Diff for /imach/src/imach.c between versions 1.17 and 1.101

version 1.17, 2002/02/20 17:15:02 version 1.101, 2004/09/15 10:38:38
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 1.101  2004/09/15 10:38:38  brouard
   individuals from different ages are interviewed on their health status    Fix on curr_time
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.100  2004/07/12 18:29:06  brouard
   Health expectancies are computed from the transistions observed between    Add version for Mac OS X. Just define UNIX in Makefile
   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 1.99  2004/06/05 08:57:40  brouard
   reach the Maximum Likelihood of the parameters involved in the model.    *** empty log message ***
   The simplest model is the multinomial logistic model where pij is  
   the probabibility to be observed in state j at the second wave conditional    Revision 1.98  2004/05/16 15:05:56  brouard
   to be observed in state i at the first wave. Therefore the model is:    New version 0.97 . First attempt to estimate force of mortality
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    directly from the data i.e. without the need of knowing the health
   is a covariate. If you want to have a more complex model than "constant and    state at each age, but using a Gompertz model: log u =a + b*age .
   age", you should modify the program where the markup    This is the basic analysis of mortality and should be done before any
     *Covariates have to be included here again* invites you to do it.    other analysis, in order to test if the mortality estimated from the
   More covariates you add, less is the speed of the convergence.    cross-longitudinal survey is different from the mortality estimated
     from other sources like vital statistic data.
   The advantage that this computer programme claims, comes from that if the  
   delay between waves is not identical for each individual, or if some    The same imach parameter file can be used but the option for mle should be -3.
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    Agnès, who wrote this part of the code, tried to keep most of the
   hPijx is the probability to be    former routines in order to include the new code within the former code.
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    The output is very simple: only an estimate of the intercept and of
   unobserved intermediate  states. This elementary transition (by month or    the slope with 95% confident intervals.
   quarter trimester, semester or year) is model as a multinomial logistic.  
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Current limitations:
   and the contribution of each individual to the likelihood is simply hPijx.    A) Even if you enter covariates, i.e. with the
     model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   Also this programme outputs the covariance matrix of the parameters but also    B) There is no computation of Life Expectancy nor Life Table.
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.97  2004/02/20 13:25:42  lievre
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Version 0.96d. Population forecasting command line is (temporarily)
            Institut national d'études démographiques, Paris.    suppressed.
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.96  2003/07/15 15:38:55  brouard
   It is copyrighted identically to a GNU software product, ie programme and    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   software can be distributed freely for non commercial use. Latest version    rewritten within the same printf. Workaround: many printfs.
   can be accessed at http://euroreves.ined.fr/imach .  
   **********************************************************************/    Revision 1.95  2003/07/08 07:54:34  brouard
      * imach.c (Repository):
 #include <math.h>    (Repository): Using imachwizard code to output a more meaningful covariance
 #include <stdio.h>    matrix (cov(a12,c31) instead of numbers.
 #include <stdlib.h>  
 #include <unistd.h>    Revision 1.94  2003/06/27 13:00:02  brouard
     Just cleaning
 #define MAXLINE 256  
 #define FILENAMELENGTH 80    Revision 1.93  2003/06/25 16:33:55  brouard
 /*#define DEBUG*/    (Module): On windows (cygwin) function asctime_r doesn't
 #define windows    exist so I changed back to asctime which exists.
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): Version 0.96b
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     Revision 1.92  2003/06/25 16:30:45  brouard
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    (Module): On windows (cygwin) function asctime_r doesn't
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    exist so I changed back to asctime which exists.
   
 #define NINTERVMAX 8    Revision 1.91  2003/06/25 15:30:29  brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    * imach.c (Repository): Duplicated warning errors corrected.
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    (Repository): Elapsed time after each iteration is now output. It
 #define NCOVMAX 8 /* Maximum number of covariates */    helps to forecast when convergence will be reached. Elapsed time
 #define MAXN 20000    is stamped in powell.  We created a new html file for the graphs
 #define YEARM 12. /* Number of months per year */    concerning matrix of covariance. It has extension -cov.htm.
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
 int nvar;    of the covariance matrix to be input.
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.89  2003/06/24 12:30:52  brouard
 int nlstate=2; /* Number of live states */    (Module): Some bugs corrected for windows. Also, when
 int ndeath=1; /* Number of dead states */    mle=-1 a template is output in file "or"mypar.txt with the design
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    of the covariance matrix to be input.
 int popbased=0;  
     Revision 1.88  2003/06/23 17:54:56  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 int maxwav; /* Maxim number of waves */  
 int jmin, jmax; /* min, max spacing between 2 waves */    Revision 1.87  2003/06/18 12:26:01  brouard
 int mle, weightopt;    Version 0.96
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Revision 1.86  2003/06/17 20:04:08  brouard
 double jmean; /* Mean space between 2 waves */    (Module): Change position of html and gnuplot routines and added
 double **oldm, **newm, **savm; /* Working pointers to matrices */    routine fileappend.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    Revision 1.85  2003/06/17 13:12:43  brouard
 FILE *ficgp, *fichtm,*ficresprob,*ficpop;    * imach.c (Repository): Check when date of death was earlier that
 FILE *ficreseij;    current date of interview. It may happen when the death was just
   char filerese[FILENAMELENGTH];    prior to the death. In this case, dh was negative and likelihood
  FILE  *ficresvij;    was wrong (infinity). We still send an "Error" but patch by
   char fileresv[FILENAMELENGTH];    assuming that the date of death was just one stepm after the
  FILE  *ficresvpl;    interview.
   char fileresvpl[FILENAMELENGTH];    (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
 #define NR_END 1    memory allocation. But we also truncated to 8 characters (left
 #define FREE_ARG char*    truncation)
 #define FTOL 1.0e-10    (Repository): No more line truncation errors.
   
 #define NRANSI    Revision 1.84  2003/06/13 21:44:43  brouard
 #define ITMAX 200    * imach.c (Repository): Replace "freqsummary" at a correct
     place. It differs from routine "prevalence" which may be called
 #define TOL 2.0e-4    many times. Probs is memory consuming and must be used with
     parcimony.
 #define CGOLD 0.3819660    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.82  2003/06/05 15:57:20  brouard
 #define TINY 1.0e-20    Add log in  imach.c and  fullversion number is now printed.
   
 static double maxarg1,maxarg2;  */
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  /*
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))     Interpolated Markov Chain
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Short summary of the programme:
 #define rint(a) floor(a+0.5)    
     This program computes Healthy Life Expectancies from
 static double sqrarg;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    first survey ("cross") where individuals from different ages are
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    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
 int imx;    second wave of interviews ("longitudinal") which measure each change
 int stepm;    (if any) in individual health status.  Health expectancies are
 /* Stepm, step in month: minimum step interpolation*/    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
 int m,nb;    Maximum Likelihood of the parameters involved in the model.  The
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    simplest model is the multinomial logistic model where pij is the
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    probability to be observed in state j at the second wave
 double **pmmij, ***probs, ***mobaverage;    conditional to be observed in state i at the first wave. Therefore
     the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 double *weight;    'age' is age and 'sex' is a covariate. If you want to have a more
 int **s; /* Status */    complex model than "constant and age", you should modify the program
 double *agedc, **covar, idx;    where the markup *Covariates have to be included here again* invites
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    you to do it.  More covariates you add, slower the
     convergence.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */    The advantage of this computer programme, compared to a simple
     multinomial logistic model, is clear when the delay between waves is not
 /**************** split *************************/    identical for each individual. Also, if a individual missed an
 static  int split( char *path, char *dirc, char *name )    intermediate interview, the information is lost, but taken into
 {    account using an interpolation or extrapolation.  
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */    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
    l1 = strlen( path );                 /* length of path */    split into an exact number (nh*stepm) of unobserved intermediate
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    states. This elementary transition (by month, quarter,
    s = strrchr( path, '\\' );           /* find last / */    semester or year) is modelled as a multinomial logistic.  The hPx
    if ( s == NULL ) {                   /* no directory, so use current */    matrix is simply the matrix product of nh*stepm elementary matrices
 #if     defined(__bsd__)                /* get current working directory */    and the contribution of each individual to the likelihood is simply
       extern char       *getwd( );    hPijx.
   
       if ( getwd( dirc ) == NULL ) {    Also this programme outputs the covariance matrix of the parameters but also
 #else    of the life expectancies. It also computes the stable prevalence. 
       extern char       *getcwd( );    
     Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {             Institut national d'études démographiques, Paris.
 #endif    This software have been partly granted by Euro-REVES, a concerted action
          return( GLOCK_ERROR_GETCWD );    from the European Union.
       }    It is copyrighted identically to a GNU software product, ie programme and
       strcpy( name, path );             /* we've got it */    software can be distributed freely for non commercial use. Latest version
    } else {                             /* strip direcotry from path */    can be accessed at http://euroreves.ined.fr/imach .
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
       strcpy( name, s );                /* save file name */    
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    **********************************************************************/
       dirc[l1-l2] = 0;                  /* add zero */  /*
    }    main
    l1 = strlen( dirc );                 /* length of directory */    read parameterfile
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    read datafile
    return( 0 );                         /* we're done */    concatwav
 }    freqsummary
     if (mle >= 1)
       mlikeli
 /******************************************/    print results files
     if mle==1 
 void replace(char *s, char*t)       computes hessian
 {    read end of parameter file: agemin, agemax, bage, fage, estepm
   int i;        begin-prev-date,...
   int lg=20;    open gnuplot file
   i=0;    open html file
   lg=strlen(t);    stable prevalence
   for(i=0; i<= lg; i++) {     for age prevalim()
     (s[i] = t[i]);    h Pij x
     if (t[i]== '\\') s[i]='/';    variance of p varprob
   }    forecasting if prevfcast==1 prevforecast call prevalence()
 }    health expectancies
     Variance-covariance of DFLE
 int nbocc(char *s, char occ)    prevalence()
 {     movingaverage()
   int i,j=0;    varevsij() 
   int lg=20;    if popbased==1 varevsij(,popbased)
   i=0;    total life expectancies
   lg=strlen(s);    Variance of stable prevalence
   for(i=0; i<= lg; i++) {   end
   if  (s[i] == occ ) j++;  */
   }  
   return j;  
 }  
    
 void cutv(char *u,char *v, char*t, char occ)  #include <math.h>
 {  #include <stdio.h>
   int i,lg,j,p=0;  #include <stdlib.h>
   i=0;  #include <unistd.h>
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  /* #include <sys/time.h> */
   }  #include <time.h>
   #include "timeval.h"
   lg=strlen(t);  
   for(j=0; j<p; j++) {  /* #include <libintl.h> */
     (u[j] = t[j]);  /* #define _(String) gettext (String) */
   }  
      u[p]='\0';  #define MAXLINE 256
   #define GNUPLOTPROGRAM "gnuplot"
    for(j=0; j<= lg; j++) {  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
     if (j>=(p+1))(v[j-p-1] = t[j]);  #define FILENAMELENGTH 132
   }  /*#define DEBUG*/
 }  /*#define windows*/
   #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 /********************** nrerror ********************/  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
 void nrerror(char error_text[])  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 {  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   fprintf(stderr,"ERREUR ...\n");  
   fprintf(stderr,"%s\n",error_text);  #define NINTERVMAX 8
   exit(1);  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 }  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 /*********************** vector *******************/  #define NCOVMAX 8 /* Maximum number of covariates */
 double *vector(int nl, int nh)  #define MAXN 20000
 {  #define YEARM 12. /* Number of months per year */
   double *v;  #define AGESUP 130
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #define AGEBASE 40
   if (!v) nrerror("allocation failure in vector");  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   return v-nl+NR_END;  #ifdef UNIX
 }  #define DIRSEPARATOR '/'
   #define ODIRSEPARATOR '\\'
 /************************ free vector ******************/  #else
 void free_vector(double*v, int nl, int nh)  #define DIRSEPARATOR '\\'
 {  #define ODIRSEPARATOR '/'
   free((FREE_ARG)(v+nl-NR_END));  #endif
 }  
   /* $Id$ */
 /************************ivector *******************************/  /* $State$ */
 int *ivector(long nl,long nh)  
 {  char version[]="Imach version 0.97b, May 2004, INED-EUROREVES ";
   int *v;  char fullversion[]="$Revision$ $Date$"; 
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   if (!v) nrerror("allocation failure in ivector");  int nvar;
   return v-nl+NR_END;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
 }  int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
 /******************free ivector **************************/  int ndeath=1; /* Number of dead states */
 void free_ivector(int *v, long nl, long nh)  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 {  int popbased=0;
   free((FREE_ARG)(v+nl-NR_END));  
 }  int *wav; /* Number of waves for this individuual 0 is possible */
   int maxwav; /* Maxim number of waves */
 /******************* imatrix *******************************/  int jmin, jmax; /* min, max spacing between 2 waves */
 int **imatrix(long nrl, long nrh, long ncl, long nch)  int gipmx, gsw; /* Global variables on the number of contributions 
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */                     to the likelihood and the sum of weights (done by funcone)*/
 {  int mle, weightopt;
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   int **m;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
    int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   /* allocate pointers to rows */             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  double jmean; /* Mean space between 2 waves */
   if (!m) nrerror("allocation failure 1 in matrix()");  double **oldm, **newm, **savm; /* Working pointers to matrices */
   m += NR_END;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   m -= nrl;  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
    FILE *ficlog, *ficrespow;
    int globpr; /* Global variable for printing or not */
   /* allocate rows and set pointers to them */  double fretone; /* Only one call to likelihood */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  long ipmx; /* Number of contributions */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  double sw; /* Sum of weights */
   m[nrl] += NR_END;  char filerespow[FILENAMELENGTH];
   m[nrl] -= ncl;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
    FILE *ficresilk;
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
    FILE *ficresprobmorprev;
   /* return pointer to array of pointers to rows */  FILE *fichtm, *fichtmcov; /* Html File */
   return m;  FILE *ficreseij;
 }  char filerese[FILENAMELENGTH];
   FILE  *ficresvij;
 /****************** free_imatrix *************************/  char fileresv[FILENAMELENGTH];
 void free_imatrix(m,nrl,nrh,ncl,nch)  FILE  *ficresvpl;
       int **m;  char fileresvpl[FILENAMELENGTH];
       long nch,ncl,nrh,nrl;  char title[MAXLINE];
      /* free an int matrix allocated by imatrix() */  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 {  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   free((FREE_ARG) (m+nrl-NR_END));  char command[FILENAMELENGTH];
 }  int  outcmd=0;
   
 /******************* matrix *******************************/  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {  char filelog[FILENAMELENGTH]; /* Log file */
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  char filerest[FILENAMELENGTH];
   double **m;  char fileregp[FILENAMELENGTH];
   char popfile[FILENAMELENGTH];
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   m += NR_END;  
   m -= nrl;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   struct timezone tzp;
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  extern int gettimeofday();
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   m[nrl] += NR_END;  long time_value;
   m[nrl] -= ncl;  extern long time();
   char strcurr[80], strfor[80];
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   return m;  #define NR_END 1
 }  #define FREE_ARG char*
   #define FTOL 1.0e-10
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #define NRANSI 
 {  #define ITMAX 200 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define TOL 2.0e-4 
 }  
   #define CGOLD 0.3819660 
 /******************* ma3x *******************************/  #define ZEPS 1.0e-10 
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define GOLD 1.618034 
   double ***m;  #define GLIMIT 100.0 
   #define TINY 1.0e-20 
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  static double maxarg1,maxarg2;
   m += NR_END;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   m -= nrl;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define rint(a) floor(a+0.5)
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int agegomp= AGEGOMP;
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  int imx; 
   m[nrl][ncl] += NR_END;  int stepm=1;
   m[nrl][ncl] -= nll;  /* Stepm, step in month: minimum step interpolation*/
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  int estepm;
    /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   for (i=nrl+1; i<=nrh; i++) {  
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  int m,nb;
     for (j=ncl+1; j<=nch; j++)  long *num;
       m[i][j]=m[i][j-1]+nlay;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   return m;  double **pmmij, ***probs;
 }  double *ageexmed,*agecens;
   double dateintmean=0;
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  double *weight;
 {  int **s; /* Status */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  double *agedc, **covar, idx;
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   free((FREE_ARG)(m+nrl-NR_END));  
 }  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   double ftolhess; /* Tolerance for computing hessian */
 /***************** f1dim *************************/  
 extern int ncom;  /**************** split *************************/
 extern double *pcom,*xicom;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 extern double (*nrfunc)(double []);  {
      /* From a file name with full path (either Unix or Windows) we extract the directory (dirc)
 double f1dim(double x)       the name of the file (name), its extension only (ext) and its first part of the name (finame)
 {    */ 
   int j;    char  *ss;                            /* pointer */
   double f;    int   l1, l2;                         /* length counters */
   double *xt;  
      l1 = strlen(path );                   /* length of path */
   xt=vector(1,ncom);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   f=(*nrfunc)(xt);    if ( ss == NULL ) {                   /* no directory, so use current */
   free_vector(xt,1,ncom);      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   return f;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
 }      /* get current working directory */
       /*    extern  char* getcwd ( char *buf , int len);*/
 /*****************brent *************************/      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)        return( GLOCK_ERROR_GETCWD );
 {      }
   int iter;      strcpy( name, path );               /* we've got it */
   double a,b,d,etemp;    } else {                              /* strip direcotry from path */
   double fu,fv,fw,fx;      ss++;                               /* after this, the filename */
   double ftemp;      l2 = strlen( ss );                  /* length of filename */
   double p,q,r,tol1,tol2,u,v,w,x,xm;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   double e=0.0;      strcpy( name, ss );         /* save file name */
        strncpy( dirc, path, l1 - l2 );     /* now the directory */
   a=(ax < cx ? ax : cx);      dirc[l1-l2] = 0;                    /* add zero */
   b=(ax > cx ? ax : cx);    }
   x=w=v=bx;    l1 = strlen( dirc );                  /* length of directory */
   fw=fv=fx=(*f)(x);    /*#ifdef windows
   for (iter=1;iter<=ITMAX;iter++) {    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
     xm=0.5*(a+b);  #else
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  #endif
     printf(".");fflush(stdout);    */
 #ifdef DEBUG    ss = strrchr( name, '.' );            /* find last / */
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);    if (ss >0){
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */      ss++;
 #endif      strcpy(ext,ss);                     /* save extension */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){      l1= strlen( name);
       *xmin=x;      l2= strlen(ss)+1;
       return fx;      strncpy( finame, name, l1-l2);
     }      finame[l1-l2]= 0;
     ftemp=fu;    }
     if (fabs(e) > tol1) {    return( 0 );                          /* we're done */
       r=(x-w)*(fx-fv);  }
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  /******************************************/
       if (q > 0.0) p = -p;  
       q=fabs(q);  void replace_back_to_slash(char *s, char*t)
       etemp=e;  {
       e=d;    int i;
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    int lg=0;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    i=0;
       else {    lg=strlen(t);
         d=p/q;    for(i=0; i<= lg; i++) {
         u=x+d;      (s[i] = t[i]);
         if (u-a < tol2 || b-u < tol2)      if (t[i]== '\\') s[i]='/';
           d=SIGN(tol1,xm-x);    }
       }  }
     } else {  
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  int nbocc(char *s, char occ)
     }  {
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    int i,j=0;
     fu=(*f)(u);    int lg=20;
     if (fu <= fx) {    i=0;
       if (u >= x) a=x; else b=x;    lg=strlen(s);
       SHFT(v,w,x,u)    for(i=0; i<= lg; i++) {
         SHFT(fv,fw,fx,fu)    if  (s[i] == occ ) j++;
         } else {    }
           if (u < x) a=u; else b=u;    return j;
           if (fu <= fw || w == x) {  }
             v=w;  
             w=u;  void cutv(char *u,char *v, char*t, char occ)
             fv=fw;  {
             fw=fu;    /* cuts string t into u and v where u is ended by char occ excluding it
           } else if (fu <= fv || v == x || v == w) {       and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)
             v=u;       gives u="abcedf" and v="ghi2j" */
             fv=fu;    int i,lg,j,p=0;
           }    i=0;
         }    for(j=0; j<=strlen(t)-1; j++) {
   }      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   nrerror("Too many iterations in brent");    }
   *xmin=x;  
   return fx;    lg=strlen(t);
 }    for(j=0; j<p; j++) {
       (u[j] = t[j]);
 /****************** mnbrak ***********************/    }
        u[p]='\0';
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))     for(j=0; j<= lg; j++) {
 {      if (j>=(p+1))(v[j-p-1] = t[j]);
   double ulim,u,r,q, dum;    }
   double fu;  }
    
   *fa=(*func)(*ax);  /********************** nrerror ********************/
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  void nrerror(char error_text[])
     SHFT(dum,*ax,*bx,dum)  {
       SHFT(dum,*fb,*fa,dum)    fprintf(stderr,"ERREUR ...\n");
       }    fprintf(stderr,"%s\n",error_text);
   *cx=(*bx)+GOLD*(*bx-*ax);    exit(EXIT_FAILURE);
   *fc=(*func)(*cx);  }
   while (*fb > *fc) {  /*********************** vector *******************/
     r=(*bx-*ax)*(*fb-*fc);  double *vector(int nl, int nh)
     q=(*bx-*cx)*(*fb-*fa);  {
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    double *v;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     ulim=(*bx)+GLIMIT*(*cx-*bx);    if (!v) nrerror("allocation failure in vector");
     if ((*bx-u)*(u-*cx) > 0.0) {    return v-nl+NR_END;
       fu=(*func)(u);  }
     } else if ((*cx-u)*(u-ulim) > 0.0) {  
       fu=(*func)(u);  /************************ free vector ******************/
       if (fu < *fc) {  void free_vector(double*v, int nl, int nh)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  {
           SHFT(*fb,*fc,fu,(*func)(u))    free((FREE_ARG)(v+nl-NR_END));
           }  }
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  /************************ivector *******************************/
       fu=(*func)(u);  int *ivector(long nl,long nh)
     } else {  {
       u=(*cx)+GOLD*(*cx-*bx);    int *v;
       fu=(*func)(u);    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     }    if (!v) nrerror("allocation failure in ivector");
     SHFT(*ax,*bx,*cx,u)    return v-nl+NR_END;
       SHFT(*fa,*fb,*fc,fu)  }
       }  
 }  /******************free ivector **************************/
   void free_ivector(int *v, long nl, long nh)
 /*************** linmin ************************/  {
     free((FREE_ARG)(v+nl-NR_END));
 int ncom;  }
 double *pcom,*xicom;  
 double (*nrfunc)(double []);  /************************lvector *******************************/
    long *lvector(long nl,long nh)
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  {
 {    long *v;
   double brent(double ax, double bx, double cx,    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
                double (*f)(double), double tol, double *xmin);    if (!v) nrerror("allocation failure in ivector");
   double f1dim(double x);    return v-nl+NR_END;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  }
               double *fc, double (*func)(double));  
   int j;  /******************free lvector **************************/
   double xx,xmin,bx,ax;  void free_lvector(long *v, long nl, long nh)
   double fx,fb,fa;  {
      free((FREE_ARG)(v+nl-NR_END));
   ncom=n;  }
   pcom=vector(1,n);  
   xicom=vector(1,n);  /******************* imatrix *******************************/
   nrfunc=func;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   for (j=1;j<=n;j++) {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     pcom[j]=p[j];  { 
     xicom[j]=xi[j];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   }    int **m; 
   ax=0.0;    
   xx=1.0;    /* allocate pointers to rows */ 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    if (!m) nrerror("allocation failure 1 in matrix()"); 
 #ifdef DEBUG    m += NR_END; 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    m -= nrl; 
 #endif    
   for (j=1;j<=n;j++) {    
     xi[j] *= xmin;    /* allocate rows and set pointers to them */ 
     p[j] += xi[j];    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   free_vector(xicom,1,n);    m[nrl] += NR_END; 
   free_vector(pcom,1,n);    m[nrl] -= ncl; 
 }    
     for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
 /*************** powell ************************/    
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    /* return pointer to array of pointers to rows */ 
             double (*func)(double []))    return m; 
 {  } 
   void linmin(double p[], double xi[], int n, double *fret,  
               double (*func)(double []));  /****************** free_imatrix *************************/
   int i,ibig,j;  void free_imatrix(m,nrl,nrh,ncl,nch)
   double del,t,*pt,*ptt,*xit;        int **m;
   double fp,fptt;        long nch,ncl,nrh,nrl; 
   double *xits;       /* free an int matrix allocated by imatrix() */ 
   pt=vector(1,n);  { 
   ptt=vector(1,n);    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   xit=vector(1,n);    free((FREE_ARG) (m+nrl-NR_END)); 
   xits=vector(1,n);  } 
   *fret=(*func)(p);  
   for (j=1;j<=n;j++) pt[j]=p[j];  /******************* matrix *******************************/
   for (*iter=1;;++(*iter)) {  double **matrix(long nrl, long nrh, long ncl, long nch)
     fp=(*fret);  {
     ibig=0;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     del=0.0;    double **m;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       printf(" %d %.12f",i, p[i]);    if (!m) nrerror("allocation failure 1 in matrix()");
     printf("\n");    m += NR_END;
     for (i=1;i<=n;i++) {    m -= nrl;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 #ifdef DEBUG    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       printf("fret=%lf \n",*fret);    m[nrl] += NR_END;
 #endif    m[nrl] -= ncl;
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       if (fabs(fptt-(*fret)) > del) {    return m;
         del=fabs(fptt-(*fret));    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
         ibig=i;     */
       }  }
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  /*************************free matrix ************************/
       for (j=1;j<=n;j++) {  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  {
         printf(" x(%d)=%.12e",j,xit[j]);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       }    free((FREE_ARG)(m+nrl-NR_END));
       for(j=1;j<=n;j++)  }
         printf(" p=%.12e",p[j]);  
       printf("\n");  /******************* ma3x *******************************/
 #endif  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     }  {
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
 #ifdef DEBUG    double ***m;
       int k[2],l;  
       k[0]=1;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       k[1]=-1;    if (!m) nrerror("allocation failure 1 in matrix()");
       printf("Max: %.12e",(*func)(p));    m += NR_END;
       for (j=1;j<=n;j++)    m -= nrl;
         printf(" %.12e",p[j]);  
       printf("\n");    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       for(l=0;l<=1;l++) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         for (j=1;j<=n;j++) {    m[nrl] += NR_END;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    m[nrl] -= ncl;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  
         }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  
       }    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
 #endif    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
       free_vector(xit,1,n);    for (j=ncl+1; j<=nch; j++) 
       free_vector(xits,1,n);      m[nrl][j]=m[nrl][j-1]+nlay;
       free_vector(ptt,1,n);    
       free_vector(pt,1,n);    for (i=nrl+1; i<=nrh; i++) {
       return;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     }      for (j=ncl+1; j<=nch; j++) 
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");        m[i][j]=m[i][j-1]+nlay;
     for (j=1;j<=n;j++) {    }
       ptt[j]=2.0*p[j]-pt[j];    return m; 
       xit[j]=p[j]-pt[j];    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
       pt[j]=p[j];             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     }    */
     fptt=(*func)(ptt);  }
     if (fptt < fp) {  
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  /*************************free ma3x ************************/
       if (t < 0.0) {  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
         linmin(p,xit,n,fret,func);  {
         for (j=1;j<=n;j++) {    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
           xi[j][ibig]=xi[j][n];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
           xi[j][n]=xit[j];    free((FREE_ARG)(m+nrl-NR_END));
         }  }
 #ifdef DEBUG  
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  /*************** function subdirf ***********/
         for(j=1;j<=n;j++)  char *subdirf(char fileres[])
           printf(" %.12e",xit[j]);  {
         printf("\n");    /* Caution optionfilefiname is hidden */
 #endif    strcpy(tmpout,optionfilefiname);
       }    strcat(tmpout,"/"); /* Add to the right */
     }    strcat(tmpout,fileres);
   }    return tmpout;
 }  }
   
 /**** Prevalence limit ****************/  /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  {
 {    
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    /* Caution optionfilefiname is hidden */
      matrix by transitions matrix until convergence is reached */    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
   int i, ii,j,k;    strcat(tmpout,preop);
   double min, max, maxmin, maxmax,sumnew=0.;    strcat(tmpout,fileres);
   double **matprod2();    return tmpout;
   double **out, cov[NCOVMAX], **pmij();  }
   double **newm;  
   double agefin, delaymax=50 ; /* Max number of years to converge */  /*************** function subdirf3 ***********/
   char *subdirf3(char fileres[], char *preop, char *preop2)
   for (ii=1;ii<=nlstate+ndeath;ii++)  {
     for (j=1;j<=nlstate+ndeath;j++){    
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    /* Caution optionfilefiname is hidden */
     }    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
    cov[1]=1.;    strcat(tmpout,preop);
      strcat(tmpout,preop2);
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    strcat(tmpout,fileres);
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    return tmpout;
     newm=savm;  }
     /* Covariates have to be included here again */  
      cov[2]=agefin;  /***************** f1dim *************************/
    extern int ncom; 
       for (k=1; k<=cptcovn;k++) {  extern double *pcom,*xicom;
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  extern double (*nrfunc)(double []); 
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/   
       }  double f1dim(double x) 
       for (k=1; k<=cptcovage;k++)  { 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    int j; 
       for (k=1; k<=cptcovprod;k++)    double f;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    double *xt; 
    
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    xt=vector(1,ncom); 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    free_vector(xt,1,ncom); 
     return f; 
     savm=oldm;  } 
     oldm=newm;  
     maxmax=0.;  /*****************brent *************************/
     for(j=1;j<=nlstate;j++){  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
       min=1.;  { 
       max=0.;    int iter; 
       for(i=1; i<=nlstate; i++) {    double a,b,d,etemp;
         sumnew=0;    double fu,fv,fw,fx;
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    double ftemp;
         prlim[i][j]= newm[i][j]/(1-sumnew);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
         max=FMAX(max,prlim[i][j]);    double e=0.0; 
         min=FMIN(min,prlim[i][j]);   
       }    a=(ax < cx ? ax : cx); 
       maxmin=max-min;    b=(ax > cx ? ax : cx); 
       maxmax=FMAX(maxmax,maxmin);    x=w=v=bx; 
     }    fw=fv=fx=(*f)(x); 
     if(maxmax < ftolpl){    for (iter=1;iter<=ITMAX;iter++) { 
       return prlim;      xm=0.5*(a+b); 
     }      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   }      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
 }      printf(".");fflush(stdout);
       fprintf(ficlog,".");fflush(ficlog);
 /*************** transition probabilities ***************/  #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);
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
 {      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   double s1, s2;  #endif
   /*double t34;*/      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   int i,j,j1, nc, ii, jj;        *xmin=x; 
         return fx; 
     for(i=1; i<= nlstate; i++){      } 
     for(j=1; j<i;j++){      ftemp=fu;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      if (fabs(e) > tol1) { 
         /*s2 += param[i][j][nc]*cov[nc];*/        r=(x-w)*(fx-fv); 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];        q=(x-v)*(fx-fw); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/        p=(x-v)*q-(x-w)*r; 
       }        q=2.0*(q-r); 
       ps[i][j]=s2;        if (q > 0.0) p = -p; 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/        q=fabs(q); 
     }        etemp=e; 
     for(j=i+1; j<=nlstate+ndeath;j++){        e=d; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/        else { 
       }          d=p/q; 
       ps[i][j]=(s2);          u=x+d; 
     }          if (u-a < tol2 || b-u < tol2) 
   }            d=SIGN(tol1,xm-x); 
     /*ps[3][2]=1;*/        } 
       } else { 
   for(i=1; i<= nlstate; i++){        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
      s1=0;      } 
     for(j=1; j<i; j++)      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       s1+=exp(ps[i][j]);      fu=(*f)(u); 
     for(j=i+1; j<=nlstate+ndeath; j++)      if (fu <= fx) { 
       s1+=exp(ps[i][j]);        if (u >= x) a=x; else b=x; 
     ps[i][i]=1./(s1+1.);        SHFT(v,w,x,u) 
     for(j=1; j<i; j++)          SHFT(fv,fw,fx,fu) 
       ps[i][j]= exp(ps[i][j])*ps[i][i];          } else { 
     for(j=i+1; j<=nlstate+ndeath; j++)            if (u < x) a=u; else b=u; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];            if (fu <= fw || w == x) { 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */              v=w; 
   } /* end i */              w=u; 
               fv=fw; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){              fw=fu; 
     for(jj=1; jj<= nlstate+ndeath; jj++){            } else if (fu <= fv || v == x || v == w) { 
       ps[ii][jj]=0;              v=u; 
       ps[ii][ii]=1;              fv=fu; 
     }            } 
   }          } 
     } 
     nrerror("Too many iterations in brent"); 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    *xmin=x; 
     for(jj=1; jj<= nlstate+ndeath; jj++){    return fx; 
      printf("%lf ",ps[ii][jj]);  } 
    }  
     printf("\n ");  /****************** mnbrak ***********************/
     }  
     printf("\n ");printf("%lf ",cov[2]);*/  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
 /*              double (*func)(double)) 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  { 
   goto end;*/    double ulim,u,r,q, dum;
     return ps;    double fu; 
 }   
     *fa=(*func)(*ax); 
 /**************** Product of 2 matrices ******************/    *fb=(*func)(*bx); 
     if (*fb > *fa) { 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      SHFT(dum,*ax,*bx,dum) 
 {        SHFT(dum,*fb,*fa,dum) 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times        } 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    *cx=(*bx)+GOLD*(*bx-*ax); 
   /* in, b, out are matrice of pointers which should have been initialized    *fc=(*func)(*cx); 
      before: only the contents of out is modified. The function returns    while (*fb > *fc) { 
      a pointer to pointers identical to out */      r=(*bx-*ax)*(*fb-*fc); 
   long i, j, k;      q=(*bx-*cx)*(*fb-*fa); 
   for(i=nrl; i<= nrh; i++)      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     for(k=ncolol; k<=ncoloh; k++)        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)      ulim=(*bx)+GLIMIT*(*cx-*bx); 
         out[i][k] +=in[i][j]*b[j][k];      if ((*bx-u)*(u-*cx) > 0.0) { 
         fu=(*func)(u); 
   return out;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 }        fu=(*func)(u); 
         if (fu < *fc) { 
           SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
 /************* Higher Matrix Product ***************/            SHFT(*fb,*fc,fu,(*func)(u)) 
             } 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
 {        u=ulim; 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        fu=(*func)(u); 
      duration (i.e. until      } else { 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.        u=(*cx)+GOLD*(*cx-*bx); 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        fu=(*func)(u); 
      (typically every 2 years instead of every month which is too big).      } 
      Model is determined by parameters x and covariates have to be      SHFT(*ax,*bx,*cx,u) 
      included manually here.        SHFT(*fa,*fb,*fc,fu) 
         } 
      */  } 
   
   int i, j, d, h, k;  /*************** linmin ************************/
   double **out, cov[NCOVMAX];  
   double **newm;  int ncom; 
   double *pcom,*xicom;
   /* Hstepm could be zero and should return the unit matrix */  double (*nrfunc)(double []); 
   for (i=1;i<=nlstate+ndeath;i++)   
     for (j=1;j<=nlstate+ndeath;j++){  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       oldm[i][j]=(i==j ? 1.0 : 0.0);  { 
       po[i][j][0]=(i==j ? 1.0 : 0.0);    double brent(double ax, double bx, double cx, 
     }                 double (*f)(double), double tol, double *xmin); 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    double f1dim(double x); 
   for(h=1; h <=nhstepm; h++){    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     for(d=1; d <=hstepm; d++){                double *fc, double (*func)(double)); 
       newm=savm;    int j; 
       /* Covariates have to be included here again */    double xx,xmin,bx,ax; 
       cov[1]=1.;    double fx,fb,fa;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;   
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    ncom=n; 
       for (k=1; k<=cptcovage;k++)    pcom=vector(1,n); 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    xicom=vector(1,n); 
       for (k=1; k<=cptcovprod;k++)    nrfunc=func; 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for (j=1;j<=n;j++) { 
       pcom[j]=p[j]; 
       xicom[j]=xi[j]; 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    } 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    ax=0.0; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    xx=1.0; 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       savm=oldm;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       oldm=newm;  #ifdef DEBUG
     }    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     for(i=1; i<=nlstate+ndeath; i++)    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       for(j=1;j<=nlstate+ndeath;j++) {  #endif
         po[i][j][h]=newm[i][j];    for (j=1;j<=n;j++) { 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      xi[j] *= xmin; 
          */      p[j] += xi[j]; 
       }    } 
   } /* end h */    free_vector(xicom,1,n); 
   return po;    free_vector(pcom,1,n); 
 }  } 
   
   char *asc_diff_time(long time_sec, char ascdiff[])
 /*************** log-likelihood *************/  {
 double func( double *x)    long sec_left, days, hours, minutes;
 {    days = (time_sec) / (60*60*24);
   int i, ii, j, k, mi, d, kk;    sec_left = (time_sec) % (60*60*24);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    hours = (sec_left) / (60*60) ;
   double **out;    sec_left = (sec_left) %(60*60);
   double sw; /* Sum of weights */    minutes = (sec_left) /60;
   double lli; /* Individual log likelihood */    sec_left = (sec_left) % (60);
   long ipmx;    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   /*extern weight */    return ascdiff;
   /* We are differentiating ll according to initial status */  }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  
   /*for(i=1;i<imx;i++)  /*************** powell ************************/
     printf(" %d\n",s[4][i]);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   */              double (*func)(double [])) 
   cov[1]=1.;  { 
     void linmin(double p[], double xi[], int n, double *fret, 
   for(k=1; k<=nlstate; k++) ll[k]=0.;                double (*func)(double [])); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    int i,ibig,j; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    double del,t,*pt,*ptt,*xit;
     for(mi=1; mi<= wav[i]-1; mi++){    double fp,fptt;
       for (ii=1;ii<=nlstate+ndeath;ii++)    double *xits;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    int niterf, itmp;
       for(d=0; d<dh[mi][i]; d++){  
         newm=savm;    pt=vector(1,n); 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    ptt=vector(1,n); 
         for (kk=1; kk<=cptcovage;kk++) {    xit=vector(1,n); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    xits=vector(1,n); 
         }    *fret=(*func)(p); 
            for (j=1;j<=n;j++) pt[j]=p[j]; 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    for (*iter=1;;++(*iter)) { 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));      fp=(*fret); 
         savm=oldm;      ibig=0; 
         oldm=newm;      del=0.0; 
              last_time=curr_time;
              (void) gettimeofday(&curr_time,&tzp);
       } /* end mult */      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
            /*    fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      */
       ipmx +=1;     for (i=1;i<=n;i++) {
       sw += weight[i];        printf(" %d %.12f",i, p[i]);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        fprintf(ficlog," %d %.12lf",i, p[i]);
     } /* end of wave */        fprintf(ficrespow," %.12lf", p[i]);
   } /* end of individual */      }
       printf("\n");
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      fprintf(ficlog,"\n");
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      fprintf(ficrespow,"\n");fflush(ficrespow);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */      if(*iter <=3){
   return -l;        tm = *localtime(&curr_time.tv_sec);
 }        strcpy(strcurr,asctime(&tm));
   /*       asctime_r(&tm,strcurr); */
         forecast_time=curr_time; 
 /*********** Maximum Likelihood Estimation ***************/        itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))          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);
   int i,j, iter;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   double **xi,*delti;        for(niterf=10;niterf<=30;niterf+=10){
   double fret;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   xi=matrix(1,npar,1,npar);          tmf = *localtime(&forecast_time.tv_sec);
   for (i=1;i<=npar;i++)  /*      asctime_r(&tmf,strfor); */
     for (j=1;j<=npar;j++)          strcpy(strfor,asctime(&tmf));
       xi[i][j]=(i==j ? 1.0 : 0.0);          itmp = strlen(strfor);
   printf("Powell\n");          if(strfor[itmp-1]=='\n')
   powell(p,xi,npar,ftol,&iter,&fret,func);          strfor[itmp-1]='\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);
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          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);
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));        }
       }
 }      for (i=1;i<=n;i++) { 
         for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 /**** Computes Hessian and covariance matrix ***/        fptt=(*fret); 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  #ifdef DEBUG
 {        printf("fret=%lf \n",*fret);
   double  **a,**y,*x,pd;        fprintf(ficlog,"fret=%lf \n",*fret);
   double **hess;  #endif
   int i, j,jk;        printf("%d",i);fflush(stdout);
   int *indx;        fprintf(ficlog,"%d",i);fflush(ficlog);
         linmin(p,xit,n,fret,func); 
   double hessii(double p[], double delta, int theta, double delti[]);        if (fabs(fptt-(*fret)) > del) { 
   double hessij(double p[], double delti[], int i, int j);          del=fabs(fptt-(*fret)); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;          ibig=i; 
   void ludcmp(double **a, int npar, int *indx, double *d) ;        } 
   #ifdef DEBUG
   hess=matrix(1,npar,1,npar);        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
   printf("\nCalculation of the hessian matrix. Wait...\n");        for (j=1;j<=n;j++) {
   for (i=1;i<=npar;i++){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     printf("%d",i);fflush(stdout);          printf(" x(%d)=%.12e",j,xit[j]);
     hess[i][i]=hessii(p,ftolhess,i,delti);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     /*printf(" %f ",p[i]);*/        }
     /*printf(" %lf ",hess[i][i]);*/        for(j=1;j<=n;j++) {
   }          printf(" p=%.12e",p[j]);
            fprintf(ficlog," p=%.12e",p[j]);
   for (i=1;i<=npar;i++) {        }
     for (j=1;j<=npar;j++)  {        printf("\n");
       if (j>i) {        fprintf(ficlog,"\n");
         printf(".%d%d",i,j);fflush(stdout);  #endif
         hess[i][j]=hessij(p,delti,i,j);      } 
         hess[j][i]=hess[i][j];          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
         /*printf(" %lf ",hess[i][j]);*/  #ifdef DEBUG
       }        int k[2],l;
     }        k[0]=1;
   }        k[1]=-1;
   printf("\n");        printf("Max: %.12e",(*func)(p));
         fprintf(ficlog,"Max: %.12e",(*func)(p));
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        for (j=1;j<=n;j++) {
            printf(" %.12e",p[j]);
   a=matrix(1,npar,1,npar);          fprintf(ficlog," %.12e",p[j]);
   y=matrix(1,npar,1,npar);        }
   x=vector(1,npar);        printf("\n");
   indx=ivector(1,npar);        fprintf(ficlog,"\n");
   for (i=1;i<=npar;i++)        for(l=0;l<=1;l++) {
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          for (j=1;j<=n;j++) {
   ludcmp(a,npar,indx,&pd);            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
             printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   for (j=1;j<=npar;j++) {            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     for (i=1;i<=npar;i++) x[i]=0;          }
     x[j]=1;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     lubksb(a,npar,indx,x);          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     for (i=1;i<=npar;i++){        }
       matcov[i][j]=x[i];  #endif
     }  
   }  
         free_vector(xit,1,n); 
   printf("\n#Hessian matrix#\n");        free_vector(xits,1,n); 
   for (i=1;i<=npar;i++) {        free_vector(ptt,1,n); 
     for (j=1;j<=npar;j++) {        free_vector(pt,1,n); 
       printf("%.3e ",hess[i][j]);        return; 
     }      } 
     printf("\n");      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   }      for (j=1;j<=n;j++) { 
         ptt[j]=2.0*p[j]-pt[j]; 
   /* Recompute Inverse */        xit[j]=p[j]-pt[j]; 
   for (i=1;i<=npar;i++)        pt[j]=p[j]; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      } 
   ludcmp(a,npar,indx,&pd);      fptt=(*func)(ptt); 
       if (fptt < fp) { 
   /*  printf("\n#Hessian matrix recomputed#\n");        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         if (t < 0.0) { 
   for (j=1;j<=npar;j++) {          linmin(p,xit,n,fret,func); 
     for (i=1;i<=npar;i++) x[i]=0;          for (j=1;j<=n;j++) { 
     x[j]=1;            xi[j][ibig]=xi[j][n]; 
     lubksb(a,npar,indx,x);            xi[j][n]=xit[j]; 
     for (i=1;i<=npar;i++){          }
       y[i][j]=x[i];  #ifdef DEBUG
       printf("%.3e ",y[i][j]);          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     printf("\n");          for(j=1;j<=n;j++){
   }            printf(" %.12e",xit[j]);
   */            fprintf(ficlog," %.12e",xit[j]);
           }
   free_matrix(a,1,npar,1,npar);          printf("\n");
   free_matrix(y,1,npar,1,npar);          fprintf(ficlog,"\n");
   free_vector(x,1,npar);  #endif
   free_ivector(indx,1,npar);        }
   free_matrix(hess,1,npar,1,npar);      } 
     } 
   } 
 }  
   /**** Prevalence limit (stable prevalence)  ****************/
 /*************** hessian matrix ****************/  
 double hessii( double x[], double delta, int theta, double delti[])  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
 {  {
   int i;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   int l=1, lmax=20;       matrix by transitions matrix until convergence is reached */
   double k1,k2;  
   double p2[NPARMAX+1];    int i, ii,j,k;
   double res;    double min, max, maxmin, maxmax,sumnew=0.;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    double **matprod2();
   double fx;    double **out, cov[NCOVMAX], **pmij();
   int k=0,kmax=10;    double **newm;
   double l1;    double agefin, delaymax=50 ; /* Max number of years to converge */
   
   fx=func(x);    for (ii=1;ii<=nlstate+ndeath;ii++)
   for (i=1;i<=npar;i++) p2[i]=x[i];      for (j=1;j<=nlstate+ndeath;j++){
   for(l=0 ; l <=lmax; l++){        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     l1=pow(10,l);      }
     delts=delt;  
     for(k=1 ; k <kmax; k=k+1){     cov[1]=1.;
       delt = delta*(l1*k);   
       p2[theta]=x[theta] +delt;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       k1=func(p2)-fx;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       p2[theta]=x[theta]-delt;      newm=savm;
       k2=func(p2)-fx;      /* Covariates have to be included here again */
       /*res= (k1-2.0*fx+k2)/delt/delt; */       cov[2]=agefin;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    
              for (k=1; k<=cptcovn;k++) {
 #ifdef DEBUG          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);          /*      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]]);*/
 #endif        }
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        for (k=1; k<=cptcovprod;k++)
         k=kmax;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       }  
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         k=kmax; l=lmax*10.;        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
       }        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
         delts=delt;  
       }      savm=oldm;
     }      oldm=newm;
   }      maxmax=0.;
   delti[theta]=delts;      for(j=1;j<=nlstate;j++){
   return res;        min=1.;
          max=0.;
 }        for(i=1; i<=nlstate; i++) {
           sumnew=0;
 double hessij( double x[], double delti[], int thetai,int thetaj)          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
 {          prlim[i][j]= newm[i][j]/(1-sumnew);
   int i;          max=FMAX(max,prlim[i][j]);
   int l=1, l1, lmax=20;          min=FMIN(min,prlim[i][j]);
   double k1,k2,k3,k4,res,fx;        }
   double p2[NPARMAX+1];        maxmin=max-min;
   int k;        maxmax=FMAX(maxmax,maxmin);
       }
   fx=func(x);      if(maxmax < ftolpl){
   for (k=1; k<=2; k++) {        return prlim;
     for (i=1;i<=npar;i++) p2[i]=x[i];      }
     p2[thetai]=x[thetai]+delti[thetai]/k;    }
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  }
     k1=func(p2)-fx;  
    /*************** transition probabilities ***************/ 
     p2[thetai]=x[thetai]+delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
     k2=func(p2)-fx;  {
      double s1, s2;
     p2[thetai]=x[thetai]-delti[thetai]/k;    /*double t34;*/
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    int i,j,j1, nc, ii, jj;
     k3=func(p2)-fx;  
        for(i=1; i<= nlstate; i++){
     p2[thetai]=x[thetai]-delti[thetai]/k;        for(j=1; j<i;j++){
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     k4=func(p2)-fx;            /*s2 += param[i][j][nc]*cov[nc];*/
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 #ifdef DEBUG  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
     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);          }
 #endif          ps[i][j]=s2;
   }  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
   return res;        }
 }        for(j=i+1; j<=nlstate+ndeath;j++){
           for (nc=1, s2=0.;nc <=ncovmodel; nc++){
 /************** Inverse of matrix **************/            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 void ludcmp(double **a, int n, int *indx, double *d)  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
 {          }
   int i,imax,j,k;          ps[i][j]=s2;
   double big,dum,sum,temp;        }
   double *vv;      }
        /*ps[3][2]=1;*/
   vv=vector(1,n);      
   *d=1.0;      for(i=1; i<= nlstate; i++){
   for (i=1;i<=n;i++) {        s1=0;
     big=0.0;        for(j=1; j<i; j++)
     for (j=1;j<=n;j++)          s1+=exp(ps[i][j]);
       if ((temp=fabs(a[i][j])) > big) big=temp;        for(j=i+1; j<=nlstate+ndeath; j++)
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          s1+=exp(ps[i][j]);
     vv[i]=1.0/big;        ps[i][i]=1./(s1+1.);
   }        for(j=1; j<i; j++)
   for (j=1;j<=n;j++) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
     for (i=1;i<j;i++) {        for(j=i+1; j<=nlstate+ndeath; j++)
       sum=a[i][j];          ps[i][j]= exp(ps[i][j])*ps[i][i];
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
       a[i][j]=sum;      } /* end i */
     }      
     big=0.0;      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     for (i=j;i<=n;i++) {        for(jj=1; jj<= nlstate+ndeath; jj++){
       sum=a[i][j];          ps[ii][jj]=0;
       for (k=1;k<j;k++)          ps[ii][ii]=1;
         sum -= a[i][k]*a[k][j];        }
       a[i][j]=sum;      }
       if ( (dum=vv[i]*fabs(sum)) >= big) {      
         big=dum;  
         imax=i;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
       }  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
     }  /*         printf("ddd %lf ",ps[ii][jj]); */
     if (j != imax) {  /*       } */
       for (k=1;k<=n;k++) {  /*       printf("\n "); */
         dum=a[imax][k];  /*        } */
         a[imax][k]=a[j][k];  /*        printf("\n ");printf("%lf ",cov[2]); */
         a[j][k]=dum;         /*
       }        for(i=1; i<= npar; i++) printf("%f ",x[i]);
       *d = -(*d);        goto end;*/
       vv[imax]=vv[j];      return ps;
     }  }
     indx[j]=imax;  
     if (a[j][j] == 0.0) a[j][j]=TINY;  /**************** Product of 2 matrices ******************/
     if (j != n) {  
       dum=1.0/(a[j][j]);  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  {
     }    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   }       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   free_vector(vv,1,n);  /* Doesn't work */    /* in, b, out are matrice of pointers which should have been initialized 
 ;       before: only the contents of out is modified. The function returns
 }       a pointer to pointers identical to out */
     long i, j, k;
 void lubksb(double **a, int n, int *indx, double b[])    for(i=nrl; i<= nrh; i++)
 {      for(k=ncolol; k<=ncoloh; k++)
   int i,ii=0,ip,j;        for(j=ncl,out[i][k]=0.; j<=nch; j++)
   double sum;          out[i][k] +=in[i][j]*b[j][k];
    
   for (i=1;i<=n;i++) {    return out;
     ip=indx[i];  }
     sum=b[ip];  
     b[ip]=b[i];  
     if (ii)  /************* Higher Matrix Product ***************/
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  
     else if (sum) ii=i;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     b[i]=sum;  {
   }    /* Computes the transition matrix starting at age 'age' over 
   for (i=n;i>=1;i--) {       'nhstepm*hstepm*stepm' months (i.e. until
     sum=b[i];       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];       nhstepm*hstepm matrices. 
     b[i]=sum/a[i][i];       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).
        Model is determined by parameters x and covariates have to be 
 /************ Frequencies ********************/       included manually here. 
 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,double **mint,double **anint)  
 {  /* Some frequencies */       */
    
   int i, m, jk, k1, k2,i1, j1, bool, z1,z2,j;    int i, j, d, h, k;
   double ***freq; /* Frequencies */    double **out, cov[NCOVMAX];
   double *pp;    double **newm;
   double pos;  
   FILE *ficresp;    /* Hstepm could be zero and should return the unit matrix */
   char fileresp[FILENAMELENGTH];    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
   pp=vector(1,nlstate);        oldm[i][j]=(i==j ? 1.0 : 0.0);
   probs= ma3x(1,130 ,1,8, 1,8);        po[i][j][0]=(i==j ? 1.0 : 0.0);
   strcpy(fileresp,"p");      }
   strcat(fileresp,fileres);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   if((ficresp=fopen(fileresp,"w"))==NULL) {    for(h=1; h <=nhstepm; h++){
     printf("Problem with prevalence resultfile: %s\n", fileresp);      for(d=1; d <=hstepm; d++){
     exit(0);        newm=savm;
   }        /* Covariates have to be included here again */
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        cov[1]=1.;
   j1=0;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   j=cptcoveff;        for (k=1; k<=cptcovage;k++)
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         for (k=1; k<=cptcovprod;k++)
   for(k1=1; k1<=j;k1++){          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
    for(i1=1; i1<=ncodemax[k1];i1++){  
        j1++;  
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          scanf("%d", i);*/        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         for (i=-1; i<=nlstate+ndeath; i++)          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
          for (jk=-1; jk<=nlstate+ndeath; jk++)                       pmij(pmmij,cov,ncovmodel,x,nlstate));
            for(m=agemin; m <= agemax+3; m++)        savm=oldm;
              freq[i][jk][m]=0;        oldm=newm;
              }
        for (i=1; i<=imx; i++) {      for(i=1; i<=nlstate+ndeath; i++)
          bool=1;        for(j=1;j<=nlstate+ndeath;j++) {
          if  (cptcovn>0) {          po[i][j][h]=newm[i][j];
            for (z1=1; z1<=cptcoveff; z1++)          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])           */
                bool=0;        }
          }    } /* end h */
           if (bool==1) {    return po;
             for(m=fprev1; m<=lprev1; m++){  }
              k2=anint[m][i]+(mint[m][i]/12.);  
              if ((k2>=1984) && (k2<=1988.5)) {  
              if(agev[m][i]==0) agev[m][i]=agemax+1;  /*************** log-likelihood *************/
              if(agev[m][i]==1) agev[m][i]=agemax+2;  double func( double *x)
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  {
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    int i, ii, j, k, mi, d, kk;
              }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
             }    double **out;
           }    double sw; /* Sum of weights */
        }    double lli; /* Individual log likelihood */
         if  (cptcovn>0) {    int s1, s2;
          fprintf(ficresp, "\n#********** Variable ");    double bbh, survp;
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    long ipmx;
        fprintf(ficresp, "**********\n#");    /*extern weight */
         }    /* We are differentiating ll according to initial status */
        for(i=1; i<=nlstate;i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    /*for(i=1;i<imx;i++) 
        fprintf(ficresp, "\n");      printf(" %d\n",s[4][i]);
            */
   for(i=(int)agemin; i <= (int)agemax+3; i++){    cov[1]=1.;
     if(i==(int)agemax+3)  
       printf("Total");    for(k=1; k<=nlstate; k++) ll[k]=0.;
     else  
       printf("Age %d", i);    if(mle==1){
     for(jk=1; jk <=nlstate ; jk++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         pp[jk] += freq[jk][m][i];        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
     for(jk=1; jk <=nlstate ; jk++){            for (j=1;j<=nlstate+ndeath;j++){
       for(m=-1, pos=0; m <=0 ; m++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         pos += freq[jk][m][i];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       if(pp[jk]>=1.e-10)            }
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          for(d=0; d<dh[mi][i]; d++){
       else            newm=savm;
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     }            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      for(jk=1; jk <=nlstate ; jk++){            }
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         pp[jk] += freq[jk][m][i];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
      }            savm=oldm;
             oldm=newm;
     for(jk=1,pos=0; jk <=nlstate ; jk++)          } /* end mult */
       pos += pp[jk];        
     for(jk=1; jk <=nlstate ; jk++){          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       if(pos>=1.e-5)          /* But now since version 0.9 we anticipate for bias at large stepm.
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       else           * (in months) between two waves is not a multiple of stepm, we rounded to 
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);           * the nearest (and in case of equal distance, to the lowest) interval but now
       if( i <= (int) agemax){           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         if(pos>=1.e-5){           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);           * probability in order to take into account the bias as a fraction of the way
           probs[i][jk][j1]= pp[jk]/pos;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/           * -stepm/2 to stepm/2 .
         }           * For stepm=1 the results are the same as for previous versions of Imach.
       else           * For stepm > 1 the results are less biased than in previous versions. 
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);           */
       }          s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
     for(jk=-1; jk <=nlstate+ndeath; jk++)          bbh=(double)bh[mi][i]/(double)stepm; 
       for(m=-1; m <=nlstate+ndeath; m++)          /* bias bh is positive if real duration
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);           * is higher than the multiple of stepm and negative otherwise.
     if(i <= (int) agemax)           */
       fprintf(ficresp,"\n");          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     printf("\n");          if( s2 > nlstate){ 
     }            /* i.e. if s2 is a death state and if the date of death is known then the contribution
     }               to the likelihood is the probability to die between last step unit time and current 
  }               step unit time, which is also equal to probability to die before dh 
                 minus probability to die before dh-stepm . 
   fclose(ficresp);               In version up to 0.92 likelihood was computed
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          as if date of death was unknown. Death was treated as any other
   free_vector(pp,1,nlstate);          health state: the date of the interview describes the actual state
           and not the date of a change in health state. The former idea was
 }  /* End of Freq */          to consider that at each interview the state was recorded
           (healthy, disable or death) and IMaCh was corrected; but when we
 /************ Prevalence ********************/          introduced the exact date of death then we should have modified
 void prevalence(int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax, int fprev1,int lprev1)          the contribution of an exact death to the likelihood. This new
 {  /* Some frequencies */          contribution is smaller and very dependent of the step unit
            stepm. It is no more the probability to die between last interview
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          and month of death but the probability to survive from last
   double ***freq; /* Frequencies */          interview up to one month before death multiplied by the
   double *pp;          probability to die within a month. Thanks to Chris
   double pos;          Jackson for correcting this bug.  Former versions increased
           mortality artificially. The bad side is that we add another loop
   pp=vector(1,nlstate);          which slows down the processing. The difference can be up to 10%
   probs= ma3x(1,130 ,1,8, 1,8);          lower mortality.
              */
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);            lli=log(out[s1][s2] - savm[s1][s2]);
   j1=0;          }else{
              lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   j=cptcoveff;            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          } 
            /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
  for(k1=1; k1<=j;k1++){          /*if(lli ==000.0)*/
     for(i1=1; i1<=ncodemax[k1];i1++){          /*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); */
       j1++;          ipmx +=1;
            sw += weight[i];
       for (i=-1; i<=nlstate+ndeath; i++)            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for (jk=-1; jk<=nlstate+ndeath; jk++)          } /* end of wave */
           for(m=agemin; m <= agemax+3; m++)      } /* end of individual */
           freq[i][jk][m]=0;    }  else if(mle==2){
            for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for (i=1; i<=imx; i++) {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         bool=1;        for(mi=1; mi<= wav[i]-1; mi++){
         if  (cptcovn>0) {          for (ii=1;ii<=nlstate+ndeath;ii++)
           for (z1=1; z1<=cptcoveff; z1++)            for (j=1;j<=nlstate+ndeath;j++){
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               bool=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
               }            }
         if (bool==1) {          for(d=0; d<=dh[mi][i]; d++){
           for(m=fprev1; m<=lprev1; m++){            newm=savm;
             if(agev[m][i]==0) agev[m][i]=agemax+1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             if(agev[m][i]==1) agev[m][i]=agemax+2;            for (kk=1; kk<=cptcovage;kk++) {
             freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];            }
           }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       }            savm=oldm;
        for(i=(int)agemin; i <= (int)agemax+3; i++){            oldm=newm;
         for(jk=1; jk <=nlstate ; jk++){          } /* end mult */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        
             pp[jk] += freq[jk][m][i];          s1=s[mw[mi][i]][i];
         }          s2=s[mw[mi+1][i]][i];
         for(jk=1; jk <=nlstate ; jk++){          bbh=(double)bh[mi][i]/(double)stepm; 
           for(m=-1, pos=0; m <=0 ; m++)          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
             pos += freq[jk][m][i];          ipmx +=1;
         }          sw += weight[i];
                  ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
          for(jk=1; jk <=nlstate ; jk++){        } /* end of wave */
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      } /* end of individual */
              pp[jk] += freq[jk][m][i];    }  else if(mle==3){  /* exponential inter-extrapolation */
          }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
                  for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
          for(jk=1; jk <=nlstate ; jk++){                      for (j=1;j<=nlstate+ndeath;j++){
            if( i <= (int) agemax){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
              if(pos>=1.e-5){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
                probs[i][jk][j1]= pp[jk]/pos;            }
              }          for(d=0; d<dh[mi][i]; d++){
            }            newm=savm;
          }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                      for (kk=1; kk<=cptcovage;kk++) {
          }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
   }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
              savm=oldm;
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);            oldm=newm;
   free_vector(pp,1,nlstate);          } /* end mult */
          
 }  /* End of Freq */          s1=s[mw[mi][i]][i];
 /************* Waves Concatenation ***************/          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
 {          ipmx +=1;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          sw += weight[i];
      Death is a valid wave (if date is known).          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        } /* end of wave */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]      } /* end of individual */
      and mw[mi+1][i]. dh depends on stepm.    }else if (mle==4){  /* ml=4 no inter-extrapolation */
      */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int i, mi, m;        for(mi=1; mi<= wav[i]-1; mi++){
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          for (ii=1;ii<=nlstate+ndeath;ii++)
      double sum=0., jmean=0.;*/            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int j, k=0,jk, ju, jl;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double sum=0.;            }
   jmin=1e+5;          for(d=0; d<dh[mi][i]; d++){
   jmax=-1;            newm=savm;
   jmean=0.;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   for(i=1; i<=imx; i++){            for (kk=1; kk<=cptcovage;kk++) {
     mi=0;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     m=firstpass;            }
     while(s[m][i] <= nlstate){          
       if(s[m][i]>=1)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         mw[++mi][i]=m;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       if(m >=lastpass)            savm=oldm;
         break;            oldm=newm;
       else          } /* end mult */
         m++;        
     }/* end while */          s1=s[mw[mi][i]][i];
     if (s[m][i] > nlstate){          s2=s[mw[mi+1][i]][i];
       mi++;     /* Death is another wave */          if( s2 > nlstate){ 
       /* if(mi==0)  never been interviewed correctly before death */            lli=log(out[s1][s2] - savm[s1][s2]);
          /* Only death is a correct wave */          }else{
       mw[mi][i]=m;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     }          }
           ipmx +=1;
     wav[i]=mi;          sw += weight[i];
     if(mi==0)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   }        } /* end of wave */
       } /* end of individual */
   for(i=1; i<=imx; i++){    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     for(mi=1; mi<wav[i];mi++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       if (stepm <=0)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         dh[mi][i]=1;        for(mi=1; mi<= wav[i]-1; mi++){
       else{          for (ii=1;ii<=nlstate+ndeath;ii++)
         if (s[mw[mi+1][i]][i] > nlstate) {            for (j=1;j<=nlstate+ndeath;j++){
           if (agedc[i] < 2*AGESUP) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           if(j==0) j=1;  /* Survives at least one month after exam */            }
           k=k+1;          for(d=0; d<dh[mi][i]; d++){
           if (j >= jmax) jmax=j;            newm=savm;
           if (j <= jmin) jmin=j;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           sum=sum+j;            for (kk=1; kk<=cptcovage;kk++) {
           /* if (j<10) printf("j=%d num=%d ",j,i); */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }            }
         }          
         else{            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           k=k+1;            savm=oldm;
           if (j >= jmax) jmax=j;            oldm=newm;
           else if (j <= jmin)jmin=j;          } /* end mult */
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */        
           sum=sum+j;          s1=s[mw[mi][i]][i];
         }          s2=s[mw[mi+1][i]][i];
         jk= j/stepm;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         jl= j -jk*stepm;          ipmx +=1;
         ju= j -(jk+1)*stepm;          sw += weight[i];
         if(jl <= -ju)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           dh[mi][i]=jk;          /*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]);*/
         else        } /* end of wave */
           dh[mi][i]=jk+1;      } /* end of individual */
         if(dh[mi][i]==0)    } /* End of if */
           dh[mi][i]=1; /* At least one step */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   }    return -l;
   jmean=sum/k;  }
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);  
  }  /*************** log-likelihood *************/
 /*********** Tricode ****************************/  double funcone( double *x)
 void tricode(int *Tvar, int **nbcode, int imx)  {
 {    /* Same as likeli but slower because of a lot of printf and if */
   int Ndum[20],ij=1, k, j, i;    int i, ii, j, k, mi, d, kk;
   int cptcode=0;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
   cptcoveff=0;    double **out;
      double lli; /* Individual log likelihood */
   for (k=0; k<19; k++) Ndum[k]=0;    double llt;
   for (k=1; k<=7; k++) ncodemax[k]=0;    int s1, s2;
     double bbh, survp;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {    /*extern weight */
     for (i=1; i<=imx; i++) {    /* We are differentiating ll according to initial status */
       ij=(int)(covar[Tvar[j]][i]);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       Ndum[ij]++;    /*for(i=1;i<imx;i++) 
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/      printf(" %d\n",s[4][i]);
       if (ij > cptcode) cptcode=ij;    */
     }    cov[1]=1.;
   
     for (i=0; i<=cptcode; i++) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
       if(Ndum[i]!=0) ncodemax[j]++;  
     }    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     ij=1;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(mi=1; mi<= wav[i]-1; mi++){
         for (ii=1;ii<=nlstate+ndeath;ii++)
     for (i=1; i<=ncodemax[j]; i++) {          for (j=1;j<=nlstate+ndeath;j++){
       for (k=0; k<=19; k++) {            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         if (Ndum[k] != 0) {            savm[ii][j]=(ii==j ? 1.0 : 0.0);
           nbcode[Tvar[j]][ij]=k;          }
           ij++;        for(d=0; d<dh[mi][i]; d++){
         }          newm=savm;
         if (ij > ncodemax[j]) break;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
     }            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   }            }
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  for (k=0; k<19; k++) Ndum[k]=0;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           savm=oldm;
  for (i=1; i<=ncovmodel-2; i++) {          oldm=newm;
       ij=Tvar[i];        } /* end mult */
       Ndum[ij]++;        
     }        s1=s[mw[mi][i]][i];
         s2=s[mw[mi+1][i]][i];
  ij=1;        bbh=(double)bh[mi][i]/(double)stepm; 
  for (i=1; i<=10; i++) {        /* bias is positive if real duration
    if((Ndum[i]!=0) && (i<=ncov)){         * is higher than the multiple of stepm and negative otherwise.
      Tvaraff[ij]=i;         */
      ij++;        if( s2 > nlstate && (mle <5) ){  /* Jackson */
    }          lli=log(out[s1][s2] - savm[s1][s2]);
  }        } else if (mle==1){
            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     cptcoveff=ij-1;        } else if(mle==2){
 }          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 */
 /*********** Health Expectancies ****************/          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 */
         } else if (mle==4){  /* mle=4 no inter-extrapolation */
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          lli=log(out[s1][s2]); /* Original formula */
 {        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   /* Health expectancies */          lli=log(out[s1][s2]); /* Original formula */
   int i, j, nhstepm, hstepm, h;        } /* End of if */
   double age, agelim,hf;        ipmx +=1;
   double ***p3mat;        sw += weight[i];
          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fprintf(ficreseij,"# Health expectancies\n");  /*       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,"# Age");        if(globpr){
   for(i=1; i<=nlstate;i++)          fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
     for(j=1; j<=nlstate;j++)   %10.6f %10.6f %10.6f ", \
       fprintf(ficreseij," %1d-%1d",i,j);                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
   fprintf(ficreseij,"\n");                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   hstepm=1*YEARM; /*  Every j years of age (in month) */            llt +=ll[k]*gipmx/gsw;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           }
   agelim=AGESUP;          fprintf(ficresilk," %10.6f\n", -llt);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        }
     /* nhstepm age range expressed in number of stepm */      } /* end of wave */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);    } /* end of individual */
     /* Typically if 20 years = 20*12/6=40 stepm */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     if (stepm >= YEARM) hstepm=1;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if(globpr==0){ /* First time we count the contributions and weights */
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      gipmx=ipmx;
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      gsw=sw;
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      }
     return -l;
   }
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++)  
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){  /*************** function likelione ***********/
           eij[i][j][(int)age] +=p3mat[i][j][h];  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
         }  {
        /* This routine should help understanding what is done with 
     hf=1;       the selection of individuals/waves and
     if (stepm >= YEARM) hf=stepm/YEARM;       to check the exact contribution to the likelihood.
     fprintf(ficreseij,"%.0f",age );       Plotting could be done.
     for(i=1; i<=nlstate;i++)     */
       for(j=1; j<=nlstate;j++){    int k;
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);  
       }    if(*globpri !=0){ /* Just counts and sums, no printings */
     fprintf(ficreseij,"\n");      strcpy(fileresilk,"ilk"); 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      strcat(fileresilk,fileres);
   }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
 }        printf("Problem with resultfile: %s\n", fileresilk);
         fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
 /************ Variance ******************/      }
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      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");
 {      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   /* Variance of health expectancies */      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      for(k=1; k<=nlstate; k++) 
   double **newm;        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   double **dnewm,**doldm;      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   int i, j, nhstepm, hstepm, h;    }
   int k, cptcode;  
   double *xp;    *fretone=(*funcone)(p);
   double **gp, **gm;    if(*globpri !=0){
   double ***gradg, ***trgradg;      fclose(ficresilk);
   double ***p3mat;      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   double age,agelim;      fflush(fichtm); 
   int theta;    } 
     return;
    fprintf(ficresvij,"# Covariances of life expectancies\n");  }
   fprintf(ficresvij,"# Age");  
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)  /*********** Maximum Likelihood Estimation ***************/
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);  
   fprintf(ficresvij,"\n");  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   {
   xp=vector(1,npar);    int i,j, iter;
   dnewm=matrix(1,nlstate,1,npar);    double **xi;
   doldm=matrix(1,nlstate,1,nlstate);    double fret;
      double fretone; /* Only one call to likelihood */
   hstepm=1*YEARM; /* Every year of age */    /*  char filerespow[FILENAMELENGTH];*/
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    xi=matrix(1,npar,1,npar);
   agelim = AGESUP;    for (i=1;i<=npar;i++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (j=1;j<=npar;j++)
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        xi[i][j]=(i==j ? 1.0 : 0.0);
     if (stepm >= YEARM) hstepm=1;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    strcpy(filerespow,"pow"); 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    strcat(filerespow,fileres);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     gp=matrix(0,nhstepm,1,nlstate);      printf("Problem with resultfile: %s\n", filerespow);
     gm=matrix(0,nhstepm,1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     }
     for(theta=1; theta <=npar; theta++){    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       for(i=1; i<=npar; i++){ /* Computes gradient */    for (i=1;i<=nlstate;i++)
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for(j=1;j<=nlstate+ndeath;j++)
       }        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      fprintf(ficrespow,"\n");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
     powell(p,xi,npar,ftol,&iter,&fret,func);
       if (popbased==1) {  
         for(i=1; i<=nlstate;i++)    fclose(ficrespow);
           prlim[i][i]=probs[(int)age][i][ij];    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
       }    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
          fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){  }
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)  
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];  /**** Computes Hessian and covariance matrix ***/
         }  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       }  {
        double  **a,**y,*x,pd;
       for(i=1; i<=npar; i++) /* Computes gradient */    double **hess;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    int i, j,jk;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      int *indx;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       if (popbased==1) {    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         for(i=1; i<=nlstate;i++)    void lubksb(double **a, int npar, int *indx, double b[]) ;
           prlim[i][i]=probs[(int)age][i][ij];    void ludcmp(double **a, int npar, int *indx, double *d) ;
       }    double gompertz(double p[]);
     hess=matrix(1,npar,1,npar);
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){    printf("\nCalculation of the hessian matrix. Wait...\n");
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    for (i=1;i<=npar;i++){
         }      printf("%d",i);fflush(stdout);
       }      fprintf(ficlog,"%d",i);fflush(ficlog);
      
       for(j=1; j<= nlstate; j++)       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
         for(h=0; h<=nhstepm; h++){      
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      /*  printf(" %f ",p[i]);
         }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     } /* End theta */    }
     
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    for (i=1;i<=npar;i++) {
       for (j=1;j<=npar;j++)  {
     for(h=0; h<=nhstepm; h++)        if (j>i) { 
       for(j=1; j<=nlstate;j++)          printf(".%d%d",i,j);fflush(stdout);
         for(theta=1; theta <=npar; theta++)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
           trgradg[h][j][theta]=gradg[h][theta][j];          hess[i][j]=hessij(p,delti,i,j,func,npar);
           
     for(i=1;i<=nlstate;i++)          hess[j][i]=hess[i][j];    
       for(j=1;j<=nlstate;j++)          /*printf(" %lf ",hess[i][j]);*/
         vareij[i][j][(int)age] =0.;        }
     for(h=0;h<=nhstepm;h++){      }
       for(k=0;k<=nhstepm;k++){    }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    printf("\n");
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    fprintf(ficlog,"\n");
         for(i=1;i<=nlstate;i++)  
           for(j=1;j<=nlstate;j++)    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
             vareij[i][j][(int)age] += doldm[i][j];    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
       }    
     }    a=matrix(1,npar,1,npar);
     h=1;    y=matrix(1,npar,1,npar);
     if (stepm >= YEARM) h=stepm/YEARM;    x=vector(1,npar);
     fprintf(ficresvij,"%.0f ",age );    indx=ivector(1,npar);
     for(i=1; i<=nlstate;i++)    for (i=1;i<=npar;i++)
       for(j=1; j<=nlstate;j++){      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);    ludcmp(a,npar,indx,&pd);
       }  
     fprintf(ficresvij,"\n");    for (j=1;j<=npar;j++) {
     free_matrix(gp,0,nhstepm,1,nlstate);      for (i=1;i<=npar;i++) x[i]=0;
     free_matrix(gm,0,nhstepm,1,nlstate);      x[j]=1;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      lubksb(a,npar,indx,x);
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);      for (i=1;i<=npar;i++){ 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        matcov[i][j]=x[i];
   } /* End age */      }
      }
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    printf("\n#Hessian matrix#\n");
   free_matrix(dnewm,1,nlstate,1,nlstate);    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
 }      for (j=1;j<=npar;j++) { 
         printf("%.3e ",hess[i][j]);
 /************ Variance of prevlim ******************/        fprintf(ficlog,"%.3e ",hess[i][j]);
 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)      }
 {      printf("\n");
   /* Variance of prevalence limit */      fprintf(ficlog,"\n");
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;  
   double **dnewm,**doldm;    /* Recompute Inverse */
   int i, j, nhstepm, hstepm;    for (i=1;i<=npar;i++)
   int k, cptcode;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   double *xp;    ludcmp(a,npar,indx,&pd);
   double *gp, *gm;  
   double **gradg, **trgradg;    /*  printf("\n#Hessian matrix recomputed#\n");
   double age,agelim;  
   int theta;    for (j=1;j<=npar;j++) {
          for (i=1;i<=npar;i++) x[i]=0;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      x[j]=1;
   fprintf(ficresvpl,"# Age");      lubksb(a,npar,indx,x);
   for(i=1; i<=nlstate;i++)      for (i=1;i<=npar;i++){ 
       fprintf(ficresvpl," %1d-%1d",i,i);        y[i][j]=x[i];
   fprintf(ficresvpl,"\n");        printf("%.3e ",y[i][j]);
         fprintf(ficlog,"%.3e ",y[i][j]);
   xp=vector(1,npar);      }
   dnewm=matrix(1,nlstate,1,npar);      printf("\n");
   doldm=matrix(1,nlstate,1,nlstate);      fprintf(ficlog,"\n");
      }
   hstepm=1*YEARM; /* Every year of age */    */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;    free_matrix(a,1,npar,1,npar);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    free_matrix(y,1,npar,1,npar);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    free_vector(x,1,npar);
     if (stepm >= YEARM) hstepm=1;    free_ivector(indx,1,npar);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    free_matrix(hess,1,npar,1,npar);
     gradg=matrix(1,npar,1,nlstate);  
     gp=vector(1,nlstate);  
     gm=vector(1,nlstate);  }
   
     for(theta=1; theta <=npar; theta++){  /*************** hessian matrix ****************/
       for(i=1; i<=npar; i++){ /* Computes gradient */  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  {
       }    int i;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    int l=1, lmax=20;
       for(i=1;i<=nlstate;i++)    double k1,k2;
         gp[i] = prlim[i][i];    double p2[NPARMAX+1];
        double res;
       for(i=1; i<=npar; i++) /* Computes gradient */    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double fx;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    int k=0,kmax=10;
       for(i=1;i<=nlstate;i++)    double l1;
         gm[i] = prlim[i][i];  
     fx=func(x);
       for(i=1;i<=nlstate;i++)    for (i=1;i<=npar;i++) p2[i]=x[i];
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    for(l=0 ; l <=lmax; l++){
     } /* End theta */      l1=pow(10,l);
       delts=delt;
     trgradg =matrix(1,nlstate,1,npar);      for(k=1 ; k <kmax; k=k+1){
         delt = delta*(l1*k);
     for(j=1; j<=nlstate;j++)        p2[theta]=x[theta] +delt;
       for(theta=1; theta <=npar; theta++)        k1=func(p2)-fx;
         trgradg[j][theta]=gradg[theta][j];        p2[theta]=x[theta]-delt;
         k2=func(p2)-fx;
     for(i=1;i<=nlstate;i++)        /*res= (k1-2.0*fx+k2)/delt/delt; */
       varpl[i][(int)age] =0.;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);        
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);  #ifdef DEBUG
     for(i=1;i<=nlstate;i++)        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);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   #endif
     fprintf(ficresvpl,"%.0f ",age );        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     for(i=1; i<=nlstate;i++)        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          k=kmax;
     fprintf(ficresvpl,"\n");        }
     free_vector(gp,1,nlstate);        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     free_vector(gm,1,nlstate);          k=kmax; l=lmax*10.;
     free_matrix(gradg,1,npar,1,nlstate);        }
     free_matrix(trgradg,1,nlstate,1,npar);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   } /* End age */          delts=delt;
         }
   free_vector(xp,1,npar);      }
   free_matrix(doldm,1,nlstate,1,npar);    }
   free_matrix(dnewm,1,nlstate,1,nlstate);    delti[theta]=delts;
     return res; 
 }    
   }
 /************ Variance of one-step probabilities  ******************/  
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
 {  {
   int i, j;    int i;
   int k=0, cptcode;    int l=1, l1, lmax=20;
   double **dnewm,**doldm;    double k1,k2,k3,k4,res,fx;
   double *xp;    double p2[NPARMAX+1];
   double *gp, *gm;    int k;
   double **gradg, **trgradg;  
   double age,agelim, cov[NCOVMAX];    fx=func(x);
   int theta;    for (k=1; k<=2; k++) {
   char fileresprob[FILENAMELENGTH];      for (i=1;i<=npar;i++) p2[i]=x[i];
       p2[thetai]=x[thetai]+delti[thetai]/k;
   strcpy(fileresprob,"prob");      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   strcat(fileresprob,fileres);      k1=func(p2)-fx;
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    
     printf("Problem with resultfile: %s\n", fileresprob);      p2[thetai]=x[thetai]+delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);      k2=func(p2)-fx;
      
       p2[thetai]=x[thetai]-delti[thetai]/k;
   xp=vector(1,npar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      k3=func(p2)-fx;
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    
        p2[thetai]=x[thetai]-delti[thetai]/k;
   cov[1]=1;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   for (age=bage; age<=fage; age ++){      k4=func(p2)-fx;
     cov[2]=age;      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     gradg=matrix(1,npar,1,9);  #ifdef DEBUG
     trgradg=matrix(1,9,1,npar);      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);
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));      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);
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));  #endif
        }
     for(theta=1; theta <=npar; theta++){    return res;
       for(i=1; i<=npar; i++)  }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
        /************** Inverse of matrix **************/
       pmij(pmmij,cov,ncovmodel,xp,nlstate);  void ludcmp(double **a, int n, int *indx, double *d) 
      { 
       k=0;    int i,imax,j,k; 
       for(i=1; i<= (nlstate+ndeath); i++){    double big,dum,sum,temp; 
         for(j=1; j<=(nlstate+ndeath);j++){    double *vv; 
            k=k+1;   
           gp[k]=pmmij[i][j];    vv=vector(1,n); 
         }    *d=1.0; 
       }    for (i=1;i<=n;i++) { 
       big=0.0; 
       for(i=1; i<=npar; i++)      for (j=1;j<=n;j++) 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        if ((temp=fabs(a[i][j])) > big) big=temp; 
          if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       vv[i]=1.0/big; 
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    } 
       k=0;    for (j=1;j<=n;j++) { 
       for(i=1; i<=(nlstate+ndeath); i++){      for (i=1;i<j;i++) { 
         for(j=1; j<=(nlstate+ndeath);j++){        sum=a[i][j]; 
           k=k+1;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
           gm[k]=pmmij[i][j];        a[i][j]=sum; 
         }      } 
       }      big=0.0; 
            for (i=j;i<=n;i++) { 
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)        sum=a[i][j]; 
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];          for (k=1;k<j;k++) 
     }          sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)        if ( (dum=vv[i]*fabs(sum)) >= big) { 
       for(theta=1; theta <=npar; theta++)          big=dum; 
       trgradg[j][theta]=gradg[theta][j];          imax=i; 
          } 
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);      } 
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);      if (j != imax) { 
         for (k=1;k<=n;k++) { 
      pmij(pmmij,cov,ncovmodel,x,nlstate);          dum=a[imax][k]; 
           a[imax][k]=a[j][k]; 
      k=0;          a[j][k]=dum; 
      for(i=1; i<=(nlstate+ndeath); i++){        } 
        for(j=1; j<=(nlstate+ndeath);j++){        *d = -(*d); 
          k=k+1;        vv[imax]=vv[j]; 
          gm[k]=pmmij[i][j];      } 
         }      indx[j]=imax; 
      }      if (a[j][j] == 0.0) a[j][j]=TINY; 
            if (j != n) { 
      /*printf("\n%d ",(int)age);        dum=1.0/(a[j][j]); 
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
              } 
     } 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    free_vector(vv,1,n);  /* Doesn't work */
      }*/  ;
   } 
   fprintf(ficresprob,"\n%d ",(int)age);  
   void lubksb(double **a, int n, int *indx, double b[]) 
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){  { 
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);    int i,ii=0,ip,j; 
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);    double sum; 
   }   
     for (i=1;i<=n;i++) { 
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));      ip=indx[i]; 
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));      sum=b[ip]; 
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      b[ip]=b[i]; 
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      if (ii) 
 }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
  free_vector(xp,1,npar);      else if (sum) ii=i; 
 fclose(ficresprob);      b[i]=sum; 
  exit(0);    } 
 }    for (i=n;i>=1;i--) { 
       sum=b[i]; 
 /***********************************************/      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
 /**************** Main Program *****************/      b[i]=sum/a[i][i]; 
 /***********************************************/    } 
   } 
 /*int main(int argc, char *argv[])*/  
 int main()  /************ Frequencies ********************/
 {  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint)
   {  /* Some frequencies */
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    
   double agedeb, agefin,hf;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   double agemin=1.e20, agemax=-1.e20;    int first;
     double ***freq; /* Frequencies */
   double fret;    double *pp, **prop;
   double **xi,tmp,delta;    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     FILE *ficresp;
   double dum; /* Dummy variable */    char fileresp[FILENAMELENGTH];
   double ***p3mat;    
   int *indx;    pp=vector(1,nlstate);
   char line[MAXLINE], linepar[MAXLINE];    prop=matrix(1,nlstate,iagemin,iagemax+3);
   char title[MAXLINE];    strcpy(fileresp,"p");
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    strcat(fileresp,fileres);
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];    if((ficresp=fopen(fileresp,"w"))==NULL) {
   char filerest[FILENAMELENGTH];      printf("Problem with prevalence resultfile: %s\n", fileresp);
   char fileregp[FILENAMELENGTH];      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   char popfile[FILENAMELENGTH];      exit(0);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    }
   int firstobs=1, lastobs=10;    freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);
   int sdeb, sfin; /* Status at beginning and end */    j1=0;
   int c,  h , cpt,l;    
   int ju,jl, mi;    j=cptcoveff;
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;  
   int mobilav=0, fprev, lprev ,fprevfore=1, lprevfore=1,nforecast,popforecast=0;    first=1;
   int hstepm, nhstepm;  
   int *popage;    for(k1=1; k1<=j;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
   double bage, fage, age, agelim, agebase;        j1++;
   double ftolpl=FTOL;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   double **prlim;          scanf("%d", i);*/
   double *severity;        for (i=-1; i<=nlstate+ndeath; i++)  
   double ***param; /* Matrix of parameters */          for (jk=-1; jk<=nlstate+ndeath; jk++)  
   double  *p;            for(m=iagemin; m <= iagemax+3; m++)
   double **matcov; /* Matrix of covariance */              freq[i][jk][m]=0;
   double ***delti3; /* Scale */  
   double *delti; /* Scale */      for (i=1; i<=nlstate; i++)  
   double ***eij, ***vareij;        for(m=iagemin; m <= iagemax+3; m++)
   double **varpl; /* Variances of prevalence limits by age */          prop[i][m]=0;
   double *epj, vepp;        
   double kk1, kk2;        dateintsum=0;
   double *popeffectif,*popcount;        k2cpt=0;
         for (i=1; i<=imx; i++) {
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";          bool=1;
   char *alph[]={"a","a","b","c","d","e"}, str[4];          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   char z[1]="c", occ;                bool=0;
 #include <sys/time.h>          }
 #include <time.h>          if (bool==1){
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];            for(m=firstpass; m<=lastpass; m++){
   /* long total_usecs;              k2=anint[m][i]+(mint[m][i]/12.);
   struct timeval start_time, end_time;              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                  if(agev[m][i]==0) agev[m][i]=iagemax+1;
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                 if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                 if (m<lastpass) {
   printf("\nIMACH, Version 0.7");                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   printf("\nEnter the parameter file name: ");                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                 }
 #ifdef windows                
   scanf("%s",pathtot);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
   getcwd(pathcd, size);                  dateintsum=dateintsum+k2;
   /*cygwin_split_path(pathtot,path,optionfile);                  k2cpt++;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/                }
   /* cutv(path,optionfile,pathtot,'\\');*/                /*}*/
             }
 split(pathtot, path,optionfile);          }
   chdir(path);        }
   replace(pathc,path);         
 #endif        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
 #ifdef unix  
   scanf("%s",optionfile);        if  (cptcovn>0) {
 #endif          fprintf(ficresp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 /*-------- arguments in the command line --------*/          fprintf(ficresp, "**********\n#");
         }
   strcpy(fileres,"r");        for(i=1; i<=nlstate;i++) 
   strcat(fileres, optionfile);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
   /*---------arguments file --------*/        
         for(i=iagemin; i <= iagemax+3; i++){
   if((ficpar=fopen(optionfile,"r"))==NULL)    {          if(i==iagemax+3){
     printf("Problem with optionfile %s\n",optionfile);            fprintf(ficlog,"Total");
     goto end;          }else{
   }            if(first==1){
               first=0;
   strcpy(filereso,"o");              printf("See log file for details...\n");
   strcat(filereso,fileres);            }
   if((ficparo=fopen(filereso,"w"))==NULL) {            fprintf(ficlog,"Age %d", i);
     printf("Problem with Output resultfile: %s\n", filereso);goto end;          }
   }          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   /* Reads comments: lines beginning with '#' */              pp[jk] += freq[jk][m][i]; 
   while((c=getc(ficpar))=='#' && c!= EOF){          }
     ungetc(c,ficpar);          for(jk=1; jk <=nlstate ; jk++){
     fgets(line, MAXLINE, ficpar);            for(m=-1, pos=0; m <=0 ; m++)
     puts(line);              pos += freq[jk][m][i];
     fputs(line,ficparo);            if(pp[jk]>=1.e-10){
   }              if(first==1){
   ungetc(c,ficpar);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               }
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   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);            }else{
   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);              if(first==1)
 while((c=getc(ficpar))=='#' && c!= EOF){                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     ungetc(c,ficpar);              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     fgets(line, MAXLINE, ficpar);            }
     puts(line);          }
     fputs(line,ficparo);  
   }          for(jk=1; jk <=nlstate ; jk++){
   ungetc(c,ficpar);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
                pp[jk] += freq[jk][m][i];
   fscanf(ficpar,"fprevalence=%d lprevalence=%d pop_based=%d\n",&fprev,&lprev,&popbased);          }       
   fprintf(ficparo,"fprevalence=%d lprevalence=%d pop_based=%d\n",fprev,lprev,popbased);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
              pos += pp[jk];
  while((c=getc(ficpar))=='#' && c!= EOF){            posprop += prop[jk][i];
     ungetc(c,ficpar);          }
     fgets(line, MAXLINE, ficpar);          for(jk=1; jk <=nlstate ; jk++){
     puts(line);            if(pos>=1.e-5){
     fputs(line,ficparo);              if(first==1)
   }                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   ungetc(c,ficpar);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
              }else{
   fscanf(ficpar,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",&fprevfore,&lprevfore,&nforecast,&mobilav);              if(first==1)
   fprintf(ficparo,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",fprevfore,lprevfore,nforecast,mobilav);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
                    fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
              }
 while((c=getc(ficpar))=='#' && c!= EOF){            if( i <= iagemax){
     ungetc(c,ficpar);              if(pos>=1.e-5){
     fgets(line, MAXLINE, ficpar);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     puts(line);                /*probs[i][jk][j1]= pp[jk]/pos;*/
     fputs(line,ficparo);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   }              }
   ungetc(c,ficpar);              else
                  fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   fscanf(ficpar,"popforecast=%d popfile=%s\n",&popforecast,popfile);            }
            }
   covar=matrix(0,NCOVMAX,1,n);          
   cptcovn=0;          for(jk=-1; jk <=nlstate+ndeath; jk++)
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;            for(m=-1; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
   ncovmodel=2+cptcovn;              if(first==1)
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                  fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   /* Read guess parameters */              }
   /* Reads comments: lines beginning with '#' */          if(i <= iagemax)
   while((c=getc(ficpar))=='#' && c!= EOF){            fprintf(ficresp,"\n");
     ungetc(c,ficpar);          if(first==1)
     fgets(line, MAXLINE, ficpar);            printf("Others in log...\n");
     puts(line);          fprintf(ficlog,"\n");
     fputs(line,ficparo);        }
   }      }
   ungetc(c,ficpar);    }
      dateintmean=dateintsum/k2cpt; 
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);   
     for(i=1; i <=nlstate; i++)    fclose(ficresp);
     for(j=1; j <=nlstate+ndeath-1; j++){    free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    free_vector(pp,1,nlstate);
       fprintf(ficparo,"%1d%1d",i1,j1);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
       printf("%1d%1d",i,j);    /* End of Freq */
       for(k=1; k<=ncovmodel;k++){  }
         fscanf(ficpar," %lf",&param[i][j][k]);  
         printf(" %lf",param[i][j][k]);  /************ Prevalence ********************/
         fprintf(ficparo," %lf",param[i][j][k]);  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)
       }  {  
       fscanf(ficpar,"\n");    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
       printf("\n");       in each health status at the date of interview (if between dateprev1 and dateprev2).
       fprintf(ficparo,"\n");       We still use firstpass and lastpass as another selection.
     }    */
     
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     double ***freq; /* Frequencies */
   p=param[1][1];    double *pp, **prop;
      double pos,posprop; 
   /* Reads comments: lines beginning with '#' */    double  y2; /* in fractional years */
   while((c=getc(ficpar))=='#' && c!= EOF){    int iagemin, iagemax;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    iagemin= (int) agemin;
     puts(line);    iagemax= (int) agemax;
     fputs(line,ficparo);    /*pp=vector(1,nlstate);*/
   }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
   ungetc(c,ficpar);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     j1=0;
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    j=cptcoveff;
   for(i=1; i <=nlstate; i++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     for(j=1; j <=nlstate+ndeath-1; j++){    
       fscanf(ficpar,"%1d%1d",&i1,&j1);    for(k1=1; k1<=j;k1++){
       printf("%1d%1d",i,j);      for(i1=1; i1<=ncodemax[k1];i1++){
       fprintf(ficparo,"%1d%1d",i1,j1);        j1++;
       for(k=1; k<=ncovmodel;k++){        
         fscanf(ficpar,"%le",&delti3[i][j][k]);        for (i=1; i<=nlstate; i++)  
         printf(" %le",delti3[i][j][k]);          for(m=iagemin; m <= iagemax+3; m++)
         fprintf(ficparo," %le",delti3[i][j][k]);            prop[i][m]=0.0;
       }       
       fscanf(ficpar,"\n");        for (i=1; i<=imx; i++) { /* Each individual */
       printf("\n");          bool=1;
       fprintf(ficparo,"\n");          if  (cptcovn>0) {
     }            for (z1=1; z1<=cptcoveff; z1++) 
   }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   delti=delti3[1][1];                bool=0;
            } 
   /* Reads comments: lines beginning with '#' */          if (bool==1) { 
   while((c=getc(ficpar))=='#' && c!= EOF){            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     ungetc(c,ficpar);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     fgets(line, MAXLINE, ficpar);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     puts(line);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     fputs(line,ficparo);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   }                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); 
   ungetc(c,ficpar);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                    /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
   matcov=matrix(1,npar,1,npar);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   for(i=1; i <=npar; i++){                  prop[s[m][i]][iagemax+3] += weight[i]; 
     fscanf(ficpar,"%s",&str);                } 
     printf("%s",str);              }
     fprintf(ficparo,"%s",str);            } /* end selection of waves */
     for(j=1; j <=i; j++){          }
       fscanf(ficpar," %le",&matcov[i][j]);        }
       printf(" %.5le",matcov[i][j]);        for(i=iagemin; i <= iagemax+3; i++){  
       fprintf(ficparo," %.5le",matcov[i][j]);          
     }          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
     fscanf(ficpar,"\n");            posprop += prop[jk][i]; 
     printf("\n");          } 
     fprintf(ficparo,"\n");  
   }          for(jk=1; jk <=nlstate ; jk++){     
   for(i=1; i <=npar; i++)            if( i <=  iagemax){ 
     for(j=i+1;j<=npar;j++)              if(posprop>=1.e-5){ 
       matcov[i][j]=matcov[j][i];                probs[i][jk][j1]= prop[jk][i]/posprop;
                  } 
   printf("\n");            } 
           }/* end jk */ 
         }/* end i */ 
     /*-------- data file ----------*/      } /* end i1 */
     if((ficres =fopen(fileres,"w"))==NULL) {    } /* end k1 */
       printf("Problem with resultfile: %s\n", fileres);goto end;    
     }    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     fprintf(ficres,"#%s\n",version);    /*free_vector(pp,1,nlstate);*/
        free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     if((fic=fopen(datafile,"r"))==NULL)    {  }  /* End of prevalence */
       printf("Problem with datafile: %s\n", datafile);goto end;  
     }  /************* Waves Concatenation ***************/
   
     n= lastobs;  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)
     severity = vector(1,maxwav);  {
     outcome=imatrix(1,maxwav+1,1,n);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
     num=ivector(1,n);       Death is a valid wave (if date is known).
     moisnais=vector(1,n);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     annais=vector(1,n);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     moisdc=vector(1,n);       and mw[mi+1][i]. dh depends on stepm.
     andc=vector(1,n);       */
     agedc=vector(1,n);  
     cod=ivector(1,n);    int i, mi, m;
     weight=vector(1,n);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */       double sum=0., jmean=0.;*/
     mint=matrix(1,maxwav,1,n);    int first;
     anint=matrix(1,maxwav,1,n);    int j, k=0,jk, ju, jl;
     s=imatrix(1,maxwav+1,1,n);    double sum=0.;
     adl=imatrix(1,maxwav+1,1,n);        first=0;
     tab=ivector(1,NCOVMAX);    jmin=1e+5;
     ncodemax=ivector(1,8);    jmax=-1;
     jmean=0.;
     i=1;    for(i=1; i<=imx; i++){
     while (fgets(line, MAXLINE, fic) != NULL)    {      mi=0;
       if ((i >= firstobs) && (i <=lastobs)) {      m=firstpass;
              while(s[m][i] <= nlstate){
         for (j=maxwav;j>=1;j--){        if(s[m][i]>=1)
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          mw[++mi][i]=m;
           strcpy(line,stra);        if(m >=lastpass)
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          break;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        else
         }          m++;
              }/* end while */
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);      if (s[m][i] > nlstate){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        mi++;     /* Death is another wave */
         /* if(mi==0)  never been interviewed correctly before death */
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);           /* Only death is a correct wave */
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        mw[mi][i]=m;
       }
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);  
         for (j=ncov;j>=1;j--){      wav[i]=mi;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      if(mi==0){
         }        nbwarn++;
         num[i]=atol(stra);        if(first==0){
                  printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){          first=1;
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/        }
         if(first==1){
         i=i+1;          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
       }        }
     }      } /* end mi==0 */
     /* printf("ii=%d", ij);    } /* End individuals */
        scanf("%d",i);*/  
   imx=i-1; /* Number of individuals */    for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
   /* for (i=1; i<=imx; i++){        if (stepm <=0)
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;          dh[mi][i]=1;
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;        else{
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     }            if (agedc[i] < 2*AGESUP) {
     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]));*/              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
               if(j==0) j=1;  /* Survives at least one month after exam */
   /* Calculation of the number of parameter from char model*/              else if(j<0){
   Tvar=ivector(1,15);                nberr++;
   Tprod=ivector(1,15);                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]);
   Tvaraff=ivector(1,15);                j=1; /* Temporary Dangerous patch */
   Tvard=imatrix(1,15,1,2);                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
   Tage=ivector(1,15);                      fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                    fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview.\n  You MUST fix the contradiction between dates.\n",stepm);
   if (strlen(model) >1){              }
     j=0, j1=0, k1=1, k2=1;              k=k+1;
     j=nbocc(model,'+');              if (j >= jmax) jmax=j;
     j1=nbocc(model,'*');              if (j <= jmin) jmin=j;
     cptcovn=j+1;              sum=sum+j;
     cptcovprod=j1;              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
                  /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
                }
     strcpy(modelsav,model);          }
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          else{
       printf("Error. Non available option model=%s ",model);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       goto end;            /*      printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     }            k=k+1;
                if (j >= jmax) jmax=j;
     for(i=(j+1); i>=1;i--){            else if (j <= jmin)jmin=j;
       cutv(stra,strb,modelsav,'+');            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);            /*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]);*/
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/            if(j<0){
       /*scanf("%d",i);*/              nberr++;
       if (strchr(strb,'*')) {              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]);
         cutv(strd,strc,strb,'*');              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]);
         if (strcmp(strc,"age")==0) {            }
           cptcovprod--;            sum=sum+j;
           cutv(strb,stre,strd,'V');          }
           Tvar[i]=atoi(stre);          jk= j/stepm;
           cptcovage++;          jl= j -jk*stepm;
             Tage[cptcovage]=i;          ju= j -(jk+1)*stepm;
             /*printf("stre=%s ", stre);*/          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
         }            if(jl==0){
         else if (strcmp(strd,"age")==0) {              dh[mi][i]=jk;
           cptcovprod--;              bh[mi][i]=0;
           cutv(strb,stre,strc,'V');            }else{ /* We want a negative bias in order to only have interpolation ie
           Tvar[i]=atoi(stre);                    * at the price of an extra matrix product in likelihood */
           cptcovage++;              dh[mi][i]=jk+1;
           Tage[cptcovage]=i;              bh[mi][i]=ju;
         }            }
         else {          }else{
           cutv(strb,stre,strc,'V');            if(jl <= -ju){
           Tvar[i]=ncov+k1;              dh[mi][i]=jk;
           cutv(strb,strc,strd,'V');              bh[mi][i]=jl;       /* bias is positive if real duration
           Tprod[k1]=i;                                   * is higher than the multiple of stepm and negative otherwise.
           Tvard[k1][1]=atoi(strc);                                   */
           Tvard[k1][2]=atoi(stre);            }
           Tvar[cptcovn+k2]=Tvard[k1][1];            else{
           Tvar[cptcovn+k2+1]=Tvard[k1][2];              dh[mi][i]=jk+1;
           for (k=1; k<=lastobs;k++)              bh[mi][i]=ju;
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];            }
           k1++;            if(dh[mi][i]==0){
           k2=k2+2;              dh[mi][i]=1; /* At least one step */
         }              bh[mi][i]=ju; /* At least one step */
       }              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
       else {            }
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          } /* end if mle */
        /*  scanf("%d",i);*/        }
       cutv(strd,strc,strb,'V');      } /* end wave */
       Tvar[i]=atoi(strc);    }
       }    jmean=sum/k;
       strcpy(modelsav,stra);      printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
         scanf("%d",i);*/   }
     }  
 }  /*********** Tricode ****************************/
    void tricode(int *Tvar, int **nbcode, int imx)
   /*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);*/    int Ndum[20],ij=1, k, j, i, maxncov=19;
     fclose(fic);    int cptcode=0;
     cptcoveff=0; 
     /*  if(mle==1){*/   
     if (weightopt != 1) { /* Maximisation without weights*/    for (k=0; k<maxncov; k++) Ndum[k]=0;
       for(i=1;i<=n;i++) weight[i]=1.0;    for (k=1; k<=7; k++) ncodemax[k]=0;
     }  
     /*-calculation of age at interview from date of interview and age at death -*/    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
     agev=matrix(1,maxwav,1,imx);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
                                  modality*/ 
    for (i=1; i<=imx; i++)        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
      for(m=2; (m<= maxwav); m++)        Ndum[ij]++; /*store the modality */
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
          anint[m][i]=9999;        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
          s[m][i]=-1;                                         Tvar[j]. If V=sex and male is 0 and 
        }                                         female is 1, then  cptcode=1.*/
          }
     for (i=1; i<=imx; i++)  {  
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);      for (i=0; i<=cptcode; i++) {
       for(m=1; (m<= maxwav); m++){        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
         if(s[m][i] >0){      }
           if (s[m][i] == nlstate+1) {  
             if(agedc[i]>0)      ij=1; 
               if(moisdc[i]!=99 && andc[i]!=9999)      for (i=1; i<=ncodemax[j]; i++) {
               agev[m][i]=agedc[i];        for (k=0; k<= maxncov; k++) {
             else {          if (Ndum[k] != 0) {
               if (andc[i]!=9999){            nbcode[Tvar[j]][ij]=k; 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            /* 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; */
               agev[m][i]=-1;            
               }            ij++;
             }          }
           }          if (ij > ncodemax[j]) break; 
           else if(s[m][i] !=9){ /* Should no more exist */        }  
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);      } 
             if(mint[m][i]==99 || anint[m][i]==9999)    }  
               agev[m][i]=1;  
             else if(agev[m][i] <agemin){   for (k=0; k< maxncov; k++) Ndum[k]=0;
               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);*/   for (i=1; i<=ncovmodel-2; i++) { 
             }     /* Listing of all covariables in staement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
             else if(agev[m][i] >agemax){     ij=Tvar[i];
               agemax=agev[m][i];     Ndum[ij]++;
              /* 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];*/   ij=1;
             /*   agev[m][i] = age[i]+2*m;*/   for (i=1; i<= maxncov; i++) {
           }     if((Ndum[i]!=0) && (i<=ncovcol)){
           else { /* =9 */       Tvaraff[ij]=i; /*For printing */
             agev[m][i]=1;       ij++;
             s[m][i]=-1;     }
           }   }
         }   
         else /*= 0 Unknown */   cptcoveff=ij-1; /*Number of simple covariates*/
           agev[m][i]=1;  }
       }  
      /*********** Health Expectancies ****************/
     }  
     for (i=1; i<=imx; 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 )
       for(m=1; (m<= maxwav); m++){  
         if (s[m][i] > (nlstate+ndeath)) {  {
           printf("Error: Wrong value in nlstate or ndeath\n");      /* Health expectancies */
           goto end;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
         }    double age, agelim, hf;
       }    double ***p3mat,***varhe;
     }    double **dnewm,**doldm;
     double *xp;
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    double **gp, **gm;
     double ***gradg, ***trgradg;
     free_vector(severity,1,maxwav);    int theta;
     free_imatrix(outcome,1,maxwav+1,1,n);  
     free_vector(moisnais,1,n);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     free_vector(annais,1,n);    xp=vector(1,npar);
     /* free_matrix(mint,1,maxwav,1,n);    dnewm=matrix(1,nlstate*nlstate,1,npar);
        free_matrix(anint,1,maxwav,1,n);*/    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     free_vector(moisdc,1,n);    
     free_vector(andc,1,n);    fprintf(ficreseij,"# Health expectancies\n");
     fprintf(ficreseij,"# Age");
        for(i=1; i<=nlstate;i++)
     wav=ivector(1,imx);      for(j=1; j<=nlstate;j++)
     dh=imatrix(1,lastpass-firstpass+1,1,imx);        fprintf(ficreseij," %1d-%1d (SE)",i,j);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    fprintf(ficreseij,"\n");
      
     /* Concatenates waves */    if(estepm < stepm){
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
       Tcode=ivector(1,100);    /* We compute the life expectancy from trapezoids spaced every estepm months
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);     * This is mainly to measure the difference between two models: for example
       ncodemax[1]=1;     * if stepm=24 months pijx are given only every 2 years and by summing them
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);     * we are calculating an estimate of the Life Expectancy assuming a linear 
           * progression in between and thus overestimating or underestimating according
    codtab=imatrix(1,100,1,10);     * to the curvature of the survival function. If, for the same date, we 
    h=0;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
    m=pow(2,cptcoveff);     * to compare the new estimate of Life expectancy with the same linear 
       * hypothesis. A more precise result, taking into account a more precise
    for(k=1;k<=cptcoveff; k++){     * curvature will be obtained if estepm is as small as stepm. */
      for(i=1; i <=(m/pow(2,k));i++){  
        for(j=1; j <= ncodemax[k]; j++){    /* For example we decided to compute the life expectancy with the smallest unit */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
            h++;       nhstepm is the number of hstepm from age to agelim 
            if (h>m) h=1;codtab[h][k]=j;       nstepm is the number of stepm from age to agelin. 
          }       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
    }       survival function given by stepm (the optimization length). Unfortunately it
           means that if the survival funtion is printed only each two years of age and if
    /* Calculates basic frequencies. Computes observed prevalence at single age       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        and prints on file fileres'p'. */       results. So we changed our mind and took the option of the best precision.
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprev, lprev,mint,anint);    */
      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   free_matrix(mint,1,maxwav,1,n);  
   free_matrix(anint,1,maxwav,1,n);    agelim=AGESUP;
      for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* nhstepm age range expressed in number of stepm */
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* if (stepm >= YEARM) hstepm=1;*/
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     /* For Powell, parameters are in a vector p[] starting at p[1]      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */      gp=matrix(0,nhstepm,1,nlstate*nlstate);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */      gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
     if(mle==1){      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
     }      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
       
     /*--------- results files --------------*/  
     fprintf(ficres,"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);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
    fprintf(ficres,"fprevalence=%d lprevalence=%d pop_based=%d\n",fprev,lprev,popbased);  
    fprintf(ficres,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",fprevfore,lprevfore,nforecast,mobilav);      /* Computing  Variances of health expectancies */
   
    jk=1;       for(theta=1; theta <=npar; theta++){
    fprintf(ficres,"# Parameters\n");        for(i=1; i<=npar; i++){ 
    printf("# Parameters\n");          xp[i] = x[i] + (i==theta ?delti[theta]:0);
    for(i=1,jk=1; i <=nlstate; i++){        }
      for(k=1; k <=(nlstate+ndeath); k++){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
        if (k != i)    
          {        cptj=0;
            printf("%d%d ",i,k);        for(j=1; j<= nlstate; j++){
            fprintf(ficres,"%1d%1d ",i,k);          for(i=1; i<=nlstate; i++){
            for(j=1; j <=ncovmodel; j++){            cptj=cptj+1;
              printf("%f ",p[jk]);            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
              fprintf(ficres,"%f ",p[jk]);              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
              jk++;            }
            }          }
            printf("\n");        }
            fprintf(ficres,"\n");       
          }       
      }        for(i=1; i<=npar; i++) 
    }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
  if(mle==1){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     /* Computing hessian and covariance matrix */        
     ftolhess=ftol; /* Usually correct */        cptj=0;
     hesscov(matcov, p, npar, delti, ftolhess, func);        for(j=1; j<= nlstate; j++){
  }          for(i=1;i<=nlstate;i++){
     fprintf(ficres,"# Scales\n");            cptj=cptj+1;
     printf("# Scales\n");            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
      for(i=1,jk=1; i <=nlstate; i++){  
       for(j=1; j <=nlstate+ndeath; j++){              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
         if (j!=i) {            }
           fprintf(ficres,"%1d%1d",i,j);          }
           printf("%1d%1d",i,j);        }
           for(k=1; k<=ncovmodel;k++){        for(j=1; j<= nlstate*nlstate; j++)
             printf(" %.5e",delti[jk]);          for(h=0; h<=nhstepm-1; h++){
             fprintf(ficres," %.5e",delti[jk]);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
             jk++;          }
           }       } 
           printf("\n");     
           fprintf(ficres,"\n");  /* End theta */
         }  
       }       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
       }  
           for(h=0; h<=nhstepm-1; h++)
     k=1;        for(j=1; j<=nlstate*nlstate;j++)
     fprintf(ficres,"# Covariance\n");          for(theta=1; theta <=npar; theta++)
     printf("# Covariance\n");            trgradg[h][j][theta]=gradg[h][theta][j];
     for(i=1;i<=npar;i++){       
       /*  if (k>nlstate) k=1;  
       i1=(i-1)/(ncovmodel*nlstate)+1;       for(i=1;i<=nlstate*nlstate;i++)
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        for(j=1;j<=nlstate*nlstate;j++)
       printf("%s%d%d",alph[k],i1,tab[i]);*/          varhe[i][j][(int)age] =0.;
       fprintf(ficres,"%3d",i);  
       printf("%3d",i);       printf("%d|",(int)age);fflush(stdout);
       for(j=1; j<=i;j++){       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         fprintf(ficres," %.5e",matcov[i][j]);       for(h=0;h<=nhstepm-1;h++){
         printf(" %.5e",matcov[i][j]);        for(k=0;k<=nhstepm-1;k++){
       }          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
       fprintf(ficres,"\n");          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       printf("\n");          for(i=1;i<=nlstate*nlstate;i++)
       k++;            for(j=1;j<=nlstate*nlstate;j++)
     }              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
            }
     while((c=getc(ficpar))=='#' && c!= EOF){      }
       ungetc(c,ficpar);      /* Computing expectancies */
       fgets(line, MAXLINE, ficpar);      for(i=1; i<=nlstate;i++)
       puts(line);        for(j=1; j<=nlstate;j++)
       fputs(line,ficparo);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     }            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     ungetc(c,ficpar);            
    /* 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]);*/
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);  
              }
     if (fage <= 2) {  
       bage = agemin;      fprintf(ficreseij,"%3.0f",age );
       fage = agemax;      cptj=0;
     }      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");          cptj++;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
         }
          fprintf(ficreseij,"\n");
 /*------------ gnuplot -------------*/     
 chdir(pathcd);      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   if((ficgp=fopen("graph.plt","w"))==NULL) {      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     printf("Problem with file graph.gp");goto end;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   }      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
 #ifdef windows      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficgp,"cd \"%s\" \n",pathc);    }
 #endif    printf("\n");
 m=pow(2,cptcoveff);    fprintf(ficlog,"\n");
    
  /* 1eme*/    free_vector(xp,1,npar);
   for (cpt=1; cpt<= nlstate ; cpt ++) {    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
    for (k1=1; k1<= m ; k1 ++) {    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
 #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);  
 #endif  /************ Variance ******************/
 #ifdef unix  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav)
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);  {
 #endif    /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
 for (i=1; i<= nlstate ; i ++) {    /* double **newm;*/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double **dnewm,**doldm;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double **dnewmp,**doldmp;
 }    int i, j, nhstepm, hstepm, h, nstepm ;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    int k, cptcode;
     for (i=1; i<= nlstate ; i ++) {    double *xp;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double **gp, **gm;  /* for var eij */
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double ***gradg, ***trgradg; /*for var eij */
 }    double **gradgp, **trgradgp; /* for var p point j */
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    double *gpp, *gmp; /* for var p point j */
      for (i=1; i<= nlstate ; i ++) {    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double ***p3mat;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double age,agelim, hf;
 }      double ***mobaverage;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    int theta;
 #ifdef unix    char digit[4];
 fprintf(ficgp,"\nset ter gif small size 400,300");    char digitp[25];
 #endif  
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    char fileresprobmorprev[FILENAMELENGTH];
    }  
   }    if(popbased==1){
   /*2 eme*/      if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
   for (k1=1; k1<= m ; k1 ++) {      else strcpy(digitp,"-populbased-nomobil-");
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    }
        else 
     for (i=1; i<= nlstate+1 ; i ++) {      strcpy(digitp,"-stablbased-");
       k=2*i;  
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    if (mobilav!=0) {
       for (j=1; j<= nlstate+1 ; j ++) {      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   else fprintf(ficgp," \%%*lf (\%%*lf)");        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
 }          printf(" Error in movingaverage mobilav=%d\n",mobilav);
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");      }
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    }
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {    strcpy(fileresprobmorprev,"prmorprev"); 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    sprintf(digit,"%-d",ij);
         else fprintf(ficgp," \%%*lf (\%%*lf)");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
 }      strcat(fileresprobmorprev,digit); /* Tvar to be done */
       fprintf(ficgp,"\" t\"\" w l 0,");    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    strcat(fileresprobmorprev,fileres);
       for (j=1; j<= nlstate+1 ; j ++) {    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      printf("Problem with resultfile: %s\n", fileresprobmorprev);
   else fprintf(ficgp," \%%*lf (\%%*lf)");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
 }      }
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       else fprintf(ficgp,"\" t\"\" w l 0,");    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     }    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   }    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
        fprintf(ficresprobmorprev," p.%-d SE",j);
   /*3eme*/      for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   for (k1=1; k1<= m ; k1 ++) {    }  
     for (cpt=1; cpt<= nlstate ; cpt ++) {    fprintf(ficresprobmorprev,"\n");
       k=2+nlstate*(cpt-1);    fprintf(ficgp,"\n# Routine varevsij");
       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);    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
       for (i=1; i< nlstate ; i ++) {    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
         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);  /*   } */
       }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  
     }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");
   }    fprintf(ficresvij,"# Age");
      for(i=1; i<=nlstate;i++)
   /* CV preval stat */      for(j=1; j<=nlstate;j++)
   for (k1=1; k1<= m ; k1 ++) {        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
     for (cpt=1; cpt<nlstate ; cpt ++) {    fprintf(ficresvij,"\n");
       k=3;  
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);    xp=vector(1,npar);
       for (i=1; i< nlstate ; i ++)    dnewm=matrix(1,nlstate,1,npar);
         fprintf(ficgp,"+$%d",k+i+1);    doldm=matrix(1,nlstate,1,nlstate);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
          doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       for (i=1; i< nlstate ; i ++) {    gpp=vector(nlstate+1,nlstate+ndeath);
         l=3+(nlstate+ndeath)*cpt;    gmp=vector(nlstate+1,nlstate+ndeath);
         fprintf(ficgp,"+$%d",l+i+1);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       }    
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      if(estepm < stepm){
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      printf ("Problem %d lower than %d\n",estepm, stepm);
     }    }
   }      else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
   /* proba elementaires */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
    for(i=1,jk=1; i <=nlstate; i++){       nhstepm is the number of hstepm from age to agelim 
     for(k=1; k <=(nlstate+ndeath); k++){       nstepm is the number of stepm from age to agelin. 
       if (k != i) {       Look at hpijx to understand the reason of that which relies in memory size
         for(j=1; j <=ncovmodel; j++){       and note for a fixed period like k years */
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           /*fprintf(ficgp,"%s",alph[1]);*/       survival function given by stepm (the optimization length). Unfortunately it
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);       means that if the survival funtion is printed every two years of age and if
           jk++;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           fprintf(ficgp,"\n");       results. So we changed our mind and took the option of the best precision.
         }    */
       }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     }    agelim = AGESUP;
     }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   for(jk=1; jk <=m; jk++) {      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
    i=1;      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
    for(k2=1; k2<=nlstate; k2++) {      gp=matrix(0,nhstepm,1,nlstate);
      k3=i;      gm=matrix(0,nhstepm,1,nlstate);
      for(k=1; k<=(nlstate+ndeath); k++) {  
        if (k != k2){  
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);      for(theta=1; theta <=npar; theta++){
 ij=1;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
         for(j=3; j <=ncovmodel; j++) {          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           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]]]);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             ij++;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           }  
           else        if (popbased==1) {
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          if(mobilav ==0){
         }            for(i=1; i<=nlstate;i++)
           fprintf(ficgp,")/(1");              prlim[i][i]=probs[(int)age][i][ij];
                  }else{ /* mobilav */ 
         for(k1=1; k1 <=nlstate; k1++){              for(i=1; i<=nlstate;i++)
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);              prlim[i][i]=mobaverage[(int)age][i][ij];
 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]]]);        for(j=1; j<= nlstate; j++){
             ij++;          for(h=0; h<=nhstepm; h++){
           }            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           else              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          }
           }        }
           fprintf(ficgp,")");        /* This for computing probability of death (h=1 means
         }           computed over hstepm matrices product = hstepm*stepm months) 
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);           as a weighted average of prlim.
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        */
         i=i+ncovmodel;        for(j=nlstate+1;j<=nlstate+ndeath;j++){
        }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
      }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
    }        }    
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);        /* end probability of death */
   }  
            for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   fclose(ficgp);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
            hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 chdir(path);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       
     free_ivector(wav,1,imx);        if (popbased==1) {
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);          if(mobilav ==0){
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);              for(i=1; i<=nlstate;i++)
     free_ivector(num,1,n);              prlim[i][i]=probs[(int)age][i][ij];
     free_vector(agedc,1,n);          }else{ /* mobilav */ 
     /*free_matrix(covar,1,NCOVMAX,1,n);*/            for(i=1; i<=nlstate;i++)
     fclose(ficparo);              prlim[i][i]=mobaverage[(int)age][i][ij];
     fclose(ficres);          }
     /*  }*/        }
      
    /*________fin mle=1_________*/        for(j=1; j<= nlstate; j++){
              for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
                gm[h][j] += prlim[i][i]*p3mat[i][j][h];
     /* No more information from the sample is required now */          }
   /* Reads comments: lines beginning with '#' */        }
   while((c=getc(ficpar))=='#' && c!= EOF){        /* This for computing probability of death (h=1 means
     ungetc(c,ficpar);           computed over hstepm matrices product = hstepm*stepm months) 
     fgets(line, MAXLINE, ficpar);           as a weighted average of prlim.
     puts(line);        */
     fputs(line,ficparo);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   }          for(i=1,gmp[j]=0.; i<= nlstate; i++)
   ungetc(c,ficpar);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
          }    
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);        /* end probability of death */
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);  
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        for(j=1; j<= nlstate; j++) /* vareij */
 /*--------- index.htm --------*/          for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   strcpy(optionfilehtm,optionfile);          }
   strcat(optionfilehtm,".htm");  
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     printf("Problem with %s \n",optionfilehtm);goto end;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
   }        }
   
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">      } /* End theta */
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>  
 Total number of observations=%d <br>      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>  
 <hr  size=\"2\" color=\"#EC5E5E\">      for(h=0; h<=nhstepm; h++) /* veij */
 <li>Outputs files<br><br>\n        for(j=1; j<=nlstate;j++)
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n          for(theta=1; theta <=npar; theta++)
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>            trgradg[h][j][theta]=gradg[h][theta][j];
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>  
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>        for(theta=1; theta <=npar; theta++)
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>          trgradgp[j][theta]=gradgp[theta][j];
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>  
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>      for(i=1;i<=nlstate;i++)
 <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);        for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
  fprintf(fichtm," <li>Graphs</li><p>");  
       for(h=0;h<=nhstepm;h++){
  m=cptcoveff;        for(k=0;k<=nhstepm;k++){
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
  j1=0;          for(i=1;i<=nlstate;i++)
  for(k1=1; k1<=m;k1++){            for(j=1;j<=nlstate;j++)
    for(i1=1; i1<=ncodemax[k1];i1++){              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
        j1++;        }
        if (cptcovn > 0) {      }
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    
          for (cpt=1; cpt<=cptcoveff;cpt++)      /* pptj */
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
        }      for(j=nlstate+1;j<=nlstate+ndeath;j++)
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>        for(i=nlstate+1;i<=nlstate+ndeath;i++)
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);              varppt[j][i]=doldmp[j][i];
        for(cpt=1; cpt<nlstate;cpt++){      /* end ppptj */
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>      /*  x centered again */
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
        }      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     for(cpt=1; cpt<=nlstate;cpt++) {   
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      if (popbased==1) {
 interval) in state (%d): v%s%d%d.gif <br>        if(mobilav ==0){
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            for(i=1; i<=nlstate;i++)
      }            prlim[i][i]=probs[(int)age][i][ij];
      for(cpt=1; cpt<=nlstate;cpt++) {        }else{ /* mobilav */ 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>          for(i=1; i<=nlstate;i++)
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            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);      /* This for computing probability of death (h=1 means
 fprintf(fichtm,"\n</body>");         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
    }         as a weighted average of prlim.
  }      */
 fclose(fichtm);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
   /*--------------- Prevalence limit --------------*/          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
        }    
   strcpy(filerespl,"pl");      /* end probability of death */
   strcat(filerespl,fileres);  
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   }        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);        for(i=1; i<=nlstate;i++){
   fprintf(ficrespl,"#Prevalence limit\n");          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
   fprintf(ficrespl,"#Age ");        }
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);      } 
   fprintf(ficrespl,"\n");      fprintf(ficresprobmorprev,"\n");
    
   prlim=matrix(1,nlstate,1,nlstate);      fprintf(ficresvij,"%.0f ",age );
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(i=1; i<=nlstate;i++)
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(j=1; j<=nlstate;j++){
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        }
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      fprintf(ficresvij,"\n");
   k=0;      free_matrix(gp,0,nhstepm,1,nlstate);
   agebase=agemin;      free_matrix(gm,0,nhstepm,1,nlstate);
   agelim=agemax;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   ftolpl=1.e-10;      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
   i1=cptcoveff;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (cptcovn < 1){i1=1;}    } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
   for(cptcov=1;cptcov<=i1;cptcov++){    free_vector(gmp,nlstate+1,nlstate+ndeath);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
         k=k+1;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
         fprintf(ficrespl,"\n#******");    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
         for(j=1;j<=cptcoveff;j++)    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
         fprintf(ficrespl,"******\n");  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
          /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
         for (age=agebase; age<=agelim; age++){    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
           fprintf(ficrespl,"%.0f",age );    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
           for(i=1; i<=nlstate;i++)    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
           fprintf(ficrespl," %.5f", prlim[i][i]);    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(ficrespl,"\n");    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
         }  */
       }  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     }    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   fclose(ficrespl);  
     free_vector(xp,1,npar);
   /*------------- h Pij x at various ages ------------*/    free_matrix(doldm,1,nlstate,1,nlstate);
      free_matrix(dnewm,1,nlstate,1,npar);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   }    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   printf("Computing pij: result on file '%s' \n", filerespij);    fclose(ficresprobmorprev);
      fflush(ficgp);
   stepsize=(int) (stepm+YEARM-1)/YEARM;    fflush(fichtm); 
   /*if (stepm<=24) stepsize=2;*/  }  /* end varevsij */
   
   agelim=AGESUP;  /************ Variance of prevlim ******************/
   hstepm=stepsize*YEARM; /* Every year of age */  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)
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  {
      /* Variance of prevalence limit */
   k=0;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   for(cptcov=1;cptcov<=i1;cptcov++){    double **newm;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double **dnewm,**doldm;
       k=k+1;    int i, j, nhstepm, hstepm;
         fprintf(ficrespij,"\n#****** ");    int k, cptcode;
         for(j=1;j<=cptcoveff;j++)    double *xp;
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    double *gp, *gm;
         fprintf(ficrespij,"******\n");    double **gradg, **trgradg;
            double age,agelim;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    int theta;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */     
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficresvpl,"# Age");
           oldm=oldms;savm=savms;    for(i=1; i<=nlstate;i++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          fprintf(ficresvpl," %1d-%1d",i,i);
           fprintf(ficrespij,"# Age");    fprintf(ficresvpl,"\n");
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)    xp=vector(1,npar);
               fprintf(ficrespij," %1d-%1d",i,j);    dnewm=matrix(1,nlstate,1,npar);
           fprintf(ficrespij,"\n");    doldm=matrix(1,nlstate,1,nlstate);
           for (h=0; h<=nhstepm; h++){    
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    hstepm=1*YEARM; /* Every year of age */
             for(i=1; i<=nlstate;i++)    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
               for(j=1; j<=nlstate+ndeath;j++)    agelim = AGESUP;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
             fprintf(ficrespij,"\n");      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
           }      if (stepm >= YEARM) hstepm=1;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
           fprintf(ficrespij,"\n");      gradg=matrix(1,npar,1,nlstate);
         }      gp=vector(1,nlstate);
     }      gm=vector(1,nlstate);
   }  
       for(theta=1; theta <=npar; theta++){
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/        for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
   fclose(ficrespij);        }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   /*---------- Forecasting ------------------*/        for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
   strcpy(fileresf,"f");      
   strcat(fileresf,fileres);        for(i=1; i<=npar; i++) /* Computes gradient */
   if((ficresf=fopen(fileresf,"w"))==NULL) {          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   }        for(i=1;i<=nlstate;i++)
   printf("Computing forecasting: result on file '%s' \n", fileresf);          gm[i] = prlim[i][i];
   
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprevfore, lprevfore);        for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
  free_matrix(agev,1,maxwav,1,imx);      } /* End theta */
   /* Mobile average */  
       trgradg =matrix(1,nlstate,1,npar);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;  
       for(j=1; j<=nlstate;j++)
   if (mobilav==1) {        for(theta=1; theta <=npar; theta++)
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          trgradg[j][theta]=gradg[theta][j];
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)  
       for (i=1; i<=nlstate;i++)      for(i=1;i<=nlstate;i++)
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)        varpl[i][(int)age] =0.;
           mobaverage[(int)agedeb][i][cptcod]=0.;      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
     for (agedeb=bage+4; agedeb<=fage; agedeb++){      for(i=1;i<=nlstate;i++)
       for (i=1; i<=nlstate;i++){        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
           for (cpt=0;cpt<=4;cpt++){      fprintf(ficresvpl,"%.0f ",age );
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];      for(i=1; i<=nlstate;i++)
           }        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      fprintf(ficresvpl,"\n");
         }      free_vector(gp,1,nlstate);
       }      free_vector(gm,1,nlstate);
     }        free_matrix(gradg,1,npar,1,nlstate);
   }      free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=12) stepsize=1;    free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
   agelim=AGESUP;    free_matrix(dnewm,1,nlstate,1,nlstate);
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */  }
    
   if (popforecast==1) {  /************ Variance of one-step probabilities  ******************/
     if((ficpop=fopen(popfile,"r"))==NULL)    {  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)
       printf("Problem with population file : %s\n",popfile);goto end;  {
     }    int i, j=0,  i1, k1, l1, t, tj;
     popage=ivector(0,AGESUP);    int k2, l2, j1,  z1;
     popeffectif=vector(0,AGESUP);    int k=0,l, cptcode;
     popcount=vector(0,AGESUP);    int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     i=1;      double **dnewm,**doldm;
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)    double *xp;
       {    double *gp, *gm;
         i=i+1;    double **gradg, **trgradg;
       }    double **mu;
     imx=i;    double age,agelim, cov[NCOVMAX];
      double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
   for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];    int theta;
   }    char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
   for(cptcov=1;cptcov<=i1;cptcov++){    char fileresprobcor[FILENAMELENGTH];
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
       k=k+1;    double ***varpij;
       fprintf(ficresf,"\n#****** ");  
       for(j=1;j<=cptcoveff;j++) {    strcpy(fileresprob,"prob"); 
         fprintf(ficresf,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    strcat(fileresprob,fileres);
       }    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       fprintf(ficresf,"******\n");      printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficresf,"# StartingAge FinalAge Horizon(in years)");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    }
       if (popforecast==1)  fprintf(ficresf," [Population]");    strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
       for (agedeb=fage; agedeb>=bage; agedeb--){    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
         fprintf(ficresf,"\n%.f %.f 0",agedeb, agedeb);      printf("Problem with resultfile: %s\n", fileresprobcov);
        if (mobilav==1) {      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
         for(j=1; j<=nlstate;j++)    }
           fprintf(ficresf," %.3f",mobaverage[(int)agedeb][j][cptcod]);    strcpy(fileresprobcor,"probcor"); 
         }    strcat(fileresprobcor,fileres);
         else {    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
           for(j=1; j<=nlstate;j++)      printf("Problem with resultfile: %s\n", fileresprobcor);
           fprintf(ficresf," %.3f",probs[(int)agedeb][j][cptcod]);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
         }      }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
        for(j=1; j<=ndeath;j++) fprintf(ficresf," 0.00000");    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
        if (popforecast==1) fprintf(ficresf," [%.f] ",popeffectif[(int)agedeb]);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
       }    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
          printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
       for (cpt=1; cpt<=nforecast;cpt++) {    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
         fprintf(ficresf,"\n");    
       for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    fprintf(ficresprob,"# Age");
         nhstepm = nhstepm/hstepm;    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/    fprintf(ficresprobcov,"# Age");
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficresprobcov,"# Age");
         oldm=oldms;savm=savms;  
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    
                    for(i=1; i<=nlstate;i++)
         for (h=0; h<=nhstepm; h++){      for(j=1; j<=(nlstate+ndeath);j++){
                fprintf(ficresprob," p%1d-%1d (SE)",i,j);
          if (h*hstepm/YEARM*stepm==cpt)        fprintf(ficresprobcov," p%1d-%1d ",i,j);
             fprintf(ficresf,"\n%.f %.f %.f",agedeb, agedeb+ h*hstepm/YEARM*stepm, h*hstepm/YEARM*stepm);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
                }  
             /* fprintf(ficresprob,"\n");
          for(j=1; j<=nlstate+ndeath;j++) {    fprintf(ficresprobcov,"\n");
            kk1=0.;kk2=0;    fprintf(ficresprobcor,"\n");
            for(i=1; i<=nlstate;i++) {           */
              if (mobilav==1)   xp=vector(1,npar);
                 kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb][i][cptcod];    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
              else kk1=kk1+p3mat[i][j][h]*probs[(int)agedeb][i][cptcod];    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
              if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
             }    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
            if (h*hstepm/YEARM*stepm==cpt) {    first=1;
              fprintf(ficresf," %.3f", kk1);    fprintf(ficgp,"\n# Routine varprob");
                if (popforecast==1) fprintf(ficresf," [%.f]", kk2);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
            }    fprintf(fichtm,"\n");
           }  
         }    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
            file %s<br>\n",optionfilehtmcov);
       }    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
       }  and drawn. It helps understanding how is the covariance between two incidences.\
     }   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
   }    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   if (popforecast==1) {  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
     free_ivector(popage,0,AGESUP);  standard deviations wide on each axis. <br>\
     free_vector(popeffectif,0,AGESUP);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
     free_vector(popcount,0,AGESUP);   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   }  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   free_imatrix(s,1,maxwav+1,1,n);  
   free_vector(weight,1,n);    cov[1]=1;
   fclose(ficresf);    tj=cptcoveff;
   /*---------- Health expectancies and variances ------------*/    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
   strcpy(filerest,"t");    for(t=1; t<=tj;t++){
   strcat(filerest,fileres);      for(i1=1; i1<=ncodemax[t];i1++){ 
   if((ficrest=fopen(filerest,"w"))==NULL) {        j1++;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;        if  (cptcovn>0) {
   }          fprintf(ficresprob, "\n#********** Variable "); 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
   strcpy(filerese,"e");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcat(filerese,fileres);          fprintf(ficresprobcov, "**********\n#\n");
   if((ficreseij=fopen(filerese,"w"))==NULL) {          
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          fprintf(ficgp, "\n#********** Variable "); 
   }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);          fprintf(ficgp, "**********\n#\n");
           
  strcpy(fileresv,"v");          
   strcat(fileresv,fileres);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   }          
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);          fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   k=0;          fprintf(ficresprobcor, "**********\n#");    
   for(cptcov=1;cptcov<=i1;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        
       k=k+1;        for (age=bage; age<=fage; age ++){ 
       fprintf(ficrest,"\n#****** ");          cov[2]=age;
       for(j=1;j<=cptcoveff;j++)          for (k=1; k<=cptcovn;k++) {
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
       fprintf(ficrest,"******\n");          }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       fprintf(ficreseij,"\n#****** ");          for (k=1; k<=cptcovprod;k++)
       for(j=1;j<=cptcoveff;j++)            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);          
       fprintf(ficreseij,"******\n");          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
       fprintf(ficresvij,"\n#****** ");          gp=vector(1,(nlstate)*(nlstate+ndeath));
       for(j=1;j<=cptcoveff;j++)          gm=vector(1,(nlstate)*(nlstate+ndeath));
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      
       fprintf(ficresvij,"******\n");          for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
       oldm=oldms;savm=savms;            
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);              pmij(pmmij,cov,ncovmodel,xp,nlstate);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            
       oldm=oldms;savm=savms;            k=0;
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);            for(i=1; i<= (nlstate); i++){
                    for(j=1; j<=(nlstate+ndeath);j++){
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");                k=k+1;
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);                gp[k]=pmmij[i][j];
       fprintf(ficrest,"\n");              }
                    }
       hf=1;            
       if (stepm >= YEARM) hf=stepm/YEARM;            for(i=1; i<=npar; i++)
       epj=vector(1,nlstate+1);              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       for(age=bage; age <=fage ;age++){      
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
         if (popbased==1) {            k=0;
           for(i=1; i<=nlstate;i++)            for(i=1; i<=(nlstate); i++){
             prlim[i][i]=probs[(int)age][i][k];              for(j=1; j<=(nlstate+ndeath);j++){
         }                k=k+1;
                        gm[k]=pmmij[i][j];
         fprintf(ficrest," %.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]*hf*eij[i][j][(int)age];            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
           }              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           epj[nlstate+1] +=epj[j];          }
         }  
         for(i=1, vepp=0.;i <=nlstate;i++)          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
           for(j=1;j <=nlstate;j++)            for(theta=1; theta <=npar; theta++)
             vepp += vareij[i][j][(int)age];              trgradg[j][theta]=gradg[theta][j];
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));          
         for(j=1;j <=nlstate;j++){          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
         }          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
         fprintf(ficrest,"\n");          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++){
  fclose(ficreseij);            for(j=1; j<=(nlstate+ndeath);j++){
  fclose(ficresvij);              k=k+1;
   fclose(ficrest);              mu[k][(int) age]=pmmij[i][j];
   fclose(ficpar);            }
   free_vector(epj,1,nlstate+1);          }
   /*  scanf("%d ",i); */          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
   /*------- Variance limit prevalence------*/                varpij[i][j][(int)age] = doldm[i][j];
   
 strcpy(fileresvpl,"vpl");          /*printf("\n%d ",(int)age);
   strcat(fileresvpl,fileres);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     exit(0);            }*/
   }  
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
  k=0;          fprintf(ficresprobcor,"\n%d ",(int)age);
  for(cptcov=1;cptcov<=i1;cptcov++){  
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
      k=k+1;            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
      fprintf(ficresvpl,"\n#****** ");          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
      for(j=1;j<=cptcoveff;j++)            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
      fprintf(ficresvpl,"******\n");          }
                i=0;
      varpl=matrix(1,nlstate,(int) bage, (int) fage);          for (k=1; k<=(nlstate);k++){
      oldm=oldms;savm=savms;            for (l=1; l<=(nlstate+ndeath);l++){ 
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);              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++){
   fclose(ficresvpl);                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 : free ----------------*/              }
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);            }
            }/* end of loop for state */
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        } /* end of loop for age */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
          /* Confidence intervalle of pij  */
          /*
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset noparametric;unset label");
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          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);
   free_matrix(matcov,1,npar,1,npar);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   free_vector(delti,1,npar);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
          */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
   printf("End of Imach\n");        first1=1;
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        for (k2=1; k2<=(nlstate);k2++){
            for (l2=1; l2<=(nlstate+ndeath);l2++){ 
   /* 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);*/            if(l2==k2) continue;
   /*printf("Total time was %d uSec.\n", total_usecs);*/            j=(k2-1)*(nlstate+ndeath)+l2;
   /*------ End -----------*/            for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
  end:                i=(k1-1)*(nlstate+ndeath)+l1;
 #ifdef windows                if(i<=j) continue;
  chdir(pathcd);                for (age=bage; age<=fage; age ++){ 
 #endif                  if ((int)age %5==0){
                      v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
  system("..\\gp37mgw\\wgnuplot graph.plt");                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
 #ifdef windows                    mu1=mu[i][(int) age]/stepm*YEARM ;
   while (z[0] != 'q') {                    mu2=mu[j][(int) age]/stepm*YEARM;
     chdir(pathcd);                    c12=cv12/sqrt(v1*v2);
     printf("\nType e to edit output files, c to start again, and q for exiting: ");                    /* Computing eigen value of matrix of covariance */
     scanf("%s",z);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
     if (z[0] == 'c') system("./imach");                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
     else if (z[0] == 'e') {                    /* Eigen vectors */
       chdir(path);                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       system(optionfilehtm);                    /*v21=sqrt(1.-v11*v11); *//* error */
     }                    v21=(lc1-v1)/cv12*v11;
     else if (z[0] == 'q') exit(0);                    v12=-v21;
   }                    v22=v11;
 #endif                    tnalp=v21/v11;
 }                    if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Stable prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - Life expectancies by age and initial health status (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: %s%d1.png<br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: %s%d2.png<br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): %s%d%d.png <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> Result files (second order: variances)</h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Health expectancies with their variances (no covariance): <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of stable prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Stable prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);
           
         } 
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       sump=sump+1;
       num=num+1;
     }
    
    
     /* for (i=1; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=0;i<=imx-1 ; i++)
       {
         if (cens[i]==1 & wav[i]>1)
           A=-x[1]/(x[2])*
             (exp(x[2]/YEARM*(agecens[i]*12-agegomp*12))-exp(x[2]/YEARM*(ageexmed[i]*12-agegomp*12)));
         
         if (cens[i]==0 & wav[i]>1)
           A=-x[1]/(x[2])*
                (exp(x[2]/YEARM*(agedc[i]*12-agegomp*12))-exp(x[2]/YEARM*(ageexmed[i]*12-agegomp*12)))
             +log(x[1]/YEARM)+x[2]/YEARM*(agedc[i]*12-agegomp*12)+log(YEARM);      
         
         if (wav[i]>1 & agecens[i]>15) {
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov){
     int i;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char strstart[80], *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("pathimach=%s, pathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     while (fgets(line, MAXLINE, fic) != NULL)    {
       if ((i >= firstobs) && (i <=lastobs)) {
           
         for (j=maxwav;j>=1;j--){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb); 
           strcpy(line,stra);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         }
           
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);
   
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);
         for (j=ncovcol;j>=1;j--){
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);
         } 
         lstra=strlen(stra);
         if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
           stratrunc = &(stra[lstra-9]);
           num[i]=atol(stratrunc);
         }
         else
           num[i]=atol(stra);
           
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
           printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
   
         i=i+1;
       }
     }
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
    for (i=1; i<=imx; i++)
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameter from char model*/
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);
     fclose(fic);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a
                                    month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<body>\n<title>IMaCh Cov %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<body>\n<title>IMaCh %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (j=1; j<=lastpass; j++)
           if (s[j][i]>nlstate) {
             dcwave[i]=j;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];agecens[i]=1.; 
           if (ageexmed[i]>1 & wav[i]>0) agecens[i]=agev[mw[j][i]][i];
           cens[i]=1;
           
           if (ageexmed[i]<1) cens[i]=-1;
           if (agedc[i]< AGESUP & agedc[i]>1 & dcwave[i]>firstpass & dcwave[i]<=lastpass) cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
   
       p[1]=0.1; p[2]=0.1;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow-mort"); 
     strcat(filerespow,fileres);
     if((ficrespow=fopen(filerespow,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
     /*  for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     */
     fprintf(ficrespow,"\n");
   
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM,delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov);
     } /* Endof if mle==-3 */
   
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%f ",p[jk]);
               fprintf(ficlog,"%f ",p[jk]);
               fprintf(ficres,"%f ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficrespl,"#Stable prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
   
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /*---------- Health expectancies and variances ------------*/
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total LEs with variances: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest); 
   
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficreseij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav);
           }
   
    
           fprintf(ficrest,"#Total LEs with variances: e.. (std) ");
           for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
           fprintf(ficrest,"\n");
   
           epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             if (popbased==1) {
               if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=probs[(int)age][i][k];
               }else{ /* mobilav */ 
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=mobaverage[(int)age][i][k];
               }
             }
           
             fprintf(ficrest," %4.0f",age);
             for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
               for(i=1, epj[j]=0.;i <=nlstate;i++) {
                 epj[j] += prlim[i][i]*eij[i][j][(int)age];
                 /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
               }
               epj[nlstate+1] +=epj[j];
             }
   
             for(i=1, vepp=0.;i <=nlstate;i++)
               for(j=1;j <=nlstate;j++)
                 vepp += vareij[i][j][(int)age];
             fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
             for(j=1;j <=nlstate;j++){
               fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
             }
             fprintf(ficrest,"\n");
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficreseij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of stable prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of stable prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of stable prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
     
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
   
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocaltime at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>",strstart, strtend);
     fclose(fichtm);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
     chdir(path);
     strcpy(plotcmd,"\"");
     strcat(plotcmd,pathimach);
     strcat(plotcmd,GNUPLOTPROGRAM);
     strcat(plotcmd,"\"");
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting graphs with: %s",plotcmd);fflush(stdout);
     if((outcmd=system(plotcmd)) != 0){
       printf(" Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

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  Added in v.1.101


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