: %s", strstart);
           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,strstart);
           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\nLocal time 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);
   #ifndef UNIX
     /*  strcpy(plotcmd,"\""); */
   #endif
     strcpy(plotcmd,pathimach);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     strcat(plotcmd,GNUPLOTPROGRAM);
   #ifndef UNIX
     strcat(plotcmd,".exe");
     /*  strcat(plotcmd,"\"");*/
   #endif
     if(stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
     }
   
   #ifndef UNIX
     strcpy(plotcmd,"\"");
   #endif
     strcat(plotcmd,pathimach);
     strcat(plotcmd,GNUPLOTPROGRAM);
   #ifndef UNIX
     strcat(plotcmd,".exe");
     strcat(plotcmd,"\"");
   #endif
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting graphs with: %s",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n 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);
     }
   }
   
   
   

Removed from v.1.15  
changed lines
  Added in v.1.110


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