Diff for /imach/src/imach.c between versions 1.41 and 1.108

version 1.41, 2002/05/07 15:53:01 version 1.108, 2006/01/19 18:05:42
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.108  2006/01/19 18:05:42  lievre
      Gnuplot problem appeared...
   This program computes Healthy Life Expectancies from    To be fixed
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a  
   first survey ("cross") where individuals from different ages are    Revision 1.107  2006/01/19 16:20:37  brouard
   interviewed on their health status or degree of disability (in the    Test existence of gnuplot in imach path
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.106  2006/01/19 13:24:36  brouard
   (if any) in individual health status.  Health expectancies are    Some cleaning and links added in html output
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.105  2006/01/05 20:23:19  lievre
   Maximum Likelihood of the parameters involved in the model.  The    *** empty log message ***
   simplest model is the multinomial logistic model where pij is the  
   probability to be observed in state j at the second wave    Revision 1.104  2005/09/30 16:11:43  lievre
   conditional to be observed in state i at the first wave. Therefore    (Module): sump fixed, loop imx fixed, and simplifications.
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    (Module): If the status is missing at the last wave but we know
   'age' is age and 'sex' is a covariate. If you want to have a more    that the person is alive, then we can code his/her status as -2
   complex model than "constant and age", you should modify the program    (instead of missing=-1 in earlier versions) and his/her
   where the markup *Covariates have to be included here again* invites    contributions to the likelihood is 1 - Prob of dying from last
   you to do it.  More covariates you add, slower the    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   convergence.    the healthy state at last known wave). Version is 0.98
   
   The advantage of this computer programme, compared to a simple    Revision 1.103  2005/09/30 15:54:49  lievre
   multinomial logistic model, is clear when the delay between waves is not    (Module): sump fixed, loop imx fixed, and simplifications.
   identical for each individual. Also, if a individual missed an  
   intermediate interview, the information is lost, but taken into    Revision 1.102  2004/09/15 17:31:30  brouard
   account using an interpolation or extrapolation.      Add the possibility to read data file including tab characters.
   
   hPijx is the probability to be observed in state i at age x+h    Revision 1.101  2004/09/15 10:38:38  brouard
   conditional to the observed state i at age x. The delay 'h' can be    Fix on curr_time
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.100  2004/07/12 18:29:06  brouard
   semester or year) is model as a multinomial logistic.  The hPx    Add version for Mac OS X. Just define UNIX in Makefile
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.99  2004/06/05 08:57:40  brouard
   hPijx.    *** empty log message ***
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.98  2004/05/16 15:05:56  brouard
   of the life expectancies. It also computes the prevalence limits.    New version 0.97 . First attempt to estimate force of mortality
      directly from the data i.e. without the need of knowing the health
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    state at each age, but using a Gompertz model: log u =a + b*age .
            Institut national d'études démographiques, Paris.    This is the basic analysis of mortality and should be done before any
   This software have been partly granted by Euro-REVES, a concerted action    other analysis, in order to test if the mortality estimated from the
   from the European Union.    cross-longitudinal survey is different from the mortality estimated
   It is copyrighted identically to a GNU software product, ie programme and    from other sources like vital statistic data.
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    The same imach parameter file can be used but the option for mle should be -3.
   **********************************************************************/  
      Agnès, who wrote this part of the code, tried to keep most of the
 #include <math.h>    former routines in order to include the new code within the former code.
 #include <stdio.h>  
 #include <stdlib.h>    The output is very simple: only an estimate of the intercept and of
 #include <unistd.h>    the slope with 95% confident intervals.
   
 #define MAXLINE 256    Current limitations:
 #define GNUPLOTPROGRAM "wgnuplot"    A) Even if you enter covariates, i.e. with the
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    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 erreur; /* Error number */    (Module): On windows (cygwin) function asctime_r doesn't
 int nvar;    exist so I changed back to asctime which exists.
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    (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, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    exist so I changed back to asctime which exists.
 int popbased=0;  
     Revision 1.91  2003/06/25 15:30:29  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    * imach.c (Repository): Duplicated warning errors corrected.
 int maxwav; /* Maxim number of waves */    (Repository): Elapsed time after each iteration is now output. It
 int jmin, jmax; /* min, max spacing between 2 waves */    helps to forecast when convergence will be reached. Elapsed time
 int mle, weightopt;    is stamped in powell.  We created a new html file for the graphs
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    concerning matrix of covariance. It has extension -cov.htm.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.90  2003/06/24 12:34:15  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Some bugs corrected for windows. Also, when
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    mle=-1 a template is output in file "or"mypar.txt with the design
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    of the covariance matrix to be input.
 FILE *ficgp,*ficresprob,*ficpop;  
 FILE *ficreseij;    Revision 1.89  2003/06/24 12:30:52  brouard
   char filerese[FILENAMELENGTH];    (Module): Some bugs corrected for windows. Also, when
  FILE  *ficresvij;    mle=-1 a template is output in file "or"mypar.txt with the design
   char fileresv[FILENAMELENGTH];    of the covariance matrix to be input.
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.88  2003/06/23 17:54:56  brouard
     * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.87  2003/06/18 12:26:01  brouard
 #define FTOL 1.0e-10    Version 0.96
   
 #define NRANSI    Revision 1.86  2003/06/17 20:04:08  brouard
 #define ITMAX 200    (Module): Change position of html and gnuplot routines and added
     routine fileappend.
 #define TOL 2.0e-4  
     Revision 1.85  2003/06/17 13:12:43  brouard
 #define CGOLD 0.3819660    * imach.c (Repository): Check when date of death was earlier that
 #define ZEPS 1.0e-10    current date of interview. It may happen when the death was just
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    prior to the death. In this case, dh was negative and likelihood
     was wrong (infinity). We still send an "Error" but patch by
 #define GOLD 1.618034    assuming that the date of death was just one stepm after the
 #define GLIMIT 100.0    interview.
 #define TINY 1.0e-20    (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
 static double maxarg1,maxarg2;    memory allocation. But we also truncated to 8 characters (left
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    truncation)
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    (Repository): No more line truncation errors.
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.84  2003/06/13 21:44:43  brouard
 #define rint(a) floor(a+0.5)    * imach.c (Repository): Replace "freqsummary" at a correct
     place. It differs from routine "prevalence" which may be called
 static double sqrarg;    many times. Probs is memory consuming and must be used with
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    parcimony.
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   
 int imx;    Revision 1.83  2003/06/10 13:39:11  lievre
 int stepm;    *** empty log message ***
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.82  2003/06/05 15:57:20  brouard
 int estepm;    Add log in  imach.c and  fullversion number is now printed.
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
   */
 int m,nb;  /*
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;     Interpolated Markov Chain
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Short summary of the programme:
 double dateintmean=0;    
     This program computes Healthy Life Expectancies from
 double *weight;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 int **s; /* Status */    first survey ("cross") where individuals from different ages are
 double *agedc, **covar, idx;    interviewed on their health status or degree of disability (in the
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    (if any) in individual health status.  Health expectancies are
 double ftolhess; /* Tolerance for computing hessian */    computed from the time spent in each health state according to a
     model. More health states you consider, more time is necessary to reach the
 /**************** split *************************/    Maximum Likelihood of the parameters involved in the model.  The
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    simplest model is the multinomial logistic model where pij is the
 {    probability to be observed in state j at the second wave
    char *s;                             /* pointer */    conditional to be observed in state i at the first wave. Therefore
    int  l1, l2;                         /* length counters */    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
    l1 = strlen( path );                 /* length of path */    complex model than "constant and age", you should modify the program
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    where the markup *Covariates have to be included here again* invites
 #ifdef windows    you to do it.  More covariates you add, slower the
    s = strrchr( path, '\\' );           /* find last / */    convergence.
 #else  
    s = strrchr( path, '/' );            /* find last / */    The advantage of this computer programme, compared to a simple
 #endif    multinomial logistic model, is clear when the delay between waves is not
    if ( s == NULL ) {                   /* no directory, so use current */    identical for each individual. Also, if a individual missed an
 #if     defined(__bsd__)                /* get current working directory */    intermediate interview, the information is lost, but taken into
       extern char       *getwd( );    account using an interpolation or extrapolation.  
   
       if ( getwd( dirc ) == NULL ) {    hPijx is the probability to be observed in state i at age x+h
 #else    conditional to the observed state i at age x. The delay 'h' can be
       extern char       *getcwd( );    split into an exact number (nh*stepm) of unobserved intermediate
     states. This elementary transition (by month, quarter,
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    semester or year) is modelled as a multinomial logistic.  The hPx
 #endif    matrix is simply the matrix product of nh*stepm elementary matrices
          return( GLOCK_ERROR_GETCWD );    and the contribution of each individual to the likelihood is simply
       }    hPijx.
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Also this programme outputs the covariance matrix of the parameters but also
       s++;                              /* after this, the filename */    of the life expectancies. It also computes the stable prevalence. 
       l2 = strlen( s );                 /* length of filename */    
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
       strcpy( name, s );                /* save file name */             Institut national d'études démographiques, Paris.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    This software have been partly granted by Euro-REVES, a concerted action
       dirc[l1-l2] = 0;                  /* add zero */    from the European Union.
    }    It is copyrighted identically to a GNU software product, ie programme and
    l1 = strlen( dirc );                 /* length of directory */    software can be distributed freely for non commercial use. Latest version
 #ifdef windows    can be accessed at http://euroreves.ined.fr/imach .
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 #endif    
    s = strrchr( name, '.' );            /* find last / */    **********************************************************************/
    s++;  /*
    strcpy(ext,s);                       /* save extension */    main
    l1= strlen( name);    read parameterfile
    l2= strlen( s)+1;    read datafile
    strncpy( finame, name, l1-l2);    concatwav
    finame[l1-l2]= 0;    freqsummary
    return( 0 );                         /* we're done */    if (mle >= 1)
 }      mlikeli
     print results files
     if mle==1 
 /******************************************/       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 void replace(char *s, char*t)        begin-prev-date,...
 {    open gnuplot file
   int i;    open html file
   int lg=20;    stable prevalence
   i=0;     for age prevalim()
   lg=strlen(t);    h Pij x
   for(i=0; i<= lg; i++) {    variance of p varprob
     (s[i] = t[i]);    forecasting if prevfcast==1 prevforecast call prevalence()
     if (t[i]== '\\') s[i]='/';    health expectancies
   }    Variance-covariance of DFLE
 }    prevalence()
      movingaverage()
 int nbocc(char *s, char occ)    varevsij() 
 {    if popbased==1 varevsij(,popbased)
   int i,j=0;    total life expectancies
   int lg=20;    Variance of stable prevalence
   i=0;   end
   lg=strlen(s);  */
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;  
   }  
   return j;   
 }  #include <math.h>
   #include <stdio.h>
 void cutv(char *u,char *v, char*t, char occ)  #include <stdlib.h>
 {  #include <string.h>
   int i,lg,j,p=0;  #include <unistd.h>
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {  #include <sys/types.h>
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  #include <sys/stat.h>
   }  #include <errno.h>
   extern int errno;
   lg=strlen(t);  
   for(j=0; j<p; j++) {  /* #include <sys/time.h> */
     (u[j] = t[j]);  #include <time.h>
   }  #include "timeval.h"
      u[p]='\0';  
   /* #include <libintl.h> */
    for(j=0; j<= lg; j++) {  /* #define _(String) gettext (String) */
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }  #define MAXLINE 256
 }  
   #define GNUPLOTPROGRAM "gnuplot"
 /********************** nrerror ********************/  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
 void nrerror(char error_text[])  
 {  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   fprintf(stderr,"ERREUR ...\n");  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   fprintf(stderr,"%s\n",error_text);  
   exit(1);  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 }  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 /*********************** vector *******************/  
 double *vector(int nl, int nh)  #define NINTERVMAX 8
 {  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   double *v;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #define NCOVMAX 8 /* Maximum number of covariates */
   if (!v) nrerror("allocation failure in vector");  #define MAXN 20000
   return v-nl+NR_END;  #define YEARM 12. /* Number of months per year */
 }  #define AGESUP 130
   #define AGEBASE 40
 /************************ free vector ******************/  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 void free_vector(double*v, int nl, int nh)  #ifdef UNIX
 {  #define DIRSEPARATOR '/'
   free((FREE_ARG)(v+nl-NR_END));  #define CHARSEPARATOR "/"
 }  #define ODIRSEPARATOR '\\'
   #else
 /************************ivector *******************************/  #define DIRSEPARATOR '\\'
 int *ivector(long nl,long nh)  #define CHARSEPARATOR "\\"
 {  #define ODIRSEPARATOR '/'
   int *v;  #endif
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");  /* $Id$ */
   return v-nl+NR_END;  /* $State$ */
 }  
   char version[]="Imach version 0.98a, January 2006, INED-EUROREVES ";
 /******************free ivector **************************/  char fullversion[]="$Revision$ $Date$"; 
 void free_ivector(int *v, long nl, long nh)  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 {  int nvar;
   free((FREE_ARG)(v+nl-NR_END));  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
 }  int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
 /******************* imatrix *******************************/  int ndeath=1; /* Number of dead states */
 int **imatrix(long nrl, long nrh, long ncl, long nch)  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  int popbased=0;
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  int *wav; /* Number of waves for this individuual 0 is possible */
   int **m;  int maxwav; /* Maxim number of waves */
    int jmin, jmax; /* min, max spacing between 2 waves */
   /* allocate pointers to rows */  int gipmx, gsw; /* Global variables on the number of contributions 
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));                     to the likelihood and the sum of weights (done by funcone)*/
   if (!m) nrerror("allocation failure 1 in matrix()");  int mle, weightopt;
   m += NR_END;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   m -= nrl;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
    int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
               * wave mi and wave mi+1 is not an exact multiple of stepm. */
   /* allocate rows and set pointers to them */  double jmean; /* Mean space between 2 waves */
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  double **oldm, **newm, **savm; /* Working pointers to matrices */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   m[nrl] += NR_END;  FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   m[nrl] -= ncl;  FILE *ficlog, *ficrespow;
    int globpr; /* Global variable for printing or not */
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  double fretone; /* Only one call to likelihood */
    long ipmx; /* Number of contributions */
   /* return pointer to array of pointers to rows */  double sw; /* Sum of weights */
   return m;  char filerespow[FILENAMELENGTH];
 }  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   FILE *ficresilk;
 /****************** free_imatrix *************************/  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 void free_imatrix(m,nrl,nrh,ncl,nch)  FILE *ficresprobmorprev;
       int **m;  FILE *fichtm, *fichtmcov; /* Html File */
       long nch,ncl,nrh,nrl;  FILE *ficreseij;
      /* free an int matrix allocated by imatrix() */  char filerese[FILENAMELENGTH];
 {  FILE  *ficresvij;
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  char fileresv[FILENAMELENGTH];
   free((FREE_ARG) (m+nrl-NR_END));  FILE  *ficresvpl;
 }  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 /******************* matrix *******************************/  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 double **matrix(long nrl, long nrh, long ncl, long nch)  char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];
 {  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  char command[FILENAMELENGTH];
   double **m;  int  outcmd=0;
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  char filelog[FILENAMELENGTH]; /* Log file */
   m -= nrl;  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  char popfile[FILENAMELENGTH];
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   m[nrl] -= ncl;  
   struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  struct timezone tzp;
   return m;  extern int gettimeofday();
 }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   long time_value;
 /*************************free matrix ************************/  extern long time();
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  char strcurr[80], strfor[80];
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define NR_END 1
   free((FREE_ARG)(m+nrl-NR_END));  #define FREE_ARG char*
 }  #define FTOL 1.0e-10
   
 /******************* ma3x *******************************/  #define NRANSI 
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #define ITMAX 200 
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define TOL 2.0e-4 
   double ***m;  
   #define CGOLD 0.3819660 
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define ZEPS 1.0e-10 
   if (!m) nrerror("allocation failure 1 in matrix()");  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   m += NR_END;  
   m -= nrl;  #define GOLD 1.618034 
   #define GLIMIT 100.0 
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define TINY 1.0e-20 
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  static double maxarg1,maxarg2;
   m[nrl] -= ncl;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #define rint(a) floor(a+0.5)
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  
   m[nrl][ncl] += NR_END;  static double sqrarg;
   m[nrl][ncl] -= nll;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   for (j=ncl+1; j<=nch; j++)  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
     m[nrl][j]=m[nrl][j-1]+nlay;  int agegomp= AGEGOMP;
    
   for (i=nrl+1; i<=nrh; i++) {  int imx; 
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  int stepm=1;
     for (j=ncl+1; j<=nch; j++)  /* Stepm, step in month: minimum step interpolation*/
       m[i][j]=m[i][j-1]+nlay;  
   }  int estepm;
   return m;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 }  
   int m,nb;
 /*************************free ma3x ************************/  long *num;
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 {  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  double **pmmij, ***probs;
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  double *ageexmed,*agecens;
   free((FREE_ARG)(m+nrl-NR_END));  double dateintmean=0;
 }  
   double *weight;
 /***************** f1dim *************************/  int **s; /* Status */
 extern int ncom;  double *agedc, **covar, idx;
 extern double *pcom,*xicom;  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 extern double (*nrfunc)(double []);  double *lsurv, *lpop, *tpop;
    
 double f1dim(double x)  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 {  double ftolhess; /* Tolerance for computing hessian */
   int j;  
   double f;  /**************** split *************************/
   double *xt;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
    {
   xt=vector(1,ncom);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   f=(*nrfunc)(xt);    */ 
   free_vector(xt,1,ncom);    char  *ss;                            /* pointer */
   return f;    int   l1, l2;                         /* length counters */
 }  
     l1 = strlen(path );                   /* length of path */
 /*****************brent *************************/    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 {    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   int iter;      strcpy( name, path );               /* we got the fullname name because no directory */
   double a,b,d,etemp;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   double fu,fv,fw,fx;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   double ftemp;      /* get current working directory */
   double p,q,r,tol1,tol2,u,v,w,x,xm;      /*    extern  char* getcwd ( char *buf , int len);*/
   double e=0.0;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
          return( GLOCK_ERROR_GETCWD );
   a=(ax < cx ? ax : cx);      }
   b=(ax > cx ? ax : cx);      /* got dirc from getcwd*/
   x=w=v=bx;      printf(" DIRC = %s \n",dirc);
   fw=fv=fx=(*f)(x);    } else {                              /* strip direcotry from path */
   for (iter=1;iter<=ITMAX;iter++) {      ss++;                               /* after this, the filename */
     xm=0.5*(a+b);      l2 = strlen( ss );                  /* length of filename */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/      strcpy( name, ss );         /* save file name */
     printf(".");fflush(stdout);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 #ifdef DEBUG      dirc[l1-l2] = 0;                    /* add zero */
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);      printf(" DIRC2 = %s \n",dirc);
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    }
 #endif    /* We add a separator at the end of dirc if not exists */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    l1 = strlen( dirc );                  /* length of directory */
       *xmin=x;    if( dirc[l1-1] != DIRSEPARATOR ){
       return fx;      dirc[l1] =  DIRSEPARATOR;
     }      dirc[l1+1] = 0; 
     ftemp=fu;      printf(" DIRC3 = %s \n",dirc);
     if (fabs(e) > tol1) {    }
       r=(x-w)*(fx-fv);    ss = strrchr( name, '.' );            /* find last / */
       q=(x-v)*(fx-fw);    if (ss >0){
       p=(x-v)*q-(x-w)*r;      ss++;
       q=2.0*(q-r);      strcpy(ext,ss);                     /* save extension */
       if (q > 0.0) p = -p;      l1= strlen( name);
       q=fabs(q);      l2= strlen(ss)+1;
       etemp=e;      strncpy( finame, name, l1-l2);
       e=d;      finame[l1-l2]= 0;
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    }
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  
       else {    return( 0 );                          /* we're done */
         d=p/q;  }
         u=x+d;  
         if (u-a < tol2 || b-u < tol2)  
           d=SIGN(tol1,xm-x);  /******************************************/
       }  
     } else {  void replace_back_to_slash(char *s, char*t)
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  {
     }    int i;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    int lg=0;
     fu=(*f)(u);    i=0;
     if (fu <= fx) {    lg=strlen(t);
       if (u >= x) a=x; else b=x;    for(i=0; i<= lg; i++) {
       SHFT(v,w,x,u)      (s[i] = t[i]);
         SHFT(fv,fw,fx,fu)      if (t[i]== '\\') s[i]='/';
         } else {    }
           if (u < x) a=u; else b=u;  }
           if (fu <= fw || w == x) {  
             v=w;  int nbocc(char *s, char occ)
             w=u;  {
             fv=fw;    int i,j=0;
             fw=fu;    int lg=20;
           } else if (fu <= fv || v == x || v == w) {    i=0;
             v=u;    lg=strlen(s);
             fv=fu;    for(i=0; i<= lg; i++) {
           }    if  (s[i] == occ ) j++;
         }    }
   }    return j;
   nrerror("Too many iterations in brent");  }
   *xmin=x;  
   return fx;  void cutv(char *u,char *v, char*t, char occ)
 }  {
     /* cuts string t into u and v where u ends before first occurence of char 'occ' 
 /****************** mnbrak ***********************/       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
        gives u="abcedf" and v="ghi2j" */
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    int i,lg,j,p=0;
             double (*func)(double))    i=0;
 {    for(j=0; j<=strlen(t)-1; j++) {
   double ulim,u,r,q, dum;      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   double fu;    }
    
   *fa=(*func)(*ax);    lg=strlen(t);
   *fb=(*func)(*bx);    for(j=0; j<p; j++) {
   if (*fb > *fa) {      (u[j] = t[j]);
     SHFT(dum,*ax,*bx,dum)    }
       SHFT(dum,*fb,*fa,dum)       u[p]='\0';
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);     for(j=0; j<= lg; j++) {
   *fc=(*func)(*cx);      if (j>=(p+1))(v[j-p-1] = t[j]);
   while (*fb > *fc) {    }
     r=(*bx-*ax)*(*fb-*fc);  }
     q=(*bx-*cx)*(*fb-*fa);  
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  /********************** nrerror ********************/
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);  void nrerror(char error_text[])
     if ((*bx-u)*(u-*cx) > 0.0) {  {
       fu=(*func)(u);    fprintf(stderr,"ERREUR ...\n");
     } else if ((*cx-u)*(u-ulim) > 0.0) {    fprintf(stderr,"%s\n",error_text);
       fu=(*func)(u);    exit(EXIT_FAILURE);
       if (fu < *fc) {  }
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  /*********************** vector *******************/
           SHFT(*fb,*fc,fu,(*func)(u))  double *vector(int nl, int nh)
           }  {
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    double *v;
       u=ulim;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       fu=(*func)(u);    if (!v) nrerror("allocation failure in vector");
     } else {    return v-nl+NR_END;
       u=(*cx)+GOLD*(*cx-*bx);  }
       fu=(*func)(u);  
     }  /************************ free vector ******************/
     SHFT(*ax,*bx,*cx,u)  void free_vector(double*v, int nl, int nh)
       SHFT(*fa,*fb,*fc,fu)  {
       }    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************** linmin ************************/  /************************ivector *******************************/
   int *ivector(long nl,long nh)
 int ncom;  {
 double *pcom,*xicom;    int *v;
 double (*nrfunc)(double []);    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
      if (!v) nrerror("allocation failure in ivector");
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    return v-nl+NR_END;
 {  }
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  /******************free ivector **************************/
   double f1dim(double x);  void free_ivector(int *v, long nl, long nh)
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  {
               double *fc, double (*func)(double));    free((FREE_ARG)(v+nl-NR_END));
   int j;  }
   double xx,xmin,bx,ax;  
   double fx,fb,fa;  /************************lvector *******************************/
    long *lvector(long nl,long nh)
   ncom=n;  {
   pcom=vector(1,n);    long *v;
   xicom=vector(1,n);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   nrfunc=func;    if (!v) nrerror("allocation failure in ivector");
   for (j=1;j<=n;j++) {    return v-nl+NR_END;
     pcom[j]=p[j];  }
     xicom[j]=xi[j];  
   }  /******************free lvector **************************/
   ax=0.0;  void free_lvector(long *v, long nl, long nh)
   xx=1.0;  {
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    free((FREE_ARG)(v+nl-NR_END));
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  }
 #ifdef DEBUG  
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  /******************* imatrix *******************************/
 #endif  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   for (j=1;j<=n;j++) {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     xi[j] *= xmin;  { 
     p[j] += xi[j];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   }    int **m; 
   free_vector(xicom,1,n);    
   free_vector(pcom,1,n);    /* allocate pointers to rows */ 
 }    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     if (!m) nrerror("allocation failure 1 in matrix()"); 
 /*************** powell ************************/    m += NR_END; 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    m -= nrl; 
             double (*func)(double []))    
 {    
   void linmin(double p[], double xi[], int n, double *fret,    /* allocate rows and set pointers to them */ 
               double (*func)(double []));    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   int i,ibig,j;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   double del,t,*pt,*ptt,*xit;    m[nrl] += NR_END; 
   double fp,fptt;    m[nrl] -= ncl; 
   double *xits;    
   pt=vector(1,n);    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   ptt=vector(1,n);    
   xit=vector(1,n);    /* return pointer to array of pointers to rows */ 
   xits=vector(1,n);    return m; 
   *fret=(*func)(p);  } 
   for (j=1;j<=n;j++) pt[j]=p[j];  
   for (*iter=1;;++(*iter)) {  /****************** free_imatrix *************************/
     fp=(*fret);  void free_imatrix(m,nrl,nrh,ncl,nch)
     ibig=0;        int **m;
     del=0.0;        long nch,ncl,nrh,nrl; 
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);       /* free an int matrix allocated by imatrix() */ 
     for (i=1;i<=n;i++)  { 
       printf(" %d %.12f",i, p[i]);    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     printf("\n");    free((FREE_ARG) (m+nrl-NR_END)); 
     for (i=1;i<=n;i++) {  } 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);  /******************* matrix *******************************/
 #ifdef DEBUG  double **matrix(long nrl, long nrh, long ncl, long nch)
       printf("fret=%lf \n",*fret);  {
 #endif    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       printf("%d",i);fflush(stdout);    double **m;
       linmin(p,xit,n,fret,func);  
       if (fabs(fptt-(*fret)) > del) {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         del=fabs(fptt-(*fret));    if (!m) nrerror("allocation failure 1 in matrix()");
         ibig=i;    m += NR_END;
       }    m -= nrl;
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       for (j=1;j<=n;j++) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    m[nrl] += NR_END;
         printf(" x(%d)=%.12e",j,xit[j]);    m[nrl] -= ncl;
       }  
       for(j=1;j<=n;j++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         printf(" p=%.12e",p[j]);    return m;
       printf("\n");    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
 #endif     */
     }  }
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG  /*************************free matrix ************************/
       int k[2],l;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       k[0]=1;  {
       k[1]=-1;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       printf("Max: %.12e",(*func)(p));    free((FREE_ARG)(m+nrl-NR_END));
       for (j=1;j<=n;j++)  }
         printf(" %.12e",p[j]);  
       printf("\n");  /******************* ma3x *******************************/
       for(l=0;l<=1;l++) {  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
         for (j=1;j<=n;j++) {  {
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    double ***m;
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       }    if (!m) nrerror("allocation failure 1 in matrix()");
 #endif    m += NR_END;
     m -= nrl;
   
       free_vector(xit,1,n);    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       free_vector(xits,1,n);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       free_vector(ptt,1,n);    m[nrl] += NR_END;
       free_vector(pt,1,n);    m[nrl] -= ncl;
       return;  
     }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  
     for (j=1;j<=n;j++) {    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       ptt[j]=2.0*p[j]-pt[j];    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       xit[j]=p[j]-pt[j];    m[nrl][ncl] += NR_END;
       pt[j]=p[j];    m[nrl][ncl] -= nll;
     }    for (j=ncl+1; j<=nch; j++) 
     fptt=(*func)(ptt);      m[nrl][j]=m[nrl][j-1]+nlay;
     if (fptt < fp) {    
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    for (i=nrl+1; i<=nrh; i++) {
       if (t < 0.0) {      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
         linmin(p,xit,n,fret,func);      for (j=ncl+1; j<=nch; j++) 
         for (j=1;j<=n;j++) {        m[i][j]=m[i][j-1]+nlay;
           xi[j][ibig]=xi[j][n];    }
           xi[j][n]=xit[j];    return m; 
         }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 #ifdef DEBUG             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    */
         for(j=1;j<=n;j++)  }
           printf(" %.12e",xit[j]);  
         printf("\n");  /*************************free ma3x ************************/
 #endif  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       }  {
     }    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 }    free((FREE_ARG)(m+nrl-NR_END));
   }
 /**** Prevalence limit ****************/  
   /*************** function subdirf ***********/
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  char *subdirf(char fileres[])
 {  {
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    /* Caution optionfilefiname is hidden */
      matrix by transitions matrix until convergence is reached */    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/"); /* Add to the right */
   int i, ii,j,k;    strcat(tmpout,fileres);
   double min, max, maxmin, maxmax,sumnew=0.;    return tmpout;
   double **matprod2();  }
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  /*************** function subdirf2 ***********/
   double agefin, delaymax=50 ; /* Max number of years to converge */  char *subdirf2(char fileres[], char *preop)
   {
   for (ii=1;ii<=nlstate+ndeath;ii++)    
     for (j=1;j<=nlstate+ndeath;j++){    /* Caution optionfilefiname is hidden */
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    strcpy(tmpout,optionfilefiname);
     }    strcat(tmpout,"/");
     strcat(tmpout,preop);
    cov[1]=1.;    strcat(tmpout,fileres);
      return tmpout;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  }
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  
     newm=savm;  /*************** function subdirf3 ***********/
     /* Covariates have to be included here again */  char *subdirf3(char fileres[], char *preop, char *preop2)
      cov[2]=agefin;  {
      
       for (k=1; k<=cptcovn;k++) {    /* Caution optionfilefiname is hidden */
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    strcpy(tmpout,optionfilefiname);
         /*      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]]);*/    strcat(tmpout,"/");
       }    strcat(tmpout,preop);
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    strcat(tmpout,preop2);
       for (k=1; k<=cptcovprod;k++)    strcat(tmpout,fileres);
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    return tmpout;
   }
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /***************** f1dim *************************/
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  extern int ncom; 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  extern double *pcom,*xicom;
   extern double (*nrfunc)(double []); 
     savm=oldm;   
     oldm=newm;  double f1dim(double x) 
     maxmax=0.;  { 
     for(j=1;j<=nlstate;j++){    int j; 
       min=1.;    double f;
       max=0.;    double *xt; 
       for(i=1; i<=nlstate; i++) {   
         sumnew=0;    xt=vector(1,ncom); 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
         prlim[i][j]= newm[i][j]/(1-sumnew);    f=(*nrfunc)(xt); 
         max=FMAX(max,prlim[i][j]);    free_vector(xt,1,ncom); 
         min=FMIN(min,prlim[i][j]);    return f; 
       }  } 
       maxmin=max-min;  
       maxmax=FMAX(maxmax,maxmin);  /*****************brent *************************/
     }  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     if(maxmax < ftolpl){  { 
       return prlim;    int iter; 
     }    double a,b,d,etemp;
   }    double fu,fv,fw,fx;
 }    double ftemp;
     double p,q,r,tol1,tol2,u,v,w,x,xm; 
 /*************** transition probabilities ***************/    double e=0.0; 
    
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    a=(ax < cx ? ax : cx); 
 {    b=(ax > cx ? ax : cx); 
   double s1, s2;    x=w=v=bx; 
   /*double t34;*/    fw=fv=fx=(*f)(x); 
   int i,j,j1, nc, ii, jj;    for (iter=1;iter<=ITMAX;iter++) { 
       xm=0.5*(a+b); 
     for(i=1; i<= nlstate; i++){      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
     for(j=1; j<i;j++){      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      printf(".");fflush(stdout);
         /*s2 += param[i][j][nc]*cov[nc];*/      fprintf(ficlog,".");fflush(ficlog);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  #ifdef DEBUG
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/      printf("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)))) { */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  #endif
     }      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     for(j=i+1; j<=nlstate+ndeath;j++){        *xmin=x; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        return fx; 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      } 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/      ftemp=fu;
       }      if (fabs(e) > tol1) { 
       ps[i][j]=s2;        r=(x-w)*(fx-fv); 
     }        q=(x-v)*(fx-fw); 
   }        p=(x-v)*q-(x-w)*r; 
     /*ps[3][2]=1;*/        q=2.0*(q-r); 
         if (q > 0.0) p = -p; 
   for(i=1; i<= nlstate; i++){        q=fabs(q); 
      s1=0;        etemp=e; 
     for(j=1; j<i; j++)        e=d; 
       s1+=exp(ps[i][j]);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     for(j=i+1; j<=nlstate+ndeath; j++)          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       s1+=exp(ps[i][j]);        else { 
     ps[i][i]=1./(s1+1.);          d=p/q; 
     for(j=1; j<i; j++)          u=x+d; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];          if (u-a < tol2 || b-u < tol2) 
     for(j=i+1; j<=nlstate+ndeath; j++)            d=SIGN(tol1,xm-x); 
       ps[i][j]= exp(ps[i][j])*ps[i][i];        } 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */      } else { 
   } /* end i */        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     for(jj=1; jj<= nlstate+ndeath; jj++){      fu=(*f)(u); 
       ps[ii][jj]=0;      if (fu <= fx) { 
       ps[ii][ii]=1;        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; 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){            if (fu <= fw || w == x) { 
     for(jj=1; jj<= nlstate+ndeath; jj++){              v=w; 
      printf("%lf ",ps[ii][jj]);              w=u; 
    }              fv=fw; 
     printf("\n ");              fw=fu; 
     }            } else if (fu <= fv || v == x || v == w) { 
     printf("\n ");printf("%lf ",cov[2]);*/              v=u; 
 /*              fv=fu; 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);            } 
   goto end;*/          } 
     return ps;    } 
 }    nrerror("Too many iterations in brent"); 
     *xmin=x; 
 /**************** Product of 2 matrices ******************/    return fx; 
   } 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  
 {  /****************** mnbrak ***********************/
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   /* in, b, out are matrice of pointers which should have been initialized              double (*func)(double)) 
      before: only the contents of out is modified. The function returns  { 
      a pointer to pointers identical to out */    double ulim,u,r,q, dum;
   long i, j, k;    double fu; 
   for(i=nrl; i<= nrh; i++)   
     for(k=ncolol; k<=ncoloh; k++)    *fa=(*func)(*ax); 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    *fb=(*func)(*bx); 
         out[i][k] +=in[i][j]*b[j][k];    if (*fb > *fa) { 
       SHFT(dum,*ax,*bx,dum) 
   return out;        SHFT(dum,*fb,*fa,dum) 
 }        } 
     *cx=(*bx)+GOLD*(*bx-*ax); 
     *fc=(*func)(*cx); 
 /************* Higher Matrix Product ***************/    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )      q=(*bx-*cx)*(*fb-*fa); 
 {      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
      duration (i.e. until      ulim=(*bx)+GLIMIT*(*cx-*bx); 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.      if ((*bx-u)*(u-*cx) > 0.0) { 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        fu=(*func)(u); 
      (typically every 2 years instead of every month which is too big).      } else if ((*cx-u)*(u-ulim) > 0.0) { 
      Model is determined by parameters x and covariates have to be        fu=(*func)(u); 
      included manually here.        if (fu < *fc) { 
           SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
      */            SHFT(*fb,*fc,fu,(*func)(u)) 
             } 
   int i, j, d, h, k;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   double **out, cov[NCOVMAX];        u=ulim; 
   double **newm;        fu=(*func)(u); 
       } else { 
   /* Hstepm could be zero and should return the unit matrix */        u=(*cx)+GOLD*(*cx-*bx); 
   for (i=1;i<=nlstate+ndeath;i++)        fu=(*func)(u); 
     for (j=1;j<=nlstate+ndeath;j++){      } 
       oldm[i][j]=(i==j ? 1.0 : 0.0);      SHFT(*ax,*bx,*cx,u) 
       po[i][j][0]=(i==j ? 1.0 : 0.0);        SHFT(*fa,*fb,*fc,fu) 
     }        } 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  } 
   for(h=1; h <=nhstepm; h++){  
     for(d=1; d <=hstepm; d++){  /*************** linmin ************************/
       newm=savm;  
       /* Covariates have to be included here again */  int ncom; 
       cov[1]=1.;  double *pcom,*xicom;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  double (*nrfunc)(double []); 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];   
       for (k=1; k<=cptcovage;k++)  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  { 
       for (k=1; k<=cptcovprod;k++)    double brent(double ax, double bx, double cx, 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];                 double (*f)(double), double tol, double *xmin); 
     double f1dim(double x); 
     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/                double *fc, double (*func)(double)); 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    int j; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    double xx,xmin,bx,ax; 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    double fx,fb,fa;
       savm=oldm;   
       oldm=newm;    ncom=n; 
     }    pcom=vector(1,n); 
     for(i=1; i<=nlstate+ndeath; i++)    xicom=vector(1,n); 
       for(j=1;j<=nlstate+ndeath;j++) {    nrfunc=func; 
         po[i][j][h]=newm[i][j];    for (j=1;j<=n;j++) { 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      pcom[j]=p[j]; 
          */      xicom[j]=xi[j]; 
       }    } 
   } /* end h */    ax=0.0; 
   return po;    xx=1.0; 
 }    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   #ifdef DEBUG
 /*************** log-likelihood *************/    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 double func( double *x)    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 {  #endif
   int i, ii, j, k, mi, d, kk;    for (j=1;j<=n;j++) { 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      xi[j] *= xmin; 
   double **out;      p[j] += xi[j]; 
   double sw; /* Sum of weights */    } 
   double lli; /* Individual log likelihood */    free_vector(xicom,1,n); 
   long ipmx;    free_vector(pcom,1,n); 
   /*extern weight */  } 
   /* We are differentiating ll according to initial status */  
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  char *asc_diff_time(long time_sec, char ascdiff[])
   /*for(i=1;i<imx;i++)  {
     printf(" %d\n",s[4][i]);    long sec_left, days, hours, minutes;
   */    days = (time_sec) / (60*60*24);
   cov[1]=1.;    sec_left = (time_sec) % (60*60*24);
     hours = (sec_left) / (60*60) ;
   for(k=1; k<=nlstate; k++) ll[k]=0.;    sec_left = (sec_left) %(60*60);
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    minutes = (sec_left) /60;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    sec_left = (sec_left) % (60);
     for(mi=1; mi<= wav[i]-1; mi++){    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
       for (ii=1;ii<=nlstate+ndeath;ii++)    return ascdiff;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  }
       for(d=0; d<dh[mi][i]; d++){  
         newm=savm;  /*************** powell ************************/
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
         for (kk=1; kk<=cptcovage;kk++) {              double (*func)(double [])) 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];  { 
         }    void linmin(double p[], double xi[], int n, double *fret, 
                        double (*func)(double [])); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    int i,ibig,j; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    double del,t,*pt,*ptt,*xit;
         savm=oldm;    double fp,fptt;
         oldm=newm;    double *xits;
            int niterf, itmp;
          
       } /* end mult */    pt=vector(1,n); 
          ptt=vector(1,n); 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    xit=vector(1,n); 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    xits=vector(1,n); 
       ipmx +=1;    *fret=(*func)(p); 
       sw += weight[i];    for (j=1;j<=n;j++) pt[j]=p[j]; 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    for (*iter=1;;++(*iter)) { 
     } /* end of wave */      fp=(*fret); 
   } /* end of individual */      ibig=0; 
       del=0.0; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      last_time=curr_time;
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      (void) gettimeofday(&curr_time,&tzp);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */      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);
   return -l;      /*    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);
 }      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
       */
      for (i=1;i<=n;i++) {
 /*********** Maximum Likelihood Estimation ***************/        printf(" %d %.12f",i, p[i]);
         fprintf(ficlog," %d %.12lf",i, p[i]);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        fprintf(ficrespow," %.12lf", p[i]);
 {      }
   int i,j, iter;      printf("\n");
   double **xi,*delti;      fprintf(ficlog,"\n");
   double fret;      fprintf(ficrespow,"\n");fflush(ficrespow);
   xi=matrix(1,npar,1,npar);      if(*iter <=3){
   for (i=1;i<=npar;i++)        tm = *localtime(&curr_time.tv_sec);
     for (j=1;j<=npar;j++)        strcpy(strcurr,asctime(&tm));
       xi[i][j]=(i==j ? 1.0 : 0.0);  /*       asctime_r(&tm,strcurr); */
   printf("Powell\n");        forecast_time=curr_time; 
   powell(p,xi,npar,ftol,&iter,&fret,func);        itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          strcurr[itmp-1]='\0';
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 }        for(niterf=10;niterf<=30;niterf+=10){
           forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
 /**** Computes Hessian and covariance matrix ***/          tmf = *localtime(&forecast_time.tv_sec);
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  /*      asctime_r(&tmf,strfor); */
 {          strcpy(strfor,asctime(&tmf));
   double  **a,**y,*x,pd;          itmp = strlen(strfor);
   double **hess;          if(strfor[itmp-1]=='\n')
   int i, j,jk;          strfor[itmp-1]='\0';
   int *indx;          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);
   double hessii(double p[], double delta, int theta, double delti[]);        }
   double hessij(double p[], double delti[], int i, int j);      }
   void lubksb(double **a, int npar, int *indx, double b[]) ;      for (i=1;i<=n;i++) { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         fptt=(*fret); 
   hess=matrix(1,npar,1,npar);  #ifdef DEBUG
         printf("fret=%lf \n",*fret);
   printf("\nCalculation of the hessian matrix. Wait...\n");        fprintf(ficlog,"fret=%lf \n",*fret);
   for (i=1;i<=npar;i++){  #endif
     printf("%d",i);fflush(stdout);        printf("%d",i);fflush(stdout);
     hess[i][i]=hessii(p,ftolhess,i,delti);        fprintf(ficlog,"%d",i);fflush(ficlog);
     /*printf(" %f ",p[i]);*/        linmin(p,xit,n,fret,func); 
     /*printf(" %lf ",hess[i][i]);*/        if (fabs(fptt-(*fret)) > del) { 
   }          del=fabs(fptt-(*fret)); 
            ibig=i; 
   for (i=1;i<=npar;i++) {        } 
     for (j=1;j<=npar;j++)  {  #ifdef DEBUG
       if (j>i) {        printf("%d %.12e",i,(*fret));
         printf(".%d%d",i,j);fflush(stdout);        fprintf(ficlog,"%d %.12e",i,(*fret));
         hess[i][j]=hessij(p,delti,i,j);        for (j=1;j<=n;j++) {
         hess[j][i]=hess[i][j];              xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
         /*printf(" %lf ",hess[i][j]);*/          printf(" x(%d)=%.12e",j,xit[j]);
       }          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     }        }
   }        for(j=1;j<=n;j++) {
   printf("\n");          printf(" p=%.12e",p[j]);
           fprintf(ficlog," p=%.12e",p[j]);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        }
          printf("\n");
   a=matrix(1,npar,1,npar);        fprintf(ficlog,"\n");
   y=matrix(1,npar,1,npar);  #endif
   x=vector(1,npar);      } 
   indx=ivector(1,npar);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   for (i=1;i<=npar;i++)  #ifdef DEBUG
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];        int k[2],l;
   ludcmp(a,npar,indx,&pd);        k[0]=1;
         k[1]=-1;
   for (j=1;j<=npar;j++) {        printf("Max: %.12e",(*func)(p));
     for (i=1;i<=npar;i++) x[i]=0;        fprintf(ficlog,"Max: %.12e",(*func)(p));
     x[j]=1;        for (j=1;j<=n;j++) {
     lubksb(a,npar,indx,x);          printf(" %.12e",p[j]);
     for (i=1;i<=npar;i++){          fprintf(ficlog," %.12e",p[j]);
       matcov[i][j]=x[i];        }
     }        printf("\n");
   }        fprintf(ficlog,"\n");
         for(l=0;l<=1;l++) {
   printf("\n#Hessian matrix#\n");          for (j=1;j<=n;j++) {
   for (i=1;i<=npar;i++) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     for (j=1;j<=npar;j++) {            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       printf("%.3e ",hess[i][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");          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   }          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         }
   /* Recompute Inverse */  #endif
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  
   ludcmp(a,npar,indx,&pd);        free_vector(xit,1,n); 
         free_vector(xits,1,n); 
   /*  printf("\n#Hessian matrix recomputed#\n");        free_vector(ptt,1,n); 
         free_vector(pt,1,n); 
   for (j=1;j<=npar;j++) {        return; 
     for (i=1;i<=npar;i++) x[i]=0;      } 
     x[j]=1;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     lubksb(a,npar,indx,x);      for (j=1;j<=n;j++) { 
     for (i=1;i<=npar;i++){        ptt[j]=2.0*p[j]-pt[j]; 
       y[i][j]=x[i];        xit[j]=p[j]-pt[j]; 
       printf("%.3e ",y[i][j]);        pt[j]=p[j]; 
     }      } 
     printf("\n");      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) { 
   free_matrix(a,1,npar,1,npar);          linmin(p,xit,n,fret,func); 
   free_matrix(y,1,npar,1,npar);          for (j=1;j<=n;j++) { 
   free_vector(x,1,npar);            xi[j][ibig]=xi[j][n]; 
   free_ivector(indx,1,npar);            xi[j][n]=xit[j]; 
   free_matrix(hess,1,npar,1,npar);          }
   #ifdef DEBUG
           printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
 }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           for(j=1;j<=n;j++){
 /*************** hessian matrix ****************/            printf(" %.12e",xit[j]);
 double hessii( double x[], double delta, int theta, double delti[])            fprintf(ficlog," %.12e",xit[j]);
 {          }
   int i;          printf("\n");
   int l=1, lmax=20;          fprintf(ficlog,"\n");
   double k1,k2;  #endif
   double p2[NPARMAX+1];        }
   double res;      } 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    } 
   double fx;  } 
   int k=0,kmax=10;  
   double l1;  /**** Prevalence limit (stable prevalence)  ****************/
   
   fx=func(x);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   for (i=1;i<=npar;i++) p2[i]=x[i];  {
   for(l=0 ; l <=lmax; l++){    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     l1=pow(10,l);       matrix by transitions matrix until convergence is reached */
     delts=delt;  
     for(k=1 ; k <kmax; k=k+1){    int i, ii,j,k;
       delt = delta*(l1*k);    double min, max, maxmin, maxmax,sumnew=0.;
       p2[theta]=x[theta] +delt;    double **matprod2();
       k1=func(p2)-fx;    double **out, cov[NCOVMAX], **pmij();
       p2[theta]=x[theta]-delt;    double **newm;
       k2=func(p2)-fx;    double agefin, delaymax=50 ; /* Max number of years to converge */
       /*res= (k1-2.0*fx+k2)/delt/delt; */  
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    for (ii=1;ii<=nlstate+ndeath;ii++)
            for (j=1;j<=nlstate+ndeath;j++){
 #ifdef DEBUG        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);      }
 #endif  
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */     cov[1]=1.;
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){   
         k=kmax;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       }    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */      newm=savm;
         k=kmax; l=lmax*10.;      /* Covariates have to be included here again */
       }       cov[2]=agefin;
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    
         delts=delt;        for (k=1; k<=cptcovn;k++) {
       }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
     }          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
   }        }
   delti[theta]=delts;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   return res;        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]]];
 }  
         /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
 double hessij( double x[], double delti[], int thetai,int thetaj)        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
 {        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   int i;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;      savm=oldm;
   double p2[NPARMAX+1];      oldm=newm;
   int k;      maxmax=0.;
       for(j=1;j<=nlstate;j++){
   fx=func(x);        min=1.;
   for (k=1; k<=2; k++) {        max=0.;
     for (i=1;i<=npar;i++) p2[i]=x[i];        for(i=1; i<=nlstate; i++) {
     p2[thetai]=x[thetai]+delti[thetai]/k;          sumnew=0;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     k1=func(p2)-fx;          prlim[i][j]= newm[i][j]/(1-sumnew);
            max=FMAX(max,prlim[i][j]);
     p2[thetai]=x[thetai]+delti[thetai]/k;          min=FMIN(min,prlim[i][j]);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        }
     k2=func(p2)-fx;        maxmin=max-min;
          maxmax=FMAX(maxmax,maxmin);
     p2[thetai]=x[thetai]-delti[thetai]/k;      }
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      if(maxmax < ftolpl){
     k3=func(p2)-fx;        return prlim;
        }
     p2[thetai]=x[thetai]-delti[thetai]/k;    }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  }
     k4=func(p2)-fx;  
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  /*************** transition probabilities ***************/ 
 #ifdef DEBUG  
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
 #endif  {
   }    double s1, s2;
   return res;    /*double t34;*/
 }    int i,j,j1, nc, ii, jj;
   
 /************** Inverse of matrix **************/      for(i=1; i<= nlstate; i++){
 void ludcmp(double **a, int n, int *indx, double *d)        for(j=1; j<i;j++){
 {          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   int i,imax,j,k;            /*s2 += param[i][j][nc]*cov[nc];*/
   double big,dum,sum,temp;            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   double *vv;  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
            }
   vv=vector(1,n);          ps[i][j]=s2;
   *d=1.0;  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
   for (i=1;i<=n;i++) {        }
     big=0.0;        for(j=i+1; j<=nlstate+ndeath;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 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
     vv[i]=1.0/big;          }
   }          ps[i][j]=s2;
   for (j=1;j<=n;j++) {        }
     for (i=1;i<j;i++) {      }
       sum=a[i][j];      /*ps[3][2]=1;*/
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];      
       a[i][j]=sum;      for(i=1; i<= nlstate; i++){
     }        s1=0;
     big=0.0;        for(j=1; j<i; j++)
     for (i=j;i<=n;i++) {          s1+=exp(ps[i][j]);
       sum=a[i][j];        for(j=i+1; j<=nlstate+ndeath; j++)
       for (k=1;k<j;k++)          s1+=exp(ps[i][j]);
         sum -= a[i][k]*a[k][j];        ps[i][i]=1./(s1+1.);
       a[i][j]=sum;        for(j=1; j<i; j++)
       if ( (dum=vv[i]*fabs(sum)) >= big) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
         big=dum;        for(j=i+1; j<=nlstate+ndeath; j++)
         imax=i;          ps[i][j]= exp(ps[i][j])*ps[i][i];
       }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     }      } /* end i */
     if (j != imax) {      
       for (k=1;k<=n;k++) {      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         dum=a[imax][k];        for(jj=1; jj<= nlstate+ndeath; jj++){
         a[imax][k]=a[j][k];          ps[ii][jj]=0;
         a[j][k]=dum;          ps[ii][ii]=1;
       }        }
       *d = -(*d);      }
       vv[imax]=vv[j];      
     }  
     indx[j]=imax;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
     if (a[j][j] == 0.0) a[j][j]=TINY;  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
     if (j != n) {  /*         printf("ddd %lf ",ps[ii][jj]); */
       dum=1.0/(a[j][j]);  /*       } */
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  /*       printf("\n "); */
     }  /*        } */
   }  /*        printf("\n ");printf("%lf ",cov[2]); */
   free_vector(vv,1,n);  /* Doesn't work */         /*
 ;        for(i=1; i<= npar; i++) printf("%f ",x[i]);
 }        goto end;*/
       return ps;
 void lubksb(double **a, int n, int *indx, double b[])  }
 {  
   int i,ii=0,ip,j;  /**************** Product of 2 matrices ******************/
   double sum;  
    double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   for (i=1;i<=n;i++) {  {
     ip=indx[i];    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     sum=b[ip];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     b[ip]=b[i];    /* in, b, out are matrice of pointers which should have been initialized 
     if (ii)       before: only the contents of out is modified. The function returns
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];       a pointer to pointers identical to out */
     else if (sum) ii=i;    long i, j, k;
     b[i]=sum;    for(i=nrl; i<= nrh; i++)
   }      for(k=ncolol; k<=ncoloh; k++)
   for (i=n;i>=1;i--) {        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     sum=b[i];          out[i][k] +=in[i][j]*b[j][k];
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];  
     b[i]=sum/a[i][i];    return out;
   }  }
 }  
   
 /************ Frequencies ********************/  /************* Higher Matrix Product ***************/
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)  
 {  /* Some frequencies */  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
    {
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;    /* Computes the transition matrix starting at age 'age' over 
   double ***freq; /* Frequencies */       'nhstepm*hstepm*stepm' months (i.e. until
   double *pp;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   double pos, k2, dateintsum=0,k2cpt=0;       nhstepm*hstepm matrices. 
   FILE *ficresp;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   char fileresp[FILENAMELENGTH];       (typically every 2 years instead of every month which is too big 
         for the memory).
   pp=vector(1,nlstate);       Model is determined by parameters x and covariates have to be 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);       included manually here. 
   strcpy(fileresp,"p");  
   strcat(fileresp,fileres);       */
   if((ficresp=fopen(fileresp,"w"))==NULL) {  
     printf("Problem with prevalence resultfile: %s\n", fileresp);    int i, j, d, h, k;
     exit(0);    double **out, cov[NCOVMAX];
   }    double **newm;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  
   j1=0;    /* Hstepm could be zero and should return the unit matrix */
      for (i=1;i<=nlstate+ndeath;i++)
   j=cptcoveff;      for (j=1;j<=nlstate+ndeath;j++){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        oldm[i][j]=(i==j ? 1.0 : 0.0);
          po[i][j][0]=(i==j ? 1.0 : 0.0);
   for(k1=1; k1<=j;k1++){      }
     for(i1=1; i1<=ncodemax[k1];i1++){    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       j1++;    for(h=1; h <=nhstepm; h++){
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      for(d=1; d <=hstepm; d++){
         scanf("%d", i);*/        newm=savm;
       for (i=-1; i<=nlstate+ndeath; i++)          /* Covariates have to be included here again */
         for (jk=-1; jk<=nlstate+ndeath; jk++)          cov[1]=1.;
           for(m=agemin; m <= agemax+3; m++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
             freq[i][jk][m]=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
              for (k=1; k<=cptcovage;k++)
       dateintsum=0;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       k2cpt=0;        for (k=1; k<=cptcovprod;k++)
       for (i=1; i<=imx; i++) {          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         bool=1;  
         if  (cptcovn>0) {  
           for (z1=1; z1<=cptcoveff; z1++)        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
               bool=0;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         }                     pmij(pmmij,cov,ncovmodel,x,nlstate));
         if (bool==1) {        savm=oldm;
           for(m=firstpass; m<=lastpass; m++){        oldm=newm;
             k2=anint[m][i]+(mint[m][i]/12.);      }
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      for(i=1; i<=nlstate+ndeath; i++)
               if(agev[m][i]==0) agev[m][i]=agemax+1;        for(j=1;j<=nlstate+ndeath;j++) {
               if(agev[m][i]==1) agev[m][i]=agemax+2;          po[i][j][h]=newm[i][j];
               if (m<lastpass) {          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];           */
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        }
               }    } /* end h */
                  return po;
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {  }
                 dateintsum=dateintsum+k2;  
                 k2cpt++;  
               }  /*************** log-likelihood *************/
             }  double func( double *x)
           }  {
         }    int i, ii, j, k, mi, d, kk;
       }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
            double **out;
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    double sw; /* Sum of weights */
     double lli; /* Individual log likelihood */
       if  (cptcovn>0) {    int s1, s2;
         fprintf(ficresp, "\n#********** Variable ");    double bbh, survp;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    long ipmx;
         fprintf(ficresp, "**********\n#");    /*extern weight */
       }    /* We are differentiating ll according to initial status */
       for(i=1; i<=nlstate;i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    /*for(i=1;i<imx;i++) 
       fprintf(ficresp, "\n");      printf(" %d\n",s[4][i]);
          */
       for(i=(int)agemin; i <= (int)agemax+3; i++){    cov[1]=1.;
         if(i==(int)agemax+3)  
           printf("Total");    for(k=1; k<=nlstate; k++) ll[k]=0.;
         else  
           printf("Age %d", i);    if(mle==1){
         for(jk=1; jk <=nlstate ; jk++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
             pp[jk] += freq[jk][m][i];        for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
         for(jk=1; jk <=nlstate ; jk++){            for (j=1;j<=nlstate+ndeath;j++){
           for(m=-1, pos=0; m <=0 ; m++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             pos += freq[jk][m][i];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           if(pp[jk]>=1.e-10)            }
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          for(d=0; d<dh[mi][i]; d++){
           else            newm=savm;
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         }            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for(jk=1; jk <=nlstate ; jk++){            }
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             pp[jk] += freq[jk][m][i];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         }            savm=oldm;
             oldm=newm;
         for(jk=1,pos=0; jk <=nlstate ; jk++)          } /* end mult */
           pos += pp[jk];        
         for(jk=1; jk <=nlstate ; jk++){          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           if(pos>=1.e-5)          /* But now since version 0.9 we anticipate for bias at large stepm.
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
           else           * (in months) between two waves is not a multiple of stepm, we rounded to 
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);           * the nearest (and in case of equal distance, to the lowest) interval but now
           if( i <= (int) agemax){           * we keep into memory the bias bh[mi][i] and also the previous matrix product
             if(pos>=1.e-5){           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);           * probability in order to take into account the bias as a fraction of the way
               probs[i][jk][j1]= pp[jk]/pos;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/           * -stepm/2 to stepm/2 .
             }           * For stepm=1 the results are the same as for previous versions of Imach.
             else           * For stepm > 1 the results are less biased than in previous versions. 
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);           */
           }          s1=s[mw[mi][i]][i];
         }          s2=s[mw[mi+1][i]][i];
                  bbh=(double)bh[mi][i]/(double)stepm; 
         for(jk=-1; jk <=nlstate+ndeath; jk++)          /* bias bh is positive if real duration
           for(m=-1; m <=nlstate+ndeath; m++)           * is higher than the multiple of stepm and negative otherwise.
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);           */
         if(i <= (int) agemax)          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           fprintf(ficresp,"\n");          if( s2 > nlstate){ 
         printf("\n");            /* i.e. if s2 is a death state and if the date of death is known 
       }               then the contribution to the likelihood is the probability to 
     }               die between last step unit time and current  step unit time, 
   }               which is also equal to probability to die before dh 
   dateintmean=dateintsum/k2cpt;               minus probability to die before dh-stepm . 
                 In version up to 0.92 likelihood was computed
   fclose(ficresp);          as if date of death was unknown. Death was treated as any other
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          health state: the date of the interview describes the actual state
   free_vector(pp,1,nlstate);          and not the date of a change in health state. The former idea was
            to consider that at each interview the state was recorded
   /* End of Freq */          (healthy, disable or death) and IMaCh was corrected; but when we
 }          introduced the exact date of death then we should have modified
           the contribution of an exact death to the likelihood. This new
 /************ Prevalence ********************/          contribution is smaller and very dependent of the step unit
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)          stepm. It is no more the probability to die between last interview
 {  /* Some frequencies */          and month of death but the probability to survive from last
            interview up to one month before death multiplied by the
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          probability to die within a month. Thanks to Chris
   double ***freq; /* Frequencies */          Jackson for correcting this bug.  Former versions increased
   double *pp;          mortality artificially. The bad side is that we add another loop
   double pos, k2;          which slows down the processing. The difference can be up to 10%
           lower mortality.
   pp=vector(1,nlstate);            */
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);            lli=log(out[s1][s2] - savm[s1][s2]);
    
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  
   j1=0;          } else if  (s2==-2) {
              for (j=1,survp=0. ; j<=nlstate; j++) 
   j=cptcoveff;              survp += out[s1][j];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            lli= survp;
            }
  for(k1=1; k1<=j;k1++){          
     for(i1=1; i1<=ncodemax[k1];i1++){          else if  (s2==-4) {
       j1++;            for (j=3,survp=0. ; j<=nlstate; j++) 
                survp += out[s1][j];
       for (i=-1; i<=nlstate+ndeath; i++)              lli= survp;
         for (jk=-1; jk<=nlstate+ndeath; jk++)            }
           for(m=agemin; m <= agemax+3; m++)          
             freq[i][jk][m]=0;          else if  (s2==-5) {
                  for (j=1,survp=0. ; j<=2; j++) 
       for (i=1; i<=imx; i++) {              survp += out[s1][j];
         bool=1;            lli= survp;
         if  (cptcovn>0) {          }
           for (z1=1; z1<=cptcoveff; z1++)  
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  
               bool=0;          else{
         }            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         if (bool==1) {            /*  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(m=firstpass; m<=lastpass; m++){          } 
             k2=anint[m][i]+(mint[m][i]/12.);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          /*if(lli ==000.0)*/
               if(agev[m][i]==0) agev[m][i]=agemax+1;          /*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); */
               if(agev[m][i]==1) agev[m][i]=agemax+2;          ipmx +=1;
               if (m<lastpass)          sw += weight[i];
                 if (calagedate>0) freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
               else        } /* end of wave */
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      } /* end of individual */
                freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];    }  else if(mle==2){
             }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
       }          for (ii=1;ii<=nlstate+ndeath;ii++)
         for(i=(int)agemin; i <= (int)agemax+3; i++){            for (j=1;j<=nlstate+ndeath;j++){
           for(jk=1; jk <=nlstate ; jk++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
               pp[jk] += freq[jk][m][i];            }
           }          for(d=0; d<=dh[mi][i]; d++){
           for(jk=1; jk <=nlstate ; jk++){            newm=savm;
             for(m=-1, pos=0; m <=0 ; m++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             pos += freq[jk][m][i];            for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
                    }
          for(jk=1; jk <=nlstate ; jk++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
              pp[jk] += freq[jk][m][i];            savm=oldm;
          }            oldm=newm;
                    } /* end mult */
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        
           s1=s[mw[mi][i]][i];
          for(jk=1; jk <=nlstate ; jk++){                    s2=s[mw[mi+1][i]][i];
            if( i <= (int) agemax){          bbh=(double)bh[mi][i]/(double)stepm; 
              if(pos>=1.e-5){          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 */
                probs[i][jk][j1]= pp[jk]/pos;          ipmx +=1;
              }          sw += weight[i];
            }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
          }        } /* end of wave */
                } /* end of individual */
         }    }  else if(mle==3){  /* exponential inter-extrapolation */
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);            for (j=1;j<=nlstate+ndeath;j++){
   free_vector(pp,1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                savm[ii][j]=(ii==j ? 1.0 : 0.0);
 }  /* End of Freq */            }
           for(d=0; d<dh[mi][i]; d++){
 /************* Waves Concatenation ***************/            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)            for (kk=1; kk<=cptcovage;kk++) {
 {              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.            }
      Death is a valid wave (if date is known).            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]            savm=oldm;
      and mw[mi+1][i]. dh depends on stepm.            oldm=newm;
      */          } /* end mult */
         
   int i, mi, m;          s1=s[mw[mi][i]][i];
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          s2=s[mw[mi+1][i]][i];
      double sum=0., jmean=0.;*/          bbh=(double)bh[mi][i]/(double)stepm; 
           lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
   int j, k=0,jk, ju, jl;          ipmx +=1;
   double sum=0.;          sw += weight[i];
   jmin=1e+5;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   jmax=-1;        } /* end of wave */
   jmean=0.;      } /* end of individual */
   for(i=1; i<=imx; i++){    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     mi=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     m=firstpass;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     while(s[m][i] <= nlstate){        for(mi=1; mi<= wav[i]-1; mi++){
       if(s[m][i]>=1)          for (ii=1;ii<=nlstate+ndeath;ii++)
         mw[++mi][i]=m;            for (j=1;j<=nlstate+ndeath;j++){
       if(m >=lastpass)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         break;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       else            }
         m++;          for(d=0; d<dh[mi][i]; d++){
     }/* end while */            newm=savm;
     if (s[m][i] > nlstate){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       mi++;     /* Death is another wave */            for (kk=1; kk<=cptcovage;kk++) {
       /* if(mi==0)  never been interviewed correctly before death */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
          /* Only death is a correct wave */            }
       mw[mi][i]=m;          
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     wav[i]=mi;            savm=oldm;
     if(mi==0)            oldm=newm;
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          } /* end mult */
   }        
           s1=s[mw[mi][i]][i];
   for(i=1; i<=imx; i++){          s2=s[mw[mi+1][i]][i];
     for(mi=1; mi<wav[i];mi++){          if( s2 > nlstate){ 
       if (stepm <=0)            lli=log(out[s1][s2] - savm[s1][s2]);
         dh[mi][i]=1;          }else{
       else{            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         if (s[mw[mi+1][i]][i] > nlstate) {          }
           if (agedc[i] < 2*AGESUP) {          ipmx +=1;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          sw += weight[i];
           if(j==0) j=1;  /* Survives at least one month after exam */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           k=k+1;  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
           if (j >= jmax) jmax=j;        } /* end of wave */
           if (j <= jmin) jmin=j;      } /* end of individual */
           sum=sum+j;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
           /*if (j<0) printf("j=%d num=%d \n",j,i); */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
         else{          for (ii=1;ii<=nlstate+ndeath;ii++)
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));            for (j=1;j<=nlstate+ndeath;j++){
           k=k+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           if (j >= jmax) jmax=j;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           else if (j <= jmin)jmin=j;            }
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */          for(d=0; d<dh[mi][i]; d++){
           sum=sum+j;            newm=savm;
         }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         jk= j/stepm;            for (kk=1; kk<=cptcovage;kk++) {
         jl= j -jk*stepm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         ju= j -(jk+1)*stepm;            }
         if(jl <= -ju)          
           dh[mi][i]=jk;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         else                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           dh[mi][i]=jk+1;            savm=oldm;
         if(dh[mi][i]==0)            oldm=newm;
           dh[mi][i]=1; /* At least one step */          } /* end mult */
       }        
     }          s1=s[mw[mi][i]][i];
   }          s2=s[mw[mi+1][i]][i];
   jmean=sum/k;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          ipmx +=1;
  }          sw += weight[i];
 /*********** Tricode ****************************/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 void tricode(int *Tvar, int **nbcode, int imx)          /*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 */
   int Ndum[20],ij=1, k, j, i;      } /* end of individual */
   int cptcode=0;    } /* End of if */
   cptcoveff=0;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   for (k=0; k<19; k++) Ndum[k]=0;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   for (k=1; k<=7; k++) ncodemax[k]=0;    return -l;
   }
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {  
     for (i=1; i<=imx; i++) {  /*************** log-likelihood *************/
       ij=(int)(covar[Tvar[j]][i]);  double funcone( double *x)
       Ndum[ij]++;  {
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    /* Same as likeli but slower because of a lot of printf and if */
       if (ij > cptcode) cptcode=ij;    int i, ii, j, k, mi, d, kk;
     }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     double **out;
     for (i=0; i<=cptcode; i++) {    double lli; /* Individual log likelihood */
       if(Ndum[i]!=0) ncodemax[j]++;    double llt;
     }    int s1, s2;
     ij=1;    double bbh, survp;
     /*extern weight */
     /* We are differentiating ll according to initial status */
     for (i=1; i<=ncodemax[j]; i++) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       for (k=0; k<=19; k++) {    /*for(i=1;i<imx;i++) 
         if (Ndum[k] != 0) {      printf(" %d\n",s[4][i]);
           nbcode[Tvar[j]][ij]=k;    */
              cov[1]=1.;
           ij++;  
         }    for(k=1; k<=nlstate; k++) ll[k]=0.;
         if (ij > ncodemax[j]) break;  
       }      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 (ii=1;ii<=nlstate+ndeath;ii++)
  for (k=0; k<19; k++) Ndum[k]=0;          for (j=1;j<=nlstate+ndeath;j++){
             oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  for (i=1; i<=ncovmodel-2; i++) {            savm[ii][j]=(ii==j ? 1.0 : 0.0);
       ij=Tvar[i];          }
       Ndum[ij]++;        for(d=0; d<dh[mi][i]; d++){
     }          newm=savm;
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
  ij=1;          for (kk=1; kk<=cptcovage;kk++) {
  for (i=1; i<=10; i++) {            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
    if((Ndum[i]!=0) && (i<=ncovcol)){          }
      Tvaraff[ij]=i;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      ij++;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
    }          savm=oldm;
  }          oldm=newm;
          } /* end mult */
     cptcoveff=ij-1;        
 }        s1=s[mw[mi][i]][i];
         s2=s[mw[mi+1][i]][i];
 /*********** Health Expectancies ****************/        bbh=(double)bh[mi][i]/(double)stepm; 
         /* bias is positive if real duration
 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 )         * is higher than the multiple of stepm and negative otherwise.
          */
 {        if( s2 > nlstate && (mle <5) ){  /* Jackson */
   /* Health expectancies */          lli=log(out[s1][s2] - savm[s1][s2]);
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;        } else if (mle==1){
   double age, agelim, hf;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   double ***p3mat,***varhe;        } else if(mle==2){
   double **dnewm,**doldm;          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
   double *xp;        } else if(mle==3){  /* exponential inter-extrapolation */
   double **gp, **gm;          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 */
   double ***gradg, ***trgradg;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   int theta;          lli=log(out[s1][s2]); /* Original formula */
         } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          lli=log(out[s1][s2]); /* Original formula */
   xp=vector(1,npar);        } /* End of if */
   dnewm=matrix(1,nlstate*2,1,npar);        ipmx +=1;
   doldm=matrix(1,nlstate*2,1,nlstate*2);        sw += weight[i];
          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fprintf(ficreseij,"# Health expectancies\n");  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   fprintf(ficreseij,"# Age");        if(globpr){
   for(i=1; i<=nlstate;i++)          fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
     for(j=1; j<=nlstate;j++)   %10.6f %10.6f %10.6f ", \
       fprintf(ficreseij," %1d-%1d (SE)",i,j);                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
   fprintf(ficreseij,"\n");                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   if(estepm < stepm){            llt +=ll[k]*gipmx/gsw;
     printf ("Problem %d lower than %d\n",estepm, stepm);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   }          }
   else  hstepm=estepm;            fprintf(ficresilk," %10.6f\n", -llt);
   /* We compute the life expectancy from trapezoids spaced every estepm months        }
    * This is mainly to measure the difference between two models: for example      } /* end of wave */
    * if stepm=24 months pijx are given only every 2 years and by summing them    } /* end of individual */
    * we are calculating an estimate of the Life Expectancy assuming a linear    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
    * progression inbetween and thus overestimating or underestimating according    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
    * to the curvature of the survival function. If, for the same date, we    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
    * estimate the model with stepm=1 month, we can keep estepm to 24 months    if(globpr==0){ /* First time we count the contributions and weights */
    * to compare the new estimate of Life expectancy with the same linear      gipmx=ipmx;
    * hypothesis. A more precise result, taking into account a more precise      gsw=sw;
    * curvature will be obtained if estepm is as small as stepm. */    }
     return -l;
   /* For example we decided to compute the life expectancy with the smallest unit */  }
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.  
      nhstepm is the number of hstepm from age to agelim  
      nstepm is the number of stepm from age to agelin.  /*************** function likelione ***********/
      Look at hpijx to understand the reason of that which relies in memory size  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
      and note for a fixed period like estepm months */  {
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    /* This routine should help understanding what is done with 
      survival function given by stepm (the optimization length). Unfortunately it       the selection of individuals/waves and
      means that if the survival funtion is printed only each two years of age and if       to check the exact contribution to the likelihood.
      you sum them up and add 1 year (area under the trapezoids) you won't get the same       Plotting could be done.
      results. So we changed our mind and took the option of the best precision.     */
   */    int k;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */  
     if(*globpri !=0){ /* Just counts and sums, no printings */
   agelim=AGESUP;      strcpy(fileresilk,"ilk"); 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      strcat(fileresilk,fileres);
     /* nhstepm age range expressed in number of stepm */      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
     nstepm=(int) rint((agelim-age)*YEARM/stepm);        printf("Problem with resultfile: %s\n", fileresilk);
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     /* if (stepm >= YEARM) hstepm=1;*/      }
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */      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");
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     gp=matrix(0,nhstepm,1,nlstate*2);      for(k=1; k<=nlstate; k++) 
     gm=matrix(0,nhstepm,1,nlstate*2);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    }
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */  
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      *fretone=(*funcone)(p);
      if(*globpri !=0){
       fclose(ficresilk);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       fflush(fichtm); 
     /* Computing Variances of health expectancies */    } 
     return;
      for(theta=1; theta <=npar; theta++){  }
       for(i=1; i<=npar; i++){  
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }  /*********** Maximum Likelihood Estimation ***************/
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
    void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       cptj=0;  {
       for(j=1; j<= nlstate; j++){    int i,j, iter;
         for(i=1; i<=nlstate; i++){    double **xi;
           cptj=cptj+1;    double fret;
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){    double fretone; /* Only one call to likelihood */
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;    /*  char filerespow[FILENAMELENGTH];*/
           }    xi=matrix(1,npar,1,npar);
         }    for (i=1;i<=npar;i++)
       }      for (j=1;j<=npar;j++)
              xi[i][j]=(i==j ? 1.0 : 0.0);
          printf("Powell\n");  fprintf(ficlog,"Powell\n");
       for(i=1; i<=npar; i++)    strcpy(filerespow,"pow"); 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    strcat(filerespow,fileres);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      if((ficrespow=fopen(filerespow,"w"))==NULL) {
            printf("Problem with resultfile: %s\n", filerespow);
       cptj=0;      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       for(j=1; j<= nlstate; j++){    }
         for(i=1;i<=nlstate;i++){    fprintf(ficrespow,"# Powell\n# iter -2*LL");
           cptj=cptj+1;    for (i=1;i<=nlstate;i++)
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){      for(j=1;j<=nlstate+ndeath;j++)
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
           }    fprintf(ficrespow,"\n");
         }  
       }    powell(p,xi,npar,ftol,&iter,&fret,func);
        
        fclose(ficrespow);
     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
       for(j=1; j<= nlstate*2; j++)    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         for(h=0; h<=nhstepm-1; h++){    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  
         }  }
   
      }  /**** Computes Hessian and covariance matrix ***/
      void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
 /* End theta */  {
     double  **a,**y,*x,pd;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);    double **hess;
     int i, j,jk;
      for(h=0; h<=nhstepm-1; h++)    int *indx;
       for(j=1; j<=nlstate*2;j++)  
         for(theta=1; theta <=npar; theta++)    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
         trgradg[h][j][theta]=gradg[h][theta][j];    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     void lubksb(double **a, int npar, int *indx, double b[]) ;
     void ludcmp(double **a, int npar, int *indx, double *d) ;
      for(i=1;i<=nlstate*2;i++)    double gompertz(double p[]);
       for(j=1;j<=nlstate*2;j++)    hess=matrix(1,npar,1,npar);
         varhe[i][j][(int)age] =0.;  
     printf("\nCalculation of the hessian matrix. Wait...\n");
     for(h=0;h<=nhstepm-1;h++){    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
       for(k=0;k<=nhstepm-1;k++){    for (i=1;i<=npar;i++){
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);      printf("%d",i);fflush(stdout);
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      fprintf(ficlog,"%d",i);fflush(ficlog);
         for(i=1;i<=nlstate*2;i++)     
           for(j=1;j<=nlstate*2;j++)       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;      
       }      /*  printf(" %f ",p[i]);
     }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
          
     /* Computing expectancies */    for (i=1;i<=npar;i++) {
     for(i=1; i<=nlstate;i++)      for (j=1;j<=npar;j++)  {
       for(j=1; j<=nlstate;j++)        if (j>i) { 
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){          printf(".%d%d",i,j);fflush(stdout);
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
                    hess[i][j]=hessij(p,delti,i,j,func,npar);
 /* 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]);*/          
           hess[j][i]=hess[i][j];    
         }          /*printf(" %lf ",hess[i][j]);*/
         }
     fprintf(ficreseij,"%3.0f",age );      }
     cptj=0;    }
     for(i=1; i<=nlstate;i++)    printf("\n");
       for(j=1; j<=nlstate;j++){    fprintf(ficlog,"\n");
         cptj++;  
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
       }    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficreseij,"\n");    
        a=matrix(1,npar,1,npar);
     free_matrix(gm,0,nhstepm,1,nlstate*2);    y=matrix(1,npar,1,npar);
     free_matrix(gp,0,nhstepm,1,nlstate*2);    x=vector(1,npar);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);    indx=ivector(1,npar);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);    for (i=1;i<=npar;i++)
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   }    ludcmp(a,npar,indx,&pd);
   free_vector(xp,1,npar);  
   free_matrix(dnewm,1,nlstate*2,1,npar);    for (j=1;j<=npar;j++) {
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);      for (i=1;i<=npar;i++) x[i]=0;
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);      x[j]=1;
 }      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
 /************ Variance ******************/        matcov[i][j]=x[i];
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)      }
 {    }
   /* Variance of health expectancies */  
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    printf("\n#Hessian matrix#\n");
   double **newm;    fprintf(ficlog,"\n#Hessian matrix#\n");
   double **dnewm,**doldm;    for (i=1;i<=npar;i++) { 
   int i, j, nhstepm, hstepm, h, nstepm ;      for (j=1;j<=npar;j++) { 
   int k, cptcode;        printf("%.3e ",hess[i][j]);
   double *xp;        fprintf(ficlog,"%.3e ",hess[i][j]);
   double **gp, **gm;      }
   double ***gradg, ***trgradg;      printf("\n");
   double ***p3mat;      fprintf(ficlog,"\n");
   double age,agelim, hf;    }
   int theta;  
     /* Recompute Inverse */
    fprintf(ficresvij,"# Covariances of life expectancies\n");    for (i=1;i<=npar;i++)
   fprintf(ficresvij,"# Age");      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   for(i=1; i<=nlstate;i++)    ludcmp(a,npar,indx,&pd);
     for(j=1; j<=nlstate;j++)  
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    /*  printf("\n#Hessian matrix recomputed#\n");
   fprintf(ficresvij,"\n");  
     for (j=1;j<=npar;j++) {
   xp=vector(1,npar);      for (i=1;i<=npar;i++) x[i]=0;
   dnewm=matrix(1,nlstate,1,npar);      x[j]=1;
   doldm=matrix(1,nlstate,1,nlstate);      lubksb(a,npar,indx,x);
        for (i=1;i<=npar;i++){ 
   if(estepm < stepm){        y[i][j]=x[i];
     printf ("Problem %d lower than %d\n",estepm, stepm);        printf("%.3e ",y[i][j]);
   }        fprintf(ficlog,"%.3e ",y[i][j]);
   else  hstepm=estepm;        }
   /* For example we decided to compute the life expectancy with the smallest unit */      printf("\n");
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.      fprintf(ficlog,"\n");
      nhstepm is the number of hstepm from age to agelim    }
      nstepm is the number of stepm from age to agelin.    */
      Look at hpijx to understand the reason of that which relies in memory size  
      and note for a fixed period like k years */    free_matrix(a,1,npar,1,npar);
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    free_matrix(y,1,npar,1,npar);
      survival function given by stepm (the optimization length). Unfortunately it    free_vector(x,1,npar);
      means that if the survival funtion is printed only each two years of age and if    free_ivector(indx,1,npar);
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    free_matrix(hess,1,npar,1,npar);
      results. So we changed our mind and took the option of the best precision.  
   */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */  }
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  /*************** hessian matrix ****************/
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  {
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int i;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    int l=1, lmax=20;
     gp=matrix(0,nhstepm,1,nlstate);    double k1,k2;
     gm=matrix(0,nhstepm,1,nlstate);    double p2[NPARMAX+1];
     double res;
     for(theta=1; theta <=npar; theta++){    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       for(i=1; i<=npar; i++){ /* Computes gradient */    double fx;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    int k=0,kmax=10;
       }    double l1;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fx=func(x);
     for (i=1;i<=npar;i++) p2[i]=x[i];
       if (popbased==1) {    for(l=0 ; l <=lmax; l++){
         for(i=1; i<=nlstate;i++)      l1=pow(10,l);
           prlim[i][i]=probs[(int)age][i][ij];      delts=delt;
       }      for(k=1 ; k <kmax; k=k+1){
          delt = delta*(l1*k);
       for(j=1; j<= nlstate; j++){        p2[theta]=x[theta] +delt;
         for(h=0; h<=nhstepm; h++){        k1=func(p2)-fx;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        p2[theta]=x[theta]-delt;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        k2=func(p2)-fx;
         }        /*res= (k1-2.0*fx+k2)/delt/delt; */
       }        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
            
       for(i=1; i<=npar; i++) /* Computes gradient */  #ifdef DEBUG
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        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);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          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);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  #endif
          /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       if (popbased==1) {        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
         for(i=1; i<=nlstate;i++)          k=kmax;
           prlim[i][i]=probs[(int)age][i][ij];        }
       }        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
           k=kmax; l=lmax*10.;
       for(j=1; j<= nlstate; j++){        }
         for(h=0; h<=nhstepm; h++){        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          delts=delt;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        }
         }      }
       }    }
     delti[theta]=delts;
       for(j=1; j<= nlstate; j++)    return res; 
         for(h=0; h<=nhstepm; h++){    
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  }
         }  
     } /* End theta */  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   {
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    int i;
     int l=1, l1, lmax=20;
     for(h=0; h<=nhstepm; h++)    double k1,k2,k3,k4,res,fx;
       for(j=1; j<=nlstate;j++)    double p2[NPARMAX+1];
         for(theta=1; theta <=npar; theta++)    int k;
           trgradg[h][j][theta]=gradg[h][theta][j];  
     fx=func(x);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    for (k=1; k<=2; k++) {
     for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++) p2[i]=x[i];
       for(j=1;j<=nlstate;j++)      p2[thetai]=x[thetai]+delti[thetai]/k;
         vareij[i][j][(int)age] =0.;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k1=func(p2)-fx;
     for(h=0;h<=nhstepm;h++){    
       for(k=0;k<=nhstepm;k++){      p2[thetai]=x[thetai]+delti[thetai]/k;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      k2=func(p2)-fx;
         for(i=1;i<=nlstate;i++)    
           for(j=1;j<=nlstate;j++)      p2[thetai]=x[thetai]-delti[thetai]/k;
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       }      k3=func(p2)-fx;
     }    
       p2[thetai]=x[thetai]-delti[thetai]/k;
     fprintf(ficresvij,"%.0f ",age );      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     for(i=1; i<=nlstate;i++)      k4=func(p2)-fx;
       for(j=1; j<=nlstate;j++){      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);  #ifdef DEBUG
       }      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
     fprintf(ficresvij,"\n");      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);
     free_matrix(gp,0,nhstepm,1,nlstate);  #endif
     free_matrix(gm,0,nhstepm,1,nlstate);    }
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    return res;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);  }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   } /* End age */  /************** Inverse of matrix **************/
    void ludcmp(double **a, int n, int *indx, double *d) 
   free_vector(xp,1,npar);  { 
   free_matrix(doldm,1,nlstate,1,npar);    int i,imax,j,k; 
   free_matrix(dnewm,1,nlstate,1,nlstate);    double big,dum,sum,temp; 
     double *vv; 
 }   
     vv=vector(1,n); 
 /************ Variance of prevlim ******************/    *d=1.0; 
 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)    for (i=1;i<=n;i++) { 
 {      big=0.0; 
   /* Variance of prevalence limit */      for (j=1;j<=n;j++) 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        if ((temp=fabs(a[i][j])) > big) big=temp; 
   double **newm;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   double **dnewm,**doldm;      vv[i]=1.0/big; 
   int i, j, nhstepm, hstepm;    } 
   int k, cptcode;    for (j=1;j<=n;j++) { 
   double *xp;      for (i=1;i<j;i++) { 
   double *gp, *gm;        sum=a[i][j]; 
   double **gradg, **trgradg;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   double age,agelim;        a[i][j]=sum; 
   int theta;      } 
          big=0.0; 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      for (i=j;i<=n;i++) { 
   fprintf(ficresvpl,"# Age");        sum=a[i][j]; 
   for(i=1; i<=nlstate;i++)        for (k=1;k<j;k++) 
       fprintf(ficresvpl," %1d-%1d",i,i);          sum -= a[i][k]*a[k][j]; 
   fprintf(ficresvpl,"\n");        a[i][j]=sum; 
         if ( (dum=vv[i]*fabs(sum)) >= big) { 
   xp=vector(1,npar);          big=dum; 
   dnewm=matrix(1,nlstate,1,npar);          imax=i; 
   doldm=matrix(1,nlstate,1,nlstate);        } 
        } 
   hstepm=1*YEARM; /* Every year of age */      if (j != imax) { 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        for (k=1;k<=n;k++) { 
   agelim = AGESUP;          dum=a[imax][k]; 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          a[imax][k]=a[j][k]; 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          a[j][k]=dum; 
     if (stepm >= YEARM) hstepm=1;        } 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        *d = -(*d); 
     gradg=matrix(1,npar,1,nlstate);        vv[imax]=vv[j]; 
     gp=vector(1,nlstate);      } 
     gm=vector(1,nlstate);      indx[j]=imax; 
       if (a[j][j] == 0.0) a[j][j]=TINY; 
     for(theta=1; theta <=npar; theta++){      if (j != n) { 
       for(i=1; i<=npar; i++){ /* Computes gradient */        dum=1.0/(a[j][j]); 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       }      } 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    } 
       for(i=1;i<=nlstate;i++)    free_vector(vv,1,n);  /* Doesn't work */
         gp[i] = prlim[i][i];  ;
      } 
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  void lubksb(double **a, int n, int *indx, double b[]) 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  { 
       for(i=1;i<=nlstate;i++)    int i,ii=0,ip,j; 
         gm[i] = prlim[i][i];    double sum; 
    
       for(i=1;i<=nlstate;i++)    for (i=1;i<=n;i++) { 
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];      ip=indx[i]; 
     } /* End theta */      sum=b[ip]; 
       b[ip]=b[i]; 
     trgradg =matrix(1,nlstate,1,npar);      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     for(j=1; j<=nlstate;j++)      else if (sum) ii=i; 
       for(theta=1; theta <=npar; theta++)      b[i]=sum; 
         trgradg[j][theta]=gradg[theta][j];    } 
     for (i=n;i>=1;i--) { 
     for(i=1;i<=nlstate;i++)      sum=b[i]; 
       varpl[i][(int)age] =0.;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      b[i]=sum/a[i][i]; 
     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 */  
   /************ Frequencies ********************/
     fprintf(ficresvpl,"%.0f ",age );  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[])
     for(i=1; i<=nlstate;i++)  {  /* Some frequencies */
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    
     fprintf(ficresvpl,"\n");    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     free_vector(gp,1,nlstate);    int first;
     free_vector(gm,1,nlstate);    double ***freq; /* Frequencies */
     free_matrix(gradg,1,npar,1,nlstate);    double *pp, **prop;
     free_matrix(trgradg,1,nlstate,1,npar);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
   } /* End age */    FILE *ficresp;
     char fileresp[FILENAMELENGTH];
   free_vector(xp,1,npar);    
   free_matrix(doldm,1,nlstate,1,npar);    pp=vector(1,nlstate);
   free_matrix(dnewm,1,nlstate,1,nlstate);    prop=matrix(1,nlstate,iagemin,iagemax+3);
     strcpy(fileresp,"p");
 }    strcat(fileresp,fileres);
     if((ficresp=fopen(fileresp,"w"))==NULL) {
 /************ Variance of one-step probabilities  ******************/      printf("Problem with prevalence resultfile: %s\n", fileresp);
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
 {      exit(0);
   int i, j, i1, k1, j1, z1;    }
   int k=0, cptcode;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
   double **dnewm,**doldm;    j1=0;
   double *xp;    
   double *gp, *gm;    j=cptcoveff;
   double **gradg, **trgradg;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   double age,agelim, cov[NCOVMAX];  
   int theta;    first=1;
   char fileresprob[FILENAMELENGTH];  
     for(k1=1; k1<=j;k1++){
   strcpy(fileresprob,"prob");      for(i1=1; i1<=ncodemax[k1];i1++){
   strcat(fileresprob,fileres);        j1++;
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
     printf("Problem with resultfile: %s\n", fileresprob);          scanf("%d", i);*/
   }        for (i=-5; i<=nlstate+ndeath; i++)  
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
              for(m=iagemin; m <= iagemax+3; m++)
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");              freq[i][jk][m]=0;
   fprintf(ficresprob,"# Age");  
   for(i=1; i<=nlstate;i++)      for (i=1; i<=nlstate; i++)  
     for(j=1; j<=(nlstate+ndeath);j++)        for(m=iagemin; m <= iagemax+3; m++)
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);          prop[i][m]=0;
         
         dateintsum=0;
   fprintf(ficresprob,"\n");        k2cpt=0;
         for (i=1; i<=imx; i++) {
           bool=1;
   xp=vector(1,npar);          if  (cptcovn>0) {
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);            for (z1=1; z1<=cptcoveff; z1++) 
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                  bool=0;
   cov[1]=1;          }
   j=cptcoveff;          if (bool==1){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            for(m=firstpass; m<=lastpass; m++){
   j1=0;              k2=anint[m][i]+(mint[m][i]/12.);
   for(k1=1; k1<=1;k1++){              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     for(i1=1; i1<=ncodemax[k1];i1++){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     j1++;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                 if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     if  (cptcovn>0) {                if (m<lastpass) {
       fprintf(ficresprob, "\n#********** Variable ");                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
       fprintf(ficresprob, "**********\n#");                }
     }                
                    if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
       for (age=bage; age<=fage; age ++){                  dateintsum=dateintsum+k2;
         cov[2]=age;                  k2cpt++;
         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]]];        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
          fprintf(ficresp, "#Local time at start: %s", strstart);
         gradg=matrix(1,npar,1,9);        if  (cptcovn>0) {
         trgradg=matrix(1,9,1,npar);          fprintf(ficresp, "\n#********** Variable "); 
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          fprintf(ficresp, "**********\n#");
            }
         for(theta=1; theta <=npar; theta++){        for(i=1; i<=nlstate;i++) 
           for(i=1; i<=npar; i++)          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
             xp[i] = x[i] + (i==theta ?delti[theta]:0);        fprintf(ficresp, "\n");
                  
           pmij(pmmij,cov,ncovmodel,xp,nlstate);        for(i=iagemin; i <= iagemax+3; i++){
                    if(i==iagemax+3){
           k=0;            fprintf(ficlog,"Total");
           for(i=1; i<= (nlstate+ndeath); i++){          }else{
             for(j=1; j<=(nlstate+ndeath);j++){            if(first==1){
               k=k+1;              first=0;
               gp[k]=pmmij[i][j];              printf("See log file for details...\n");
             }            }
           }            fprintf(ficlog,"Age %d", i);
                    }
           for(i=1; i<=npar; i++)          for(jk=1; jk <=nlstate ; jk++){
             xp[i] = x[i] - (i==theta ?delti[theta]:0);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                  pp[jk] += freq[jk][m][i]; 
           pmij(pmmij,cov,ncovmodel,xp,nlstate);          }
           k=0;          for(jk=1; jk <=nlstate ; jk++){
           for(i=1; i<=(nlstate+ndeath); i++){            for(m=-1, pos=0; m <=0 ; m++)
             for(j=1; j<=(nlstate+ndeath);j++){              pos += freq[jk][m][i];
               k=k+1;            if(pp[jk]>=1.e-10){
               gm[k]=pmmij[i][j];              if(first==1){
             }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           }              }
                    fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)            }else{
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];                if(first==1)
         }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)            }
           for(theta=1; theta <=npar; theta++)          }
             trgradg[j][theta]=gradg[theta][j];  
                  for(jk=1; jk <=nlstate ; jk++){
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);              pp[jk] += freq[jk][m][i];
                  }       
         pmij(pmmij,cov,ncovmodel,x,nlstate);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
                    pos += pp[jk];
         k=0;            posprop += prop[jk][i];
         for(i=1; i<=(nlstate+ndeath); i++){          }
           for(j=1; j<=(nlstate+ndeath);j++){          for(jk=1; jk <=nlstate ; jk++){
             k=k+1;            if(pos>=1.e-5){
             gm[k]=pmmij[i][j];              if(first==1)
           }                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         }              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                  }else{
      /*printf("\n%d ",(int)age);              if(first==1)
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
      }*/            }
             if( i <= iagemax){
         fprintf(ficresprob,"\n%d ",(int)age);              if(pos>=1.e-5){
                 fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)                /*probs[i][jk][j1]= pp[jk]/pos;*/
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][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]);*/
                }
       }              else
     }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     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);          for(jk=-1; jk <=nlstate+ndeath; jk++)
   }            for(m=-1; m <=nlstate+ndeath; m++)
   free_vector(xp,1,npar);              if(freq[jk][m][i] !=0 ) {
   fclose(ficresprob);              if(first==1)
                  printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
 }                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
 /******************* Printing html file ***********/          if(i <= iagemax)
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \            fprintf(ficresp,"\n");
  int lastpass, int stepm, int weightopt, char model[],\          if(first==1)
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \            printf("Others in log...\n");
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\          fprintf(ficlog,"\n");
  char version[], int popforecast, int estepm ){        }
   int jj1, k1, i1, cpt;      }
   FILE *fichtm;    }
   /*char optionfilehtm[FILENAMELENGTH];*/    dateintmean=dateintsum/k2cpt; 
    
   strcpy(optionfilehtm,optionfile);    fclose(ficresp);
   strcat(optionfilehtm,".htm");    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    free_vector(pp,1,nlstate);
     printf("Problem with %s \n",optionfilehtm), exit(0);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
   }    /* End of Freq */
   }
  fprintf(fichtm,"<body> <font size=\"2\">%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  /************ Prevalence ********************/
 \n  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
 Total number of observations=%d <br>\n  {  
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
 <hr  size=\"2\" color=\"#EC5E5E\">       in each health status at the date of interview (if between dateprev1 and dateprev2).
  <ul><li>Outputs files<br>\n       We still use firstpass and lastpass as another selection.
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n    */
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n   
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n    double ***freq; /* Frequencies */
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n    double *pp, **prop;
  - Life expectancies by age and initial health status (estepm=%2d months): <a href=\"e%s\">e%s</a> <br>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot,fileres,fileres,fileres,fileres,fileres,fileres,estepm,fileres,fileres);    double pos,posprop; 
     double  y2; /* in fractional years */
  fprintf(fichtm,"\n    int iagemin, iagemax;
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n  
   - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n    iagemin= (int) agemin;
  - Variances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n    iagemax= (int) agemax;
  - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>\n    /*pp=vector(1,nlstate);*/
  - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
  if(popforecast==1) fprintf(fichtm,"\n    j1=0;
  - 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    j=cptcoveff;
         <br>",fileres,fileres,fileres,fileres);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
  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);    for(k1=1; k1<=j;k1++){
 fprintf(fichtm," <li>Graphs</li><p>");      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
  m=cptcoveff;        
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}        for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
  jj1=0;            prop[i][m]=0.0;
  for(k1=1; k1<=m;k1++){       
    for(i1=1; i1<=ncodemax[k1];i1++){        for (i=1; i<=imx; i++) { /* Each individual */
        jj1++;          bool=1;
        if (cptcovn > 0) {          if  (cptcovn>0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");            for (z1=1; z1<=cptcoveff; z1++) 
          for (cpt=1; cpt<=cptcoveff;cpt++)              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);                bool=0;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");          } 
        }          if (bool==1) { 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                  y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
        for(cpt=1; cpt<nlstate;cpt++){              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>                if(agev[m][i]==0) agev[m][i]=iagemax+1;
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
        }                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
     for(cpt=1; cpt<=nlstate;cpt++) {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident                  /*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]]);*/
 interval) in state (%d): v%s%d%d.gif <br>                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                    prop[s[m][i]][iagemax+3] += weight[i]; 
      }                } 
      for(cpt=1; cpt<=nlstate;cpt++) {              }
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>            } /* end selection of waves */
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          }
      }        }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and        for(i=iagemin; i <= iagemax+3; i++){  
 health expectancies in states (1) and (2): e%s%d.gif<br>          
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
 fprintf(fichtm,"\n</body>");            posprop += prop[jk][i]; 
    }          } 
    }  
 fclose(fichtm);          for(jk=1; jk <=nlstate ; jk++){     
 }            if( i <=  iagemax){ 
               if(posprop>=1.e-5){ 
 /******************* Gnuplot file **************/                probs[i][jk][j1]= prop[jk][i]/posprop;
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){              } 
             } 
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;          }/* end jk */ 
         }/* end i */ 
   strcpy(optionfilegnuplot,optionfilefiname);      } /* end i1 */
   strcat(optionfilegnuplot,".gp.txt");    } /* end k1 */
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {    
     printf("Problem with file %s",optionfilegnuplot);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
   }    /*free_vector(pp,1,nlstate);*/
     free_matrix(prop,1,nlstate, iagemin,iagemax+3);
 #ifdef windows  }  /* End of prevalence */
     fprintf(ficgp,"cd \"%s\" \n",pathc);  
 #endif  /************* Waves Concatenation ***************/
 m=pow(2,cptcoveff);  
    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)
  /* 1eme*/  {
   for (cpt=1; cpt<= nlstate ; cpt ++) {    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
    for (k1=1; k1<= m ; k1 ++) {       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
 #ifdef windows       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     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",ageminpar,fage,fileres,k1-1,k1-1);       and mw[mi+1][i]. dh depends on stepm.
 #endif       */
 #ifdef unix  
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);    int i, mi, m;
 #endif    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
 for (i=1; i<= nlstate ; i ++) {    int first;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    int j, k=0,jk, ju, jl;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double sum=0.;
 }    first=0;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    jmin=1e+5;
     for (i=1; i<= nlstate ; i ++) {    jmax=-1;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    jmean=0.;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for(i=1; i<=imx; i++){
 }      mi=0;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);      m=firstpass;
      for (i=1; i<= nlstate ; i ++) {      while(s[m][i] <= nlstate){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
   else fprintf(ficgp," \%%*lf (\%%*lf)");          mw[++mi][i]=m;
 }          if(m >=lastpass)
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          break;
 #ifdef unix        else
 fprintf(ficgp,"\nset ter gif small size 400,300");          m++;
 #endif      }/* end while */
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      if (s[m][i] > nlstate){
    }        mi++;     /* Death is another wave */
   }        /* if(mi==0)  never been interviewed correctly before death */
   /*2 eme*/           /* Only death is a correct wave */
         mw[mi][i]=m;
   for (k1=1; k1<= m ; k1 ++) {      }
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",ageminpar,fage);  
          wav[i]=mi;
     for (i=1; i<= nlstate+1 ; i ++) {      if(mi==0){
       k=2*i;        nbwarn++;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);        if(first==0){
       for (j=1; j<= nlstate+1 ; j ++) {          printf("Warning! None valid information for:%ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          first=1;
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }          if(first==1){
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");          fprintf(ficlog,"Warning! None valid information for:%ld line=%d (skipped)\n",num[i],i);
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);        }
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);      } /* end mi==0 */
       for (j=1; j<= nlstate+1 ; j ++) {    } /* End individuals */
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
         else fprintf(ficgp," \%%*lf (\%%*lf)");    for(i=1; i<=imx; i++){
 }        for(mi=1; mi<wav[i];mi++){
       fprintf(ficgp,"\" t\"\" w l 0,");        if (stepm <=0)
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);          dh[mi][i]=1;
       for (j=1; j<= nlstate+1 ; j ++) {        else{
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
   else fprintf(ficgp," \%%*lf (\%%*lf)");            if (agedc[i] < 2*AGESUP) {
 }                j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");              if(j==0) j=1;  /* Survives at least one month after exam */
       else fprintf(ficgp,"\" t\"\" w l 0,");              else if(j<0){
     }                nberr++;
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
   }                j=1; /* Temporary Dangerous patch */
                  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);
   /*3eme*/                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);
   for (k1=1; k1<= m ; k1 ++) {              }
     for (cpt=1; cpt<= nlstate ; cpt ++) {              k=k+1;
       k=2+nlstate*(2*cpt-2);              if (j >= jmax) jmax=j;
       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",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);              if (j <= jmin) jmin=j;
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              sum=sum+j;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%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);          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
 */  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
       for (i=1; i< nlstate ; i ++) {  
         fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);            k=k+1;
             if (j >= jmax) jmax=j;
       }            else if (j <= jmin)jmin=j;
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     }            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
     }            if(j<0){
                nberr++;
   /* CV preval stat */              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 (k1=1; k1<= m ; k1 ++) {              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]);
     for (cpt=1; cpt<nlstate ; cpt ++) {            }
       k=3;            sum=sum+j;
       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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);          }
           jk= j/stepm;
       for (i=1; i< nlstate ; i ++)          jl= j -jk*stepm;
         fprintf(ficgp,"+$%d",k+i+1);          ju= j -(jk+1)*stepm;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
                  if(jl==0){
       l=3+(nlstate+ndeath)*cpt;              dh[mi][i]=jk;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);              bh[mi][i]=0;
       for (i=1; i< nlstate ; i ++) {            }else{ /* We want a negative bias in order to only have interpolation ie
         l=3+(nlstate+ndeath)*cpt;                    * at the price of an extra matrix product in likelihood */
         fprintf(ficgp,"+$%d",l+i+1);              dh[mi][i]=jk+1;
       }              bh[mi][i]=ju;
       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);          }else{
     }            if(jl <= -ju){
   }                dh[mi][i]=jk;
                bh[mi][i]=jl;       /* bias is positive if real duration
   /* proba elementaires */                                   * is higher than the multiple of stepm and negative otherwise.
    for(i=1,jk=1; i <=nlstate; i++){                                   */
     for(k=1; k <=(nlstate+ndeath); k++){            }
       if (k != i) {            else{
         for(j=1; j <=ncovmodel; j++){              dh[mi][i]=jk+1;
                      bh[mi][i]=ju;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);            }
           jk++;            if(dh[mi][i]==0){
           fprintf(ficgp,"\n");              dh[mi][i]=1; /* At least one step */
         }              bh[mi][i]=ju; /* At least one step */
       }              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
     }            }
     }          } /* end if mle */
         }
     for(jk=1; jk <=m; jk++) {      } /* end wave */
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);    }
    i=1;    jmean=sum/k;
    for(k2=1; k2<=nlstate; k2++) {    printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
      k3=i;    fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);
      for(k=1; k<=(nlstate+ndeath); k++) {   }
        if (k != k2){  
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);  /*********** Tricode ****************************/
 ij=1;  void tricode(int *Tvar, int **nbcode, int imx)
         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]]]);    int Ndum[20],ij=1, k, j, i, maxncov=19;
             ij++;    int cptcode=0;
           }    cptcoveff=0; 
           else   
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    for (k=0; k<maxncov; k++) Ndum[k]=0;
         }    for (k=1; k<=7; k++) ncodemax[k]=0;
           fprintf(ficgp,")/(1");  
            for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
         for(k1=1; k1 <=nlstate; k1++){        for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);                                 modality*/ 
 ij=1;        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
           for(j=3; j <=ncovmodel; j++){        Ndum[ij]++; /*store the modality */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
             ij++;                                         Tvar[j]. If V=sex and male is 0 and 
           }                                         female is 1, then  cptcode=1.*/
           else      }
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  
           }      for (i=0; i<=cptcode; i++) {
           fprintf(ficgp,")");        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
         }      }
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);  
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      ij=1; 
         i=i+ncovmodel;      for (i=1; i<=ncodemax[j]; i++) {
        }        for (k=0; k<= maxncov; k++) {
      }          if (Ndum[k] != 0) {
    }            nbcode[Tvar[j]][ij]=k; 
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);            /* 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; */
    }            
                ij++;
   fclose(ficgp);          }
 }  /* end gnuplot */          if (ij > ncodemax[j]) break; 
         }  
       } 
 /*************** Moving average **************/    }  
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){  
    for (k=0; k< maxncov; k++) Ndum[k]=0;
   int i, cpt, cptcod;  
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)   for (i=1; i<=ncovmodel-2; i++) { 
       for (i=1; i<=nlstate;i++)     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)     ij=Tvar[i];
           mobaverage[(int)agedeb][i][cptcod]=0.;     Ndum[ij]++;
       }
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){  
       for (i=1; i<=nlstate;i++){   ij=1;
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){   for (i=1; i<= maxncov; i++) {
           for (cpt=0;cpt<=4;cpt++){     if((Ndum[i]!=0) && (i<=ncovcol)){
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];       Tvaraff[ij]=i; /*For printing */
           }       ij++;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;     }
         }   }
       }   
     }   cptcoveff=ij-1; /*Number of simple covariates*/
      }
 }  
   /*********** Health Expectancies ****************/
   
 /************** Forecasting ******************/  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[] )
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){  
    {
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    /* Health expectancies */
   int *popage;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    double age, agelim, hf;
   double *popeffectif,*popcount;    double ***p3mat,***varhe;
   double ***p3mat;    double **dnewm,**doldm;
   char fileresf[FILENAMELENGTH];    double *xp;
     double **gp, **gm;
  agelim=AGESUP;    double ***gradg, ***trgradg;
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    int theta;
   
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
      xp=vector(1,npar);
      dnewm=matrix(1,nlstate*nlstate,1,npar);
   strcpy(fileresf,"f");    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   strcat(fileresf,fileres);    
   if((ficresf=fopen(fileresf,"w"))==NULL) {    fprintf(ficreseij,"# Local time at start: %s", strstart);
     printf("Problem with forecast resultfile: %s\n", fileresf);    fprintf(ficreseij,"# Health expectancies\n");
   }    fprintf(ficreseij,"# Age");
   printf("Computing forecasting: result on file '%s' \n", fileresf);    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        fprintf(ficreseij," %1d-%1d (SE)",i,j);
     fprintf(ficreseij,"\n");
   if (mobilav==1) {  
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    if(estepm < stepm){
     movingaverage(agedeb, fage, ageminpar, mobaverage);      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
     else  hstepm=estepm;   
   stepsize=(int) (stepm+YEARM-1)/YEARM;    /* We compute the life expectancy from trapezoids spaced every estepm months
   if (stepm<=12) stepsize=1;     * 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
   agelim=AGESUP;     * we are calculating an estimate of the Life Expectancy assuming a linear 
       * progression in between and thus overestimating or underestimating according
   hstepm=1;     * to the curvature of the survival function. If, for the same date, we 
   hstepm=hstepm/stepm;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   yp1=modf(dateintmean,&yp);     * to compare the new estimate of Life expectancy with the same linear 
   anprojmean=yp;     * hypothesis. A more precise result, taking into account a more precise
   yp2=modf((yp1*12),&yp);     * curvature will be obtained if estepm is as small as stepm. */
   mprojmean=yp;  
   yp1=modf((yp2*30.5),&yp);    /* For example we decided to compute the life expectancy with the smallest unit */
   jprojmean=yp;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   if(jprojmean==0) jprojmean=1;       nhstepm is the number of hstepm from age to agelim 
   if(mprojmean==0) jprojmean=1;       nstepm is the number of stepm from age to agelin. 
         Look at hpijx to understand the reason of that which relies in memory size
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);       and note for a fixed period like estepm months */
      /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   for(cptcov=1;cptcov<=i2;cptcov++){       survival function given by stepm (the optimization length). Unfortunately it
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){       means that if the survival funtion is printed only each two years of age and if
       k=k+1;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       fprintf(ficresf,"\n#******");       results. So we changed our mind and took the option of the best precision.
       for(j=1;j<=cptcoveff;j++) {    */
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       }  
       fprintf(ficresf,"******\n");    agelim=AGESUP;
       fprintf(ficresf,"# StartingAge FinalAge");    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);      /* nhstepm age range expressed in number of stepm */
            nstepm=(int) rint((agelim-age)*YEARM/stepm); 
            /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {      /* if (stepm >= YEARM) hstepm=1;*/
         fprintf(ficresf,"\n");      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      gp=matrix(0,nhstepm,1,nlstate*nlstate);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      gm=matrix(0,nhstepm,1,nlstate*nlstate);
           nhstepm = nhstepm/hstepm;  
                /* Computed by stepm unit matrices, product of hstepm matrices, stored
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
           oldm=oldms;savm=savms;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);     
          
           for (h=0; h<=nhstepm; h++){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
             if (h==(int) (calagedate+YEARM*cpt)) {  
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);      /* Computing  Variances of health expectancies */
             }  
             for(j=1; j<=nlstate+ndeath;j++) {       for(theta=1; theta <=npar; theta++){
               kk1=0.;kk2=0;        for(i=1; i<=npar; i++){ 
               for(i=1; i<=nlstate;i++) {                        xp[i] = x[i] + (i==theta ?delti[theta]:0);
                 if (mobilav==1)        }
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
                 else {    
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];        cptj=0;
                 }        for(j=1; j<= nlstate; j++){
                          for(i=1; i<=nlstate; i++){
               }            cptj=cptj+1;
               if (h==(int)(calagedate+12*cpt)){            for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){
                 fprintf(ficresf," %.3f", kk1);              gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
                                    }
               }          }
             }        }
           }       
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       
         }        for(i=1; i<=npar; i++) 
       }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   }        
                cptj=0;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(j=1; j<= nlstate; j++){
           for(i=1;i<=nlstate;i++){
   fclose(ficresf);            cptj=cptj+1;
 }            for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){
 /************** Forecasting ******************/  
 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){              gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;
              }
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;          }
   int *popage;        }
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;        for(j=1; j<= nlstate*nlstate; j++)
   double *popeffectif,*popcount;          for(h=0; h<=nhstepm-1; h++){
   double ***p3mat,***tabpop,***tabpopprev;            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   char filerespop[FILENAMELENGTH];          }
        } 
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);     
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  /* End theta */
   agelim=AGESUP;  
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;       trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
    
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);       for(h=0; h<=nhstepm-1; h++)
          for(j=1; j<=nlstate*nlstate;j++)
            for(theta=1; theta <=npar; theta++)
   strcpy(filerespop,"pop");            trgradg[h][j][theta]=gradg[h][theta][j];
   strcat(filerespop,fileres);       
   if((ficrespop=fopen(filerespop,"w"))==NULL) {  
     printf("Problem with forecast resultfile: %s\n", filerespop);       for(i=1;i<=nlstate*nlstate;i++)
   }        for(j=1;j<=nlstate*nlstate;j++)
   printf("Computing forecasting: result on file '%s' \n", filerespop);          varhe[i][j][(int)age] =0.;
   
   if (cptcoveff==0) ncodemax[cptcoveff]=1;       printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   if (mobilav==1) {       for(h=0;h<=nhstepm-1;h++){
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(k=0;k<=nhstepm-1;k++){
     movingaverage(agedeb, fage, ageminpar, mobaverage);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   }          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(i=1;i<=nlstate*nlstate;i++)
   stepsize=(int) (stepm+YEARM-1)/YEARM;            for(j=1;j<=nlstate*nlstate;j++)
   if (stepm<=12) stepsize=1;              varhe[i][j][(int)age] += doldm[i][j]*hf*hf;
          }
   agelim=AGESUP;      }
        /* Computing expectancies */
   hstepm=1;      for(i=1; i<=nlstate;i++)
   hstepm=hstepm/stepm;        for(j=1; j<=nlstate;j++)
            for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   if (popforecast==1) {            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     if((ficpop=fopen(popfile,"r"))==NULL) {            
       printf("Problem with population file : %s\n",popfile);exit(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]);*/
     }  
     popage=ivector(0,AGESUP);          }
     popeffectif=vector(0,AGESUP);  
     popcount=vector(0,AGESUP);      fprintf(ficreseij,"%3.0f",age );
          cptj=0;
     i=1;        for(i=1; i<=nlstate;i++)
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;        for(j=1; j<=nlstate;j++){
              cptj++;
     imx=i;          fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];        }
   }      fprintf(ficreseij,"\n");
      
   for(cptcov=1;cptcov<=i2;cptcov++){      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
       k=k+1;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       fprintf(ficrespop,"\n#******");      free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       for(j=1;j<=cptcoveff;j++) {      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    }
       }    printf("\n");
       fprintf(ficrespop,"******\n");    fprintf(ficlog,"\n");
       fprintf(ficrespop,"# Age");  
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    free_vector(xp,1,npar);
       if (popforecast==1)  fprintf(ficrespop," [Population]");    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
          free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       for (cpt=0; cpt<=0;cpt++) {    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);    }
          
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){  /************ Variance ******************/
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  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[])
           nhstepm = nhstepm/hstepm;  {
              /* Variance of health expectancies */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
           oldm=oldms;savm=savms;    /* double **newm;*/
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double **dnewm,**doldm;
            double **dnewmp,**doldmp;
           for (h=0; h<=nhstepm; h++){    int i, j, nhstepm, hstepm, h, nstepm ;
             if (h==(int) (calagedate+YEARM*cpt)) {    int k, cptcode;
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    double *xp;
             }    double **gp, **gm;  /* for var eij */
             for(j=1; j<=nlstate+ndeath;j++) {    double ***gradg, ***trgradg; /*for var eij */
               kk1=0.;kk2=0;    double **gradgp, **trgradgp; /* for var p point j */
               for(i=1; i<=nlstate;i++) {                  double *gpp, *gmp; /* for var p point j */
                 if (mobilav==1)    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    double ***p3mat;
                 else {    double age,agelim, hf;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    double ***mobaverage;
                 }    int theta;
               }    char digit[4];
               if (h==(int)(calagedate+12*cpt)){    char digitp[25];
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;  
                   /*fprintf(ficrespop," %.3f", kk1);    char fileresprobmorprev[FILENAMELENGTH];
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/  
               }    if(popbased==1){
             }      if(mobilav!=0)
             for(i=1; i<=nlstate;i++){        strcpy(digitp,"-populbased-mobilav-");
               kk1=0.;      else strcpy(digitp,"-populbased-nomobil-");
                 for(j=1; j<=nlstate;j++){    }
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];    else 
                 }      strcpy(digitp,"-stablbased-");
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];  
             }    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      }
         }    }
       }  
      strcpy(fileresprobmorprev,"prmorprev"); 
   /******/    sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    strcat(fileresprobmorprev,digit); /* Tvar to be done */
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    strcat(fileresprobmorprev,fileres);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
           nhstepm = nhstepm/hstepm;      printf("Problem with resultfile: %s\n", fileresprobmorprev);
                fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    }
           oldm=oldms;savm=savms;    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);     
           for (h=0; h<=nhstepm; h++){    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
             if (h==(int) (calagedate+YEARM*cpt)) {    fprintf(ficresprobmorprev, "#Local time at start: %s", strstart);
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    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=1; j<=nlstate+ndeath;j++) {    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
               kk1=0.;kk2=0;      fprintf(ficresprobmorprev," p.%-d SE",j);
               for(i=1; i<=nlstate;i++) {                    for(i=1; i<=nlstate;i++)
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];            fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
               }    }  
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    fprintf(ficresprobmorprev,"\n");
             }    fprintf(ficgp,"\n# Routine varevsij");
           }    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    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");
         }    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       }  /*   } */
    }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   }   fprintf(ficresvij, "#Local time at start: %s", strstart);
      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");
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
   if (popforecast==1) {      for(j=1; j<=nlstate;j++)
     free_ivector(popage,0,AGESUP);        fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
     free_vector(popeffectif,0,AGESUP);    fprintf(ficresvij,"\n");
     free_vector(popcount,0,AGESUP);  
   }    xp=vector(1,npar);
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    dnewm=matrix(1,nlstate,1,npar);
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    doldm=matrix(1,nlstate,1,nlstate);
   fclose(ficrespop);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
 }    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
 /***********************************************/    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
 /**************** Main Program *****************/    gpp=vector(nlstate+1,nlstate+ndeath);
 /***********************************************/    gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
 int main(int argc, char *argv[])    
 {    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    }
   double agedeb, agefin,hf;    else  hstepm=estepm;   
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;    /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   double fret;       nhstepm is the number of hstepm from age to agelim 
   double **xi,tmp,delta;       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   double dum; /* Dummy variable */       and note for a fixed period like k years */
   double ***p3mat;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   int *indx;       survival function given by stepm (the optimization length). Unfortunately it
   char line[MAXLINE], linepar[MAXLINE];       means that if the survival funtion is printed every two years of age and if
   char title[MAXLINE];       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];       results. So we changed our mind and took the option of the best precision.
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    */
      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   char filerest[FILENAMELENGTH];      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   char fileregp[FILENAMELENGTH];      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   char popfile[FILENAMELENGTH];      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   int firstobs=1, lastobs=10;      gp=matrix(0,nhstepm,1,nlstate);
   int sdeb, sfin; /* Status at beginning and end */      gm=matrix(0,nhstepm,1,nlstate);
   int c,  h , cpt,l;  
   int ju,jl, mi;  
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      for(theta=1; theta <=npar; theta++){
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   int mobilav=0,popforecast=0;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   int hstepm, nhstepm;        }
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   double bage, fage, age, agelim, agebase;  
   double ftolpl=FTOL;        if (popbased==1) {
   double **prlim;          if(mobilav ==0){
   double *severity;            for(i=1; i<=nlstate;i++)
   double ***param; /* Matrix of parameters */              prlim[i][i]=probs[(int)age][i][ij];
   double  *p;          }else{ /* mobilav */ 
   double **matcov; /* Matrix of covariance */            for(i=1; i<=nlstate;i++)
   double ***delti3; /* Scale */              prlim[i][i]=mobaverage[(int)age][i][ij];
   double *delti; /* Scale */          }
   double ***eij, ***vareij;        }
   double **varpl; /* Variances of prevalence limits by age */    
   double *epj, vepp;        for(j=1; j<= nlstate; j++){
   double kk1, kk2;          for(h=0; h<=nhstepm; h++){
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
                gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
   char version[80]="Imach version 0.8a, May 2002, INED-EUROREVES ";        }
   char *alph[]={"a","a","b","c","d","e"}, str[4];        /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
   char z[1]="c", occ;        */
 #include <sys/time.h>        for(j=nlstate+1;j<=nlstate+ndeath;j++){
 #include <time.h>          for(i=1,gpp[j]=0.; i<= nlstate; i++)
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];            gpp[j] += prlim[i][i]*p3mat[i][j][1];
          }    
   /* long total_usecs;        /* end probability of death */
   struct timeval start_time, end_time;  
          for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   getcwd(pathcd, size);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   printf("\n%s",version);   
   if(argc <=1){        if (popbased==1) {
     printf("\nEnter the parameter file name: ");          if(mobilav ==0){
     scanf("%s",pathtot);            for(i=1; i<=nlstate;i++)
   }              prlim[i][i]=probs[(int)age][i][ij];
   else{          }else{ /* mobilav */ 
     strcpy(pathtot,argv[1]);            for(i=1; i<=nlstate;i++)
   }              prlim[i][i]=mobaverage[(int)age][i][ij];
   /*if(getcwd(pathcd, 80)!= 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,'\\');*/        for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   chdir(path);          }
   replace(pathc,path);        }
         /* This for computing probability of death (h=1 means
 /*-------- arguments in the command line --------*/           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
   strcpy(fileres,"r");        */
   strcat(fileres, optionfilefiname);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   strcat(fileres,".txt");    /* Other files have txt extension */          for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
   /*---------arguments file --------*/        }    
         /* end probability of death */
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  
     printf("Problem with optionfile %s\n",optionfile);        for(j=1; j<= nlstate; j++) /* vareij */
     goto end;          for(h=0; h<=nhstepm; h++){
   }            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   strcpy(filereso,"o");  
   strcat(filereso,fileres);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   if((ficparo=fopen(filereso,"w"))==NULL) {          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        }
   }  
       } /* End theta */
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);      for(h=0; h<=nhstepm; h++) /* veij */
     puts(line);        for(j=1; j<=nlstate;j++)
     fputs(line,ficparo);          for(theta=1; theta <=npar; theta++)
   }            trgradg[h][j][theta]=gradg[h][theta][j];
   ungetc(c,ficpar);  
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   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\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);        for(theta=1; theta <=npar; theta++)
   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);          trgradgp[j][theta]=gradgp[theta][j];
   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);    
 while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     fgets(line, MAXLINE, ficpar);      for(i=1;i<=nlstate;i++)
     puts(line);        for(j=1;j<=nlstate;j++)
     fputs(line,ficparo);          vareij[i][j][(int)age] =0.;
   }  
   ungetc(c,ficpar);      for(h=0;h<=nhstepm;h++){
          for(k=0;k<=nhstepm;k++){
              matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
   covar=matrix(0,NCOVMAX,1,n);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   cptcovn=0;          for(i=1;i<=nlstate;i++)
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;            for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
   ncovmodel=2+cptcovn;        }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      }
      
   /* Read guess parameters */      /* pptj */
   /* Reads comments: lines beginning with '#' */      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
   while((c=getc(ficpar))=='#' && c!= EOF){      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
     ungetc(c,ficpar);      for(j=nlstate+1;j<=nlstate+ndeath;j++)
     fgets(line, MAXLINE, ficpar);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
     puts(line);          varppt[j][i]=doldmp[j][i];
     fputs(line,ficparo);      /* end ppptj */
   }      /*  x centered again */
   ungetc(c,ficpar);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
        prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);   
     for(i=1; i <=nlstate; i++)      if (popbased==1) {
     for(j=1; j <=nlstate+ndeath-1; j++){        if(mobilav ==0){
       fscanf(ficpar,"%1d%1d",&i1,&j1);          for(i=1; i<=nlstate;i++)
       fprintf(ficparo,"%1d%1d",i1,j1);            prlim[i][i]=probs[(int)age][i][ij];
       printf("%1d%1d",i,j);        }else{ /* mobilav */ 
       for(k=1; k<=ncovmodel;k++){          for(i=1; i<=nlstate;i++)
         fscanf(ficpar," %lf",&param[i][j][k]);            prlim[i][i]=mobaverage[(int)age][i][ij];
         printf(" %lf",param[i][j][k]);        }
         fprintf(ficparo," %lf",param[i][j][k]);      }
       }               
       fscanf(ficpar,"\n");      /* This for computing probability of death (h=1 means
       printf("\n");         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
       fprintf(ficparo,"\n");         as a weighted average of prlim.
     }      */
        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   p=param[1][1];      }    
        /* end probability of death */
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     ungetc(c,ficpar);      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     fgets(line, MAXLINE, ficpar);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
     puts(line);        for(i=1; i<=nlstate;i++){
     fputs(line,ficparo);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
   }        }
   ungetc(c,ficpar);      } 
       fprintf(ficresprobmorprev,"\n");
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      fprintf(ficresvij,"%.0f ",age );
   for(i=1; i <=nlstate; i++){      for(i=1; i<=nlstate;i++)
     for(j=1; j <=nlstate+ndeath-1; j++){        for(j=1; j<=nlstate;j++){
       fscanf(ficpar,"%1d%1d",&i1,&j1);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       printf("%1d%1d",i,j);        }
       fprintf(ficparo,"%1d%1d",i1,j1);      fprintf(ficresvij,"\n");
       for(k=1; k<=ncovmodel;k++){      free_matrix(gp,0,nhstepm,1,nlstate);
         fscanf(ficpar,"%le",&delti3[i][j][k]);      free_matrix(gm,0,nhstepm,1,nlstate);
         printf(" %le",delti3[i][j][k]);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
         fprintf(ficparo," %le",delti3[i][j][k]);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       }      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fscanf(ficpar,"\n");    } /* End age */
       printf("\n");    free_vector(gpp,nlstate+1,nlstate+ndeath);
       fprintf(ficparo,"\n");    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*/
   delti=delti3[1][1];    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 */
   /* Reads comments: lines beginning with '#' */    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   while((c=getc(ficpar))=='#' && c!= EOF){  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
     ungetc(c,ficpar);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fgets(line, MAXLINE, ficpar);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     puts(line);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     fputs(line,ficparo);    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));
   ungetc(c,ficpar);    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);
   matcov=matrix(1,npar,1,npar);    /*  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);
   for(i=1; i <=npar; i++){  */
     fscanf(ficpar,"%s",&str);  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     printf("%s",str);    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     fprintf(ficparo,"%s",str);  
     for(j=1; j <=i; j++){    free_vector(xp,1,npar);
       fscanf(ficpar," %le",&matcov[i][j]);    free_matrix(doldm,1,nlstate,1,nlstate);
       printf(" %.5le",matcov[i][j]);    free_matrix(dnewm,1,nlstate,1,npar);
       fprintf(ficparo," %.5le",matcov[i][j]);    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     }    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     fscanf(ficpar,"\n");    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     printf("\n");    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fprintf(ficparo,"\n");    fclose(ficresprobmorprev);
   }    fflush(ficgp);
   for(i=1; i <=npar; i++)    fflush(fichtm); 
     for(j=i+1;j<=npar;j++)  }  /* end varevsij */
       matcov[i][j]=matcov[j][i];  
      /************ Variance of prevlim ******************/
   printf("\n");  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 */
     /*-------- Rewriting paramater file ----------*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
      strcpy(rfileres,"r");    /* "Rparameterfile */    double **newm;
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/    double **dnewm,**doldm;
      strcat(rfileres,".");    /* */    int i, j, nhstepm, hstepm;
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    int k, cptcode;
     if((ficres =fopen(rfileres,"w"))==NULL) {    double *xp;
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    double *gp, *gm;
     }    double **gradg, **trgradg;
     fprintf(ficres,"#%s\n",version);    double age,agelim;
        int theta;
     /*-------- data file ----------*/    fprintf(ficresvpl, "#Local time at start: %s", strstart); 
     if((fic=fopen(datafile,"r"))==NULL)    {    fprintf(ficresvpl,"# Standard deviation of stable prevalences \n");
       printf("Problem with datafile: %s\n", datafile);goto end;    fprintf(ficresvpl,"# Age");
     }    for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     n= lastobs;    fprintf(ficresvpl,"\n");
     severity = vector(1,maxwav);  
     outcome=imatrix(1,maxwav+1,1,n);    xp=vector(1,npar);
     num=ivector(1,n);    dnewm=matrix(1,nlstate,1,npar);
     moisnais=vector(1,n);    doldm=matrix(1,nlstate,1,nlstate);
     annais=vector(1,n);    
     moisdc=vector(1,n);    hstepm=1*YEARM; /* Every year of age */
     andc=vector(1,n);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agedc=vector(1,n);    agelim = AGESUP;
     cod=ivector(1,n);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     weight=vector(1,n);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */      if (stepm >= YEARM) hstepm=1;
     mint=matrix(1,maxwav,1,n);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
     anint=matrix(1,maxwav,1,n);      gradg=matrix(1,npar,1,nlstate);
     s=imatrix(1,maxwav+1,1,n);      gp=vector(1,nlstate);
     adl=imatrix(1,maxwav+1,1,n);          gm=vector(1,nlstate);
     tab=ivector(1,NCOVMAX);  
     ncodemax=ivector(1,8);      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
     i=1;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     while (fgets(line, MAXLINE, fic) != NULL)    {        }
       if ((i >= firstobs) && (i <=lastobs)) {        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
                for(i=1;i<=nlstate;i++)
         for (j=maxwav;j>=1;j--){          gp[i] = prlim[i][i];
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);      
           strcpy(line,stra);        for(i=1; i<=npar; i++) /* Computes gradient */
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         }        for(i=1;i<=nlstate;i++)
                  gm[i] = prlim[i][i];
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      } /* End theta */
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);  
       trgradg =matrix(1,nlstate,1,npar);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);  
         for (j=ncovcol;j>=1;j--){      for(j=1; j<=nlstate;j++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        for(theta=1; theta <=npar; theta++)
         }          trgradg[j][theta]=gradg[theta][j];
         num[i]=atol(stra);  
              for(i=1;i<=nlstate;i++)
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){        varpl[i][(int)age] =0.;
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
         i=i+1;      for(i=1;i<=nlstate;i++)
       }        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     }  
     /* printf("ii=%d", ij);      fprintf(ficresvpl,"%.0f ",age );
        scanf("%d",i);*/      for(i=1; i<=nlstate;i++)
   imx=i-1; /* Number of individuals */        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
   /* for (i=1; i<=imx; i++){      free_vector(gp,1,nlstate);
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      free_vector(gm,1,nlstate);
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;      free_matrix(gradg,1,npar,1,nlstate);
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;      free_matrix(trgradg,1,nlstate,1,npar);
     }*/    } /* End age */
    /*  for (i=1; i<=imx; i++){  
      if (s[4][i]==9)  s[4][i]=-1;    free_vector(xp,1,npar);
      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]));}*/    free_matrix(doldm,1,nlstate,1,npar);
      free_matrix(dnewm,1,nlstate,1,nlstate);
    
   /* Calculation of the number of parameter from char model*/  }
   Tvar=ivector(1,15);  
   Tprod=ivector(1,15);  /************ Variance of one-step probabilities  ******************/
   Tvaraff=ivector(1,15);  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[])
   Tvard=imatrix(1,15,1,2);  {
   Tage=ivector(1,15);          int i, j=0,  i1, k1, l1, t, tj;
        int k2, l2, j1,  z1;
   if (strlen(model) >1){    int k=0,l, cptcode;
     j=0, j1=0, k1=1, k2=1;    int first=1, first1;
     j=nbocc(model,'+');    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     j1=nbocc(model,'*');    double **dnewm,**doldm;
     cptcovn=j+1;    double *xp;
     cptcovprod=j1;    double *gp, *gm;
        double **gradg, **trgradg;
     strcpy(modelsav,model);    double **mu;
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    double age,agelim, cov[NCOVMAX];
       printf("Error. Non available option model=%s ",model);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
       goto end;    int theta;
     }    char fileresprob[FILENAMELENGTH];
        char fileresprobcov[FILENAMELENGTH];
     for(i=(j+1); i>=1;i--){    char fileresprobcor[FILENAMELENGTH];
       cutv(stra,strb,modelsav,'+');  
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    double ***varpij;
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/  
       /*scanf("%d",i);*/    strcpy(fileresprob,"prob"); 
       if (strchr(strb,'*')) {    strcat(fileresprob,fileres);
         cutv(strd,strc,strb,'*');    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
         if (strcmp(strc,"age")==0) {      printf("Problem with resultfile: %s\n", fileresprob);
           cptcovprod--;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
           cutv(strb,stre,strd,'V');    }
           Tvar[i]=atoi(stre);    strcpy(fileresprobcov,"probcov"); 
           cptcovage++;    strcat(fileresprobcov,fileres);
             Tage[cptcovage]=i;    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
             /*printf("stre=%s ", stre);*/      printf("Problem with resultfile: %s\n", fileresprobcov);
         }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
         else if (strcmp(strd,"age")==0) {    }
           cptcovprod--;    strcpy(fileresprobcor,"probcor"); 
           cutv(strb,stre,strc,'V');    strcat(fileresprobcor,fileres);
           Tvar[i]=atoi(stre);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
           cptcovage++;      printf("Problem with resultfile: %s\n", fileresprobcor);
           Tage[cptcovage]=i;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
         }    }
         else {    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           cutv(strb,stre,strc,'V');    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           Tvar[i]=ncovcol+k1;    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
           cutv(strb,strc,strd,'V');    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
           Tprod[k1]=i;    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
           Tvard[k1][1]=atoi(strc);    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
           Tvard[k1][2]=atoi(stre);    fprintf(ficresprob, "#Local time at start: %s", strstart);
           Tvar[cptcovn+k2]=Tvard[k1][1];    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    fprintf(ficresprob,"# Age");
           for (k=1; k<=lastobs;k++)    fprintf(ficresprobcov, "#Local time at start: %s", strstart);
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
           k1++;    fprintf(ficresprobcov,"# Age");
           k2=k2+2;    fprintf(ficresprobcor, "#Local time at start: %s", strstart);
         }    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
       }    fprintf(ficresprobcov,"# Age");
       else {  
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/  
        /*  scanf("%d",i);*/    for(i=1; i<=nlstate;i++)
       cutv(strd,strc,strb,'V');      for(j=1; j<=(nlstate+ndeath);j++){
       Tvar[i]=atoi(strc);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
       }        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       strcpy(modelsav,stra);          fprintf(ficresprobcor," p%1d-%1d ",i,j);
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);      }  
         scanf("%d",i);*/   /* fprintf(ficresprob,"\n");
     }    fprintf(ficresprobcov,"\n");
 }    fprintf(ficresprobcor,"\n");
     */
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);   xp=vector(1,npar);
   printf("cptcovprod=%d ", cptcovprod);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   scanf("%d ",i);*/    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     fclose(fic);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     /*  if(mle==1){*/    first=1;
     if (weightopt != 1) { /* Maximisation without weights*/    fprintf(ficgp,"\n# Routine varprob");
       for(i=1;i<=n;i++) weight[i]=1.0;    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     }    fprintf(fichtm,"\n");
     /*-calculation of age at interview from date of interview and age at death -*/  
     agev=matrix(1,maxwav,1,imx);    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\
     for (i=1; i<=imx; i++) {    file %s<br>\n",optionfilehtmcov);
       for(m=2; (m<= maxwav); m++) {    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){  and drawn. It helps understanding how is the covariance between two incidences.\
          anint[m][i]=9999;   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
          s[m][i]=-1;    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 \
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;  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>\
     for (i=1; i<=imx; i++)  {  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  
       for(m=1; (m<= maxwav); m++){    cov[1]=1;
         if(s[m][i] >0){    tj=cptcoveff;
           if (s[m][i] >= nlstate+1) {    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
             if(agedc[i]>0)    j1=0;
               if(moisdc[i]!=99 && andc[i]!=9999)    for(t=1; t<=tj;t++){
                 agev[m][i]=agedc[i];      for(i1=1; i1<=ncodemax[t];i1++){ 
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/        j1++;
            else {        if  (cptcovn>0) {
               if (andc[i]!=9999){          fprintf(ficresprob, "\n#********** Variable "); 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
               agev[m][i]=-1;          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");
           else if(s[m][i] !=9){ /* Should no more exist */          
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          fprintf(ficgp, "\n#********** Variable "); 
             if(mint[m][i]==99 || anint[m][i]==9999)          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
               agev[m][i]=1;          fprintf(ficgp, "**********\n#\n");
             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);*/          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]]);
             else if(agev[m][i] >agemax){          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
               agemax=agev[m][i];          
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/          fprintf(ficresprobcor, "\n#********** Variable ");    
             }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             /*agev[m][i]=anint[m][i]-annais[i];*/          fprintf(ficresprobcor, "**********\n#");    
             /*   agev[m][i] = age[i]+2*m;*/        }
           }        
           else { /* =9 */        for (age=bage; age<=fage; age ++){ 
             agev[m][i]=1;          cov[2]=age;
             s[m][i]=-1;          for (k=1; k<=cptcovn;k++) {
           }            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
         }          }
         else /*= 0 Unknown */          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           agev[m][i]=1;          for (k=1; k<=cptcovprod;k++)
       }            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
              
     }          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
     for (i=1; i<=imx; i++)  {          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
       for(m=1; (m<= maxwav); m++){          gp=vector(1,(nlstate)*(nlstate+ndeath));
         if (s[m][i] > (nlstate+ndeath)) {          gm=vector(1,(nlstate)*(nlstate+ndeath));
           printf("Error: Wrong value in nlstate or ndeath\n");        
           goto end;          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);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);            
             k=0;
     free_vector(severity,1,maxwav);            for(i=1; i<= (nlstate); i++){
     free_imatrix(outcome,1,maxwav+1,1,n);              for(j=1; j<=(nlstate+ndeath);j++){
     free_vector(moisnais,1,n);                k=k+1;
     free_vector(annais,1,n);                gp[k]=pmmij[i][j];
     /* free_matrix(mint,1,maxwav,1,n);              }
        free_matrix(anint,1,maxwav,1,n);*/            }
     free_vector(moisdc,1,n);            
     free_vector(andc,1,n);            for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
          
     wav=ivector(1,imx);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);            k=0;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);            for(i=1; i<=(nlstate); i++){
                  for(j=1; j<=(nlstate+ndeath);j++){
     /* Concatenates waves */                k=k+1;
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);                gm[k]=pmmij[i][j];
               }
             }
       Tcode=ivector(1,100);       
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
       ncodemax[1]=1;              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          }
        
    codtab=imatrix(1,100,1,10);          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
    h=0;            for(theta=1; theta <=npar; theta++)
    m=pow(2,cptcoveff);              trgradg[j][theta]=gradg[theta][j];
            
    for(k=1;k<=cptcoveff; k++){          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
      for(i=1; i <=(m/pow(2,k));i++){          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
        for(j=1; j <= ncodemax[k]; j++){          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
            h++;          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/  
          }          pmij(pmmij,cov,ncovmodel,x,nlstate);
        }          
      }          k=0;
    }          for(i=1; i<=(nlstate); i++){
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);            for(j=1; j<=(nlstate+ndeath);j++){
       codtab[1][2]=1;codtab[2][2]=2; */              k=k+1;
    /* for(i=1; i <=m ;i++){              mu[k][(int) age]=pmmij[i][j];
       for(k=1; k <=cptcovn; k++){            }
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);          }
       }          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
       printf("\n");            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
       }              varpij[i][j][(int)age] = doldm[i][j];
       scanf("%d",i);*/  
              /*printf("\n%d ",(int)age);
    /* Calculates basic frequencies. Computes observed prevalence at single age            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
        and prints on file fileres'p'. */            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]));
                }*/
      
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresprob,"\n%d ",(int)age);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresprobcov,"\n%d ",(int)age);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresprobcor,"\n%d ",(int)age);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          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 Powell, parameters are in a vector p[] starting at p[1]          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
     if(mle==1){          i=0;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);          for (k=1; k<=(nlstate);k++){
     }            for (l=1; l<=(nlstate+ndeath);l++){ 
                  i=i++;
     /*--------- results files --------------*/              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
     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(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
                for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
    jk=1;                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");              }
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");            }
    for(i=1,jk=1; i <=nlstate; i++){          }/* end of loop for state */
      for(k=1; k <=(nlstate+ndeath); k++){        } /* end of loop for age */
        if (k != i)  
          {        /* Confidence intervalle of pij  */
            printf("%d%d ",i,k);        /*
            fprintf(ficres,"%1d%1d ",i,k);          fprintf(ficgp,"\nset noparametric;unset label");
            for(j=1; j <=ncovmodel; j++){          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
              printf("%f ",p[jk]);          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
              fprintf(ficres,"%f ",p[jk]);          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);
              jk++;          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
            }          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
            printf("\n");          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
            fprintf(ficres,"\n");        */
          }  
      }        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
    }        first1=1;
  if(mle==1){        for (k2=1; k2<=(nlstate);k2++){
     /* Computing hessian and covariance matrix */          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
     ftolhess=ftol; /* Usually correct */            if(l2==k2) continue;
     hesscov(matcov, p, npar, delti, ftolhess, func);            j=(k2-1)*(nlstate+ndeath)+l2;
  }            for (k1=1; k1<=(nlstate);k1++){
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
     printf("# Scales (for hessian or gradient estimation)\n");                if(l1==k1) continue;
      for(i=1,jk=1; i <=nlstate; i++){                i=(k1-1)*(nlstate+ndeath)+l1;
       for(j=1; j <=nlstate+ndeath; j++){                if(i<=j) continue;
         if (j!=i) {                for (age=bage; age<=fage; age ++){ 
           fprintf(ficres,"%1d%1d",i,j);                  if ((int)age %5==0){
           printf("%1d%1d",i,j);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
           for(k=1; k<=ncovmodel;k++){                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
             printf(" %.5e",delti[jk]);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
             fprintf(ficres," %.5e",delti[jk]);                    mu1=mu[i][(int) age]/stepm*YEARM ;
             jk++;                    mu2=mu[j][(int) age]/stepm*YEARM;
           }                    c12=cv12/sqrt(v1*v2);
           printf("\n");                    /* Computing eigen value of matrix of covariance */
           fprintf(ficres,"\n");                    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 */
     k=1;                    v21=(lc1-v1)/cv12*v11;
     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");                    v12=-v21;
     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");                    v22=v11;
     for(i=1;i<=npar;i++){                    tnalp=v21/v11;
       /*  if (k>nlstate) k=1;                    if(first1==1){
       i1=(i-1)/(ncovmodel*nlstate)+1;                      first1=0;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);                      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);
       printf("%s%d%d",alph[k],i1,tab[i]);*/                    }
       fprintf(ficres,"%3d",i);                    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("%3d",i);                    /*printf(fignu*/
       for(j=1; j<=i;j++){                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
         fprintf(ficres," %.5e",matcov[i][j]);                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
         printf(" %.5e",matcov[i][j]);                    if(first==1){
       }                      first=0;
       fprintf(ficres,"\n");                      fprintf(ficgp,"\nset parametric;unset label");
       printf("\n");                      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);
       k++;                      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\">\
     while((c=getc(ficpar))=='#' && c!= EOF){  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
       ungetc(c,ficpar);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
       fgets(line, MAXLINE, ficpar);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
       puts(line);                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
       fputs(line,ficparo);                      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);
     ungetc(c,ficpar);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
     estepm=0;                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);                      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",\
     if (estepm==0 || estepm < stepm) estepm=stepm;                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
     if (fage <= 2) {                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
       bage = ageminpar;                    }else{
       fage = agemaxpar;                      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(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);                      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",\
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                                mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
     while((c=getc(ficpar))=='#' && c!= EOF){                    }/* if first */
     ungetc(c,ficpar);                  } /* age mod 5 */
     fgets(line, MAXLINE, ficpar);                } /* end loop age */
     puts(line);                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
     fputs(line,ficparo);                first=1;
   }              } /*l12 */
   ungetc(c,ficpar);            } /* k12 */
            } /*l1 */
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);        }/* k1 */
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      } /* loop covariates */
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    }
          free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     ungetc(c,ficpar);    free_vector(xp,1,npar);
     fgets(line, MAXLINE, ficpar);    fclose(ficresprob);
     puts(line);    fclose(ficresprobcov);
     fputs(line,ficparo);    fclose(ficresprobcor);
   }    fflush(ficgp);
   ungetc(c,ficpar);    fflush(fichtmcov);
    }
   
    dateprev1=anprev1+mprev1/12.+jprev1/365.;  
    dateprev2=anprev2+mprev2/12.+jprev2/365.;  /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
   fscanf(ficpar,"pop_based=%d\n",&popbased);                    int lastpass, int stepm, int weightopt, char model[],\
   fprintf(ficparo,"pop_based=%d\n",popbased);                      int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
   fprintf(ficres,"pop_based=%d\n",popbased);                      int popforecast, int estepm ,\
                      double jprev1, double mprev1,double anprev1, \
   while((c=getc(ficpar))=='#' && c!= EOF){                    double jprev2, double mprev2,double anprev2){
     ungetc(c,ficpar);    int jj1, k1, i1, cpt;
     fgets(line, MAXLINE, ficpar);  
     puts(line);     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
     fputs(line,ficparo);     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   }  </ul>");
   ungetc(c,ficpar);     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);     fprintf(fichtm,"\
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
 while((c=getc(ficpar))=='#' && c!= EOF){   - Stable prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
     ungetc(c,ficpar);             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
     fgets(line, MAXLINE, ficpar);     fprintf(fichtm,"\
     puts(line);   - Life expectancies by age and initial health status (estepm=%2d months): \
     fputs(line,ficparo);     <a href=\"%s\">%s</a> <br>\n</li>",
   }             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   ungetc(c,ficpar);  
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);  
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);   m=cptcoveff;
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);   jj1=0;
    for(k1=1; k1<=m;k1++){
 /*------------ gnuplot -------------*/     for(i1=1; i1<=ncodemax[k1];i1++){
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);       jj1++;
         if (cptcovn > 0) {
 /*------------ free_vector  -------------*/         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
  chdir(path);         for (cpt=1; cpt<=cptcoveff;cpt++) 
             fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
  free_ivector(wav,1,imx);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);       }
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);         /* Pij */
  free_ivector(num,1,n);       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> \
  free_vector(agedc,1,n);  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
  /*free_matrix(covar,1,NCOVMAX,1,n);*/       /* Quasi-incidences */
  fclose(ficparo);       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
  fclose(ficres);   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); 
 /*--------- index.htm --------*/         /* Stable prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);           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);
           }
   /*--------------- Prevalence limit --------------*/       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> \
   strcpy(filerespl,"pl");  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
   strcat(filerespl,fileres);       }
   if((ficrespl=fopen(filerespl,"w"))==NULL) {     } /* end i1 */
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;   }/* End k1 */
   }   fprintf(fichtm,"</ul>");
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);  
   fprintf(ficrespl,"#Prevalence limit\n");  
   fprintf(ficrespl,"#Age ");   fprintf(fichtm,"\
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
   fprintf(ficrespl,"\n");   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
    
   prlim=matrix(1,nlstate,1,nlstate);   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   fprintf(fichtm,"\
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  
   k=0;   fprintf(fichtm,"\
   agebase=ageminpar;   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   agelim=agemaxpar;           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
   ftolpl=1.e-10;   fprintf(fichtm,"\
   i1=cptcoveff;   - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
   if (cptcovn < 1){i1=1;}           estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
   for(cptcov=1;cptcov<=i1;cptcov++){   - Health expectancies with their variances (no covariance): <a href=\"%s\">%s</a> <br>\n",
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){           subdirf2(fileres,"t"),subdirf2(fileres,"t"));
         k=k+1;   fprintf(fichtm,"\
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/   - Standard deviation of stable prevalences: <a href=\"%s\">%s</a> <br>\n",\
         fprintf(ficrespl,"\n#******");           subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
         for(j=1;j<=cptcoveff;j++)  
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  /*  if(popforecast==1) fprintf(fichtm,"\n */
         fprintf(ficrespl,"******\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 */
         for (age=agebase; age<=agelim; age++){  /*      <br>",fileres,fileres,fileres,fileres); */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  /*  else  */
           fprintf(ficrespl,"%.0f",age );  /*    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); */
           for(i=1; i<=nlstate;i++)   fflush(fichtm);
           fprintf(ficrespl," %.5f", prlim[i][i]);   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
           fprintf(ficrespl,"\n");  
         }   m=cptcoveff;
       }   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
     }  
   fclose(ficrespl);   jj1=0;
    for(k1=1; k1<=m;k1++){
   /*------------- h Pij x at various ages ------------*/     for(i1=1; i1<=ncodemax[k1];i1++){
         jj1++;
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);       if (cptcovn > 0) {
   if((ficrespij=fopen(filerespij,"w"))==NULL) {         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;         for (cpt=1; cpt<=cptcoveff;cpt++) 
   }           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   printf("Computing pij: result on file '%s' \n", filerespij);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
         }
   stepsize=(int) (stepm+YEARM-1)/YEARM;       for(cpt=1; cpt<=nlstate;cpt++) {
   /*if (stepm<=24) stepsize=2;*/         fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   agelim=AGESUP;  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
   hstepm=stepsize*YEARM; /* Every year of age */       }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
    health expectancies in states (1) and (2): %s%d.png<br>\
   k=0;  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
   for(cptcov=1;cptcov<=i1;cptcov++){     } /* end i1 */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   }/* End k1 */
       k=k+1;   fprintf(fichtm,"</ul>");
         fprintf(ficrespij,"\n#****** ");   fflush(fichtm);
         for(j=1;j<=cptcoveff;j++)  }
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
         fprintf(ficrespij,"******\n");  /******************* Gnuplot file **************/
          void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
         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 dirfileres[132],optfileres[132];
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int ng;
           oldm=oldms;savm=savms;  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    /*     printf("Problem with file %s",optionfilegnuplot); */
           fprintf(ficrespij,"# Age");  /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
           for(i=1; i<=nlstate;i++)  /*   } */
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);    /*#ifdef windows */
           fprintf(ficrespij,"\n");    fprintf(ficgp,"cd \"%s\" \n",pathc);
            for (h=0; h<=nhstepm; h++){      /*#endif */
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    m=pow(2,cptcoveff);
             for(i=1; i<=nlstate;i++)  
               for(j=1; j<=nlstate+ndeath;j++)    strcpy(dirfileres,optionfilefiname);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    strcpy(optfileres,"vpl");
             fprintf(ficrespij,"\n");   /* 1eme*/
              }    for (cpt=1; cpt<= nlstate ; cpt ++) {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     for (k1=1; k1<= m ; k1 ++) {
           fprintf(ficrespij,"\n");       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\
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);  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);
   fclose(ficrespij);  
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
   /*---------- Forecasting ------------------*/         else fprintf(ficgp," \%%*lf (\%%*lf)");
   if((stepm == 1) && (strcmp(model,".")==0)){       }
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);       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);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);       for (i=1; i<= nlstate ; i ++) {
   }         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
   else{         else fprintf(ficgp," \%%*lf (\%%*lf)");
     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(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
   }       for (i=1; i<= nlstate ; i ++) {
           if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
   /*---------- Health expectancies and variances ------------*/       }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
   strcpy(filerest,"t");     }
   strcat(filerest,fileres);    }
   if((ficrest=fopen(filerest,"w"))==NULL) {    /*2 eme*/
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    
   }    for (k1=1; k1<= m ; k1 ++) { 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      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);
       
   strcpy(filerese,"e");      for (i=1; i<= nlstate+1 ; i ++) {
   strcat(filerese,fileres);        k=2*i;
   if((ficreseij=fopen(filerese,"w"))==NULL) {        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);        for (j=1; j<= nlstate+1 ; j ++) {
   }          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);          else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
  strcpy(fileresv,"v");        if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
   strcat(fileresv,fileres);        else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);        for (j=1; j<= nlstate+1 ; j ++) {
   }          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);          else fprintf(ficgp," \%%*lf (\%%*lf)");
   calagedate=-1;        }   
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        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);
   k=0;        for (j=1; j<= nlstate+1 ; j ++) {
   for(cptcov=1;cptcov<=i1;cptcov++){          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          else fprintf(ficgp," \%%*lf (\%%*lf)");
       k=k+1;        }   
       fprintf(ficrest,"\n#****** ");        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
       for(j=1;j<=cptcoveff;j++)        else fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      }
       fprintf(ficrest,"******\n");    }
     
       fprintf(ficreseij,"\n#****** ");    /*3eme*/
       for(j=1;j<=cptcoveff;j++)    
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficreseij,"******\n");      for (cpt=1; cpt<= nlstate ; cpt ++) {
         k=2+nlstate*(2*cpt-2);
       fprintf(ficresvij,"\n#****** ");        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
       for(j=1;j<=cptcoveff;j++)        fprintf(ficgp,"set ter png small\n\
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  set size 0.65,0.65\n\
       fprintf(ficresvij,"******\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);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
       oldm=oldms;savm=savms;          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);            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) ");
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
       oldm=oldms;savm=savms;          
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);        */
            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);
            
       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);    /* CV preval stable (period) */
       for(age=bage; age <=fage ;age++){    for (k1=1; k1<= m ; k1 ++) { 
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      for (cpt=1; cpt<=nlstate ; cpt ++) {
         if (popbased==1) {        k=3;
           for(i=1; i<=nlstate;i++)        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
             prlim[i][i]=probs[(int)age][i][k];        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
         }  set ter png small\nset size 0.65,0.65\n\
          unset log y\n\
         fprintf(ficrest," %4.0f",age);  plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){        
           for(i=1, epj[j]=0.;i <=nlstate;i++) {        for (i=1; i< nlstate ; i ++)
             epj[j] += prlim[i][i]*eij[i][j][(int)age];          fprintf(ficgp,"+$%d",k+i+1);
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/        fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
           }        
           epj[nlstate+1] +=epj[j];        l=3+(nlstate+ndeath)*cpt;
         }        fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
         for(i=1, vepp=0.;i <=nlstate;i++)          l=3+(nlstate+ndeath)*cpt;
           for(j=1;j <=nlstate;j++)          fprintf(ficgp,"+$%d",l+i+1);
             vepp += vareij[i][j][(int)age];        }
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));        fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
         for(j=1;j <=nlstate;j++){      } 
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));    }  
         }    
         fprintf(ficrest,"\n");    /* proba elementaires */
       }    for(i=1,jk=1; i <=nlstate; i++){
     }      for(k=1; k <=(nlstate+ndeath); k++){
   }        if (k != i) {
 free_matrix(mint,1,maxwav,1,n);          for(j=1; j <=ncovmodel; j++){
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);            fprintf(ficgp,"p%d=%f ",jk,p[jk]);
     free_vector(weight,1,n);            jk++; 
   fclose(ficreseij);            fprintf(ficgp,"\n");
   fclose(ficresvij);          }
   fclose(ficrest);        }
   fclose(ficpar);      }
   free_vector(epj,1,nlstate+1);     }
    
   /*------- Variance limit prevalence------*/       for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
   strcpy(fileresvpl,"vpl");         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
   strcat(fileresvpl,fileres);         if (ng==2)
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {           fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);         else
     exit(0);           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);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);         i=1;
          for(k2=1; k2<=nlstate; k2++) {
   k=0;           k3=i;
   for(cptcov=1;cptcov<=i1;cptcov++){           for(k=1; k<=(nlstate+ndeath); k++) {
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){             if (k != k2){
       k=k+1;               if(ng==2)
       fprintf(ficresvpl,"\n#****** ");                 fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
       for(j=1;j<=cptcoveff;j++)               else
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                 fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
       fprintf(ficresvpl,"******\n");               ij=1;
                     for(j=3; j <=ncovmodel; j++) {
       varpl=matrix(1,nlstate,(int) bage, (int) fage);                 if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
       oldm=oldms;savm=savms;                   fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);                   ij++;
     }                 }
  }                 else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
   fclose(ficresvpl);               }
                fprintf(ficgp,")/(1");
   /*---------- End : free ----------------*/               
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);               for(k1=1; k1 <=nlstate; k1++){   
                   fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                 ij=1;
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);                 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]]]);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);                     ij++;
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);                   }
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);                   else
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);                     fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                   }
   free_matrix(matcov,1,npar,1,npar);                 fprintf(ficgp,")");
   free_vector(delti,1,npar);               }
   free_matrix(agev,1,maxwav,1,imx);               fprintf(ficgp,") t \"p%d%d\" ", k2,k);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);               if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
   if(erreur >0)             }
     printf("End of Imach with error or warning %d\n",erreur);           } /* end k */
   else   printf("End of Imach\n");         } /* end k2 */
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */       } /* end jk */
       } /* end ng */
   /* 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);*/     fflush(ficgp); 
   /*printf("Total time was %d uSec.\n", total_usecs);*/  }  /* end gnuplot */
   /*------ End -----------*/  
   
   /*************** Moving average **************/
  end:  int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
 #ifdef windows  
   /* chdir(pathcd);*/    int i, cpt, cptcod;
 #endif    int modcovmax =1;
  /*system("wgnuplot graph.plt");*/    int mobilavrange, mob;
  /*system("../gp37mgw/wgnuplot graph.plt");*/    double age;
  /*system("cd ../gp37mgw");*/  
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/    modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
  strcpy(plotcmd,GNUPLOTPROGRAM);                             a covariate has 2 modalities */
  strcat(plotcmd," ");    if (cptcovn<1) modcovmax=1; /* At least 1 pass */
  strcat(plotcmd,optionfilegnuplot);  
  system(plotcmd);    if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
 #ifdef windows      else mobilavrange=mobilav;
   while (z[0] != 'q') {      for (age=bage; age<=fage; age++)
     /* chdir(path); */        for (i=1; i<=nlstate;i++)
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");          for (cptcod=1;cptcod<=modcovmax;cptcod++)
     scanf("%s",z);            mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
     if (z[0] == 'c') system("./imach");      /* We keep the original values on the extreme ages bage, fage and for 
     else if (z[0] == 'e') system(optionfilehtm);         fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
     else if (z[0] == 'g') system(plotcmd);         we use a 5 terms etc. until the borders are no more concerned. 
     else if (z[0] == 'q') exit(0);      */ 
   }      for (mob=3;mob <=mobilavrange;mob=mob+2){
 #endif        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   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char strstart[80], *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       scanf("%s",pathtot);
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     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 parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);
     fclose(fic);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<body>\n<title>IMaCh Cov %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<body>\n<title>IMaCh %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (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);
   #ifndef UNIX
     /*  strcpy(plotcmd,"\""); */
   #endif
     strcpy(plotcmd,pathimach);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     strcat(plotcmd,GNUPLOTPROGRAM);
   #ifndef UNIX
     strcat(plotcmd,".exe");
     /*  strcat(plotcmd,"\"");*/
   #endif
     if(stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
     }
   
   #ifndef UNIX
     strcpy(plotcmd,"\"");
   #endif
     strcat(plotcmd,pathimach);
     strcat(plotcmd,GNUPLOTPROGRAM);
   #ifndef UNIX
     strcat(plotcmd,".exe");
     strcat(plotcmd,"\"");
   #endif
     strcat(plotcmd," ");
     strcat(plotcmd,optionfilegnuplot);
     printf("Starting graphs with: %s",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.41  
changed lines
  Added in v.1.108


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