Diff for /imach/src/imach.c between versions 1.7 and 1.105

version 1.7, 2001/05/02 17:50:24 version 1.105, 2006/01/05 20:23:19
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 1.105  2006/01/05 20:23:19  lievre
   individuals from different ages are interviewed on their health status    *** empty log message ***
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.104  2005/09/30 16:11:43  lievre
   Health expectancies are computed from the transistions observed between    (Module): sump fixed, loop imx fixed, and simplifications.
   waves and are computed for each degree of severity of disability (number    (Module): If the status is missing at the last wave but we know
   of life states). More degrees you consider, more time is necessary to    that the person is alive, then we can code his/her status as -2
   reach the Maximum Likelihood of the parameters involved in the model.    (instead of missing=-1 in earlier versions) and his/her
   The simplest model is the multinomial logistic model where pij is    contributions to the likelihood is 1 - Prob of dying from last
   the probabibility to be observed in state j at the second wave conditional    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   to be observed in state i at the first wave. Therefore the model is:    the healthy state at last known wave). Version is 0.98
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'  
   is a covariate. If you want to have a more complex model than "constant and    Revision 1.103  2005/09/30 15:54:49  lievre
   age", you should modify the program where the markup    (Module): sump fixed, loop imx fixed, and simplifications.
     *Covariates have to be included here again* invites you to do it.  
   More covariates you add, less is the speed of the convergence.    Revision 1.102  2004/09/15 17:31:30  brouard
     Add the possibility to read data file including tab characters.
   The advantage that this computer programme claims, comes from that if the  
   delay between waves is not identical for each individual, or if some    Revision 1.101  2004/09/15 10:38:38  brouard
   individual missed an interview, the information is not rounded or lost, but    Fix on curr_time
   taken into account using an interpolation or extrapolation.  
   hPijx is the probability to be    Revision 1.100  2004/07/12 18:29:06  brouard
   observed in state i at age x+h conditional to the observed state i at age    Add version for Mac OS X. Just define UNIX in Makefile
   x. The delay 'h' can be split into an exact number (nh*stepm) of  
   unobserved intermediate  states. This elementary transition (by month or    Revision 1.99  2004/06/05 08:57:40  brouard
   quarter trimester, semester or year) is model as a multinomial logistic.    *** empty log message ***
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply hPijx.    Revision 1.98  2004/05/16 15:05:56  brouard
     New version 0.97 . First attempt to estimate force of mortality
   Also this programme outputs the covariance matrix of the parameters but also    directly from the data i.e. without the need of knowing the health
   of the life expectancies. It also computes the prevalence limits.    state at each age, but using a Gompertz model: log u =a + b*age .
      This is the basic analysis of mortality and should be done before any
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    other analysis, in order to test if the mortality estimated from the
            Institut national d'études démographiques, Paris.    cross-longitudinal survey is different from the mortality estimated
   This software have been partly granted by Euro-REVES, a concerted action    from other sources like vital statistic data.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    The same imach parameter file can be used but the option for mle should be -3.
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Agnès, who wrote this part of the code, tried to keep most of the
   **********************************************************************/    former routines in order to include the new code within the former code.
    
 #include <math.h>    The output is very simple: only an estimate of the intercept and of
 #include <stdio.h>    the slope with 95% confident intervals.
 #include <stdlib.h>  
 #include <unistd.h>    Current limitations:
     A) Even if you enter covariates, i.e. with the
 #define MAXLINE 256    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 #define FILENAMELENGTH 80    B) There is no computation of Life Expectancy nor Life Table.
 /*#define DEBUG*/  
 #define windows    Revision 1.97  2004/02/20 13:25:42  lievre
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Version 0.96d. Population forecasting command line is (temporarily)
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    suppressed.
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.96  2003/07/15 15:38:55  brouard
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
     rewritten within the same printf. Workaround: many printfs.
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.95  2003/07/08 07:54:34  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    * imach.c (Repository):
 #define NCOVMAX 8 /* Maximum number of covariates */    (Repository): Using imachwizard code to output a more meaningful covariance
 #define MAXN 20000    matrix (cov(a12,c31) instead of numbers.
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.94  2003/06/27 13:00:02  brouard
 #define AGEBASE 40    Just cleaning
   
     Revision 1.93  2003/06/25 16:33:55  brouard
 int nvar;    (Module): On windows (cygwin) function asctime_r doesn't
 static int cptcov;    exist so I changed back to asctime which exists.
 int cptcovn, cptcovage=0, cptcoveff=0;    (Module): Version 0.96b
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.92  2003/06/25 16:30:45  brouard
 int ndeath=1; /* Number of dead states */    (Module): On windows (cygwin) function asctime_r doesn't
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    exist so I changed back to asctime which exists.
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.91  2003/06/25 15:30:29  brouard
 int maxwav; /* Maxim number of waves */    * imach.c (Repository): Duplicated warning errors corrected.
 int mle, weightopt;    (Repository): Elapsed time after each iteration is now output. It
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    helps to forecast when convergence will be reached. Elapsed time
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    is stamped in powell.  We created a new html file for the graphs
 double **oldm, **newm, **savm; /* Working pointers to matrices */    concerning matrix of covariance. It has extension -cov.htm.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    Revision 1.90  2003/06/24 12:34:15  brouard
 FILE *ficgp, *fichtm;    (Module): Some bugs corrected for windows. Also, when
 FILE *ficreseij;    mle=-1 a template is output in file "or"mypar.txt with the design
   char filerese[FILENAMELENGTH];    of the covariance matrix to be input.
  FILE  *ficresvij;  
   char fileresv[FILENAMELENGTH];    Revision 1.89  2003/06/24 12:30:52  brouard
  FILE  *ficresvpl;    (Module): Some bugs corrected for windows. Also, when
   char fileresvpl[FILENAMELENGTH];    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.88  2003/06/23 17:54:56  brouard
 #define FTOL 1.0e-10    * 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.
   
 #define NRANSI    Revision 1.87  2003/06/18 12:26:01  brouard
 #define ITMAX 200    Version 0.96
   
 #define TOL 2.0e-4    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 #define CGOLD 0.3819660    routine fileappend.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
 #define GOLD 1.618034    current date of interview. It may happen when the death was just
 #define GLIMIT 100.0    prior to the death. In this case, dh was negative and likelihood
 #define TINY 1.0e-20    was wrong (infinity). We still send an "Error" but patch by
     assuming that the date of death was just one stepm after the
 static double maxarg1,maxarg2;    interview.
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    (Repository): Because some people have very long ID (first column)
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    we changed int to long in num[] and we added a new lvector for
      memory allocation. But we also truncated to 8 characters (left
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    truncation)
 #define rint(a) floor(a+0.5)    (Repository): No more line truncation errors.
   
 static double sqrarg;    Revision 1.84  2003/06/13 21:44:43  brouard
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    * imach.c (Repository): Replace "freqsummary" at a correct
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    place. It differs from routine "prevalence" which may be called
     many times. Probs is memory consuming and must be used with
 int imx;    parcimony.
 int stepm;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.83  2003/06/10 13:39:11  lievre
 int m,nb;    *** empty log message ***
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Revision 1.82  2003/06/05 15:57:20  brouard
 double **pmmij;    Add log in  imach.c and  fullversion number is now printed.
   
 double *weight;  */
 int **s; /* Status */  /*
 double *agedc, **covar, idx;     Interpolated Markov Chain
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Short summary of the programme:
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    
 double ftolhess; /* Tolerance for computing hessian */    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /**************** split *************************/    first survey ("cross") where individuals from different ages are
 static  int split( char *path, char *dirc, char *name )    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
    char *s;                             /* pointer */    second wave of interviews ("longitudinal") which measure each change
    int  l1, l2;                         /* length counters */    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
    l1 = strlen( path );                 /* length of path */    model. More health states you consider, more time is necessary to reach the
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Maximum Likelihood of the parameters involved in the model.  The
    s = strrchr( path, '\\' );           /* find last / */    simplest model is the multinomial logistic model where pij is the
    if ( s == NULL ) {                   /* no directory, so use current */    probability to be observed in state j at the second wave
 #if     defined(__bsd__)                /* get current working directory */    conditional to be observed in state i at the first wave. Therefore
       extern char       *getwd( );    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
     'age' is age and 'sex' is a covariate. If you want to have a more
       if ( getwd( dirc ) == NULL ) {    complex model than "constant and age", you should modify the program
 #else    where the markup *Covariates have to be included here again* invites
       extern char       *getcwd( );    you to do it.  More covariates you add, slower the
     convergence.
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    The advantage of this computer programme, compared to a simple
          return( GLOCK_ERROR_GETCWD );    multinomial logistic model, is clear when the delay between waves is not
       }    identical for each individual. Also, if a individual missed an
       strcpy( name, path );             /* we've got it */    intermediate interview, the information is lost, but taken into
    } else {                             /* strip direcotry from path */    account using an interpolation or extrapolation.  
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    hPijx is the probability to be observed in state i at age x+h
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    conditional to the observed state i at age x. The delay 'h' can be
       strcpy( name, s );                /* save file name */    split into an exact number (nh*stepm) of unobserved intermediate
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    states. This elementary transition (by month, quarter,
       dirc[l1-l2] = 0;                  /* add zero */    semester or year) is modelled as a multinomial logistic.  The hPx
    }    matrix is simply the matrix product of nh*stepm elementary matrices
    l1 = strlen( dirc );                 /* length of directory */    and the contribution of each individual to the likelihood is simply
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    hPijx.
    return( 0 );                         /* we're done */  
 }    Also this programme outputs the covariance matrix of the parameters but also
     of the life expectancies. It also computes the stable prevalence. 
     
 /******************************************/    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
              Institut national d'études démographiques, Paris.
 void replace(char *s, char*t)    This software have been partly granted by Euro-REVES, a concerted action
 {    from the European Union.
   int i;    It is copyrighted identically to a GNU software product, ie programme and
   int lg=20;    software can be distributed freely for non commercial use. Latest version
   i=0;    can be accessed at http://euroreves.ined.fr/imach .
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
     (s[i] = t[i]);    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     if (t[i]== '\\') s[i]='/';    
   }    **********************************************************************/
 }  /*
     main
 int nbocc(char *s, char occ)    read parameterfile
 {    read datafile
   int i,j=0;    concatwav
   int lg=20;    freqsummary
   i=0;    if (mle >= 1)
   lg=strlen(s);      mlikeli
   for(i=0; i<= lg; i++) {    print results files
   if  (s[i] == occ ) j++;    if mle==1 
   }       computes hessian
   return j;    read end of parameter file: agemin, agemax, bage, fage, estepm
 }        begin-prev-date,...
     open gnuplot file
 void cutv(char *u,char *v, char*t, char occ)    open html file
 {    stable prevalence
   int i,lg,j,p=0;     for age prevalim()
   i=0;    h Pij x
   for(j=0; j<=strlen(t)-1; j++) {    variance of p varprob
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    forecasting if prevfcast==1 prevforecast call prevalence()
   }    health expectancies
     Variance-covariance of DFLE
   lg=strlen(t);    prevalence()
   for(j=0; j<p; j++) {     movingaverage()
     (u[j] = t[j]);    varevsij() 
   }    if popbased==1 varevsij(,popbased)
      u[p]='\0';    total life expectancies
     Variance of stable prevalence
    for(j=0; j<= lg; j++) {   end
     if (j>=(p+1))(v[j-p-1] = t[j]);  */
   }  
 }  
   
 /********************** nrerror ********************/   
   #include <math.h>
 void nrerror(char error_text[])  #include <stdio.h>
 {  #include <stdlib.h>
   fprintf(stderr,"ERREUR ...\n");  #include <unistd.h>
   fprintf(stderr,"%s\n",error_text);  
   exit(1);  /* #include <sys/time.h> */
 }  #include <time.h>
 /*********************** vector *******************/  #include "timeval.h"
 double *vector(int nl, int nh)  
 {  /* #include <libintl.h> */
   double *v;  /* #define _(String) gettext (String) */
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");  #define MAXLINE 256
   return v-nl+NR_END;  #define GNUPLOTPROGRAM "gnuplot"
 }  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
 /************************ free vector ******************/  /*#define DEBUG*/
 void free_vector(double*v, int nl, int nh)  /*#define windows*/
 {  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   free((FREE_ARG)(v+nl-NR_END));  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 }  
   #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 /************************ivector *******************************/  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 int *ivector(long nl,long nh)  
 {  #define NINTERVMAX 8
   int *v;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   if (!v) nrerror("allocation failure in ivector");  #define NCOVMAX 8 /* Maximum number of covariates */
   return v-nl+NR_END;  #define MAXN 20000
 }  #define YEARM 12. /* Number of months per year */
   #define AGESUP 130
 /******************free ivector **************************/  #define AGEBASE 40
 void free_ivector(int *v, long nl, long nh)  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 {  #ifdef UNIX
   free((FREE_ARG)(v+nl-NR_END));  #define DIRSEPARATOR '/'
 }  #define ODIRSEPARATOR '\\'
   #else
 /******************* imatrix *******************************/  #define DIRSEPARATOR '\\'
 int **imatrix(long nrl, long nrh, long ncl, long nch)  #define ODIRSEPARATOR '/'
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  #endif
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  /* $Id$ */
   int **m;  /* $State$ */
    
   /* allocate pointers to rows */  char version[]="Imach version 0.98, September 2005, INED-EUROREVES ";
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  char fullversion[]="$Revision$ $Date$"; 
   if (!m) nrerror("allocation failure 1 in matrix()");  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   m += NR_END;  int nvar;
   m -= nrl;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
    int npar=NPARMAX;
    int nlstate=2; /* Number of live states */
   /* allocate rows and set pointers to them */  int ndeath=1; /* Number of dead states */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  int popbased=0;
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  int *wav; /* Number of waves for this individuual 0 is possible */
    int maxwav; /* Maxim number of waves */
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  int jmin, jmax; /* min, max spacing between 2 waves */
    int gipmx, gsw; /* Global variables on the number of contributions 
   /* return pointer to array of pointers to rows */                     to the likelihood and the sum of weights (done by funcone)*/
   return m;  int mle, weightopt;
 }  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 */
 /****************** free_imatrix *************************/  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
 void free_imatrix(m,nrl,nrh,ncl,nch)             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       int **m;  double jmean; /* Mean space between 2 waves */
       long nch,ncl,nrh,nrl;  double **oldm, **newm, **savm; /* Working pointers to matrices */
      /* free an int matrix allocated by imatrix() */  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 {  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  FILE *ficlog, *ficrespow;
   free((FREE_ARG) (m+nrl-NR_END));  int globpr; /* Global variable for printing or not */
 }  double fretone; /* Only one call to likelihood */
   long ipmx; /* Number of contributions */
 /******************* matrix *******************************/  double sw; /* Sum of weights */
 double **matrix(long nrl, long nrh, long ncl, long nch)  char filerespow[FILENAMELENGTH];
 {  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  FILE *ficresilk;
   double **m;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   FILE *ficresprobmorprev;
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  FILE *fichtm, *fichtmcov; /* Html File */
   if (!m) nrerror("allocation failure 1 in matrix()");  FILE *ficreseij;
   m += NR_END;  char filerese[FILENAMELENGTH];
   m -= nrl;  FILE  *ficresvij;
   char fileresv[FILENAMELENGTH];
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  FILE  *ficresvpl;
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  char fileresvpl[FILENAMELENGTH];
   m[nrl] += NR_END;  char title[MAXLINE];
   m[nrl] -= ncl;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   return m;  char command[FILENAMELENGTH];
 }  int  outcmd=0;
   
 /*************************free matrix ************************/  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  
 {  char filelog[FILENAMELENGTH]; /* Log file */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  char filerest[FILENAMELENGTH];
   free((FREE_ARG)(m+nrl-NR_END));  char fileregp[FILENAMELENGTH];
 }  char popfile[FILENAMELENGTH];
   
 /******************* ma3x *******************************/  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  
 {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  struct timezone tzp;
   double ***m;  extern int gettimeofday();
   struct tm tmg, tm, tmf, *gmtime(), *localtime();
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  long time_value;
   if (!m) nrerror("allocation failure 1 in matrix()");  extern long time();
   m += NR_END;  char strcurr[80], strfor[80];
   m -= nrl;  
   #define NR_END 1
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define FREE_ARG char*
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define FTOL 1.0e-10
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  #define NRANSI 
   #define ITMAX 200 
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   #define TOL 2.0e-4 
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #define CGOLD 0.3819660 
   m[nrl][ncl] += NR_END;  #define ZEPS 1.0e-10 
   m[nrl][ncl] -= nll;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  #define GOLD 1.618034 
    #define GLIMIT 100.0 
   for (i=nrl+1; i<=nrh; i++) {  #define TINY 1.0e-20 
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  static double maxarg1,maxarg2;
       m[i][j]=m[i][j-1]+nlay;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   return m;    
 }  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   #define rint(a) floor(a+0.5)
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  static double sqrarg;
 {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  int agegomp= AGEGOMP;
   free((FREE_ARG)(m+nrl-NR_END));  
 }  int imx; 
   int stepm=1;
 /***************** f1dim *************************/  /* Stepm, step in month: minimum step interpolation*/
 extern int ncom;  
 extern double *pcom,*xicom;  int estepm;
 extern double (*nrfunc)(double []);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
    
 double f1dim(double x)  int m,nb;
 {  long *num;
   int j;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   double f;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double *xt;  double **pmmij, ***probs;
    double *ageexmed,*agecens;
   xt=vector(1,ncom);  double dateintmean=0;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);  double *weight;
   free_vector(xt,1,ncom);  int **s; /* Status */
   return f;  double *agedc, **covar, idx;
 }  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   double *lsurv, *lpop, *tpop;
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 {  double ftolhess; /* Tolerance for computing hessian */
   int iter;  
   double a,b,d,etemp;  /**************** split *************************/
   double fu,fv,fw,fx;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   double ftemp;  {
   double p,q,r,tol1,tol2,u,v,w,x,xm;    /* From a file name with full path (either Unix or Windows) we extract the directory (dirc)
   double e=0.0;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
      */ 
   a=(ax < cx ? ax : cx);    char  *ss;                            /* pointer */
   b=(ax > cx ? ax : cx);    int   l1, l2;                         /* length counters */
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);    l1 = strlen(path );                   /* length of path */
   for (iter=1;iter<=ITMAX;iter++) {    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     xm=0.5*(a+b);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    if ( ss == NULL ) {                   /* no directory, so use current */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     printf(".");fflush(stdout);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
 #ifdef DEBUG      /* get current working directory */
     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);      /*    extern  char* getcwd ( char *buf , int len);*/
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 #endif        return( GLOCK_ERROR_GETCWD );
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){      }
       *xmin=x;      strcpy( name, path );               /* we've got it */
       return fx;    } else {                              /* strip direcotry from path */
     }      ss++;                               /* after this, the filename */
     ftemp=fu;      l2 = strlen( ss );                  /* length of filename */
     if (fabs(e) > tol1) {      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       r=(x-w)*(fx-fv);      strcpy( name, ss );         /* save file name */
       q=(x-v)*(fx-fw);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       p=(x-v)*q-(x-w)*r;      dirc[l1-l2] = 0;                    /* add zero */
       q=2.0*(q-r);    }
       if (q > 0.0) p = -p;    l1 = strlen( dirc );                  /* length of directory */
       q=fabs(q);    /*#ifdef windows
       etemp=e;    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }
       e=d;  #else
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #endif
       else {    */
         d=p/q;    ss = strrchr( name, '.' );            /* find last / */
         u=x+d;    if (ss >0){
         if (u-a < tol2 || b-u < tol2)      ss++;
           d=SIGN(tol1,xm-x);      strcpy(ext,ss);                     /* save extension */
       }      l1= strlen( name);
     } else {      l2= strlen(ss)+1;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));      strncpy( finame, name, l1-l2);
     }      finame[l1-l2]= 0;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    }
     fu=(*f)(u);    return( 0 );                          /* we're done */
     if (fu <= fx) {  }
       if (u >= x) a=x; else b=x;  
       SHFT(v,w,x,u)  
         SHFT(fv,fw,fx,fu)  /******************************************/
         } else {  
           if (u < x) a=u; else b=u;  void replace_back_to_slash(char *s, char*t)
           if (fu <= fw || w == x) {  {
             v=w;    int i;
             w=u;    int lg=0;
             fv=fw;    i=0;
             fw=fu;    lg=strlen(t);
           } else if (fu <= fv || v == x || v == w) {    for(i=0; i<= lg; i++) {
             v=u;      (s[i] = t[i]);
             fv=fu;      if (t[i]== '\\') s[i]='/';
           }    }
         }  }
   }  
   nrerror("Too many iterations in brent");  int nbocc(char *s, char occ)
   *xmin=x;  {
   return fx;    int i,j=0;
 }    int lg=20;
     i=0;
 /****************** mnbrak ***********************/    lg=strlen(s);
     for(i=0; i<= lg; i++) {
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    if  (s[i] == occ ) j++;
             double (*func)(double))    }
 {    return j;
   double ulim,u,r,q, dum;  }
   double fu;  
    void cutv(char *u,char *v, char*t, char occ)
   *fa=(*func)(*ax);  {
   *fb=(*func)(*bx);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
   if (*fb > *fa) {       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
     SHFT(dum,*ax,*bx,dum)       gives u="abcedf" and v="ghi2j" */
       SHFT(dum,*fb,*fa,dum)    int i,lg,j,p=0;
       }    i=0;
   *cx=(*bx)+GOLD*(*bx-*ax);    for(j=0; j<=strlen(t)-1; j++) {
   *fc=(*func)(*cx);      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   while (*fb > *fc) {    }
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);    lg=strlen(t);
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    for(j=0; j<p; j++) {
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));      (u[j] = t[j]);
     ulim=(*bx)+GLIMIT*(*cx-*bx);    }
     if ((*bx-u)*(u-*cx) > 0.0) {       u[p]='\0';
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {     for(j=0; j<= lg; j++) {
       fu=(*func)(u);      if (j>=(p+1))(v[j-p-1] = t[j]);
       if (fu < *fc) {    }
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  }
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  /********************** nrerror ********************/
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  void nrerror(char error_text[])
       fu=(*func)(u);  {
     } else {    fprintf(stderr,"ERREUR ...\n");
       u=(*cx)+GOLD*(*cx-*bx);    fprintf(stderr,"%s\n",error_text);
       fu=(*func)(u);    exit(EXIT_FAILURE);
     }  }
     SHFT(*ax,*bx,*cx,u)  /*********************** vector *******************/
       SHFT(*fa,*fb,*fc,fu)  double *vector(int nl, int nh)
       }  {
 }    double *v;
     v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 /*************** linmin ************************/    if (!v) nrerror("allocation failure in vector");
     return v-nl+NR_END;
 int ncom;  }
 double *pcom,*xicom;  
 double (*nrfunc)(double []);  /************************ free vector ******************/
    void free_vector(double*v, int nl, int nh)
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  {
 {    free((FREE_ARG)(v+nl-NR_END));
   double brent(double ax, double bx, double cx,  }
                double (*f)(double), double tol, double *xmin);  
   double f1dim(double x);  /************************ivector *******************************/
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  int *ivector(long nl,long nh)
               double *fc, double (*func)(double));  {
   int j;    int *v;
   double xx,xmin,bx,ax;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   double fx,fb,fa;    if (!v) nrerror("allocation failure in ivector");
      return v-nl+NR_END;
   ncom=n;  }
   pcom=vector(1,n);  
   xicom=vector(1,n);  /******************free ivector **************************/
   nrfunc=func;  void free_ivector(int *v, long nl, long nh)
   for (j=1;j<=n;j++) {  {
     pcom[j]=p[j];    free((FREE_ARG)(v+nl-NR_END));
     xicom[j]=xi[j];  }
   }  
   ax=0.0;  /************************lvector *******************************/
   xx=1.0;  long *lvector(long nl,long nh)
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  {
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    long *v;
 #ifdef DEBUG    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    if (!v) nrerror("allocation failure in ivector");
 #endif    return v-nl+NR_END;
   for (j=1;j<=n;j++) {  }
     xi[j] *= xmin;  
     p[j] += xi[j];  /******************free lvector **************************/
   }  void free_lvector(long *v, long nl, long nh)
   free_vector(xicom,1,n);  {
   free_vector(pcom,1,n);    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************** powell ************************/  /******************* imatrix *******************************/
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  int **imatrix(long nrl, long nrh, long ncl, long nch) 
             double (*func)(double []))       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
 {  { 
   void linmin(double p[], double xi[], int n, double *fret,    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
               double (*func)(double []));    int **m; 
   int i,ibig,j;    
   double del,t,*pt,*ptt,*xit;    /* allocate pointers to rows */ 
   double fp,fptt;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   double *xits;    if (!m) nrerror("allocation failure 1 in matrix()"); 
   pt=vector(1,n);    m += NR_END; 
   ptt=vector(1,n);    m -= nrl; 
   xit=vector(1,n);    
   xits=vector(1,n);    
   *fret=(*func)(p);    /* allocate rows and set pointers to them */ 
   for (j=1;j<=n;j++) pt[j]=p[j];    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   for (*iter=1;;++(*iter)) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     fp=(*fret);    m[nrl] += NR_END; 
     ibig=0;    m[nrl] -= ncl; 
     del=0.0;    
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     for (i=1;i<=n;i++)    
       printf(" %d %.12f",i, p[i]);    /* return pointer to array of pointers to rows */ 
     printf("\n");    return m; 
     for (i=1;i<=n;i++) {  } 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);  /****************** free_imatrix *************************/
 #ifdef DEBUG  void free_imatrix(m,nrl,nrh,ncl,nch)
       printf("fret=%lf \n",*fret);        int **m;
 #endif        long nch,ncl,nrh,nrl; 
       printf("%d",i);fflush(stdout);       /* free an int matrix allocated by imatrix() */ 
       linmin(p,xit,n,fret,func);  { 
       if (fabs(fptt-(*fret)) > del) {    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
         del=fabs(fptt-(*fret));    free((FREE_ARG) (m+nrl-NR_END)); 
         ibig=i;  } 
       }  
 #ifdef DEBUG  /******************* matrix *******************************/
       printf("%d %.12e",i,(*fret));  double **matrix(long nrl, long nrh, long ncl, long nch)
       for (j=1;j<=n;j++) {  {
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
         printf(" x(%d)=%.12e",j,xit[j]);    double **m;
       }  
       for(j=1;j<=n;j++)    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         printf(" p=%.12e",p[j]);    if (!m) nrerror("allocation failure 1 in matrix()");
       printf("\n");    m += NR_END;
 #endif    m -= nrl;
     }  
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 #ifdef DEBUG    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       int k[2],l;    m[nrl] += NR_END;
       k[0]=1;    m[nrl] -= ncl;
       k[1]=-1;  
       printf("Max: %.12e",(*func)(p));    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       for (j=1;j<=n;j++)    return m;
         printf(" %.12e",p[j]);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       printf("\n");     */
       for(l=0;l<=1;l++) {  }
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  /*************************free matrix ************************/
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         }  {
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       }    free((FREE_ARG)(m+nrl-NR_END));
 #endif  }
   
   /******************* ma3x *******************************/
       free_vector(xit,1,n);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       free_vector(xits,1,n);  {
       free_vector(ptt,1,n);    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       free_vector(pt,1,n);    double ***m;
       return;  
     }    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    if (!m) nrerror("allocation failure 1 in matrix()");
     for (j=1;j<=n;j++) {    m += NR_END;
       ptt[j]=2.0*p[j]-pt[j];    m -= nrl;
       xit[j]=p[j]-pt[j];  
       pt[j]=p[j];    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     fptt=(*func)(ptt);    m[nrl] += NR_END;
     if (fptt < fp) {    m[nrl] -= ncl;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  
       if (t < 0.0) {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
           xi[j][ibig]=xi[j][n];    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
           xi[j][n]=xit[j];    m[nrl][ncl] += NR_END;
         }    m[nrl][ncl] -= nll;
 #ifdef DEBUG    for (j=ncl+1; j<=nch; j++) 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      m[nrl][j]=m[nrl][j-1]+nlay;
         for(j=1;j<=n;j++)    
           printf(" %.12e",xit[j]);    for (i=nrl+1; i<=nrh; i++) {
         printf("\n");      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
 #endif      for (j=ncl+1; j<=nch; j++) 
       }        m[i][j]=m[i][j-1]+nlay;
     }    }
   }    return m; 
 }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
              &(m[i][j][k]) <=> *((*(m+i) + j)+k)
 /**** Prevalence limit ****************/    */
   }
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  
 {  /*************************free ma3x ************************/
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
      matrix by transitions matrix until convergence is reached */  {
     free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   int i, ii,j,k;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   double min, max, maxmin, maxmax,sumnew=0.;    free((FREE_ARG)(m+nrl-NR_END));
   double **matprod2();  }
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  /*************** function subdirf ***********/
   double agefin, delaymax=50 ; /* Max number of years to converge */  char *subdirf(char fileres[])
   {
   for (ii=1;ii<=nlstate+ndeath;ii++)    /* Caution optionfilefiname is hidden */
     for (j=1;j<=nlstate+ndeath;j++){    strcpy(tmpout,optionfilefiname);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    strcat(tmpout,"/"); /* Add to the right */
     }    strcat(tmpout,fileres);
     return tmpout;
    cov[1]=1.;  }
    
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /*************** function subdirf2 ***********/
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  char *subdirf2(char fileres[], char *preop)
     newm=savm;  {
     /* Covariates have to be included here again */    
      cov[2]=agefin;    /* Caution optionfilefiname is hidden */
      strcpy(tmpout,optionfilefiname);
       for (k=1; k<=cptcovn;k++) {    strcat(tmpout,"/");
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    strcat(tmpout,preop);
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    strcat(tmpout,fileres);
       }    return tmpout;
       for (k=1; k<=cptcovage;k++)  }
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  
       for (k=1; k<=cptcovprod;k++)  /*************** function subdirf3 ***********/
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  char *subdirf3(char fileres[], char *preop, char *preop2)
   {
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    
     /* Caution optionfilefiname is hidden */
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    strcat(tmpout,preop);
     strcat(tmpout,preop2);
     savm=oldm;    strcat(tmpout,fileres);
     oldm=newm;    return tmpout;
     maxmax=0.;  }
     for(j=1;j<=nlstate;j++){  
       min=1.;  /***************** f1dim *************************/
       max=0.;  extern int ncom; 
       for(i=1; i<=nlstate; i++) {  extern double *pcom,*xicom;
         sumnew=0;  extern double (*nrfunc)(double []); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];   
         prlim[i][j]= newm[i][j]/(1-sumnew);  double f1dim(double x) 
         max=FMAX(max,prlim[i][j]);  { 
         min=FMIN(min,prlim[i][j]);    int j; 
       }    double f;
       maxmin=max-min;    double *xt; 
       maxmax=FMAX(maxmax,maxmin);   
     }    xt=vector(1,ncom); 
     if(maxmax < ftolpl){    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       return prlim;    f=(*nrfunc)(xt); 
     }    free_vector(xt,1,ncom); 
   }    return f; 
 }  } 
   
 /*************** transition probabilities **********/  /*****************brent *************************/
   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  { 
 {    int iter; 
   double s1, s2;    double a,b,d,etemp;
   /*double t34;*/    double fu,fv,fw,fx;
   int i,j,j1, nc, ii, jj;    double ftemp;
     double p,q,r,tol1,tol2,u,v,w,x,xm; 
     for(i=1; i<= nlstate; i++){    double e=0.0; 
     for(j=1; j<i;j++){   
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    a=(ax < cx ? ax : cx); 
         /*s2 += param[i][j][nc]*cov[nc];*/    b=(ax > cx ? ax : cx); 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    x=w=v=bx; 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    fw=fv=fx=(*f)(x); 
       }    for (iter=1;iter<=ITMAX;iter++) { 
       ps[i][j]=s2;      xm=0.5*(a+b); 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
     }      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     for(j=i+1; j<=nlstate+ndeath;j++){      printf(".");fflush(stdout);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      fprintf(ficlog,".");fflush(ficlog);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  #ifdef DEBUG
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       }      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       ps[i][j]=s2;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     }  #endif
   }      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for(i=1; i<= nlstate; i++){        *xmin=x; 
      s1=0;        return fx; 
     for(j=1; j<i; j++)      } 
       s1+=exp(ps[i][j]);      ftemp=fu;
     for(j=i+1; j<=nlstate+ndeath; j++)      if (fabs(e) > tol1) { 
       s1+=exp(ps[i][j]);        r=(x-w)*(fx-fv); 
     ps[i][i]=1./(s1+1.);        q=(x-v)*(fx-fw); 
     for(j=1; j<i; j++)        p=(x-v)*q-(x-w)*r; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];        q=2.0*(q-r); 
     for(j=i+1; j<=nlstate+ndeath; j++)        if (q > 0.0) p = -p; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];        q=fabs(q); 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */        etemp=e; 
   } /* end i */        e=d; 
         if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     for(jj=1; jj<= nlstate+ndeath; jj++){        else { 
       ps[ii][jj]=0;          d=p/q; 
       ps[ii][ii]=1;          u=x+d; 
     }          if (u-a < tol2 || b-u < tol2) 
   }            d=SIGN(tol1,xm-x); 
         } 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      } else { 
     for(jj=1; jj<= nlstate+ndeath; jj++){        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
      printf("%lf ",ps[ii][jj]);      } 
    }      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     printf("\n ");      fu=(*f)(u); 
     }      if (fu <= fx) { 
     printf("\n ");printf("%lf ",cov[2]);*/        if (u >= x) a=x; else b=x; 
 /*        SHFT(v,w,x,u) 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);          SHFT(fv,fw,fx,fu) 
   goto end;*/          } else { 
     return ps;            if (u < x) a=u; else b=u; 
 }            if (fu <= fw || w == x) { 
               v=w; 
 /**************** Product of 2 matrices ******************/              w=u; 
               fv=fw; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)              fw=fu; 
 {            } else if (fu <= fv || v == x || v == w) { 
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times              v=u; 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */              fv=fu; 
   /* 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;    nrerror("Too many iterations in brent"); 
   for(i=nrl; i<= nrh; i++)    *xmin=x; 
     for(k=ncolol; k<=ncoloh; k++)    return fx; 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  } 
         out[i][k] +=in[i][j]*b[j][k];  
   /****************** mnbrak ***********************/
   return out;  
 }  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
               double (*func)(double)) 
   { 
 /************* Higher Matrix Product ***************/    double ulim,u,r,q, dum;
     double fu; 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )   
 {    *fa=(*func)(*ax); 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    *fb=(*func)(*bx); 
      duration (i.e. until    if (*fb > *fa) { 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.      SHFT(dum,*ax,*bx,dum) 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        SHFT(dum,*fb,*fa,dum) 
      (typically every 2 years instead of every month which is too big).        } 
      Model is determined by parameters x and covariates have to be    *cx=(*bx)+GOLD*(*bx-*ax); 
      included manually here.    *fc=(*func)(*cx); 
     while (*fb > *fc) { 
      */      r=(*bx-*ax)*(*fb-*fc); 
       q=(*bx-*cx)*(*fb-*fa); 
   int i, j, d, h, k;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   double **out, cov[NCOVMAX];        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   double **newm;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if ((*bx-u)*(u-*cx) > 0.0) { 
   /* Hstepm could be zero and should return the unit matrix */        fu=(*func)(u); 
   for (i=1;i<=nlstate+ndeath;i++)      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     for (j=1;j<=nlstate+ndeath;j++){        fu=(*func)(u); 
       oldm[i][j]=(i==j ? 1.0 : 0.0);        if (fu < *fc) { 
       po[i][j][0]=(i==j ? 1.0 : 0.0);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
     }            SHFT(*fb,*fc,fu,(*func)(u)) 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */            } 
   for(h=1; h <=nhstepm; h++){      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     for(d=1; d <=hstepm; d++){        u=ulim; 
       newm=savm;        fu=(*func)(u); 
       /* Covariates have to be included here again */      } else { 
       cov[1]=1.;        u=(*cx)+GOLD*(*cx-*bx); 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        fu=(*func)(u); 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      } 
 for (k=1; k<=cptcovage;k++)      SHFT(*ax,*bx,*cx,u) 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];        SHFT(*fa,*fb,*fc,fu) 
    for (k=1; k<=cptcovprod;k++)        } 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  } 
   
   /*************** linmin ************************/
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  int ncom; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  double *pcom,*xicom;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  double (*nrfunc)(double []); 
       savm=oldm;   
       oldm=newm;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
     }  { 
     for(i=1; i<=nlstate+ndeath; i++)    double brent(double ax, double bx, double cx, 
       for(j=1;j<=nlstate+ndeath;j++) {                 double (*f)(double), double tol, double *xmin); 
         po[i][j][h]=newm[i][j];    double f1dim(double x); 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
          */                double *fc, double (*func)(double)); 
       }    int j; 
   } /* end h */    double xx,xmin,bx,ax; 
   return po;    double fx,fb,fa;
 }   
     ncom=n; 
     pcom=vector(1,n); 
 /*************** log-likelihood *************/    xicom=vector(1,n); 
 double func( double *x)    nrfunc=func; 
 {    for (j=1;j<=n;j++) { 
   int i, ii, j, k, mi, d, kk;      pcom[j]=p[j]; 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      xicom[j]=xi[j]; 
   double **out;    } 
   double sw; /* Sum of weights */    ax=0.0; 
   double lli; /* Individual log likelihood */    xx=1.0; 
   long ipmx;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   /*extern weight */    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   /* We are differentiating ll according to initial status */  #ifdef DEBUG
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   /*for(i=1;i<imx;i++)    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 printf(" %d\n",s[4][i]);  #endif
   */    for (j=1;j<=n;j++) { 
   cov[1]=1.;      xi[j] *= xmin; 
       p[j] += xi[j]; 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    } 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    free_vector(xicom,1,n); 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    free_vector(pcom,1,n); 
        for(mi=1; mi<= wav[i]-1; mi++){  } 
       for (ii=1;ii<=nlstate+ndeath;ii++)  
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  char *asc_diff_time(long time_sec, char ascdiff[])
             for(d=0; d<dh[mi][i]; d++){  {
               newm=savm;    long sec_left, days, hours, minutes;
               cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    days = (time_sec) / (60*60*24);
               for (kk=1; kk<=cptcovage;kk++) {    sec_left = (time_sec) % (60*60*24);
                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    hours = (sec_left) / (60*60) ;
                  /*printf("%d %d",kk,Tage[kk]);*/    sec_left = (sec_left) %(60*60);
               }    minutes = (sec_left) /60;
               /*cov[4]=covar[1][i]*cov[2];scanf("%d", i);*/    sec_left = (sec_left) % (60);
               /*cov[3]=pow(cov[2],2)/1000.;*/    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
     return ascdiff;
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  }
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  
           savm=oldm;  /*************** powell ************************/
           oldm=newm;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
               double (*func)(double [])) 
   { 
       } /* end mult */    void linmin(double p[], double xi[], int n, double *fret, 
                    double (*func)(double [])); 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    int i,ibig,j; 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    double del,t,*pt,*ptt,*xit;
       ipmx +=1;    double fp,fptt;
       sw += weight[i];    double *xits;
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    int niterf, itmp;
     } /* end of wave */  
   } /* end of individual */    pt=vector(1,n); 
     ptt=vector(1,n); 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    xit=vector(1,n); 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    xits=vector(1,n); 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    *fret=(*func)(p); 
   return -l;    for (j=1;j<=n;j++) pt[j]=p[j]; 
 }    for (*iter=1;;++(*iter)) { 
       fp=(*fret); 
       ibig=0; 
 /*********** Maximum Likelihood Estimation ***************/      del=0.0; 
       last_time=curr_time;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      (void) gettimeofday(&curr_time,&tzp);
 {      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
   int i,j, iter;      /*    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);
   double **xi,*delti;      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
   double fret;      */
   xi=matrix(1,npar,1,npar);     for (i=1;i<=n;i++) {
   for (i=1;i<=npar;i++)        printf(" %d %.12f",i, p[i]);
     for (j=1;j<=npar;j++)        fprintf(ficlog," %d %.12lf",i, p[i]);
       xi[i][j]=(i==j ? 1.0 : 0.0);        fprintf(ficrespow," %.12lf", p[i]);
   printf("Powell\n");      }
   powell(p,xi,npar,ftol,&iter,&fret,func);      printf("\n");
       fprintf(ficlog,"\n");
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));      fprintf(ficrespow,"\n");fflush(ficrespow);
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));      if(*iter <=3){
         tm = *localtime(&curr_time.tv_sec);
 }        strcpy(strcurr,asctime(&tm));
   /*       asctime_r(&tm,strcurr); */
 /**** Computes Hessian and covariance matrix ***/        forecast_time=curr_time; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))        itmp = strlen(strcurr);
 {        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   double  **a,**y,*x,pd;          strcurr[itmp-1]='\0';
   double **hess;        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,jk;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   int *indx;        for(niterf=10;niterf<=30;niterf+=10){
           forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   double hessii(double p[], double delta, int theta, double delti[]);          tmf = *localtime(&forecast_time.tv_sec);
   double hessij(double p[], double delti[], int i, int j);  /*      asctime_r(&tmf,strfor); */
   void lubksb(double **a, int npar, int *indx, double b[]) ;          strcpy(strfor,asctime(&tmf));
   void ludcmp(double **a, int npar, int *indx, double *d) ;          itmp = strlen(strfor);
           if(strfor[itmp-1]=='\n')
           strfor[itmp-1]='\0';
   hess=matrix(1,npar,1,npar);          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);
           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);
   printf("\nCalculation of the hessian matrix. Wait...\n");        }
   for (i=1;i<=npar;i++){      }
     printf("%d",i);fflush(stdout);      for (i=1;i<=n;i++) { 
     hess[i][i]=hessii(p,ftolhess,i,delti);        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     /*printf(" %f ",p[i]);*/        fptt=(*fret); 
   }  #ifdef DEBUG
         printf("fret=%lf \n",*fret);
   for (i=1;i<=npar;i++) {        fprintf(ficlog,"fret=%lf \n",*fret);
     for (j=1;j<=npar;j++)  {  #endif
       if (j>i) {        printf("%d",i);fflush(stdout);
         printf(".%d%d",i,j);fflush(stdout);        fprintf(ficlog,"%d",i);fflush(ficlog);
         hess[i][j]=hessij(p,delti,i,j);        linmin(p,xit,n,fret,func); 
         hess[j][i]=hess[i][j];        if (fabs(fptt-(*fret)) > del) { 
       }          del=fabs(fptt-(*fret)); 
     }          ibig=i; 
   }        } 
   printf("\n");  #ifdef DEBUG
         printf("%d %.12e",i,(*fret));
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        fprintf(ficlog,"%d %.12e",i,(*fret));
          for (j=1;j<=n;j++) {
   a=matrix(1,npar,1,npar);          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   y=matrix(1,npar,1,npar);          printf(" x(%d)=%.12e",j,xit[j]);
   x=vector(1,npar);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   indx=ivector(1,npar);        }
   for (i=1;i<=npar;i++)        for(j=1;j<=n;j++) {
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          printf(" p=%.12e",p[j]);
   ludcmp(a,npar,indx,&pd);          fprintf(ficlog," p=%.12e",p[j]);
         }
   for (j=1;j<=npar;j++) {        printf("\n");
     for (i=1;i<=npar;i++) x[i]=0;        fprintf(ficlog,"\n");
     x[j]=1;  #endif
     lubksb(a,npar,indx,x);      } 
     for (i=1;i<=npar;i++){      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       matcov[i][j]=x[i];  #ifdef DEBUG
     }        int k[2],l;
   }        k[0]=1;
         k[1]=-1;
   printf("\n#Hessian matrix#\n");        printf("Max: %.12e",(*func)(p));
   for (i=1;i<=npar;i++) {        fprintf(ficlog,"Max: %.12e",(*func)(p));
     for (j=1;j<=npar;j++) {        for (j=1;j<=n;j++) {
       printf("%.3e ",hess[i][j]);          printf(" %.12e",p[j]);
     }          fprintf(ficlog," %.12e",p[j]);
     printf("\n");        }
   }        printf("\n");
         fprintf(ficlog,"\n");
   /* Recompute Inverse */        for(l=0;l<=1;l++) {
   for (i=1;i<=npar;i++)          for (j=1;j<=n;j++) {
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   ludcmp(a,npar,indx,&pd);            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   /*  printf("\n#Hessian matrix recomputed#\n");          }
           printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   for (j=1;j<=npar;j++) {          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     for (i=1;i<=npar;i++) x[i]=0;        }
     x[j]=1;  #endif
     lubksb(a,npar,indx,x);  
     for (i=1;i<=npar;i++){  
       y[i][j]=x[i];        free_vector(xit,1,n); 
       printf("%.3e ",y[i][j]);        free_vector(xits,1,n); 
     }        free_vector(ptt,1,n); 
     printf("\n");        free_vector(pt,1,n); 
   }        return; 
   */      } 
       if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   free_matrix(a,1,npar,1,npar);      for (j=1;j<=n;j++) { 
   free_matrix(y,1,npar,1,npar);        ptt[j]=2.0*p[j]-pt[j]; 
   free_vector(x,1,npar);        xit[j]=p[j]-pt[j]; 
   free_ivector(indx,1,npar);        pt[j]=p[j]; 
   free_matrix(hess,1,npar,1,npar);      } 
       fptt=(*func)(ptt); 
       if (fptt < fp) { 
 }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         if (t < 0.0) { 
 /*************** hessian matrix ****************/          linmin(p,xit,n,fret,func); 
 double hessii( double x[], double delta, int theta, double delti[])          for (j=1;j<=n;j++) { 
 {            xi[j][ibig]=xi[j][n]; 
   int i;            xi[j][n]=xit[j]; 
   int l=1, lmax=20;          }
   double k1,k2;  #ifdef DEBUG
   double p2[NPARMAX+1];          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   double res;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;          for(j=1;j<=n;j++){
   double fx;            printf(" %.12e",xit[j]);
   int k=0,kmax=10;            fprintf(ficlog," %.12e",xit[j]);
   double l1;          }
           printf("\n");
   fx=func(x);          fprintf(ficlog,"\n");
   for (i=1;i<=npar;i++) p2[i]=x[i];  #endif
   for(l=0 ; l <=lmax; l++){        }
     l1=pow(10,l);      } 
     delts=delt;    } 
     for(k=1 ; k <kmax; k=k+1){  } 
       delt = delta*(l1*k);  
       p2[theta]=x[theta] +delt;  /**** Prevalence limit (stable prevalence)  ****************/
       k1=func(p2)-fx;  
       p2[theta]=x[theta]-delt;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       k2=func(p2)-fx;  {
       /*res= (k1-2.0*fx+k2)/delt/delt; */    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */       matrix by transitions matrix until convergence is reached */
        
 #ifdef DEBUG    int i, ii,j,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);    double min, max, maxmin, maxmax,sumnew=0.;
 #endif    double **matprod2();
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    double **out, cov[NCOVMAX], **pmij();
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    double **newm;
         k=kmax;    double agefin, delaymax=50 ; /* Max number of years to converge */
       }  
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    for (ii=1;ii<=nlstate+ndeath;ii++)
         k=kmax; l=lmax*10.;      for (j=1;j<=nlstate+ndeath;j++){
       }        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){      }
         delts=delt;  
       }     cov[1]=1.;
     }   
   }   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   delti[theta]=delts;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   return res;      newm=savm;
        /* Covariates have to be included here again */
 }       cov[2]=agefin;
     
 double hessij( double x[], double delti[], int thetai,int thetaj)        for (k=1; k<=cptcovn;k++) {
 {          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   int i;          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
   int l=1, l1, lmax=20;        }
   double k1,k2,k3,k4,res,fx;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   double p2[NPARMAX+1];        for (k=1; k<=cptcovprod;k++)
   int k;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
   fx=func(x);        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   for (k=1; k<=2; k++) {        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
     for (i=1;i<=npar;i++) p2[i]=x[i];        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
     p2[thetai]=x[thetai]+delti[thetai]/k;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k1=func(p2)-fx;      savm=oldm;
        oldm=newm;
     p2[thetai]=x[thetai]+delti[thetai]/k;      maxmax=0.;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      for(j=1;j<=nlstate;j++){
     k2=func(p2)-fx;        min=1.;
          max=0.;
     p2[thetai]=x[thetai]-delti[thetai]/k;        for(i=1; i<=nlstate; i++) {
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          sumnew=0;
     k3=func(p2)-fx;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
            prlim[i][j]= newm[i][j]/(1-sumnew);
     p2[thetai]=x[thetai]-delti[thetai]/k;          max=FMAX(max,prlim[i][j]);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          min=FMIN(min,prlim[i][j]);
     k4=func(p2)-fx;        }
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        maxmin=max-min;
 #ifdef DEBUG        maxmax=FMAX(maxmax,maxmin);
     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      if(maxmax < ftolpl){
   }        return prlim;
   return res;      }
 }    }
   }
 /************** Inverse of matrix **************/  
 void ludcmp(double **a, int n, int *indx, double *d)  /*************** transition probabilities ***************/ 
 {  
   int i,imax,j,k;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   double big,dum,sum,temp;  {
   double *vv;    double s1, s2;
      /*double t34;*/
   vv=vector(1,n);    int i,j,j1, nc, ii, jj;
   *d=1.0;  
   for (i=1;i<=n;i++) {      for(i=1; i<= nlstate; i++){
     big=0.0;        for(j=1; j<i;j++){
     for (j=1;j<=n;j++)          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
       if ((temp=fabs(a[i][j])) > big) big=temp;            /*s2 += param[i][j][nc]*cov[nc];*/
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     vv[i]=1.0/big;  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
   }          }
   for (j=1;j<=n;j++) {          ps[i][j]=s2;
     for (i=1;i<j;i++) {  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
       sum=a[i][j];        }
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        for(j=i+1; j<=nlstate+ndeath;j++){
       a[i][j]=sum;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     }            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     big=0.0;  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
     for (i=j;i<=n;i++) {          }
       sum=a[i][j];          ps[i][j]=s2;
       for (k=1;k<j;k++)        }
         sum -= a[i][k]*a[k][j];      }
       a[i][j]=sum;      /*ps[3][2]=1;*/
       if ( (dum=vv[i]*fabs(sum)) >= big) {      
         big=dum;      for(i=1; i<= nlstate; i++){
         imax=i;        s1=0;
       }        for(j=1; j<i; j++)
     }          s1+=exp(ps[i][j]);
     if (j != imax) {        for(j=i+1; j<=nlstate+ndeath; j++)
       for (k=1;k<=n;k++) {          s1+=exp(ps[i][j]);
         dum=a[imax][k];        ps[i][i]=1./(s1+1.);
         a[imax][k]=a[j][k];        for(j=1; j<i; j++)
         a[j][k]=dum;          ps[i][j]= exp(ps[i][j])*ps[i][i];
       }        for(j=i+1; j<=nlstate+ndeath; j++)
       *d = -(*d);          ps[i][j]= exp(ps[i][j])*ps[i][i];
       vv[imax]=vv[j];        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     }      } /* end i */
     indx[j]=imax;      
     if (a[j][j] == 0.0) a[j][j]=TINY;      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     if (j != n) {        for(jj=1; jj<= nlstate+ndeath; jj++){
       dum=1.0/(a[j][j]);          ps[ii][jj]=0;
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          ps[ii][ii]=1;
     }        }
   }      }
   free_vector(vv,1,n);  /* Doesn't work */      
 ;  
 }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
 void lubksb(double **a, int n, int *indx, double b[])  /*         printf("ddd %lf ",ps[ii][jj]); */
 {  /*       } */
   int i,ii=0,ip,j;  /*       printf("\n "); */
   double sum;  /*        } */
    /*        printf("\n ");printf("%lf ",cov[2]); */
   for (i=1;i<=n;i++) {         /*
     ip=indx[i];        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     sum=b[ip];        goto end;*/
     b[ip]=b[i];      return ps;
     if (ii)  }
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  
     else if (sum) ii=i;  /**************** Product of 2 matrices ******************/
     b[i]=sum;  
   }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   for (i=n;i>=1;i--) {  {
     sum=b[i];    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     b[i]=sum/a[i][i];    /* 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;
 /************ Frequencies ********************/    for(i=nrl; i<= nrh; i++)
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)      for(k=ncolol; k<=ncoloh; k++)
 {  /* Some frequencies */        for(j=ncl,out[i][k]=0.; j<=nch; j++)
            out[i][k] +=in[i][j]*b[j][k];
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  
   double ***freq; /* Frequencies */    return out;
   double *pp;  }
   double pos;  
   FILE *ficresp;  
   char fileresp[FILENAMELENGTH];  /************* Higher Matrix Product ***************/
   
   pp=vector(1,nlstate);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   {
   strcpy(fileresp,"p");    /* Computes the transition matrix starting at age 'age' over 
   strcat(fileresp,fileres);       'nhstepm*hstepm*stepm' months (i.e. until
   if((ficresp=fopen(fileresp,"w"))==NULL) {       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     printf("Problem with prevalence resultfile: %s\n", fileresp);       nhstepm*hstepm matrices. 
     exit(0);       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 
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);       for the memory).
   j1=0;       Model is determined by parameters x and covariates have to be 
        included manually here. 
   j=cptcoveff;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}       */
   
   for(k1=1; k1<=j;k1++){    int i, j, d, h, k;
    for(i1=1; i1<=ncodemax[k1];i1++){    double **out, cov[NCOVMAX];
        j1++;    double **newm;
   
         for (i=-1; i<=nlstate+ndeath; i++)      /* Hstepm could be zero and should return the unit matrix */
          for (jk=-1; jk<=nlstate+ndeath; jk++)      for (i=1;i<=nlstate+ndeath;i++)
            for(m=agemin; m <= agemax+3; m++)      for (j=1;j<=nlstate+ndeath;j++){
              freq[i][jk][m]=0;        oldm[i][j]=(i==j ? 1.0 : 0.0);
                po[i][j][0]=(i==j ? 1.0 : 0.0);
        for (i=1; i<=imx; i++) {      }
          bool=1;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
          if  (cptcovn>0) {    for(h=1; h <=nhstepm; h++){
            for (z1=1; z1<=cptcoveff; z1++)      for(d=1; d <=hstepm; d++){
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) bool=0;        newm=savm;
          }        /* Covariates have to be included here again */
           if (bool==1) {        cov[1]=1.;
            for(m=firstpass; m<=lastpass-1; m++){        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
              if(agev[m][i]==0) agev[m][i]=agemax+1;        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
              if(agev[m][i]==1) agev[m][i]=agemax+2;        for (k=1; k<=cptcovage;k++)
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        for (k=1; k<=cptcovprod;k++)
            }          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
          }  
        }  
         if  (cptcovn>0) {        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          fprintf(ficresp, "\n#********** Variable ");        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
        }                     pmij(pmmij,cov,ncovmodel,x,nlstate));
        fprintf(ficresp, "**********\n#");        savm=oldm;
        for(i=1; i<=nlstate;i++)        oldm=newm;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      }
        fprintf(ficresp, "\n");      for(i=1; i<=nlstate+ndeath; i++)
                for(j=1;j<=nlstate+ndeath;j++) {
   for(i=(int)agemin; i <= (int)agemax+3; i++){          po[i][j][h]=newm[i][j];
     if(i==(int)agemax+3)          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       printf("Total");           */
     else        }
       printf("Age %d", i);    } /* end h */
     for(jk=1; jk <=nlstate ; jk++){    return po;
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  }
         pp[jk] += freq[jk][m][i];  
     }  
     for(jk=1; jk <=nlstate ; jk++){  /*************** log-likelihood *************/
       for(m=-1, pos=0; m <=0 ; m++)  double func( double *x)
         pos += freq[jk][m][i];  {
       if(pp[jk]>=1.e-10)    int i, ii, j, k, mi, d, kk;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
       else    double **out;
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);    double sw; /* Sum of weights */
     }    double lli; /* Individual log likelihood */
     for(jk=1; jk <=nlstate ; jk++){    int s1, s2;
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)    double bbh, survp;
         pp[jk] += freq[jk][m][i];    long ipmx;
     }    /*extern weight */
     for(jk=1,pos=0; jk <=nlstate ; jk++)    /* We are differentiating ll according to initial status */
       pos += pp[jk];    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     for(jk=1; jk <=nlstate ; jk++){    /*for(i=1;i<imx;i++) 
       if(pos>=1.e-5)      printf(" %d\n",s[4][i]);
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    */
       else    cov[1]=1.;
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  
       if( i <= (int) agemax){    for(k=1; k<=nlstate; k++) ll[k]=0.;
         if(pos>=1.e-5)  
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    if(mle==1){
       else      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        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(jk=-1; jk <=nlstate+ndeath; jk++)            for (j=1;j<=nlstate+ndeath;j++){
       for(m=-1; m <=nlstate+ndeath; m++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     if(i <= (int) agemax)            }
       fprintf(ficresp,"\n");          for(d=0; d<dh[mi][i]; d++){
     printf("\n");            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];
              }
   fclose(ficresp);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   free_vector(pp,1,nlstate);            savm=oldm;
             oldm=newm;
 }  /* End of Freq */          } /* end mult */
         
 /************* Waves Concatenation ***************/          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           /* But now since version 0.9 we anticipate for bias at large 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)           * If stepm is larger than one month (smallest stepm) and if the exact delay 
 {           * (in months) between two waves is not a multiple of stepm, we rounded to 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.           * the nearest (and in case of equal distance, to the lowest) interval but now
      Death is a valid wave (if date is known).           * we keep into memory the bias bh[mi][i] and also the previous matrix product
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]           * probability in order to take into account the bias as a fraction of the way
      and mw[mi+1][i]. dh depends on stepm.           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
      */           * -stepm/2 to stepm/2 .
            * For stepm=1 the results are the same as for previous versions of Imach.
   int i, mi, m;           * For stepm > 1 the results are less biased than in previous versions. 
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;           */
 float sum=0.;          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   for(i=1; i<=imx; i++){          bbh=(double)bh[mi][i]/(double)stepm; 
     mi=0;          /* bias bh is positive if real duration
     m=firstpass;           * is higher than the multiple of stepm and negative otherwise.
     while(s[m][i] <= nlstate){           */
       if(s[m][i]>=1)          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
         mw[++mi][i]=m;          if( s2 > nlstate){ 
       if(m >=lastpass)            /* i.e. if s2 is a death state and if the date of death is known 
         break;               then the contribution to the likelihood is the probability to 
       else               die between last step unit time and current  step unit time, 
         m++;               which is also equal to probability to die before dh 
     }/* end while */               minus probability to die before dh-stepm . 
     if (s[m][i] > nlstate){               In version up to 0.92 likelihood was computed
       mi++;     /* Death is another wave */          as if date of death was unknown. Death was treated as any other
       /* if(mi==0)  never been interviewed correctly before death */          health state: the date of the interview describes the actual state
          /* Only death is a correct wave */          and not the date of a change in health state. The former idea was
       mw[mi][i]=m;          to consider that at each interview the state was recorded
     }          (healthy, disable or death) and IMaCh was corrected; but when we
           introduced the exact date of death then we should have modified
     wav[i]=mi;          the contribution of an exact death to the likelihood. This new
     if(mi==0)          contribution is smaller and very dependent of the step unit
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          stepm. It is no more the probability to die between last interview
   }          and month of death but the probability to survive from last
           interview up to one month before death multiplied by the
   for(i=1; i<=imx; i++){          probability to die within a month. Thanks to Chris
     for(mi=1; mi<wav[i];mi++){          Jackson for correcting this bug.  Former versions increased
       if (stepm <=0)          mortality artificially. The bad side is that we add another loop
         dh[mi][i]=1;          which slows down the processing. The difference can be up to 10%
       else{          lower mortality.
         if (s[mw[mi+1][i]][i] > nlstate) {            */
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            lli=log(out[s1][s2] - savm[s1][s2]);
           if(j=0) j=1;  /* Survives at least one month after exam */  
         }  
         else{          } else if  (s2==-2) {
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));            for (j=1,survp=0. ; j<=nlstate; j++) 
           k=k+1;              survp += out[s1][j];
           if (j >= jmax) jmax=j;            lli= survp;
           else if (j <= jmin)jmin=j;          }
           sum=sum+j;          
         }          else if  (s2==-4) {
         jk= j/stepm;            for (j=3,survp=0. ; j<=nlstate; j++) 
         jl= j -jk*stepm;              survp += out[s1][j];
         ju= j -(jk+1)*stepm;            lli= survp;
         if(jl <= -ju)          }
           dh[mi][i]=jk;          
         else          else if  (s2==-5) {
           dh[mi][i]=jk+1;            for (j=1,survp=0. ; j<=2; j++) 
         if(dh[mi][i]==0)              survp += out[s1][j];
           dh[mi][i]=1; /* At least one step */            lli= survp;
       }          }
     }  
   }  
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);          else{
 }            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 /*********** Tricode ****************************/            /*  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 */
 void tricode(int *Tvar, int **nbcode, int imx)          } 
 {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   int Ndum[20],ij=1, k, j, i;          /*if(lli ==000.0)*/
   int cptcode=0;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
   cptcoveff=0;          ipmx +=1;
            sw += weight[i];
   for (k=0; k<19; k++) Ndum[k]=0;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   for (k=1; k<=7; k++) ncodemax[k]=0;        } /* end of wave */
       } /* end of individual */
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {    }  else if(mle==2){
     for (i=1; i<=imx; i++) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       ij=(int)(covar[Tvar[j]][i]);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       Ndum[ij]++;        for(mi=1; mi<= wav[i]-1; mi++){
       if (ij > cptcode) cptcode=ij;          for (ii=1;ii<=nlstate+ndeath;ii++)
     }            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=0; i<=cptcode; i++) {            }
       if(Ndum[i]!=0) ncodemax[j]++;          for(d=0; d<=dh[mi][i]; d++){
     }            newm=savm;
     ij=1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
     for (i=1; i<=ncodemax[j]; i++) {              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for (k=0; k<=19; k++) {            }
         if (Ndum[k] != 0) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           nbcode[Tvar[j]][ij]=k;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           /*   printf("ij=%d ",nbcode[Tvar[2]][1]);*/            savm=oldm;
           ij++;            oldm=newm;
         }          } /* end mult */
         if (ij > ncodemax[j]) break;        
       }            s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
   }            bbh=(double)bh[mi][i]/(double)stepm; 
  for (i=1; i<=10; i++) {          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       ij=Tvar[i];          ipmx +=1;
       Ndum[ij]++;          sw += weight[i];
     }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
  ij=1;        } /* end of wave */
  for (i=1; i<=cptcovn; i++) {      } /* end of individual */
    if((Ndum[i]!=0) && (i<=ncov)){    }  else if(mle==3){  /* exponential inter-extrapolation */
      Tvaraff[i]=ij;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
    ij++;        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 (j=1;j<=nlstate+ndeath;j++){
  for (j=1; j<=(cptcovn+2*cptcovprod); j++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
    if ((Tvar[j]>= cptcoveff) && (Tvar[j] <=ncov)) cptcoveff=Tvar[j];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    /*printf("j=%d %d\n",j,Tvar[j]);*/            }
  }          for(d=0; d<dh[mi][i]; d++){
              newm=savm;
  /* printf("cptcoveff=%d Tvaraff=%d %d\n",cptcoveff, Tvaraff[1],Tvaraff[2]);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     scanf("%d",i);*/            for (kk=1; kk<=cptcovage;kk++) {
 }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
 /*********** Health Expectancies ****************/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)            savm=oldm;
 {            oldm=newm;
   /* Health expectancies */          } /* end mult */
   int i, j, nhstepm, hstepm, h;        
   double age, agelim,hf;          s1=s[mw[mi][i]][i];
   double ***p3mat;          s2=s[mw[mi+1][i]][i];
            bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficreseij,"# Health expectancies\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])); /* exponential inter-extrapolation */
   fprintf(ficreseij,"# Age");          ipmx +=1;
   for(i=1; i<=nlstate;i++)          sw += weight[i];
     for(j=1; j<=nlstate;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficreseij," %1d-%1d",i,j);        } /* end of wave */
   fprintf(ficreseij,"\n");      } /* end of individual */
     }else if (mle==4){  /* ml=4 no inter-extrapolation */
   hstepm=1*YEARM; /*  Every j years of age (in month) */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
   agelim=AGESUP;          for (ii=1;ii<=nlstate+ndeath;ii++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            for (j=1;j<=nlstate+ndeath;j++){
     /* nhstepm age range expressed in number of stepm */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* Typically if 20 years = 20*12/6=40 stepm */            }
     if (stepm >= YEARM) hstepm=1;          for(d=0; d<dh[mi][i]; d++){
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */            newm=savm;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            for (kk=1; kk<=cptcovage;kk++) {
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              }
           
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1; j<=nlstate;j++)            savm=oldm;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){            oldm=newm;
           eij[i][j][(int)age] +=p3mat[i][j][h];          } /* end mult */
         }        
              s1=s[mw[mi][i]][i];
     hf=1;          s2=s[mw[mi+1][i]][i];
     if (stepm >= YEARM) hf=stepm/YEARM;          if( s2 > nlstate){ 
     fprintf(ficreseij,"%.0f",age );            lli=log(out[s1][s2] - savm[s1][s2]);
     for(i=1; i<=nlstate;i++)          }else{
       for(j=1; j<=nlstate;j++){            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);          }
       }          ipmx +=1;
     fprintf(ficreseij,"\n");          sw += weight[i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   }  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
 }        } /* end of wave */
       } /* end of individual */
 /************ Variance ******************/    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   /* Variance of health expectancies */        for(mi=1; mi<= wav[i]-1; mi++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          for (ii=1;ii<=nlstate+ndeath;ii++)
   double **newm;            for (j=1;j<=nlstate+ndeath;j++){
   double **dnewm,**doldm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j, nhstepm, hstepm, h;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int k, cptcode;            }
    double *xp;          for(d=0; d<dh[mi][i]; d++){
   double **gp, **gm;            newm=savm;
   double ***gradg, ***trgradg;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double ***p3mat;            for (kk=1; kk<=cptcovage;kk++) {
   double age,agelim;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int theta;            }
           
    fprintf(ficresvij,"# Covariances of life expectancies\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   fprintf(ficresvij,"# Age");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   for(i=1; i<=nlstate;i++)            savm=oldm;
     for(j=1; j<=nlstate;j++)            oldm=newm;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          } /* end mult */
   fprintf(ficresvij,"\n");        
           s1=s[mw[mi][i]][i];
   xp=vector(1,npar);          s2=s[mw[mi+1][i]][i];
   dnewm=matrix(1,nlstate,1,npar);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   doldm=matrix(1,nlstate,1,nlstate);          ipmx +=1;
            sw += weight[i];
   hstepm=1*YEARM; /* Every year of age */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          /*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]);*/
   agelim = AGESUP;        } /* end of wave */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      } /* end of individual */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    } /* End of if */
     if (stepm >= YEARM) hstepm=1;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    return -l;
     gp=matrix(0,nhstepm,1,nlstate);  }
     gm=matrix(0,nhstepm,1,nlstate);  
   /*************** log-likelihood *************/
     for(theta=1; theta <=npar; theta++){  double funcone( double *x)
       for(i=1; i<=npar; i++){ /* Computes gradient */  {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    /* Same as likeli but slower because of a lot of printf and if */
       }    int i, ii, j, k, mi, d, kk;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      double l, ll[NLSTATEMAX], cov[NCOVMAX];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double **out;
       for(j=1; j<= nlstate; j++){    double lli; /* Individual log likelihood */
         for(h=0; h<=nhstepm; h++){    double llt;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    int s1, s2;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    double bbh, survp;
         }    /*extern weight */
       }    /* We are differentiating ll according to initial status */
        /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       for(i=1; i<=npar; i++) /* Computes gradient */    /*for(i=1;i<imx;i++) 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      printf(" %d\n",s[4][i]);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    cov[1]=1.;
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){    for(k=1; k<=nlstate; k++) ll[k]=0.;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }      for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j<= nlstate; j++)        for (ii=1;ii<=nlstate+ndeath;ii++)
         for(h=0; h<=nhstepm; h++){          for (j=1;j<=nlstate+ndeath;j++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            savm[ii][j]=(ii==j ? 1.0 : 0.0);
     } /* End theta */          }
         for(d=0; d<dh[mi][i]; d++){
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          newm=savm;
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(h=0; h<=nhstepm; h++)          for (kk=1; kk<=cptcovage;kk++) {
       for(j=1; j<=nlstate;j++)            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for(theta=1; theta <=npar; theta++)          }
           trgradg[h][j][theta]=gradg[h][theta][j];          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(i=1;i<=nlstate;i++)          savm=oldm;
       for(j=1;j<=nlstate;j++)          oldm=newm;
         vareij[i][j][(int)age] =0.;        } /* end mult */
     for(h=0;h<=nhstepm;h++){        
       for(k=0;k<=nhstepm;k++){        s1=s[mw[mi][i]][i];
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);        s2=s[mw[mi+1][i]][i];
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        bbh=(double)bh[mi][i]/(double)stepm; 
         for(i=1;i<=nlstate;i++)        /* bias is positive if real duration
           for(j=1;j<=nlstate;j++)         * is higher than the multiple of stepm and negative otherwise.
             vareij[i][j][(int)age] += doldm[i][j];         */
       }        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     }          lli=log(out[s1][s2] - savm[s1][s2]);
     h=1;        } else if (mle==1){
     if (stepm >= YEARM) h=stepm/YEARM;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     fprintf(ficresvij,"%.0f ",age );        } else if(mle==2){
     for(i=1; i<=nlstate;i++)          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       for(j=1; j<=nlstate;j++){        } else if(mle==3){  /* exponential inter-extrapolation */
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       }        } else if (mle==4){  /* mle=4 no inter-extrapolation */
     fprintf(ficresvij,"\n");          lli=log(out[s1][s2]); /* Original formula */
     free_matrix(gp,0,nhstepm,1,nlstate);        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
     free_matrix(gm,0,nhstepm,1,nlstate);          lli=log(out[s1][s2]); /* Original formula */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        } /* End of if */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        ipmx +=1;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        sw += weight[i];
   } /* End age */        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   free_vector(xp,1,npar);        if(globpr){
   free_matrix(doldm,1,nlstate,1,npar);          fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
   free_matrix(dnewm,1,nlstate,1,nlstate);   %10.6f %10.6f %10.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
 }                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
 /************ Variance of prevlim ******************/            llt +=ll[k]*gipmx/gsw;
 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)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
 {          }
   /* Variance of prevalence limit */          fprintf(ficresilk," %10.6f\n", -llt);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        }
   double **newm;      } /* end of wave */
   double **dnewm,**doldm;    } /* end of individual */
   int i, j, nhstepm, hstepm;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   int k, cptcode;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double *xp;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double *gp, *gm;    if(globpr==0){ /* First time we count the contributions and weights */
   double **gradg, **trgradg;      gipmx=ipmx;
   double age,agelim;      gsw=sw;
   int theta;    }
        return -l;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  }
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)  
       fprintf(ficresvpl," %1d-%1d",i,i);  /*************** function likelione ***********/
   fprintf(ficresvpl,"\n");  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
   xp=vector(1,npar);    /* This routine should help understanding what is done with 
   dnewm=matrix(1,nlstate,1,npar);       the selection of individuals/waves and
   doldm=matrix(1,nlstate,1,nlstate);       to check the exact contribution to the likelihood.
         Plotting could be done.
   hstepm=1*YEARM; /* Every year of age */     */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    int k;
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    if(*globpri !=0){ /* Just counts and sums, no printings */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      strcpy(fileresilk,"ilk"); 
     if (stepm >= YEARM) hstepm=1;      strcat(fileresilk,fileres);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
     gradg=matrix(1,npar,1,nlstate);        printf("Problem with resultfile: %s\n", fileresilk);
     gp=vector(1,nlstate);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     gm=vector(1,nlstate);      }
       fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
     for(theta=1; theta <=npar; theta++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       for(i=1; i<=npar; i++){ /* Computes gradient */      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for(k=1; k<=nlstate; k++) 
       }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       for(i=1;i<=nlstate;i++)    }
         gp[i] = prlim[i][i];  
        *fretone=(*funcone)(p);
       for(i=1; i<=npar; i++) /* Computes gradient */    if(*globpri !=0){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      fclose(ficresilk);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       for(i=1;i<=nlstate;i++)      fflush(fichtm); 
         gm[i] = prlim[i][i];    } 
     return;
       for(i=1;i<=nlstate;i++)  }
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */  
   /*********** Maximum Likelihood Estimation ***************/
     trgradg =matrix(1,nlstate,1,npar);  
   void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     for(j=1; j<=nlstate;j++)  {
       for(theta=1; theta <=npar; theta++)    int i,j, iter;
         trgradg[j][theta]=gradg[theta][j];    double **xi;
     double fret;
     for(i=1;i<=nlstate;i++)    double fretone; /* Only one call to likelihood */
       varpl[i][(int)age] =0.;    /*  char filerespow[FILENAMELENGTH];*/
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    xi=matrix(1,npar,1,npar);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    for (i=1;i<=npar;i++)
     for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++)
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     fprintf(ficresvpl,"%.0f ",age );    strcpy(filerespow,"pow"); 
     for(i=1; i<=nlstate;i++)    strcat(filerespow,fileres);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     fprintf(ficresvpl,"\n");      printf("Problem with resultfile: %s\n", filerespow);
     free_vector(gp,1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     free_vector(gm,1,nlstate);    }
     free_matrix(gradg,1,npar,1,nlstate);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     free_matrix(trgradg,1,nlstate,1,npar);    for (i=1;i<=nlstate;i++)
   } /* End age */      for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   free_vector(xp,1,npar);    fprintf(ficrespow,"\n");
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    powell(p,xi,npar,ftol,&iter,&fret,func);
   
 }    fclose(ficrespow);
     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));
 /***********************************************/  
 /**************** Main Program *****************/  }
 /***********************************************/  
   /**** Computes Hessian and covariance matrix ***/
 /*int main(int argc, char *argv[])*/  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
 int main()  {
 {    double  **a,**y,*x,pd;
     double **hess;
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;    int i, j,jk;
   double agedeb, agefin,hf;    int *indx;
   double agemin=1.e20, agemax=-1.e20;  
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   double fret;    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   double **xi,tmp,delta;    void lubksb(double **a, int npar, int *indx, double b[]) ;
     void ludcmp(double **a, int npar, int *indx, double *d) ;
   double dum; /* Dummy variable */    double gompertz(double p[]);
   double ***p3mat;    hess=matrix(1,npar,1,npar);
   int *indx;  
   char line[MAXLINE], linepar[MAXLINE];    printf("\nCalculation of the hessian matrix. Wait...\n");
   char title[MAXLINE];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    for (i=1;i<=npar;i++){
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];      printf("%d",i);fflush(stdout);
   char filerest[FILENAMELENGTH];      fprintf(ficlog,"%d",i);fflush(ficlog);
   char fileregp[FILENAMELENGTH];     
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   int firstobs=1, lastobs=10;      
   int sdeb, sfin; /* Status at beginning and end */      /*  printf(" %f ",p[i]);
   int c,  h , cpt,l;          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   int ju,jl, mi;    }
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    for (i=1;i<=npar;i++) {
        for (j=1;j<=npar;j++)  {
   int hstepm, nhstepm;        if (j>i) { 
   double bage, fage, age, agelim, agebase;          printf(".%d%d",i,j);fflush(stdout);
   double ftolpl=FTOL;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double **prlim;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double *severity;          
   double ***param; /* Matrix of parameters */          hess[j][i]=hess[i][j];    
   double  *p;          /*printf(" %lf ",hess[i][j]);*/
   double **matcov; /* Matrix of covariance */        }
   double ***delti3; /* Scale */      }
   double *delti; /* Scale */    }
   double ***eij, ***vareij;    printf("\n");
   double **varpl; /* Variances of prevalence limits by age */    fprintf(ficlog,"\n");
   double *epj, vepp;  
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   char *alph[]={"a","a","b","c","d","e"}, str[4];    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     
   char z[1]="c", occ;    a=matrix(1,npar,1,npar);
 #include <sys/time.h>    y=matrix(1,npar,1,npar);
 #include <time.h>    x=vector(1,npar);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    indx=ivector(1,npar);
   /* long total_usecs;    for (i=1;i<=npar;i++)
   struct timeval start_time, end_time;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
      ludcmp(a,npar,indx,&pd);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
     for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   printf("\nIMACH, Version 0.64a");      x[j]=1;
   printf("\nEnter the parameter file name: ");      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
 #ifdef windows        matcov[i][j]=x[i];
   scanf("%s",pathtot);      }
   getcwd(pathcd, size);    }
   /*cygwin_split_path(pathtot,path,optionfile);  
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    printf("\n#Hessian matrix#\n");
   /* cutv(path,optionfile,pathtot,'\\');*/    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
 split(pathtot, path,optionfile);      for (j=1;j<=npar;j++) { 
   chdir(path);        printf("%.3e ",hess[i][j]);
   replace(pathc,path);        fprintf(ficlog,"%.3e ",hess[i][j]);
 #endif      }
 #ifdef unix      printf("\n");
   scanf("%s",optionfile);      fprintf(ficlog,"\n");
 #endif    }
   
 /*-------- arguments in the command line --------*/    /* Recompute Inverse */
     for (i=1;i<=npar;i++)
   strcpy(fileres,"r");      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   strcat(fileres, optionfile);    ludcmp(a,npar,indx,&pd);
   
   /*---------arguments file --------*/    /*  printf("\n#Hessian matrix recomputed#\n");
   
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    for (j=1;j<=npar;j++) {
     printf("Problem with optionfile %s\n",optionfile);      for (i=1;i<=npar;i++) x[i]=0;
     goto end;      x[j]=1;
   }      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
   strcpy(filereso,"o");        y[i][j]=x[i];
   strcat(filereso,fileres);        printf("%.3e ",y[i][j]);
   if((ficparo=fopen(filereso,"w"))==NULL) {        fprintf(ficlog,"%.3e ",y[i][j]);
     printf("Problem with Output resultfile: %s\n", filereso);goto end;      }
   }      printf("\n");
       fprintf(ficlog,"\n");
   /* Reads comments: lines beginning with '#' */    }
   while((c=getc(ficpar))=='#' && c!= EOF){    */
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    free_matrix(a,1,npar,1,npar);
     puts(line);    free_matrix(y,1,npar,1,npar);
     fputs(line,ficparo);    free_vector(x,1,npar);
   }    free_ivector(indx,1,npar);
   ungetc(c,ficpar);    free_matrix(hess,1,npar,1,npar);
   
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);  
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);  }
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);  
   /*************** hessian matrix ****************/
   covar=matrix(0,NCOVMAX,1,n);      double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   if (strlen(model)<=1) cptcovn=0;  {
   else {    int i;
     j=0;    int l=1, lmax=20;
     j=nbocc(model,'+');    double k1,k2;
     cptcovn=j+1;    double p2[NPARMAX+1];
   }    double res;
     double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   ncovmodel=2+cptcovn;    double fx;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    int k=0,kmax=10;
      double l1;
   /* Read guess parameters */  
   /* Reads comments: lines beginning with '#' */    fx=func(x);
   while((c=getc(ficpar))=='#' && c!= EOF){    for (i=1;i<=npar;i++) p2[i]=x[i];
     ungetc(c,ficpar);    for(l=0 ; l <=lmax; l++){
     fgets(line, MAXLINE, ficpar);      l1=pow(10,l);
     puts(line);      delts=delt;
     fputs(line,ficparo);      for(k=1 ; k <kmax; k=k+1){
   }        delt = delta*(l1*k);
   ungetc(c,ficpar);        p2[theta]=x[theta] +delt;
          k1=func(p2)-fx;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        p2[theta]=x[theta]-delt;
     for(i=1; i <=nlstate; i++)        k2=func(p2)-fx;
     for(j=1; j <=nlstate+ndeath-1; j++){        /*res= (k1-2.0*fx+k2)/delt/delt; */
       fscanf(ficpar,"%1d%1d",&i1,&j1);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
       fprintf(ficparo,"%1d%1d",i1,j1);        
       printf("%1d%1d",i,j);  #ifdef DEBUG
       for(k=1; k<=ncovmodel;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);
         fscanf(ficpar," %lf",&param[i][j][k]);        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);
         printf(" %lf",param[i][j][k]);  #endif
         fprintf(ficparo," %lf",param[i][j][k]);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       fscanf(ficpar,"\n");          k=kmax;
       printf("\n");        }
       fprintf(ficparo,"\n");        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     }          k=kmax; l=lmax*10.;
          }
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   p=param[1][1];          delts=delt;
          }
   /* Reads comments: lines beginning with '#' */      }
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    delti[theta]=delts;
     fgets(line, MAXLINE, ficpar);    return res; 
     puts(line);    
     fputs(line,ficparo);  }
   }  
   ungetc(c,ficpar);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   {
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    int i;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    int l=1, l1, lmax=20;
   for(i=1; i <=nlstate; i++){    double k1,k2,k3,k4,res,fx;
     for(j=1; j <=nlstate+ndeath-1; j++){    double p2[NPARMAX+1];
       fscanf(ficpar,"%1d%1d",&i1,&j1);    int k;
       printf("%1d%1d",i,j);  
       fprintf(ficparo,"%1d%1d",i1,j1);    fx=func(x);
       for(k=1; k<=ncovmodel;k++){    for (k=1; k<=2; k++) {
         fscanf(ficpar,"%le",&delti3[i][j][k]);      for (i=1;i<=npar;i++) p2[i]=x[i];
         printf(" %le",delti3[i][j][k]);      p2[thetai]=x[thetai]+delti[thetai]/k;
         fprintf(ficparo," %le",delti3[i][j][k]);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       }      k1=func(p2)-fx;
       fscanf(ficpar,"\n");    
       printf("\n");      p2[thetai]=x[thetai]+delti[thetai]/k;
       fprintf(ficparo,"\n");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     }      k2=func(p2)-fx;
   }    
   delti=delti3[1][1];      p2[thetai]=x[thetai]-delti[thetai]/k;
        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   /* Reads comments: lines beginning with '#' */      k3=func(p2)-fx;
   while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);      p2[thetai]=x[thetai]-delti[thetai]/k;
     fgets(line, MAXLINE, ficpar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     puts(line);      k4=func(p2)-fx;
     fputs(line,ficparo);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   }  #ifdef DEBUG
   ungetc(c,ficpar);      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
        fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   matcov=matrix(1,npar,1,npar);  #endif
   for(i=1; i <=npar; i++){    }
     fscanf(ficpar,"%s",&str);    return res;
     printf("%s",str);  }
     fprintf(ficparo,"%s",str);  
     for(j=1; j <=i; j++){  /************** Inverse of matrix **************/
       fscanf(ficpar," %le",&matcov[i][j]);  void ludcmp(double **a, int n, int *indx, double *d) 
       printf(" %.5le",matcov[i][j]);  { 
       fprintf(ficparo," %.5le",matcov[i][j]);    int i,imax,j,k; 
     }    double big,dum,sum,temp; 
     fscanf(ficpar,"\n");    double *vv; 
     printf("\n");   
     fprintf(ficparo,"\n");    vv=vector(1,n); 
   }    *d=1.0; 
   for(i=1; i <=npar; i++)    for (i=1;i<=n;i++) { 
     for(j=i+1;j<=npar;j++)      big=0.0; 
       matcov[i][j]=matcov[j][i];      for (j=1;j<=n;j++) 
            if ((temp=fabs(a[i][j])) > big) big=temp; 
   printf("\n");      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       vv[i]=1.0/big; 
     } 
     /*-------- data file ----------*/    for (j=1;j<=n;j++) { 
     if((ficres =fopen(fileres,"w"))==NULL) {      for (i=1;i<j;i++) { 
       printf("Problem with resultfile: %s\n", fileres);goto end;        sum=a[i][j]; 
     }        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     fprintf(ficres,"#%s\n",version);        a[i][j]=sum; 
          } 
     if((fic=fopen(datafile,"r"))==NULL)    {      big=0.0; 
       printf("Problem with datafile: %s\n", datafile);goto end;      for (i=j;i<=n;i++) { 
     }        sum=a[i][j]; 
         for (k=1;k<j;k++) 
     n= lastobs;          sum -= a[i][k]*a[k][j]; 
     severity = vector(1,maxwav);        a[i][j]=sum; 
     outcome=imatrix(1,maxwav+1,1,n);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
     num=ivector(1,n);          big=dum; 
     moisnais=vector(1,n);          imax=i; 
     annais=vector(1,n);        } 
     moisdc=vector(1,n);      } 
     andc=vector(1,n);      if (j != imax) { 
     agedc=vector(1,n);        for (k=1;k<=n;k++) { 
     cod=ivector(1,n);          dum=a[imax][k]; 
     weight=vector(1,n);          a[imax][k]=a[j][k]; 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */          a[j][k]=dum; 
     mint=matrix(1,maxwav,1,n);        } 
     anint=matrix(1,maxwav,1,n);        *d = -(*d); 
     s=imatrix(1,maxwav+1,1,n);        vv[imax]=vv[j]; 
     adl=imatrix(1,maxwav+1,1,n);          } 
     tab=ivector(1,NCOVMAX);      indx[j]=imax; 
     ncodemax=ivector(1,8);      if (a[j][j] == 0.0) a[j][j]=TINY; 
       if (j != n) { 
     i=1;        dum=1.0/(a[j][j]); 
     while (fgets(line, MAXLINE, fic) != NULL)    {        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       if ((i >= firstobs) && (i <=lastobs)) {      } 
            } 
         for (j=maxwav;j>=1;j--){    free_vector(vv,1,n);  /* Doesn't work */
           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);  void lubksb(double **a, int n, int *indx, double b[]) 
         }  { 
            int i,ii=0,ip,j; 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    double sum; 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);   
     for (i=1;i<=n;i++) { 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      ip=indx[i]; 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      sum=b[ip]; 
       b[ip]=b[i]; 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      if (ii) 
         for (j=ncov;j>=1;j--){        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      else if (sum) ii=i; 
         }      b[i]=sum; 
         num[i]=atol(stra);    } 
     for (i=n;i>=1;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]));*/      sum=b[i]; 
       for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
         i=i+1;      b[i]=sum/a[i][i]; 
       }    } 
     }  } 
   
     /*scanf("%d",i);*/  /************ Frequencies ********************/
   imx=i-1; /* Number of individuals */  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
   {  /* Some frequencies */
   /* Calculation of the number of parameter from char model*/    
   Tvar=ivector(1,15);    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   Tprod=ivector(1,15);    int first;
   Tvaraff=ivector(1,15);    double ***freq; /* Frequencies */
   Tvard=imatrix(1,15,1,2);    double *pp, **prop;
   Tage=ivector(1,15);          double pos,posprop, k2, dateintsum=0,k2cpt=0;
        FILE *ficresp;
   if (strlen(model) >1){    char fileresp[FILENAMELENGTH];
     j=0, j1=0, k1=1, k2=1;    
     j=nbocc(model,'+');    pp=vector(1,nlstate);
     j1=nbocc(model,'*');    prop=matrix(1,nlstate,iagemin,iagemax+3);
     cptcovn=j+1;    strcpy(fileresp,"p");
     cptcovprod=j1;    strcat(fileresp,fileres);
        if((ficresp=fopen(fileresp,"w"))==NULL) {
     strcpy(modelsav,model);      printf("Problem with prevalence resultfile: %s\n", fileresp);
    if (j==0) {      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
       if (j1==0){      exit(0);
         cutv(stra,strb,modelsav,'V');    }
         Tvar[1]=atoi(strb);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
       }    j1=0;
       else if (j1==1) {    
         cutv(stra,strb,modelsav,'*');    j=cptcoveff;
         Tage[1]=1; cptcovage++;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
         if (strcmp(stra,"age")==0) {  
           cptcovprod--;    first=1;
           cutv(strd,strc,strb,'V');  
           Tvar[1]=atoi(strc);    for(k1=1; k1<=j;k1++){
         }      for(i1=1; i1<=ncodemax[k1];i1++){
         else if (strcmp(strb,"age")==0) {        j1++;
           cptcovprod--;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           cutv(strd,strc,stra,'V');          scanf("%d", i);*/
           Tvar[1]=atoi(strc);        for (i=-5; i<=nlstate+ndeath; i++)  
         }          for (jk=-5; jk<=nlstate+ndeath; jk++)  
         else {            for(m=iagemin; m <= iagemax+3; m++)
           cutv(strd,strc,strb,'V');              freq[i][jk][m]=0;
           cutv(stre,strd,stra,'V');  
           Tvar[1]=ncov+1;      for (i=1; i<=nlstate; i++)  
           for (k=1; k<=lastobs;k++)        for(m=iagemin; m <= iagemax+3; m++)
               covar[ncov+1][k]=covar[atoi(strc)][k]*covar[atoi(strd)][k];          prop[i][m]=0;
         }        
         /*printf("%s %s %s\n", stra,strb,modelsav);        dateintsum=0;
 printf("%d ",Tvar[1]);        k2cpt=0;
 scanf("%d",i);*/        for (i=1; i<=imx; i++) {
       }          bool=1;
     }          if  (cptcovn>0) {
    else {            for (z1=1; z1<=cptcoveff; z1++) 
       for(i=j; i>=1;i--){              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
         cutv(stra,strb,modelsav,'+');                bool=0;
         /*printf("%s %s %s\n", stra,strb,modelsav);          }
           scanf("%d",i);*/          if (bool==1){
         if (strchr(strb,'*')) {            for(m=firstpass; m<=lastpass; m++){
           cutv(strd,strc,strb,'*');              k2=anint[m][i]+(mint[m][i]/12.);
           if (strcmp(strc,"age")==0) {              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
             cptcovprod--;                if(agev[m][i]==0) agev[m][i]=iagemax+1;
             cutv(strb,stre,strd,'V');                if(agev[m][i]==1) agev[m][i]=iagemax+2;
             Tvar[i+1]=atoi(stre);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
             cptcovage++;                if (m<lastpass) {
             Tage[cptcovage]=i+1;                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
             printf("stre=%s ", stre);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
           }                }
           else if (strcmp(strd,"age")==0) {                
             cptcovprod--;                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
             cutv(strb,stre,strc,'V');                  dateintsum=dateintsum+k2;
             Tvar[i+1]=atoi(stre);                  k2cpt++;
             cptcovage++;                }
             Tage[cptcovage]=i+1;                /*}*/
           }            }
           else {          }
             cutv(strb,stre,strc,'V');        }
             Tvar[i+1]=ncov+k1;         
             cutv(strb,strc,strd,'V');        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
             Tprod[k1]=i+1;  fprintf(ficresp, "#Local time at start: %s", strstart);
             Tvard[k1][1]=atoi(strc);        if  (cptcovn>0) {
             Tvard[k1][2]=atoi(stre);          fprintf(ficresp, "\n#********** Variable "); 
             Tvar[cptcovn+k2]=Tvard[k1][1];          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             Tvar[cptcovn+k2+1]=Tvard[k1][2];          fprintf(ficresp, "**********\n#");
             for (k=1; k<=lastobs;k++)        }
               covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        for(i=1; i<=nlstate;i++) 
             k1++;          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
             k2=k2+2;        fprintf(ficresp, "\n");
           }        
         }        for(i=iagemin; i <= iagemax+3; i++){
         else {          if(i==iagemax+3){
           cutv(strd,strc,strb,'V');            fprintf(ficlog,"Total");
           /* printf("%s %s %s", strd,strc,strb);*/          }else{
           Tvar[i+1]=atoi(strc);            if(first==1){
         }              first=0;
         strcpy(modelsav,stra);                printf("See log file for details...\n");
       }            }
       cutv(strd,strc,stra,'V');            fprintf(ficlog,"Age %d", i);
       Tvar[1]=atoi(strc);          }
     }          for(jk=1; jk <=nlstate ; jk++){
   }            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   /* for (i=1; i<=5; i++)              pp[jk] += freq[jk][m][i]; 
      printf("i=%d %d ",i,Tvar[i]);*/          }
   /* printf("tvar=%d %d cptcovage=%d %d",Tvar[1],Tvar[2],cptcovage,Tage[1]);*/          for(jk=1; jk <=nlstate ; jk++){
  /*printf("cptcovprod=%d ", cptcovprod);*/            for(m=-1, pos=0; m <=0 ; m++)
   /*  scanf("%d ",i);*/              pos += freq[jk][m][i];
     fclose(fic);            if(pp[jk]>=1.e-10){
               if(first==1){
     /*  if(mle==1){*/              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     if (weightopt != 1) { /* Maximisation without weights*/              }
       for(i=1;i<=n;i++) weight[i]=1.0;              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     }            }else{
     /*-calculation of age at interview from date of interview and age at death -*/              if(first==1)
     agev=matrix(1,maxwav,1,imx);                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                  fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     for (i=1; i<=imx; i++)  {            }
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          }
       for(m=1; (m<= maxwav); m++){  
         if(s[m][i] >0){          for(jk=1; jk <=nlstate ; jk++){
           if (s[m][i] == nlstate+1) {            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
             if(agedc[i]>0)              pp[jk] += freq[jk][m][i];
               if(moisdc[i]!=99 && andc[i]!=9999)          }       
               agev[m][i]=agedc[i];          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
             else{            pos += pp[jk];
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            posprop += prop[jk][i];
               agev[m][i]=-1;          }
             }          for(jk=1; jk <=nlstate ; jk++){
           }            if(pos>=1.e-5){
           else if(s[m][i] !=9){ /* Should no more exist */              if(first==1)
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             if(mint[m][i]==99 || anint[m][i]==9999)              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
               agev[m][i]=1;            }else{
             else if(agev[m][i] <agemin){              if(first==1)
               agemin=agev[m][i];                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }            }
             else if(agev[m][i] >agemax){            if( i <= iagemax){
               agemax=agev[m][i];              if(pos>=1.e-5){
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
             }                /*probs[i][jk][j1]= pp[jk]/pos;*/
             /*agev[m][i]=anint[m][i]-annais[i];*/                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
             /*   agev[m][i] = age[i]+2*m;*/              }
           }              else
           else { /* =9 */                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             agev[m][i]=1;            }
             s[m][i]=-1;          }
           }          
         }          for(jk=-1; jk <=nlstate+ndeath; jk++)
         else /*= 0 Unknown */            for(m=-1; m <=nlstate+ndeath; m++)
           agev[m][i]=1;              if(freq[jk][m][i] !=0 ) {
       }              if(first==1)
                    printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     }                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     for (i=1; i<=imx; i++)  {              }
       for(m=1; (m<= maxwav); m++){          if(i <= iagemax)
         if (s[m][i] > (nlstate+ndeath)) {            fprintf(ficresp,"\n");
           printf("Error: Wrong value in nlstate or ndeath\n");            if(first==1)
           goto end;            printf("Others in log...\n");
         }          fprintf(ficlog,"\n");
       }        }
     }      }
     }
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    dateintmean=dateintsum/k2cpt; 
    
     free_vector(severity,1,maxwav);    fclose(ficresp);
     free_imatrix(outcome,1,maxwav+1,1,n);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     free_vector(moisnais,1,n);    free_vector(pp,1,nlstate);
     free_vector(annais,1,n);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     free_matrix(mint,1,maxwav,1,n);    /* End of Freq */
     free_matrix(anint,1,maxwav,1,n);  }
     free_vector(moisdc,1,n);  
     free_vector(andc,1,n);  /************ Prevalence ********************/
   void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
      {  
     wav=ivector(1,imx);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
     dh=imatrix(1,lastpass-firstpass+1,1,imx);       in each health status at the date of interview (if between dateprev1 and dateprev2).
     mw=imatrix(1,lastpass-firstpass+1,1,imx);       We still use firstpass and lastpass as another selection.
        */
     /* Concatenates waves */   
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     double ***freq; /* Frequencies */
     double *pp, **prop;
       Tcode=ivector(1,100);    double pos,posprop; 
       nbcode=imatrix(1,nvar,1,8);    double  y2; /* in fractional years */
       ncodemax[1]=1;    int iagemin, iagemax;
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);  
          iagemin= (int) agemin;
    codtab=imatrix(1,100,1,10);    iagemax= (int) agemax;
    h=0;    /*pp=vector(1,nlstate);*/
    m=pow(2,cptcoveff);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
      /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
    for(k=1;k<=cptcoveff; k++){    j1=0;
      for(i=1; i <=(m/pow(2,k));i++){    
        for(j=1; j <= ncodemax[k]; j++){    j=cptcoveff;
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
            h++;    
            if (h>m) h=1;codtab[h][k]=j;    for(k1=1; k1<=j;k1++){
          }      for(i1=1; i1<=ncodemax[k1];i1++){
        }        j1++;
      }        
    }        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
    /*for(i=1; i <=m ;i++){       
      for(k=1; k <=cptcovn; k++){        for (i=1; i<=imx; i++) { /* Each individual */
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);          bool=1;
      }          if  (cptcovn>0) {
      printf("\n");            for (z1=1; z1<=cptcoveff; z1++) 
    }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
    scanf("%d",i);*/                bool=0;
              } 
    /* Calculates basic frequencies. Computes observed prevalence at single age          if (bool==1) { 
        and prints on file fileres'p'. */            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
               if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                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); 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */                  /*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]]);*/
                      prop[s[m][i]][(int)agev[m][i]] += weight[i];
     /* For Powell, parameters are in a vector p[] starting at p[1]                  prop[s[m][i]][iagemax+3] += weight[i]; 
        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) */              }
             } /* end selection of waves */
     if(mle==1){          }
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);        }
     }        for(i=iagemin; i <= iagemax+3; i++){  
              
     /*--------- results files --------------*/          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);            posprop += prop[jk][i]; 
              } 
    jk=1;  
    fprintf(ficres,"# Parameters\n");          for(jk=1; jk <=nlstate ; jk++){     
    printf("# Parameters\n");            if( i <=  iagemax){ 
    for(i=1,jk=1; i <=nlstate; i++){              if(posprop>=1.e-5){ 
      for(k=1; k <=(nlstate+ndeath); k++){                probs[i][jk][j1]= prop[jk][i]/posprop;
        if (k != i)              } 
          {            } 
            printf("%d%d ",i,k);          }/* end jk */ 
            fprintf(ficres,"%1d%1d ",i,k);        }/* end i */ 
            for(j=1; j <=ncovmodel; j++){      } /* end i1 */
              printf("%f ",p[jk]);    } /* end k1 */
              fprintf(ficres,"%f ",p[jk]);    
              jk++;    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
            }    /*free_vector(pp,1,nlstate);*/
            printf("\n");    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
            fprintf(ficres,"\n");  }  /* End of prevalence */
          }  
      }  /************* Waves Concatenation ***************/
    }  
  if(mle==1){  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
     /* Computing hessian and covariance matrix */  {
     ftolhess=ftol; /* Usually correct */    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
     hesscov(matcov, p, npar, delti, ftolhess, func);       Death is a valid wave (if date is known).
  }       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     fprintf(ficres,"# Scales\n");       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     printf("# Scales\n");       and mw[mi+1][i]. dh depends on stepm.
      for(i=1,jk=1; i <=nlstate; i++){       */
       for(j=1; j <=nlstate+ndeath; j++){  
         if (j!=i) {    int i, mi, m;
           fprintf(ficres,"%1d%1d",i,j);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
           printf("%1d%1d",i,j);       double sum=0., jmean=0.;*/
           for(k=1; k<=ncovmodel;k++){    int first;
             printf(" %.5e",delti[jk]);    int j, k=0,jk, ju, jl;
             fprintf(ficres," %.5e",delti[jk]);    double sum=0.;
             jk++;    first=0;
           }    jmin=1e+5;
           printf("\n");    jmax=-1;
           fprintf(ficres,"\n");    jmean=0.;
         }    for(i=1; i<=imx; i++){
       }      mi=0;
       }      m=firstpass;
          while(s[m][i] <= nlstate){
     k=1;        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     fprintf(ficres,"# Covariance\n");          mw[++mi][i]=m;
     printf("# Covariance\n");        if(m >=lastpass)
     for(i=1;i<=npar;i++){          break;
       /*  if (k>nlstate) k=1;        else
       i1=(i-1)/(ncovmodel*nlstate)+1;          m++;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);      }/* end while */
       printf("%s%d%d",alph[k],i1,tab[i]);*/      if (s[m][i] > nlstate){
       fprintf(ficres,"%3d",i);        mi++;     /* Death is another wave */
       printf("%3d",i);        /* if(mi==0)  never been interviewed correctly before death */
       for(j=1; j<=i;j++){           /* Only death is a correct wave */
         fprintf(ficres," %.5e",matcov[i][j]);        mw[mi][i]=m;
         printf(" %.5e",matcov[i][j]);      }
       }  
       fprintf(ficres,"\n");      wav[i]=mi;
       printf("\n");      if(mi==0){
       k++;        nbwarn++;
     }        if(first==0){
              printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     while((c=getc(ficpar))=='#' && c!= EOF){          first=1;
       ungetc(c,ficpar);        }
       fgets(line, MAXLINE, ficpar);        if(first==1){
       puts(line);          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
       fputs(line,ficparo);        }
     }      } /* end mi==0 */
     ungetc(c,ficpar);    } /* End individuals */
    
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    for(i=1; i<=imx; i++){
          for(mi=1; mi<wav[i];mi++){
     if (fage <= 2) {        if (stepm <=0)
       bage = agemin;          dh[mi][i]=1;
       fage = agemax;        else{
     }          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
             if (agedc[i] < 2*AGESUP) {
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);              if(j==0) j=1;  /* Survives at least one month after exam */
               else if(j<0){
                    nberr++;
 /*------------ gnuplot -------------*/                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]);
 chdir(pathcd);                j=1; /* Temporary Dangerous patch */
   if((ficgp=fopen("graph.plt","w"))==NULL) {                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     printf("Problem with file graph.gp");goto end;                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. You MUST fix the contradiction between dates.\n",stepm);
 #ifdef windows              }
   fprintf(ficgp,"cd \"%s\" \n",pathc);              k=k+1;
 #endif              if (j >= jmax) jmax=j;
 m=pow(2,cptcoveff);              if (j <= jmin) jmin=j;
                sum=sum+j;
  /* 1eme*/              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   for (cpt=1; cpt<= nlstate ; cpt ++) {              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
    for (k1=1; k1<= m ; k1 ++) {            }
           }
 #ifdef windows          else{
     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);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
 #endif  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
 #ifdef unix  
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);            k=k+1;
 #endif            if (j >= jmax) jmax=j;
             else if (j <= jmin)jmin=j;
 for (i=1; i<= nlstate ; i ++) {            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            /*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]);*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");            if(j<0){
 }              nberr++;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);              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]);
     for (i=1; i<= nlstate ; i ++) {              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            sum=sum+j;
 }          }
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);          jk= j/stepm;
      for (i=1; i<= nlstate ; i ++) {          jl= j -jk*stepm;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          ju= j -(jk+1)*stepm;
   else fprintf(ficgp," \%%*lf (\%%*lf)");          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
 }              if(jl==0){
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));              dh[mi][i]=jk;
 #ifdef unix              bh[mi][i]=0;
 fprintf(ficgp,"\nset ter gif small size 400,300");            }else{ /* We want a negative bias in order to only have interpolation ie
 #endif                    * at the price of an extra matrix product in likelihood */
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);              dh[mi][i]=jk+1;
    }              bh[mi][i]=ju;
   }            }
   /*2 eme*/          }else{
             if(jl <= -ju){
   for (k1=1; k1<= m ; k1 ++) {              dh[mi][i]=jk;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);              bh[mi][i]=jl;       /* bias is positive if real duration
                                       * is higher than the multiple of stepm and negative otherwise.
     for (i=1; i<= nlstate+1 ; i ++) {                                   */
       k=2*i;            }
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);            else{
       for (j=1; j<= nlstate+1 ; j ++) {              dh[mi][i]=jk+1;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              bh[mi][i]=ju;
   else fprintf(ficgp," \%%*lf (\%%*lf)");            }
 }              if(dh[mi][i]==0){
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");              dh[mi][i]=1; /* At least one step */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);              bh[mi][i]=ju; /* At least one step */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);              /*  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);*/
       for (j=1; j<= nlstate+1 ; j ++) {            }
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          } /* end if mle */
         else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }        } /* end wave */
       fprintf(ficgp,"\" t\"\" w l 0,");    }
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    jmean=sum/k;
       for (j=1; j<= nlstate+1 ; j ++) {    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
   else fprintf(ficgp," \%%*lf (\%%*lf)");   }
 }    
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  /*********** Tricode ****************************/
       else fprintf(ficgp,"\" t\"\" w l 0,");  void tricode(int *Tvar, int **nbcode, int imx)
     }  {
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);    
   }    int Ndum[20],ij=1, k, j, i, maxncov=19;
      int cptcode=0;
   /*3eme*/    cptcoveff=0; 
    
   for (k1=1; k1<= m ; k1 ++) {    for (k=0; k<maxncov; k++) Ndum[k]=0;
     for (cpt=1; cpt<= nlstate ; cpt ++) {    for (k=1; k<=7; k++) ncodemax[k]=0;
       k=2+nlstate*(cpt-1);  
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       for (i=1; i< nlstate ; i ++) {      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
         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);                                 modality*/ 
       }        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        Ndum[ij]++; /*store the modality */
     }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
   }        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
                                           Tvar[j]. If V=sex and male is 0 and 
   /* CV preval stat */                                         female is 1, then  cptcode=1.*/
   for (k1=1; k1<= m ; k1 ++) {      }
     for (cpt=1; cpt<nlstate ; cpt ++) {  
       k=3;      for (i=0; i<=cptcode; i++) {
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
       for (i=1; i< nlstate ; i ++)      }
         fprintf(ficgp,"+$%d",k+i+1);  
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);      ij=1; 
            for (i=1; i<=ncodemax[j]; i++) {
       l=3+(nlstate+ndeath)*cpt;        for (k=0; k<= maxncov; k++) {
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);          if (Ndum[k] != 0) {
       for (i=1; i< nlstate ; i ++) {            nbcode[Tvar[j]][ij]=k; 
         l=3+(nlstate+ndeath)*cpt;            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
         fprintf(ficgp,"+$%d",l+i+1);            
       }            ij++;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);            }
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          if (ij > ncodemax[j]) break; 
     }        }  
   }      } 
     }  
   /* proba elementaires */  
    for(i=1,jk=1; i <=nlstate; i++){   for (k=0; k< maxncov; k++) Ndum[k]=0;
     for(k=1; k <=(nlstate+ndeath); k++){  
       if (k != i) {   for (i=1; i<=ncovmodel-2; i++) { 
         for(j=1; j <=ncovmodel; j++){     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/     ij=Tvar[i];
           /*fprintf(ficgp,"%s",alph[1]);*/     Ndum[ij]++;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);   }
           jk++;  
           fprintf(ficgp,"\n");   ij=1;
         }   for (i=1; i<= maxncov; i++) {
       }     if((Ndum[i]!=0) && (i<=ncovcol)){
     }       Tvaraff[ij]=i; /*For printing */
     }       ij++;
      }
   for(jk=1; jk <=m; jk++) {   }
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);   
    i=1;   cptcoveff=ij-1; /*Number of simple covariates*/
    for(k2=1; k2<=nlstate; k2++) {  }
      k3=i;  
      for(k=1; k<=(nlstate+ndeath); k++) {  /*********** Health Expectancies ****************/
        if (k != k2){  
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov,char strstart[] )
 ij=1;  
         for(j=3; j <=ncovmodel; j++) {  {
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    /* Health expectancies */
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
             ij++;    double age, agelim, hf;
           }    double ***p3mat,***varhe;
           else    double **dnewm,**doldm;
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    double *xp;
         }    double **gp, **gm;
           fprintf(ficgp,")/(1");    double ***gradg, ***trgradg;
            int theta;
         for(k1=1; k1 <=nlstate; k1++){    
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
 ij=1;    xp=vector(1,npar);
           for(j=3; j <=ncovmodel; j++){    dnewm=matrix(1,nlstate*nlstate,1,npar);
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    
             ij++;    fprintf(ficreseij,"# Local time at start: %s", strstart);
           }    fprintf(ficreseij,"# Health expectancies\n");
           else    fprintf(ficreseij,"# Age");
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    for(i=1; i<=nlstate;i++)
           }      for(j=1; j<=nlstate;j++)
           fprintf(ficgp,")");        fprintf(ficreseij," %1d-%1d (SE)",i,j);
         }    fprintf(ficreseij,"\n");
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);  
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    if(estepm < stepm){
         i=i+ncovmodel;      printf ("Problem %d lower than %d\n",estepm, stepm);
        }    }
      }    else  hstepm=estepm;   
    }    /* We compute the life expectancy from trapezoids spaced every estepm months
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);     * This is mainly to measure the difference between two models: for example
   }     * if stepm=24 months pijx are given only every 2 years and by summing them
         * we are calculating an estimate of the Life Expectancy assuming a linear 
   fclose(ficgp);     * progression in between and thus overestimating or underestimating according
         * to the curvature of the survival function. If, for the same date, we 
 chdir(path);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     free_matrix(agev,1,maxwav,1,imx);     * to compare the new estimate of Life expectancy with the same linear 
     free_ivector(wav,1,imx);     * hypothesis. A more precise result, taking into account a more precise
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);     * curvature will be obtained if estepm is as small as stepm. */
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);  
        /* For example we decided to compute the life expectancy with the smallest unit */
     free_imatrix(s,1,maxwav+1,1,n);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           nhstepm is the number of hstepm from age to agelim 
           nstepm is the number of stepm from age to agelin. 
     free_ivector(num,1,n);       Look at hpijx to understand the reason of that which relies in memory size
     free_vector(agedc,1,n);       and note for a fixed period like estepm months */
     free_vector(weight,1,n);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     /*free_matrix(covar,1,NCOVMAX,1,n);*/       survival function given by stepm (the optimization length). Unfortunately it
     fclose(ficparo);       means that if the survival funtion is printed only each two years of age and if
     fclose(ficres);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     /*  }*/       results. So we changed our mind and took the option of the best precision.
        */
    /*________fin mle=1_________*/    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 */
     /* No more information from the sample is required now */      /* nhstepm age range expressed in number of stepm */
   /* Reads comments: lines beginning with '#' */      nstepm=(int) rint((agelim-age)*YEARM/stepm); 
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     ungetc(c,ficpar);      /* if (stepm >= YEARM) hstepm=1;*/
     fgets(line, MAXLINE, ficpar);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     puts(line);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     fputs(line,ficparo);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   }      gp=matrix(0,nhstepm,1,nlstate*nlstate);
   ungetc(c,ficpar);      gm=matrix(0,nhstepm,1,nlstate*nlstate);
    
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
 /*--------- index.htm --------*/   
   
   if((fichtm=fopen("index.htm","w"))==NULL)    {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     printf("Problem with index.htm \n");goto end;  
   }      /* Computing  Variances of health expectancies */
   
  fprintf(fichtm,"<body><ul> Imach, Version 0.64a<hr> <li>Outputs files<br><br>\n       for(theta=1; theta <=npar; theta++){
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        for(i=1; i<=npar; i++){ 
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>        }
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>        cptj=0;
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>        for(j=1; j<= nlstate; j++){
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>          for(i=1; i<=nlstate; i++){
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);            cptj=cptj+1;
             for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
  fprintf(fichtm," <li>Graphs</li>\n<p>");              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
             }
  m=cptcoveff;          }
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}        }
        
  j1=0;       
  for(k1=1; k1<=m;k1++){        for(i=1; i<=npar; i++) 
    for(i1=1; i1<=ncodemax[k1];i1++){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
        j1++;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
        if (cptcovn > 0) {        
          fprintf(fichtm,"<hr>************ Results for covariates");        cptj=0;
          for (cpt=1; cpt<=cptcoveff;cpt++)        for(j=1; j<= nlstate; j++){
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);          for(i=1;i<=nlstate;i++){
          fprintf(fichtm," ************\n<hr>");            cptj=cptj+1;
        }            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>  
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);                  gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
        for(cpt=1; cpt<nlstate;cpt++){            }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>          }
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        }
        }        for(j=1; j<= nlstate*nlstate; j++)
     for(cpt=1; cpt<=nlstate;cpt++) {          for(h=0; h<=nhstepm-1; h++){
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 interval) in state (%d): v%s%d%d.gif <br>          }
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);         } 
      }     
      for(cpt=1; cpt<=nlstate;cpt++) {  /* End theta */
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>  
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
      }  
      fprintf(fichtm,"\n<br>- Total life expectancy by age and       for(h=0; h<=nhstepm-1; h++)
 health expectancies in states (1) and (2): e%s%d.gif<br>        for(j=1; j<=nlstate*nlstate;j++)
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          for(theta=1; theta <=npar; theta++)
 fprintf(fichtm,"\n</body>");            trgradg[h][j][theta]=gradg[h][theta][j];
    }       
  }  
 fclose(fichtm);       for(i=1;i<=nlstate*nlstate;i++)
         for(j=1;j<=nlstate*nlstate;j++)
   /*--------------- Prevalence limit --------------*/          varhe[i][j][(int)age] =0.;
    
   strcpy(filerespl,"pl");       printf("%d|",(int)age);fflush(stdout);
   strcat(filerespl,fileres);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {       for(h=0;h<=nhstepm-1;h++){
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        for(k=0;k<=nhstepm-1;k++){
   }          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   fprintf(ficrespl,"#Prevalence limit\n");          for(i=1;i<=nlstate*nlstate;i++)
   fprintf(ficrespl,"#Age ");            for(j=1;j<=nlstate*nlstate;j++)
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
   fprintf(ficrespl,"\n");        }
        }
   prlim=matrix(1,nlstate,1,nlstate);      /* Computing expectancies */
   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 */          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            
   k=0;  /* 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]);*/
   agebase=agemin;  
   agelim=agemax;          }
   ftolpl=1.e-10;  
   i1=cptcoveff;      fprintf(ficreseij,"%3.0f",age );
   if (cptcovn < 1){i1=1;}      cptj=0;
       for(i=1; i<=nlstate;i++)
   for(cptcov=1;cptcov<=i1;cptcov++){        for(j=1; j<=nlstate;j++){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          cptj++;
         k=k+1;          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/        }
         fprintf(ficrespl,"\n#******");      fprintf(ficreseij,"\n");
         for(j=1;j<=cptcoveff;j++)     
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         fprintf(ficrespl,"******\n");      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
              free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
         for (age=agebase; age<=agelim; age++){      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespl,"%.0f",age );    }
           for(i=1; i<=nlstate;i++)    printf("\n");
           fprintf(ficrespl," %.5f", prlim[i][i]);    fprintf(ficlog,"\n");
           fprintf(ficrespl,"\n");  
         }    free_vector(xp,1,npar);
       }    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     }    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   fclose(ficrespl);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   /*------------- h Pij x at various ages ------------*/  }
    
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  /************ Variance ******************/
   if((ficrespij=fopen(filerespij,"w"))==NULL) {  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  {
   }    /* Variance of health expectancies */
   printf("Computing pij: result on file '%s' \n", filerespij);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
      /* double **newm;*/
   stepsize=(int) (stepm+YEARM-1)/YEARM;    double **dnewm,**doldm;
   if (stepm<=24) stepsize=2;    double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
   agelim=AGESUP;    int k, cptcode;
   hstepm=stepsize*YEARM; /* Every year of age */    double *xp;
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    double **gp, **gm;  /* for var eij */
      double ***gradg, ***trgradg; /*for var eij */
   k=0;    double **gradgp, **trgradgp; /* for var p point j */
   for(cptcov=1;cptcov<=i1;cptcov++){    double *gpp, *gmp; /* for var p point j */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       k=k+1;    double ***p3mat;
         fprintf(ficrespij,"\n#****** ");    double age,agelim, hf;
         for(j=1;j<=cptcoveff;j++)    double ***mobaverage;
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    int theta;
         fprintf(ficrespij,"******\n");    char digit[4];
            char digitp[25];
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    char fileresprobmorprev[FILENAMELENGTH];
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if(popbased==1){
           oldm=oldms;savm=savms;      if(mobilav!=0)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          strcpy(digitp,"-populbased-mobilav-");
           fprintf(ficrespij,"# Age");      else strcpy(digitp,"-populbased-nomobil-");
           for(i=1; i<=nlstate;i++)    }
             for(j=1; j<=nlstate+ndeath;j++)    else 
               fprintf(ficrespij," %1d-%1d",i,j);      strcpy(digitp,"-stablbased-");
           fprintf(ficrespij,"\n");  
           for (h=0; h<=nhstepm; h++){    if (mobilav!=0) {
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
             for(i=1; i<=nlstate;i++)      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
               for(j=1; j<=nlstate+ndeath;j++)        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
             fprintf(ficrespij,"\n");      }
           }    }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           fprintf(ficrespij,"\n");    strcpy(fileresprobmorprev,"prmorprev"); 
         }    sprintf(digit,"%-d",ij);
     }    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   }    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   fclose(ficrespij);    strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   /*---------- Health expectancies and variances ------------*/      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   strcpy(filerest,"t");    }
   strcat(filerest,fileres);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   if((ficrest=fopen(filerest,"w"))==NULL) {   
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   }    fprintf(ficresprobmorprev, "#Local time at start: %s", strstart);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   strcpy(filerese,"e");      fprintf(ficresprobmorprev," p.%-d SE",j);
   strcat(filerese,fileres);      for(i=1; i<=nlstate;i++)
   if((ficreseij=fopen(filerese,"w"))==NULL) {        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    }  
   }    fprintf(ficresprobmorprev,"\n");
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    fprintf(ficgp,"\n# Routine varevsij");
    fprintf(fichtm, "#Local time at start: %s", strstart);
  strcpy(fileresv,"v");    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");
   strcat(fileresv,fileres);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {  /*   } */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   }   fprintf(ficresvij, "#Local time at start: %s", strstart);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    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");
   k=0;    for(i=1; i<=nlstate;i++)
   for(cptcov=1;cptcov<=i1;cptcov++){      for(j=1; j<=nlstate;j++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
       k=k+1;    fprintf(ficresvij,"\n");
       fprintf(ficrest,"\n#****** ");  
       for(j=1;j<=cptcoveff;j++)    xp=vector(1,npar);
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    dnewm=matrix(1,nlstate,1,npar);
       fprintf(ficrest,"******\n");    doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       fprintf(ficreseij,"\n#****** ");    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       for(j=1;j<=cptcoveff;j++)  
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       fprintf(ficreseij,"******\n");    gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
       fprintf(ficresvij,"\n#****** ");    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       for(j=1;j<=cptcoveff;j++)    
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    if(estepm < stepm){
       fprintf(ficresvij,"******\n");      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    else  hstepm=estepm;   
       oldm=oldms;savm=savms;    /* For example we decided to compute the life expectancy with the smallest unit */
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);       nhstepm is the number of hstepm from age to agelim 
       oldm=oldms;savm=savms;       nstepm is the number of stepm from age to agelin. 
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);       Look at hpijx to understand the reason of that which relies in memory size
             and note for a fixed period like k years */
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);       survival function given by stepm (the optimization length). Unfortunately it
       fprintf(ficrest,"\n");       means that if the survival funtion is printed every two years of age and if
               you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       hf=1;       results. So we changed our mind and took the option of the best precision.
       if (stepm >= YEARM) hf=stepm/YEARM;    */
       epj=vector(1,nlstate+1);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       for(age=bage; age <=fage ;age++){    agelim = AGESUP;
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         fprintf(ficrest," %.0f",age);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
           for(i=1, epj[j]=0.;i <=nlstate;i++) {      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
           }      gp=matrix(0,nhstepm,1,nlstate);
           epj[nlstate+1] +=epj[j];      gm=matrix(0,nhstepm,1,nlstate);
         }  
         for(i=1, vepp=0.;i <=nlstate;i++)  
           for(j=1;j <=nlstate;j++)      for(theta=1; theta <=npar; theta++){
             vepp += vareij[i][j][(int)age];        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         for(j=1;j <=nlstate;j++){        }
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         fprintf(ficrest,"\n");  
       }        if (popbased==1) {
     }          if(mobilav ==0){
   }            for(i=1; i<=nlstate;i++)
                      prlim[i][i]=probs[(int)age][i][ij];
  fclose(ficreseij);          }else{ /* mobilav */ 
  fclose(ficresvij);            for(i=1; i<=nlstate;i++)
   fclose(ficrest);              prlim[i][i]=mobaverage[(int)age][i][ij];
   fclose(ficpar);          }
   free_vector(epj,1,nlstate+1);        }
   /*  scanf("%d ",i); */    
         for(j=1; j<= nlstate; j++){
   /*------- Variance limit prevalence------*/            for(h=0; h<=nhstepm; h++){
             for(i=1, gp[h][j]=0.;i<=nlstate;i++)
 strcpy(fileresvpl,"vpl");              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
   strcat(fileresvpl,fileres);          }
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        }
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);        /* This for computing probability of death (h=1 means
     exit(0);           computed over hstepm matrices product = hstepm*stepm months) 
   }           as a weighted average of prlim.
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);        */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
  k=0;          for(i=1,gpp[j]=0.; i<= nlstate; i++)
  for(cptcov=1;cptcov<=i1;cptcov++){            gpp[j] += prlim[i][i]*p3mat[i][j][1];
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        }    
      k=k+1;        /* end probability of death */
      fprintf(ficresvpl,"\n#****** ");  
      for(j=1;j<=cptcoveff;j++)        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
      fprintf(ficresvpl,"******\n");        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
              prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
      varpl=matrix(1,nlstate,(int) bage, (int) fage);   
      oldm=oldms;savm=savms;        if (popbased==1) {
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);          if(mobilav ==0){
    }            for(i=1; i<=nlstate;i++)
  }              prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
   fclose(ficresvpl);            for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
   /*---------- End : free ----------------*/          }
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        }
    
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        for(j=1; j<= nlstate; j++){
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);          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];
   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);        /* This for computing probability of death (h=1 means
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);           computed over hstepm matrices product = hstepm*stepm months) 
             as a weighted average of prlim.
   free_matrix(matcov,1,npar,1,npar);        */
   free_vector(delti,1,npar);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
            for(i=1,gmp[j]=0.; i<= nlstate; i++)
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
   printf("End of Imach\n");        /* end probability of death */
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  
          for(j=1; j<= nlstate; j++) /* vareij */
   /* 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);*/          for(h=0; h<=nhstepm; h++){
   /*printf("Total time was %d uSec.\n", total_usecs);*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   /*------ End -----------*/          }
   
  end:        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
 #ifdef windows          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
  chdir(pathcd);        }
 #endif  
  system("wgnuplot graph.plt");      } /* End theta */
   
 #ifdef windows      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   while (z[0] != 'q') {  
     chdir(pathcd);      for(h=0; h<=nhstepm; h++) /* veij */
     printf("\nType e to edit output files, c to start again, and q for exiting: ");        for(j=1; j<=nlstate;j++)
     scanf("%s",z);          for(theta=1; theta <=npar; theta++)
     if (z[0] == 'c') system("./imach");            trgradg[h][j][theta]=gradg[h][theta][j];
     else if (z[0] == 'e') {  
       chdir(path);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
       system("index.htm");        for(theta=1; theta <=npar; theta++)
     }          trgradgp[j][theta]=gradgp[theta][j];
     else if (z[0] == 'q') exit(0);    
   }  
 #endif      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 }      for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;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);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     fprintf(ficresvpl, "#Local time at start: %s", strstart); 
     fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficresprob, "#Local time at start: %s", strstart);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     fprintf(ficresprobcov, "#Local time at start: %s", strstart);
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     fprintf(ficresprobcor, "#Local time at start: %s", strstart);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcov,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     fprintf(fichtm,"\n");
   
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
   standard deviations wide on each axis. <br>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Stable prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - Life expectancies by age and initial health status (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: %s%d1.png<br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: %s%d2.png<br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): %s%d%d.png <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> Result files (second order: variances)</h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Health expectancies with their variances (no covariance): <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of stable prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Stable prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);
           
         } 
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i]==1 & wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i]==0 & wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         if (wav[i]>1 & agecens[i]>15) {
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   lx     qx    dx    Lx     Tx     e(x)<br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int 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;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char strstart[80], *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     split(argv[0],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=0; line[j] != '\n';j++){  /* Untabifies line */
           if(line[j] == '\t')
             line[j] = ' ';
         }
         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 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a
                                    month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<body>\n<title>IMaCh Cov %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<body>\n<title>IMaCh %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (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]));
   
   lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
      
        for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
      
         for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
   
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
   
    tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
          }
      
      
          printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
   
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
   
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* Endof if mle==-3 */
   
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%f ",p[jk]);
               fprintf(ficlog,"%f ",p[jk]);
               fprintf(ficres,"%f ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,path); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with stable prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing stable prevalence: result on file '%s' \n", filerespl);
       fprintf(ficrespl, "#Local time at start: %s", strstart);
       fprintf(ficrespl,"#Stable prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       fprintf(ficrespij, "#Local time at start: %s", strstart);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /*---------- Health expectancies and variances ------------*/
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total LEs with variances: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest); 
   
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficreseij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav, strstart);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav, strstart);
           }
   
           fprintf(ficrest, "#Local time at start: %s", strstart);
           fprintf(ficrest,"#Total LEs with variances: e.. (std) ");
           for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
           fprintf(ficrest,"\n");
   
           epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             if (popbased==1) {
               if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=probs[(int)age][i][k];
               }else{ /* mobilav */ 
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=mobaverage[(int)age][i][k];
               }
             }
           
             fprintf(ficrest," %4.0f",age);
             for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
               for(i=1, epj[j]=0.;i <=nlstate;i++) {
                 epj[j] += prlim[i][i]*eij[i][j][(int)age];
                 /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
               }
               epj[nlstate+1] +=epj[j];
             }
   
             for(i=1, vepp=0.;i <=nlstate;i++)
               for(j=1;j <=nlstate;j++)
                 vepp += vareij[i][j][(int)age];
             fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
             for(j=1;j <=nlstate;j++){
               fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
             }
             fprintf(ficrest,"\n");
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficreseij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of stable prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of stable prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of stable prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
     
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
   
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>",strstart, strtend);
     fclose(fichtm);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
     chdir(path);
     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);
     }
   }
   
   
   

Removed from v.1.7  
changed lines
  Added in v.1.105


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