Diff for /imach/src/imach.c between versions 1.48 and 1.117

version 1.48, 2002/06/10 13:12:49 version 1.117, 2006/03/14 17:16:22
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.117  2006/03/14 17:16:22  brouard
      (Module): varevsij Comments added explaining the second
   This program computes Healthy Life Expectancies from    table of variances if popbased=1 .
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   first survey ("cross") where individuals from different ages are    (Module): Function pstamp added
   interviewed on their health status or degree of disability (in the    (Module): Version 0.98d
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.116  2006/03/06 10:29:27  brouard
   (if any) in individual health status.  Health expectancies are    (Module): Variance-covariance wrong links and
   computed from the time spent in each health state according to a    varian-covariance of ej. is needed (Saito).
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.115  2006/02/27 12:17:45  brouard
   simplest model is the multinomial logistic model where pij is the    (Module): One freematrix added in mlikeli! 0.98c
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.114  2006/02/26 12:57:58  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    (Module): Some improvements in processing parameter
   'age' is age and 'sex' is a covariate. If you want to have a more    filename with strsep.
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.113  2006/02/24 14:20:24  brouard
   you to do it.  More covariates you add, slower the    (Module): Memory leaks checks with valgrind and:
   convergence.    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.112  2006/01/30 09:55:26  brouard
   identical for each individual. Also, if a individual missed an    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.111  2006/01/25 20:38:18  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
   hPijx is the probability to be observed in state i at age x+h    (Module): Comments can be added in data file. Missing date values
   conditional to the observed state i at age x. The delay 'h' can be    can be a simple dot '.'.
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.110  2006/01/25 00:51:50  brouard
   semester or year) is model as a multinomial logistic.  The hPx    (Module): Lots of cleaning and bugs added (Gompertz)
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.109  2006/01/24 19:37:15  brouard
   hPijx.    (Module): Comments (lines starting with a #) are allowed in data.
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.108  2006/01/19 18:05:42  lievre
   of the life expectancies. It also computes the prevalence limits.    Gnuplot problem appeared...
      To be fixed
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).  
            Institut national d'études démographiques, Paris.    Revision 1.107  2006/01/19 16:20:37  brouard
   This software have been partly granted by Euro-REVES, a concerted action    Test existence of gnuplot in imach path
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.106  2006/01/19 13:24:36  brouard
   software can be distributed freely for non commercial use. Latest version    Some cleaning and links added in html output
   can be accessed at http://euroreves.ined.fr/imach .  
   **********************************************************************/    Revision 1.105  2006/01/05 20:23:19  lievre
      *** empty log message ***
 #include <math.h>  
 #include <stdio.h>    Revision 1.104  2005/09/30 16:11:43  lievre
 #include <stdlib.h>    (Module): sump fixed, loop imx fixed, and simplifications.
 #include <unistd.h>    (Module): If the status is missing at the last wave but we know
     that the person is alive, then we can code his/her status as -2
 #define MAXLINE 256    (instead of missing=-1 in earlier versions) and his/her
 #define GNUPLOTPROGRAM "gnuplot"    contributions to the likelihood is 1 - Prob of dying from last
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 #define FILENAMELENGTH 80    the healthy state at last known wave). Version is 0.98
 /*#define DEBUG*/  
 #define windows    Revision 1.103  2005/09/30 15:54:49  lievre
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): sump fixed, loop imx fixed, and simplifications.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     Revision 1.102  2004/09/15 17:31:30  brouard
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Add the possibility to read data file including tab characters.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.101  2004/09/15 10:38:38  brouard
 #define NINTERVMAX 8    Fix on curr_time
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.100  2004/07/12 18:29:06  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    Add version for Mac OS X. Just define UNIX in Makefile
 #define MAXN 20000  
 #define YEARM 12. /* Number of months per year */    Revision 1.99  2004/06/05 08:57:40  brouard
 #define AGESUP 130    *** empty log message ***
 #define AGEBASE 40  
 #ifdef windows    Revision 1.98  2004/05/16 15:05:56  brouard
 #define DIRSEPARATOR '\\'    New version 0.97 . First attempt to estimate force of mortality
 #else    directly from the data i.e. without the need of knowing the health
 #define DIRSEPARATOR '/'    state at each age, but using a Gompertz model: log u =a + b*age .
 #endif    This is the basic analysis of mortality and should be done before any
     other analysis, in order to test if the mortality estimated from the
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    cross-longitudinal survey is different from the mortality estimated
 int erreur; /* Error number */    from other sources like vital statistic data.
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    The same imach parameter file can be used but the option for mle should be -3.
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Agnès, who wrote this part of the code, tried to keep most of the
 int ndeath=1; /* Number of dead states */    former routines in order to include the new code within the former code.
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    The output is very simple: only an estimate of the intercept and of
     the slope with 95% confident intervals.
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Current limitations:
 int jmin, jmax; /* min, max spacing between 2 waves */    A) Even if you enter covariates, i.e. with the
 int mle, weightopt;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    B) There is no computation of Life Expectancy nor Life Table.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.97  2004/02/20 13:25:42  lievre
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Version 0.96d. Population forecasting command line is (temporarily)
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    suppressed.
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    Revision 1.96  2003/07/15 15:38:55  brouard
 FILE *fichtm; /* Html File */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 FILE *ficreseij;    rewritten within the same printf. Workaround: many printfs.
 char filerese[FILENAMELENGTH];  
 FILE  *ficresvij;    Revision 1.95  2003/07/08 07:54:34  brouard
 char fileresv[FILENAMELENGTH];    * imach.c (Repository):
 FILE  *ficresvpl;    (Repository): Using imachwizard code to output a more meaningful covariance
 char fileresvpl[FILENAMELENGTH];    matrix (cov(a12,c31) instead of numbers.
 char title[MAXLINE];  
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    Revision 1.94  2003/06/27 13:00:02  brouard
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    Just cleaning
   
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    Revision 1.93  2003/06/25 16:33:55  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 char filerest[FILENAMELENGTH];    exist so I changed back to asctime which exists.
 char fileregp[FILENAMELENGTH];    (Module): Version 0.96b
 char popfile[FILENAMELENGTH];  
     Revision 1.92  2003/06/25 16:30:45  brouard
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.91  2003/06/25 15:30:29  brouard
 #define FTOL 1.0e-10    * imach.c (Repository): Duplicated warning errors corrected.
     (Repository): Elapsed time after each iteration is now output. It
 #define NRANSI    helps to forecast when convergence will be reached. Elapsed time
 #define ITMAX 200    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
 #define TOL 2.0e-4  
     Revision 1.90  2003/06/24 12:34:15  brouard
 #define CGOLD 0.3819660    (Module): Some bugs corrected for windows. Also, when
 #define ZEPS 1.0e-10    mle=-1 a template is output in file "or"mypar.txt with the design
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    of the covariance matrix to be input.
   
 #define GOLD 1.618034    Revision 1.89  2003/06/24 12:30:52  brouard
 #define GLIMIT 100.0    (Module): Some bugs corrected for windows. Also, when
 #define TINY 1.0e-20    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.88  2003/06/23 17:54:56  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    * 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 SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.87  2003/06/18 12:26:01  brouard
 #define rint(a) floor(a+0.5)    Version 0.96
   
 static double sqrarg;    Revision 1.86  2003/06/17 20:04:08  brouard
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    (Module): Change position of html and gnuplot routines and added
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    routine fileappend.
   
 int imx;    Revision 1.85  2003/06/17 13:12:43  brouard
 int stepm;    * imach.c (Repository): Check when date of death was earlier that
 /* Stepm, step in month: minimum step interpolation*/    current date of interview. It may happen when the death was just
     prior to the death. In this case, dh was negative and likelihood
 int estepm;    was wrong (infinity). We still send an "Error" but patch by
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    assuming that the date of death was just one stepm after the
     interview.
 int m,nb;    (Repository): Because some people have very long ID (first column)
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    we changed int to long in num[] and we added a new lvector for
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    memory allocation. But we also truncated to 8 characters (left
 double **pmmij, ***probs, ***mobaverage;    truncation)
 double dateintmean=0;    (Repository): No more line truncation errors.
   
 double *weight;    Revision 1.84  2003/06/13 21:44:43  brouard
 int **s; /* Status */    * imach.c (Repository): Replace "freqsummary" at a correct
 double *agedc, **covar, idx;    place. It differs from routine "prevalence" which may be called
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    many times. Probs is memory consuming and must be used with
     parcimony.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.83  2003/06/10 13:39:11  lievre
 /**************** split *************************/    *** empty log message ***
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.82  2003/06/05 15:57:20  brouard
    char *s;                             /* pointer */    Add log in  imach.c and  fullversion number is now printed.
    int  l1, l2;                         /* length counters */  
   */
    l1 = strlen( path );                 /* length of path */  /*
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );     Interpolated Markov Chain
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */    Short summary of the programme:
 #if     defined(__bsd__)                /* get current working directory */    
       extern char       *getwd( );    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
       if ( getwd( dirc ) == NULL ) {    first survey ("cross") where individuals from different ages are
 #else    interviewed on their health status or degree of disability (in the
       extern char       *getcwd( );    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    (if any) in individual health status.  Health expectancies are
 #endif    computed from the time spent in each health state according to a
          return( GLOCK_ERROR_GETCWD );    model. More health states you consider, more time is necessary to reach the
       }    Maximum Likelihood of the parameters involved in the model.  The
       strcpy( name, path );             /* we've got it */    simplest model is the multinomial logistic model where pij is the
    } else {                             /* strip direcotry from path */    probability to be observed in state j at the second wave
       s++;                              /* after this, the filename */    conditional to be observed in state i at the first wave. Therefore
       l2 = strlen( s );                 /* length of filename */    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    'age' is age and 'sex' is a covariate. If you want to have a more
       strcpy( name, s );                /* save file name */    complex model than "constant and age", you should modify the program
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    where the markup *Covariates have to be included here again* invites
       dirc[l1-l2] = 0;                  /* add zero */    you to do it.  More covariates you add, slower the
    }    convergence.
    l1 = strlen( dirc );                 /* length of directory */  
 #ifdef windows    The advantage of this computer programme, compared to a simple
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    multinomial logistic model, is clear when the delay between waves is not
 #else    identical for each individual. Also, if a individual missed an
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    intermediate interview, the information is lost, but taken into
 #endif    account using an interpolation or extrapolation.  
    s = strrchr( name, '.' );            /* find last / */  
    s++;    hPijx is the probability to be observed in state i at age x+h
    strcpy(ext,s);                       /* save extension */    conditional to the observed state i at age x. The delay 'h' can be
    l1= strlen( name);    split into an exact number (nh*stepm) of unobserved intermediate
    l2= strlen( s)+1;    states. This elementary transition (by month, quarter,
    strncpy( finame, name, l1-l2);    semester or year) is modelled as a multinomial logistic.  The hPx
    finame[l1-l2]= 0;    matrix is simply the matrix product of nh*stepm elementary matrices
    return( 0 );                         /* we're done */    and the contribution of each individual to the likelihood is simply
 }    hPijx.
   
     Also this programme outputs the covariance matrix of the parameters but also
 /******************************************/    of the life expectancies. It also computes the period (stable) prevalence. 
     
 void replace(char *s, char*t)    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 {             Institut national d'études démographiques, Paris.
   int i;    This software have been partly granted by Euro-REVES, a concerted action
   int lg=20;    from the European Union.
   i=0;    It is copyrighted identically to a GNU software product, ie programme and
   lg=strlen(t);    software can be distributed freely for non commercial use. Latest version
   for(i=0; i<= lg; i++) {    can be accessed at http://euroreves.ined.fr/imach .
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 }    
     **********************************************************************/
 int nbocc(char *s, char occ)  /*
 {    main
   int i,j=0;    read parameterfile
   int lg=20;    read datafile
   i=0;    concatwav
   lg=strlen(s);    freqsummary
   for(i=0; i<= lg; i++) {    if (mle >= 1)
   if  (s[i] == occ ) j++;      mlikeli
   }    print results files
   return j;    if mle==1 
 }       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 void cutv(char *u,char *v, char*t, char occ)        begin-prev-date,...
 {    open gnuplot file
   int i,lg,j,p=0;    open html file
   i=0;    period (stable) prevalence
   for(j=0; j<=strlen(t)-1; j++) {     for age prevalim()
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    h Pij x
   }    variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
   lg=strlen(t);    health expectancies
   for(j=0; j<p; j++) {    Variance-covariance of DFLE
     (u[j] = t[j]);    prevalence()
   }     movingaverage()
      u[p]='\0';    varevsij() 
     if popbased==1 varevsij(,popbased)
    for(j=0; j<= lg; j++) {    total life expectancies
     if (j>=(p+1))(v[j-p-1] = t[j]);    Variance of period (stable) prevalence
   }   end
 }  */
   
 /********************** nrerror ********************/  
   
 void nrerror(char error_text[])   
 {  #include <math.h>
   fprintf(stderr,"ERREUR ...\n");  #include <stdio.h>
   fprintf(stderr,"%s\n",error_text);  #include <stdlib.h>
   exit(1);  #include <string.h>
 }  #include <unistd.h>
 /*********************** vector *******************/  
 double *vector(int nl, int nh)  #include <limits.h>
 {  #include <sys/types.h>
   double *v;  #include <sys/stat.h>
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  #include <errno.h>
   if (!v) nrerror("allocation failure in vector");  extern int errno;
   return v-nl+NR_END;  
 }  /* #include <sys/time.h> */
   #include <time.h>
 /************************ free vector ******************/  #include "timeval.h"
 void free_vector(double*v, int nl, int nh)  
 {  /* #include <libintl.h> */
   free((FREE_ARG)(v+nl-NR_END));  /* #define _(String) gettext (String) */
 }  
   #define MAXLINE 256
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)  #define GNUPLOTPROGRAM "gnuplot"
 {  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   int *v;  #define FILENAMELENGTH 132
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   return v-nl+NR_END;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 }  
   #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 /******************free ivector **************************/  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 void free_ivector(int *v, long nl, long nh)  
 {  #define NINTERVMAX 8
   free((FREE_ARG)(v+nl-NR_END));  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 }  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   #define NCOVMAX 8 /* Maximum number of covariates */
 /******************* imatrix *******************************/  #define MAXN 20000
 int **imatrix(long nrl, long nrh, long ncl, long nch)  #define YEARM 12. /* Number of months per year */
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  #define AGESUP 130
 {  #define AGEBASE 40
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   int **m;  #ifdef UNIX
    #define DIRSEPARATOR '/'
   /* allocate pointers to rows */  #define CHARSEPARATOR "/"
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  #define ODIRSEPARATOR '\\'
   if (!m) nrerror("allocation failure 1 in matrix()");  #else
   m += NR_END;  #define DIRSEPARATOR '\\'
   m -= nrl;  #define CHARSEPARATOR "\\"
    #define ODIRSEPARATOR '/'
    #endif
   /* allocate rows and set pointers to them */  
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  /* $Id$ */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /* $State$ */
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  char version[]="Imach version 0.98d, March 2006, INED-EUROREVES-Institut de longevite ";
    char fullversion[]="$Revision$ $Date$"; 
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  char strstart[80];
    char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   /* return pointer to array of pointers to rows */  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   return m;  int nvar;
 }  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int npar=NPARMAX;
 /****************** free_imatrix *************************/  int nlstate=2; /* Number of live states */
 void free_imatrix(m,nrl,nrh,ncl,nch)  int ndeath=1; /* Number of dead states */
       int **m;  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       long nch,ncl,nrh,nrl;  int popbased=0;
      /* free an int matrix allocated by imatrix() */  
 {  int *wav; /* Number of waves for this individuual 0 is possible */
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  int maxwav; /* Maxim number of waves */
   free((FREE_ARG) (m+nrl-NR_END));  int jmin, jmax; /* min, max spacing between 2 waves */
 }  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
   int gipmx, gsw; /* Global variables on the number of contributions 
 /******************* matrix *******************************/                     to the likelihood and the sum of weights (done by funcone)*/
 double **matrix(long nrl, long nrh, long ncl, long nch)  int mle, weightopt;
 {  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   double **m;  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. */
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  double jmean; /* Mean space between 2 waves */
   if (!m) nrerror("allocation failure 1 in matrix()");  double **oldm, **newm, **savm; /* Working pointers to matrices */
   m += NR_END;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   m -= nrl;  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   FILE *ficlog, *ficrespow;
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  int globpr; /* Global variable for printing or not */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  double fretone; /* Only one call to likelihood */
   m[nrl] += NR_END;  long ipmx; /* Number of contributions */
   m[nrl] -= ncl;  double sw; /* Sum of weights */
   char filerespow[FILENAMELENGTH];
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   return m;  FILE *ficresilk;
 }  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   FILE *ficresprobmorprev;
 /*************************free matrix ************************/  FILE *fichtm, *fichtmcov; /* Html File */
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  FILE *ficreseij;
 {  char filerese[FILENAMELENGTH];
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  FILE *ficresstdeij;
   free((FREE_ARG)(m+nrl-NR_END));  char fileresstde[FILENAMELENGTH];
 }  FILE *ficrescveij;
   char filerescve[FILENAMELENGTH];
 /******************* ma3x *******************************/  FILE  *ficresvij;
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  char fileresv[FILENAMELENGTH];
 {  FILE  *ficresvpl;
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  char fileresvpl[FILENAMELENGTH];
   double ***m;  char title[MAXLINE];
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   if (!m) nrerror("allocation failure 1 in matrix()");  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   m += NR_END;  char command[FILENAMELENGTH];
   m -= nrl;  int  outcmd=0;
   
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  char filelog[FILENAMELENGTH]; /* Log file */
   m[nrl] -= ncl;  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  char popfile[FILENAMELENGTH];
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  
   m[nrl][ncl] += NR_END;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   m[nrl][ncl] -= nll;  struct timezone tzp;
   for (j=ncl+1; j<=nch; j++)  extern int gettimeofday();
     m[nrl][j]=m[nrl][j-1]+nlay;  struct tm tmg, tm, tmf, *gmtime(), *localtime();
    long time_value;
   for (i=nrl+1; i<=nrh; i++) {  extern long time();
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  char strcurr[80], strfor[80];
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;  char *endptr;
   }  long lval;
   return m;  
 }  #define NR_END 1
   #define FREE_ARG char*
 /*************************free ma3x ************************/  #define FTOL 1.0e-10
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  
 {  #define NRANSI 
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #define ITMAX 200 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define TOL 2.0e-4 
 }  
   #define CGOLD 0.3819660 
 /***************** f1dim *************************/  #define ZEPS 1.0e-10 
 extern int ncom;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 extern double *pcom,*xicom;  
 extern double (*nrfunc)(double []);  #define GOLD 1.618034 
    #define GLIMIT 100.0 
 double f1dim(double x)  #define TINY 1.0e-20 
 {  
   int j;  static double maxarg1,maxarg2;
   double f;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   double *xt;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
      
   xt=vector(1,ncom);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define rint(a) floor(a+0.5)
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  static double sqrarg;
   return f;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int agegomp= AGEGOMP;
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  int imx; 
 {  int stepm=1;
   int iter;  /* Stepm, step in month: minimum step interpolation*/
   double a,b,d,etemp;  
   double fu,fv,fw,fx;  int estepm;
   double ftemp;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;  int m,nb;
    long *num;
   a=(ax < cx ? ax : cx);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   b=(ax > cx ? ax : cx);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   x=w=v=bx;  double **pmmij, ***probs;
   fw=fv=fx=(*f)(x);  double *ageexmed,*agecens;
   for (iter=1;iter<=ITMAX;iter++) {  double dateintmean=0;
     xm=0.5*(a+b);  
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  double *weight;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  int **s; /* Status */
     printf(".");fflush(stdout);  double *agedc, **covar, idx;
 #ifdef DEBUG  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  double *lsurv, *lpop, *tpop;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  double ftolhess; /* Tolerance for computing hessian */
       *xmin=x;  
       return fx;  /**************** split *************************/
     }  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     ftemp=fu;  {
     if (fabs(e) > tol1) {    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       r=(x-w)*(fx-fv);       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       q=(x-v)*(fx-fw);    */ 
       p=(x-v)*q-(x-w)*r;    char  *ss;                            /* pointer */
       q=2.0*(q-r);    int   l1, l2;                         /* length counters */
       if (q > 0.0) p = -p;  
       q=fabs(q);    l1 = strlen(path );                   /* length of path */
       etemp=e;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       e=d;    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    if ( ss == NULL ) {                   /* no directory, so determine current directory */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));      strcpy( name, path );               /* we got the fullname name because no directory */
       else {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
         d=p/q;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
         u=x+d;      /* get current working directory */
         if (u-a < tol2 || b-u < tol2)      /*    extern  char* getcwd ( char *buf , int len);*/
           d=SIGN(tol1,xm-x);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       }        return( GLOCK_ERROR_GETCWD );
     } else {      }
       d=CGOLD*(e=(x >= xm ? a-x : b-x));      /* got dirc from getcwd*/
     }      printf(" DIRC = %s \n",dirc);
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    } else {                              /* strip direcotry from path */
     fu=(*f)(u);      ss++;                               /* after this, the filename */
     if (fu <= fx) {      l2 = strlen( ss );                  /* length of filename */
       if (u >= x) a=x; else b=x;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       SHFT(v,w,x,u)      strcpy( name, ss );         /* save file name */
         SHFT(fv,fw,fx,fu)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
         } else {      dirc[l1-l2] = 0;                    /* add zero */
           if (u < x) a=u; else b=u;      printf(" DIRC2 = %s \n",dirc);
           if (fu <= fw || w == x) {    }
             v=w;    /* We add a separator at the end of dirc if not exists */
             w=u;    l1 = strlen( dirc );                  /* length of directory */
             fv=fw;    if( dirc[l1-1] != DIRSEPARATOR ){
             fw=fu;      dirc[l1] =  DIRSEPARATOR;
           } else if (fu <= fv || v == x || v == w) {      dirc[l1+1] = 0; 
             v=u;      printf(" DIRC3 = %s \n",dirc);
             fv=fu;    }
           }    ss = strrchr( name, '.' );            /* find last / */
         }    if (ss >0){
   }      ss++;
   nrerror("Too many iterations in brent");      strcpy(ext,ss);                     /* save extension */
   *xmin=x;      l1= strlen( name);
   return fx;      l2= strlen(ss)+1;
 }      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
 /****************** mnbrak ***********************/    }
   
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    return( 0 );                          /* we're done */
             double (*func)(double))  }
 {  
   double ulim,u,r,q, dum;  
   double fu;  /******************************************/
    
   *fa=(*func)(*ax);  void replace_back_to_slash(char *s, char*t)
   *fb=(*func)(*bx);  {
   if (*fb > *fa) {    int i;
     SHFT(dum,*ax,*bx,dum)    int lg=0;
       SHFT(dum,*fb,*fa,dum)    i=0;
       }    lg=strlen(t);
   *cx=(*bx)+GOLD*(*bx-*ax);    for(i=0; i<= lg; i++) {
   *fc=(*func)(*cx);      (s[i] = t[i]);
   while (*fb > *fc) {      if (t[i]== '\\') s[i]='/';
     r=(*bx-*ax)*(*fb-*fc);    }
     q=(*bx-*cx)*(*fb-*fa);  }
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  int nbocc(char *s, char occ)
     ulim=(*bx)+GLIMIT*(*cx-*bx);  {
     if ((*bx-u)*(u-*cx) > 0.0) {    int i,j=0;
       fu=(*func)(u);    int lg=20;
     } else if ((*cx-u)*(u-ulim) > 0.0) {    i=0;
       fu=(*func)(u);    lg=strlen(s);
       if (fu < *fc) {    for(i=0; i<= lg; i++) {
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    if  (s[i] == occ ) j++;
           SHFT(*fb,*fc,fu,(*func)(u))    }
           }    return j;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  }
       u=ulim;  
       fu=(*func)(u);  void cutv(char *u,char *v, char*t, char occ)
     } else {  {
       u=(*cx)+GOLD*(*cx-*bx);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
       fu=(*func)(u);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
     }       gives u="abcedf" and v="ghi2j" */
     SHFT(*ax,*bx,*cx,u)    int i,lg,j,p=0;
       SHFT(*fa,*fb,*fc,fu)    i=0;
       }    for(j=0; j<=strlen(t)-1; j++) {
 }      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     }
 /*************** linmin ************************/  
     lg=strlen(t);
 int ncom;    for(j=0; j<p; j++) {
 double *pcom,*xicom;      (u[j] = t[j]);
 double (*nrfunc)(double []);    }
         u[p]='\0';
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {     for(j=0; j<= lg; j++) {
   double brent(double ax, double bx, double cx,      if (j>=(p+1))(v[j-p-1] = t[j]);
                double (*f)(double), double tol, double *xmin);    }
   double f1dim(double x);  }
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  
               double *fc, double (*func)(double));  /********************** nrerror ********************/
   int j;  
   double xx,xmin,bx,ax;  void nrerror(char error_text[])
   double fx,fb,fa;  {
      fprintf(stderr,"ERREUR ...\n");
   ncom=n;    fprintf(stderr,"%s\n",error_text);
   pcom=vector(1,n);    exit(EXIT_FAILURE);
   xicom=vector(1,n);  }
   nrfunc=func;  /*********************** vector *******************/
   for (j=1;j<=n;j++) {  double *vector(int nl, int nh)
     pcom[j]=p[j];  {
     xicom[j]=xi[j];    double *v;
   }    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   ax=0.0;    if (!v) nrerror("allocation failure in vector");
   xx=1.0;    return v-nl+NR_END;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  }
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  /************************ free vector ******************/
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  void free_vector(double*v, int nl, int nh)
 #endif  {
   for (j=1;j<=n;j++) {    free((FREE_ARG)(v+nl-NR_END));
     xi[j] *= xmin;  }
     p[j] += xi[j];  
   }  /************************ivector *******************************/
   free_vector(xicom,1,n);  int *ivector(long nl,long nh)
   free_vector(pcom,1,n);  {
 }    int *v;
     v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
 /*************** powell ************************/    if (!v) nrerror("allocation failure in ivector");
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    return v-nl+NR_END;
             double (*func)(double []))  }
 {  
   void linmin(double p[], double xi[], int n, double *fret,  /******************free ivector **************************/
               double (*func)(double []));  void free_ivector(int *v, long nl, long nh)
   int i,ibig,j;  {
   double del,t,*pt,*ptt,*xit;    free((FREE_ARG)(v+nl-NR_END));
   double fp,fptt;  }
   double *xits;  
   pt=vector(1,n);  /************************lvector *******************************/
   ptt=vector(1,n);  long *lvector(long nl,long nh)
   xit=vector(1,n);  {
   xits=vector(1,n);    long *v;
   *fret=(*func)(p);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   for (j=1;j<=n;j++) pt[j]=p[j];    if (!v) nrerror("allocation failure in ivector");
   for (*iter=1;;++(*iter)) {    return v-nl+NR_END;
     fp=(*fret);  }
     ibig=0;  
     del=0.0;  /******************free lvector **************************/
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  void free_lvector(long *v, long nl, long nh)
     for (i=1;i<=n;i++)  {
       printf(" %d %.12f",i, p[i]);    free((FREE_ARG)(v+nl-NR_END));
     printf("\n");  }
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  /******************* imatrix *******************************/
       fptt=(*fret);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
 #ifdef DEBUG       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       printf("fret=%lf \n",*fret);  { 
 #endif    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       printf("%d",i);fflush(stdout);    int **m; 
       linmin(p,xit,n,fret,func);    
       if (fabs(fptt-(*fret)) > del) {    /* allocate pointers to rows */ 
         del=fabs(fptt-(*fret));    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
         ibig=i;    if (!m) nrerror("allocation failure 1 in matrix()"); 
       }    m += NR_END; 
 #ifdef DEBUG    m -= nrl; 
       printf("%d %.12e",i,(*fret));    
       for (j=1;j<=n;j++) {    
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    /* allocate rows and set pointers to them */ 
         printf(" x(%d)=%.12e",j,xit[j]);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       for(j=1;j<=n;j++)    m[nrl] += NR_END; 
         printf(" p=%.12e",p[j]);    m[nrl] -= ncl; 
       printf("\n");    
 #endif    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     }    
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    /* return pointer to array of pointers to rows */ 
 #ifdef DEBUG    return m; 
       int k[2],l;  } 
       k[0]=1;  
       k[1]=-1;  /****************** free_imatrix *************************/
       printf("Max: %.12e",(*func)(p));  void free_imatrix(m,nrl,nrh,ncl,nch)
       for (j=1;j<=n;j++)        int **m;
         printf(" %.12e",p[j]);        long nch,ncl,nrh,nrl; 
       printf("\n");       /* free an int matrix allocated by imatrix() */ 
       for(l=0;l<=1;l++) {  { 
         for (j=1;j<=n;j++) {    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    free((FREE_ARG) (m+nrl-NR_END)); 
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  } 
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  /******************* matrix *******************************/
       }  double **matrix(long nrl, long nrh, long ncl, long nch)
 #endif  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     double **m;
       free_vector(xit,1,n);  
       free_vector(xits,1,n);    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       free_vector(ptt,1,n);    if (!m) nrerror("allocation failure 1 in matrix()");
       free_vector(pt,1,n);    m += NR_END;
       return;    m -= nrl;
     }  
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    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()");
       ptt[j]=2.0*p[j]-pt[j];    m[nrl] += NR_END;
       xit[j]=p[j]-pt[j];    m[nrl] -= ncl;
       pt[j]=p[j];  
     }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     fptt=(*func)(ptt);    return m;
     if (fptt < fp) {    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);     */
       if (t < 0.0) {  }
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {  /*************************free matrix ************************/
           xi[j][ibig]=xi[j][n];  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
           xi[j][n]=xit[j];  {
         }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 #ifdef DEBUG    free((FREE_ARG)(m+nrl-NR_END));
         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]);  /******************* ma3x *******************************/
         printf("\n");  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
 #endif  {
       }    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     }    double ***m;
   }  
 }    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
 /**** Prevalence limit ****************/    m += NR_END;
     m -= nrl;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  
 {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
      matrix by transitions matrix until convergence is reached */    m[nrl] += NR_END;
     m[nrl] -= ncl;
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   double **matprod2();  
   double **out, cov[NCOVMAX], **pmij();    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   double **newm;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   double agefin, delaymax=50 ; /* Max number of years to converge */    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
   for (ii=1;ii<=nlstate+ndeath;ii++)    for (j=ncl+1; j<=nch; j++) 
     for (j=1;j<=nlstate+ndeath;j++){      m[nrl][j]=m[nrl][j-1]+nlay;
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    
     }    for (i=nrl+1; i<=nrh; i++) {
       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
    cov[1]=1.;      for (j=ncl+1; j<=nch; j++) 
          m[i][j]=m[i][j-1]+nlay;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    }
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    return m; 
     newm=savm;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     /* Covariates have to be included here again */             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
      cov[2]=agefin;    */
    }
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /*************************free ma3x ************************/
         /*      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]]);*/  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       }  {
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
       for (k=1; k<=cptcovprod;k++)    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    free((FREE_ARG)(m+nrl-NR_END));
   }
       /*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]);*/  /*************** function subdirf ***********/
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  char *subdirf(char fileres[])
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  {
     /* Caution optionfilefiname is hidden */
     savm=oldm;    strcpy(tmpout,optionfilefiname);
     oldm=newm;    strcat(tmpout,"/"); /* Add to the right */
     maxmax=0.;    strcat(tmpout,fileres);
     for(j=1;j<=nlstate;j++){    return tmpout;
       min=1.;  }
       max=0.;  
       for(i=1; i<=nlstate; i++) {  /*************** function subdirf2 ***********/
         sumnew=0;  char *subdirf2(char fileres[], char *preop)
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  {
         prlim[i][j]= newm[i][j]/(1-sumnew);    
         max=FMAX(max,prlim[i][j]);    /* Caution optionfilefiname is hidden */
         min=FMIN(min,prlim[i][j]);    strcpy(tmpout,optionfilefiname);
       }    strcat(tmpout,"/");
       maxmin=max-min;    strcat(tmpout,preop);
       maxmax=FMAX(maxmax,maxmin);    strcat(tmpout,fileres);
     }    return tmpout;
     if(maxmax < ftolpl){  }
       return prlim;  
     }  /*************** function subdirf3 ***********/
   }  char *subdirf3(char fileres[], char *preop, char *preop2)
 }  {
     
 /*************** transition probabilities ***************/    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    strcat(tmpout,"/");
 {    strcat(tmpout,preop);
   double s1, s2;    strcat(tmpout,preop2);
   /*double t34;*/    strcat(tmpout,fileres);
   int i,j,j1, nc, ii, jj;    return tmpout;
   }
     for(i=1; i<= nlstate; i++){  
     for(j=1; j<i;j++){  /***************** f1dim *************************/
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  extern int ncom; 
         /*s2 += param[i][j][nc]*cov[nc];*/  extern double *pcom,*xicom;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  extern double (*nrfunc)(double []); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/   
       }  double f1dim(double x) 
       ps[i][j]=s2;  { 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    int j; 
     }    double f;
     for(j=i+1; j<=nlstate+ndeath;j++){    double *xt; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){   
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    xt=vector(1,ncom); 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       }    f=(*nrfunc)(xt); 
       ps[i][j]=s2;    free_vector(xt,1,ncom); 
     }    return f; 
   }  } 
     /*ps[3][2]=1;*/  
   /*****************brent *************************/
   for(i=1; i<= nlstate; i++){  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
      s1=0;  { 
     for(j=1; j<i; j++)    int iter; 
       s1+=exp(ps[i][j]);    double a,b,d,etemp;
     for(j=i+1; j<=nlstate+ndeath; j++)    double fu,fv,fw,fx;
       s1+=exp(ps[i][j]);    double ftemp;
     ps[i][i]=1./(s1+1.);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     for(j=1; j<i; j++)    double e=0.0; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];   
     for(j=i+1; j<=nlstate+ndeath; j++)    a=(ax < cx ? ax : cx); 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    b=(ax > cx ? ax : cx); 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    x=w=v=bx; 
   } /* end i */    fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      xm=0.5*(a+b); 
     for(jj=1; jj<= nlstate+ndeath; jj++){      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       ps[ii][jj]=0;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       ps[ii][ii]=1;      printf(".");fflush(stdout);
     }      fprintf(ficlog,".");fflush(ficlog);
   }  #ifdef DEBUG
       printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       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);
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     for(jj=1; jj<= nlstate+ndeath; jj++){  #endif
      printf("%lf ",ps[ii][jj]);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
    }        *xmin=x; 
     printf("\n ");        return fx; 
     }      } 
     printf("\n ");printf("%lf ",cov[2]);*/      ftemp=fu;
 /*      if (fabs(e) > tol1) { 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        r=(x-w)*(fx-fv); 
   goto end;*/        q=(x-v)*(fx-fw); 
     return ps;        p=(x-v)*q-(x-w)*r; 
 }        q=2.0*(q-r); 
         if (q > 0.0) p = -p; 
 /**************** Product of 2 matrices ******************/        q=fabs(q); 
         etemp=e; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)        e=d; 
 {        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */        else { 
   /* in, b, out are matrice of pointers which should have been initialized          d=p/q; 
      before: only the contents of out is modified. The function returns          u=x+d; 
      a pointer to pointers identical to out */          if (u-a < tol2 || b-u < tol2) 
   long i, j, k;            d=SIGN(tol1,xm-x); 
   for(i=nrl; i<= nrh; i++)        } 
     for(k=ncolol; k<=ncoloh; k++)      } else { 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         out[i][k] +=in[i][j]*b[j][k];      } 
       u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   return out;      fu=(*f)(u); 
 }      if (fu <= fx) { 
         if (u >= x) a=x; else b=x; 
         SHFT(v,w,x,u) 
 /************* Higher Matrix Product ***************/          SHFT(fv,fw,fx,fu) 
           } else { 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )            if (u < x) a=u; else b=u; 
 {            if (fu <= fw || w == x) { 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month              v=w; 
      duration (i.e. until              w=u; 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.              fv=fw; 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step              fw=fu; 
      (typically every 2 years instead of every month which is too big).            } else if (fu <= fv || v == x || v == w) { 
      Model is determined by parameters x and covariates have to be              v=u; 
      included manually here.              fv=fu; 
             } 
      */          } 
     } 
   int i, j, d, h, k;    nrerror("Too many iterations in brent"); 
   double **out, cov[NCOVMAX];    *xmin=x; 
   double **newm;    return fx; 
   } 
   /* Hstepm could be zero and should return the unit matrix */  
   for (i=1;i<=nlstate+ndeath;i++)  /****************** mnbrak ***********************/
     for (j=1;j<=nlstate+ndeath;j++){  
       oldm[i][j]=(i==j ? 1.0 : 0.0);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       po[i][j][0]=(i==j ? 1.0 : 0.0);              double (*func)(double)) 
     }  { 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    double ulim,u,r,q, dum;
   for(h=1; h <=nhstepm; h++){    double fu; 
     for(d=1; d <=hstepm; d++){   
       newm=savm;    *fa=(*func)(*ax); 
       /* Covariates have to be included here again */    *fb=(*func)(*bx); 
       cov[1]=1.;    if (*fb > *fa) { 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      SHFT(dum,*ax,*bx,dum) 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];        SHFT(dum,*fb,*fa,dum) 
       for (k=1; k<=cptcovage;k++)        } 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    *cx=(*bx)+GOLD*(*bx-*ax); 
       for (k=1; k<=cptcovprod;k++)    *fc=(*func)(*cx); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
       q=(*bx-*cx)*(*fb-*fa); 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,      ulim=(*bx)+GLIMIT*(*cx-*bx); 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      if ((*bx-u)*(u-*cx) > 0.0) { 
       savm=oldm;        fu=(*func)(u); 
       oldm=newm;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     }        fu=(*func)(u); 
     for(i=1; i<=nlstate+ndeath; i++)        if (fu < *fc) { 
       for(j=1;j<=nlstate+ndeath;j++) {          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
         po[i][j][h]=newm[i][j];            SHFT(*fb,*fc,fu,(*func)(u)) 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);            } 
          */      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       }        u=ulim; 
   } /* end h */        fu=(*func)(u); 
   return po;      } else { 
 }        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
       } 
 /*************** log-likelihood *************/      SHFT(*ax,*bx,*cx,u) 
 double func( double *x)        SHFT(*fa,*fb,*fc,fu) 
 {        } 
   int i, ii, j, k, mi, d, kk;  } 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;  /*************** linmin ************************/
   double sw; /* Sum of weights */  
   double lli; /* Individual log likelihood */  int ncom; 
   long ipmx;  double *pcom,*xicom;
   /*extern weight */  double (*nrfunc)(double []); 
   /* We are differentiating ll according to initial status */   
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   /*for(i=1;i<imx;i++)  { 
     printf(" %d\n",s[4][i]);    double brent(double ax, double bx, double cx, 
   */                 double (*f)(double), double tol, double *xmin); 
   cov[1]=1.;    double f1dim(double x); 
     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   for(k=1; k<=nlstate; k++) ll[k]=0.;                double *fc, double (*func)(double)); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    int j; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    double xx,xmin,bx,ax; 
     for(mi=1; mi<= wav[i]-1; mi++){    double fx,fb,fa;
       for (ii=1;ii<=nlstate+ndeath;ii++)   
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    ncom=n; 
       for(d=0; d<dh[mi][i]; d++){    pcom=vector(1,n); 
         newm=savm;    xicom=vector(1,n); 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    nrfunc=func; 
         for (kk=1; kk<=cptcovage;kk++) {    for (j=1;j<=n;j++) { 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      pcom[j]=p[j]; 
         }      xicom[j]=xi[j]; 
            } 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    ax=0.0; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    xx=1.0; 
         savm=oldm;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
         oldm=newm;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
          #ifdef DEBUG
            printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       } /* end mult */    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
        #endif
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    for (j=1;j<=n;j++) { 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      xi[j] *= xmin; 
       ipmx +=1;      p[j] += xi[j]; 
       sw += weight[i];    } 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    free_vector(xicom,1,n); 
     } /* end of wave */    free_vector(pcom,1,n); 
   } /* end of individual */  } 
   
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  char *asc_diff_time(long time_sec, char ascdiff[])
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  {
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    long sec_left, days, hours, minutes;
   return -l;    days = (time_sec) / (60*60*24);
 }    sec_left = (time_sec) % (60*60*24);
     hours = (sec_left) / (60*60) ;
     sec_left = (sec_left) %(60*60);
 /*********** Maximum Likelihood Estimation ***************/    minutes = (sec_left) /60;
     sec_left = (sec_left) % (60);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
 {    return ascdiff;
   int i,j, iter;  }
   double **xi,*delti;  
   double fret;  /*************** powell ************************/
   xi=matrix(1,npar,1,npar);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   for (i=1;i<=npar;i++)              double (*func)(double [])) 
     for (j=1;j<=npar;j++)  { 
       xi[i][j]=(i==j ? 1.0 : 0.0);    void linmin(double p[], double xi[], int n, double *fret, 
   printf("Powell\n");                double (*func)(double [])); 
   powell(p,xi,npar,ftol,&iter,&fret,func);    int i,ibig,j; 
     double del,t,*pt,*ptt,*xit;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    double fp,fptt;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    double *xits;
     int niterf, itmp;
 }  
     pt=vector(1,n); 
 /**** Computes Hessian and covariance matrix ***/    ptt=vector(1,n); 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    xit=vector(1,n); 
 {    xits=vector(1,n); 
   double  **a,**y,*x,pd;    *fret=(*func)(p); 
   double **hess;    for (j=1;j<=n;j++) pt[j]=p[j]; 
   int i, j,jk;    for (*iter=1;;++(*iter)) { 
   int *indx;      fp=(*fret); 
       ibig=0; 
   double hessii(double p[], double delta, int theta, double delti[]);      del=0.0; 
   double hessij(double p[], double delti[], int i, int j);      last_time=curr_time;
   void lubksb(double **a, int npar, int *indx, double b[]) ;      (void) gettimeofday(&curr_time,&tzp);
   void ludcmp(double **a, int npar, int *indx, double *d) ;      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
       /*    fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);
   hess=matrix(1,npar,1,npar);      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
       */
   printf("\nCalculation of the hessian matrix. Wait...\n");     for (i=1;i<=n;i++) {
   for (i=1;i<=npar;i++){        printf(" %d %.12f",i, p[i]);
     printf("%d",i);fflush(stdout);        fprintf(ficlog," %d %.12lf",i, p[i]);
     hess[i][i]=hessii(p,ftolhess,i,delti);        fprintf(ficrespow," %.12lf", p[i]);
     /*printf(" %f ",p[i]);*/      }
     /*printf(" %lf ",hess[i][i]);*/      printf("\n");
   }      fprintf(ficlog,"\n");
        fprintf(ficrespow,"\n");fflush(ficrespow);
   for (i=1;i<=npar;i++) {      if(*iter <=3){
     for (j=1;j<=npar;j++)  {        tm = *localtime(&curr_time.tv_sec);
       if (j>i) {        strcpy(strcurr,asctime(&tm));
         printf(".%d%d",i,j);fflush(stdout);  /*       asctime_r(&tm,strcurr); */
         hess[i][j]=hessij(p,delti,i,j);        forecast_time=curr_time; 
         hess[j][i]=hess[i][j];            itmp = strlen(strcurr);
         /*printf(" %lf ",hess[i][j]);*/        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       }          strcurr[itmp-1]='\0';
     }        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   }        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   printf("\n");        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);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");          tmf = *localtime(&forecast_time.tv_sec);
    /*      asctime_r(&tmf,strfor); */
   a=matrix(1,npar,1,npar);          strcpy(strfor,asctime(&tmf));
   y=matrix(1,npar,1,npar);          itmp = strlen(strfor);
   x=vector(1,npar);          if(strfor[itmp-1]=='\n')
   indx=ivector(1,npar);          strfor[itmp-1]='\0';
   for (i=1;i<=npar;i++)          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);
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          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);
   ludcmp(a,npar,indx,&pd);        }
       }
   for (j=1;j<=npar;j++) {      for (i=1;i<=n;i++) { 
     for (i=1;i<=npar;i++) x[i]=0;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     x[j]=1;        fptt=(*fret); 
     lubksb(a,npar,indx,x);  #ifdef DEBUG
     for (i=1;i<=npar;i++){        printf("fret=%lf \n",*fret);
       matcov[i][j]=x[i];        fprintf(ficlog,"fret=%lf \n",*fret);
     }  #endif
   }        printf("%d",i);fflush(stdout);
         fprintf(ficlog,"%d",i);fflush(ficlog);
   printf("\n#Hessian matrix#\n");        linmin(p,xit,n,fret,func); 
   for (i=1;i<=npar;i++) {        if (fabs(fptt-(*fret)) > del) { 
     for (j=1;j<=npar;j++) {          del=fabs(fptt-(*fret)); 
       printf("%.3e ",hess[i][j]);          ibig=i; 
     }        } 
     printf("\n");  #ifdef DEBUG
   }        printf("%d %.12e",i,(*fret));
         fprintf(ficlog,"%d %.12e",i,(*fret));
   /* Recompute Inverse */        for (j=1;j<=n;j++) {
   for (i=1;i<=npar;i++)          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];          printf(" x(%d)=%.12e",j,xit[j]);
   ludcmp(a,npar,indx,&pd);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         }
   /*  printf("\n#Hessian matrix recomputed#\n");        for(j=1;j<=n;j++) {
           printf(" p=%.12e",p[j]);
   for (j=1;j<=npar;j++) {          fprintf(ficlog," p=%.12e",p[j]);
     for (i=1;i<=npar;i++) x[i]=0;        }
     x[j]=1;        printf("\n");
     lubksb(a,npar,indx,x);        fprintf(ficlog,"\n");
     for (i=1;i<=npar;i++){  #endif
       y[i][j]=x[i];      } 
       printf("%.3e ",y[i][j]);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     }  #ifdef DEBUG
     printf("\n");        int k[2],l;
   }        k[0]=1;
   */        k[1]=-1;
         printf("Max: %.12e",(*func)(p));
   free_matrix(a,1,npar,1,npar);        fprintf(ficlog,"Max: %.12e",(*func)(p));
   free_matrix(y,1,npar,1,npar);        for (j=1;j<=n;j++) {
   free_vector(x,1,npar);          printf(" %.12e",p[j]);
   free_ivector(indx,1,npar);          fprintf(ficlog," %.12e",p[j]);
   free_matrix(hess,1,npar,1,npar);        }
         printf("\n");
         fprintf(ficlog,"\n");
 }        for(l=0;l<=1;l++) {
           for (j=1;j<=n;j++) {
 /*************** hessian matrix ****************/            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
 double hessii( double x[], double delta, int theta, double delti[])            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
 {            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   int i;          }
   int l=1, lmax=20;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   double k1,k2;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   double p2[NPARMAX+1];        }
   double res;  #endif
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  
   double fx;  
   int k=0,kmax=10;        free_vector(xit,1,n); 
   double l1;        free_vector(xits,1,n); 
         free_vector(ptt,1,n); 
   fx=func(x);        free_vector(pt,1,n); 
   for (i=1;i<=npar;i++) p2[i]=x[i];        return; 
   for(l=0 ; l <=lmax; l++){      } 
     l1=pow(10,l);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     delts=delt;      for (j=1;j<=n;j++) { 
     for(k=1 ; k <kmax; k=k+1){        ptt[j]=2.0*p[j]-pt[j]; 
       delt = delta*(l1*k);        xit[j]=p[j]-pt[j]; 
       p2[theta]=x[theta] +delt;        pt[j]=p[j]; 
       k1=func(p2)-fx;      } 
       p2[theta]=x[theta]-delt;      fptt=(*func)(ptt); 
       k2=func(p2)-fx;      if (fptt < fp) { 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        if (t < 0.0) { 
                linmin(p,xit,n,fret,func); 
 #ifdef DEBUG          for (j=1;j<=n;j++) { 
       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);            xi[j][ibig]=xi[j][n]; 
 #endif            xi[j][n]=xit[j]; 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          }
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  #ifdef DEBUG
         k=kmax;          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);
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */          for(j=1;j<=n;j++){
         k=kmax; l=lmax*10.;            printf(" %.12e",xit[j]);
       }            fprintf(ficlog," %.12e",xit[j]);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){          }
         delts=delt;          printf("\n");
       }          fprintf(ficlog,"\n");
     }  #endif
   }        }
   delti[theta]=delts;      } 
   return res;    } 
    } 
 }  
   /**** Prevalence limit (stable or period prevalence)  ****************/
 double hessij( double x[], double delti[], int thetai,int thetaj)  
 {  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   int i;  {
   int l=1, l1, lmax=20;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   double k1,k2,k3,k4,res,fx;       matrix by transitions matrix until convergence is reached */
   double p2[NPARMAX+1];  
   int k;    int i, ii,j,k;
     double min, max, maxmin, maxmax,sumnew=0.;
   fx=func(x);    double **matprod2();
   for (k=1; k<=2; k++) {    double **out, cov[NCOVMAX], **pmij();
     for (i=1;i<=npar;i++) p2[i]=x[i];    double **newm;
     p2[thetai]=x[thetai]+delti[thetai]/k;    double agefin, delaymax=50 ; /* Max number of years to converge */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k1=func(p2)-fx;    for (ii=1;ii<=nlstate+ndeath;ii++)
        for (j=1;j<=nlstate+ndeath;j++){
     p2[thetai]=x[thetai]+delti[thetai]/k;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      }
     k2=func(p2)-fx;  
       cov[1]=1.;
     p2[thetai]=x[thetai]-delti[thetai]/k;   
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     k3=func(p2)-fx;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
        newm=savm;
     p2[thetai]=x[thetai]-delti[thetai]/k;      /* Covariates have to be included here again */
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;       cov[2]=agefin;
     k4=func(p2)-fx;    
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        for (k=1; k<=cptcovn;k++) {
 #ifdef DEBUG          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
     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);          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
 #endif        }
   }        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]]];
   
 /************** Inverse of matrix **************/        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
 void ludcmp(double **a, int n, int *indx, double *d)        /*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,imax,j,k;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   double big,dum,sum,temp;  
   double *vv;      savm=oldm;
        oldm=newm;
   vv=vector(1,n);      maxmax=0.;
   *d=1.0;      for(j=1;j<=nlstate;j++){
   for (i=1;i<=n;i++) {        min=1.;
     big=0.0;        max=0.;
     for (j=1;j<=n;j++)        for(i=1; i<=nlstate; i++) {
       if ((temp=fabs(a[i][j])) > big) big=temp;          sumnew=0;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     vv[i]=1.0/big;          prlim[i][j]= newm[i][j]/(1-sumnew);
   }          max=FMAX(max,prlim[i][j]);
   for (j=1;j<=n;j++) {          min=FMIN(min,prlim[i][j]);
     for (i=1;i<j;i++) {        }
       sum=a[i][j];        maxmin=max-min;
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        maxmax=FMAX(maxmax,maxmin);
       a[i][j]=sum;      }
     }      if(maxmax < ftolpl){
     big=0.0;        return prlim;
     for (i=j;i<=n;i++) {      }
       sum=a[i][j];    }
       for (k=1;k<j;k++)  }
         sum -= a[i][k]*a[k][j];  
       a[i][j]=sum;  /*************** transition probabilities ***************/ 
       if ( (dum=vv[i]*fabs(sum)) >= big) {  
         big=dum;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         imax=i;  {
       }    double s1, s2;
     }    /*double t34;*/
     if (j != imax) {    int i,j,j1, nc, ii, jj;
       for (k=1;k<=n;k++) {  
         dum=a[imax][k];      for(i=1; i<= nlstate; i++){
         a[imax][k]=a[j][k];        for(j=1; j<i;j++){
         a[j][k]=dum;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
       }            /*s2 += param[i][j][nc]*cov[nc];*/
       *d = -(*d);            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
       vv[imax]=vv[j];  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
     }          }
     indx[j]=imax;          ps[i][j]=s2;
     if (a[j][j] == 0.0) a[j][j]=TINY;  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
     if (j != n) {        }
       dum=1.0/(a[j][j]);        for(j=i+1; j<=nlstate+ndeath;j++){
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     }            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   }  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
   free_vector(vv,1,n);  /* Doesn't work */          }
 ;          ps[i][j]=s2;
 }        }
       }
 void lubksb(double **a, int n, int *indx, double b[])      /*ps[3][2]=1;*/
 {      
   int i,ii=0,ip,j;      for(i=1; i<= nlstate; i++){
   double sum;        s1=0;
          for(j=1; j<i; j++)
   for (i=1;i<=n;i++) {          s1+=exp(ps[i][j]);
     ip=indx[i];        for(j=i+1; j<=nlstate+ndeath; j++)
     sum=b[ip];          s1+=exp(ps[i][j]);
     b[ip]=b[i];        ps[i][i]=1./(s1+1.);
     if (ii)        for(j=1; j<i; j++)
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          ps[i][j]= exp(ps[i][j])*ps[i][i];
     else if (sum) ii=i;        for(j=i+1; j<=nlstate+ndeath; j++)
     b[i]=sum;          ps[i][j]= exp(ps[i][j])*ps[i][i];
   }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   for (i=n;i>=1;i--) {      } /* end i */
     sum=b[i];      
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     b[i]=sum/a[i][i];        for(jj=1; jj<= nlstate+ndeath; jj++){
   }          ps[ii][jj]=0;
 }          ps[ii][ii]=1;
         }
 /************ Frequencies ********************/      }
 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 */  
    /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   double ***freq; /* Frequencies */  /*         printf("ddd %lf ",ps[ii][jj]); */
   double *pp;  /*       } */
   double pos, k2, dateintsum=0,k2cpt=0;  /*       printf("\n "); */
   FILE *ficresp;  /*        } */
   char fileresp[FILENAMELENGTH];  /*        printf("\n ");printf("%lf ",cov[2]); */
           /*
   pp=vector(1,nlstate);        for(i=1; i<= npar; i++) printf("%f ",x[i]);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        goto end;*/
   strcpy(fileresp,"p");      return ps;
   strcat(fileresp,fileres);  }
   if((ficresp=fopen(fileresp,"w"))==NULL) {  
     printf("Problem with prevalence resultfile: %s\n", fileresp);  /**************** Product of 2 matrices ******************/
     exit(0);  
   }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  {
   j1=0;    /* 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(...) */
   j=cptcoveff;    /* in, b, out are matrice of pointers which should have been initialized 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}       before: only the contents of out is modified. The function returns
         a pointer to pointers identical to out */
   for(k1=1; k1<=j;k1++){    long i, j, k;
     for(i1=1; i1<=ncodemax[k1];i1++){    for(i=nrl; i<= nrh; i++)
       j1++;      for(k=ncolol; k<=ncoloh; k++)
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
         scanf("%d", i);*/          out[i][k] +=in[i][j]*b[j][k];
       for (i=-1; i<=nlstate+ndeath; i++)    
         for (jk=-1; jk<=nlstate+ndeath; jk++)      return out;
           for(m=agemin; m <= agemax+3; m++)  }
             freq[i][jk][m]=0;  
        
       dateintsum=0;  /************* Higher Matrix Product ***************/
       k2cpt=0;  
       for (i=1; i<=imx; i++) {  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
         bool=1;  {
         if  (cptcovn>0) {    /* Computes the transition matrix starting at age 'age' over 
           for (z1=1; z1<=cptcoveff; z1++)       'nhstepm*hstepm*stepm' months (i.e. until
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
               bool=0;       nhstepm*hstepm matrices. 
         }       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         if (bool==1) {       (typically every 2 years instead of every month which is too big 
           for(m=firstpass; m<=lastpass; m++){       for the memory).
             k2=anint[m][i]+(mint[m][i]/12.);       Model is determined by parameters x and covariates have to be 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {       included manually here. 
               if(agev[m][i]==0) agev[m][i]=agemax+1;  
               if(agev[m][i]==1) agev[m][i]=agemax+2;       */
               if (m<lastpass) {  
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    int i, j, d, h, k;
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    double **out, cov[NCOVMAX];
               }    double **newm;
                
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {    /* Hstepm could be zero and should return the unit matrix */
                 dateintsum=dateintsum+k2;    for (i=1;i<=nlstate+ndeath;i++)
                 k2cpt++;      for (j=1;j<=nlstate+ndeath;j++){
               }        oldm[i][j]=(i==j ? 1.0 : 0.0);
             }        po[i][j][0]=(i==j ? 1.0 : 0.0);
           }      }
         }    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       }    for(h=1; h <=nhstepm; h++){
              for(d=1; d <=hstepm; d++){
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        newm=savm;
         /* Covariates have to be included here again */
       if  (cptcovn>0) {        cov[1]=1.;
         fprintf(ficresp, "\n#********** Variable ");        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         fprintf(ficresp, "**********\n#");        for (k=1; k<=cptcovage;k++)
       }          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       for(i=1; i<=nlstate;i++)        for (k=1; k<=cptcovprod;k++)
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       fprintf(ficresp, "\n");  
        
       for(i=(int)agemin; i <= (int)agemax+3; i++){        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
         if(i==(int)agemax+3)        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           printf("Total");        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         else                     pmij(pmmij,cov,ncovmodel,x,nlstate));
           printf("Age %d", i);        savm=oldm;
         for(jk=1; jk <=nlstate ; jk++){        oldm=newm;
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      }
             pp[jk] += freq[jk][m][i];      for(i=1; i<=nlstate+ndeath; i++)
         }        for(j=1;j<=nlstate+ndeath;j++) {
         for(jk=1; jk <=nlstate ; jk++){          po[i][j][h]=newm[i][j];
           for(m=-1, pos=0; m <=0 ; m++)          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
             pos += freq[jk][m][i];           */
           if(pp[jk]>=1.e-10)        }
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);    } /* end h */
           else    return po;
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  }
         }  
   
         for(jk=1; jk <=nlstate ; jk++){  /*************** log-likelihood *************/
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  double func( double *x)
             pp[jk] += freq[jk][m][i];  {
         }    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX], cov[NCOVMAX];
         for(jk=1,pos=0; jk <=nlstate ; jk++)    double **out;
           pos += pp[jk];    double sw; /* Sum of weights */
         for(jk=1; jk <=nlstate ; jk++){    double lli; /* Individual log likelihood */
           if(pos>=1.e-5)    int s1, s2;
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    double bbh, survp;
           else    long ipmx;
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    /*extern weight */
           if( i <= (int) agemax){    /* We are differentiating ll according to initial status */
             if(pos>=1.e-5){    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    /*for(i=1;i<imx;i++) 
               probs[i][jk][j1]= pp[jk]/pos;      printf(" %d\n",s[4][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]);*/    */
             }    cov[1]=1.;
             else  
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    for(k=1; k<=nlstate; k++) ll[k]=0.;
           }  
         }    if(mle==1){
              for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for(jk=-1; jk <=nlstate+ndeath; jk++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           for(m=-1; m <=nlstate+ndeath; m++)        for(mi=1; mi<= wav[i]-1; mi++){
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          for (ii=1;ii<=nlstate+ndeath;ii++)
         if(i <= (int) agemax)            for (j=1;j<=nlstate+ndeath;j++){
           fprintf(ficresp,"\n");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         printf("\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
     }          for(d=0; d<dh[mi][i]; d++){
   }            newm=savm;
   dateintmean=dateintsum/k2cpt;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
   fclose(ficresp);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);            }
   free_vector(pp,1,nlstate);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* End of Freq */            savm=oldm;
 }            oldm=newm;
           } /* end mult */
 /************ Prevalence ********************/        
 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)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
 {  /* Some frequencies */          /* But now since version 0.9 we anticipate for bias at large stepm.
             * If stepm is larger than one month (smallest stepm) and if the exact delay 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;           * (in months) between two waves is not a multiple of stepm, we rounded to 
   double ***freq; /* Frequencies */           * the nearest (and in case of equal distance, to the lowest) interval but now
   double *pp;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   double pos, k2;           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
            * probability in order to take into account the bias as a fraction of the way
   pp=vector(1,nlstate);           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);           * -stepm/2 to stepm/2 .
             * For stepm=1 the results are the same as for previous versions of Imach.
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);           * For stepm > 1 the results are less biased than in previous versions. 
   j1=0;           */
            s1=s[mw[mi][i]][i];
   j=cptcoveff;          s2=s[mw[mi+1][i]][i];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          bbh=(double)bh[mi][i]/(double)stepm; 
            /* bias bh is positive if real duration
   for(k1=1; k1<=j;k1++){           * is higher than the multiple of stepm and negative otherwise.
     for(i1=1; i1<=ncodemax[k1];i1++){           */
       j1++;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
                if( s2 > nlstate){ 
       for (i=-1; i<=nlstate+ndeath; i++)              /* i.e. if s2 is a death state and if the date of death is known 
         for (jk=-1; jk<=nlstate+ndeath; jk++)                 then the contribution to the likelihood is the probability to 
           for(m=agemin; m <= agemax+3; m++)               die between last step unit time and current  step unit time, 
             freq[i][jk][m]=0;               which is also equal to probability to die before dh 
                     minus probability to die before dh-stepm . 
       for (i=1; i<=imx; i++) {               In version up to 0.92 likelihood was computed
         bool=1;          as if date of death was unknown. Death was treated as any other
         if  (cptcovn>0) {          health state: the date of the interview describes the actual state
           for (z1=1; z1<=cptcoveff; z1++)          and not the date of a change in health state. The former idea was
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          to consider that at each interview the state was recorded
               bool=0;          (healthy, disable or death) and IMaCh was corrected; but when we
         }          introduced the exact date of death then we should have modified
         if (bool==1) {          the contribution of an exact death to the likelihood. This new
           for(m=firstpass; m<=lastpass; m++){          contribution is smaller and very dependent of the step unit
             k2=anint[m][i]+(mint[m][i]/12.);          stepm. It is no more the probability to die between last interview
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          and month of death but the probability to survive from last
               if(agev[m][i]==0) agev[m][i]=agemax+1;          interview up to one month before death multiplied by the
               if(agev[m][i]==1) agev[m][i]=agemax+2;          probability to die within a month. Thanks to Chris
               if (m<lastpass) {          Jackson for correcting this bug.  Former versions increased
                 if (calagedate>0)          mortality artificially. The bad side is that we add another loop
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          which slows down the processing. The difference can be up to 10%
                 else          lower mortality.
                   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];            lli=log(out[s1][s2] - savm[s1][s2]);
               }  
             }  
           }          } else if  (s2==-2) {
         }            for (j=1,survp=0. ; j<=nlstate; j++) 
       }              survp += out[s1][j];
       for(i=(int)agemin; i <= (int)agemax+3; i++){            lli= survp;
         for(jk=1; jk <=nlstate ; jk++){          }
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          
             pp[jk] += freq[jk][m][i];          else if  (s2==-4) {
         }            for (j=3,survp=0. ; j<=nlstate; j++) 
         for(jk=1; jk <=nlstate ; jk++){              survp += out[s1][j];
           for(m=-1, pos=0; m <=0 ; m++)            lli= survp;
             pos += freq[jk][m][i];          }
         }          
                  else if  (s2==-5) {
         for(jk=1; jk <=nlstate ; jk++){            for (j=1,survp=0. ; j<=2; j++) 
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)              survp += out[s1][j];
             pp[jk] += freq[jk][m][i];            lli= survp;
         }          }
          
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];  
                  else{
         for(jk=1; jk <=nlstate ; jk++){                lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           if( i <= (int) agemax){            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
             if(pos>=1.e-5){          } 
               probs[i][jk][j1]= pp[jk]/pos;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
             }          /*if(lli ==000.0)*/
           }          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
         }          ipmx +=1;
                  sw += weight[i];
       }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        } /* end of wave */
   }      } /* end of individual */
     }  else if(mle==2){
        for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   free_vector(pp,1,nlstate);        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
 }  /* End of Freq */            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /************* Waves Concatenation ***************/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
 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(d=0; d<=dh[mi][i]; d++){
 {            newm=savm;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      Death is a valid wave (if date is known).            for (kk=1; kk<=cptcovage;kk++) {
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]            }
      and mw[mi+1][i]. dh depends on stepm.            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   int i, mi, m;            oldm=newm;
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          } /* end mult */
      double sum=0., jmean=0.;*/        
           s1=s[mw[mi][i]][i];
   int j, k=0,jk, ju, jl;          s2=s[mw[mi+1][i]][i];
   double sum=0.;          bbh=(double)bh[mi][i]/(double)stepm; 
   jmin=1e+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 */
   jmax=-1;          ipmx +=1;
   jmean=0.;          sw += weight[i];
   for(i=1; i<=imx; i++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     mi=0;        } /* end of wave */
     m=firstpass;      } /* end of individual */
     while(s[m][i] <= nlstate){    }  else if(mle==3){  /* exponential inter-extrapolation */
       if(s[m][i]>=1)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         mw[++mi][i]=m;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       if(m >=lastpass)        for(mi=1; mi<= wav[i]-1; mi++){
         break;          for (ii=1;ii<=nlstate+ndeath;ii++)
       else            for (j=1;j<=nlstate+ndeath;j++){
         m++;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }/* end while */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     if (s[m][i] > nlstate){            }
       mi++;     /* Death is another wave */          for(d=0; d<dh[mi][i]; d++){
       /* if(mi==0)  never been interviewed correctly before death */            newm=savm;
          /* Only death is a correct wave */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       mw[mi][i]=m;            for (kk=1; kk<=cptcovage;kk++) {
     }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
     wav[i]=mi;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     if(mi==0)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);            savm=oldm;
   }            oldm=newm;
           } /* end mult */
   for(i=1; i<=imx; i++){        
     for(mi=1; mi<wav[i];mi++){          s1=s[mw[mi][i]][i];
       if (stepm <=0)          s2=s[mw[mi+1][i]][i];
         dh[mi][i]=1;          bbh=(double)bh[mi][i]/(double)stepm; 
       else{          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 */
         if (s[mw[mi+1][i]][i] > nlstate) {          ipmx +=1;
           if (agedc[i] < 2*AGESUP) {          sw += weight[i];
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           if(j==0) j=1;  /* Survives at least one month after exam */        } /* end of wave */
           k=k+1;      } /* end of individual */
           if (j >= jmax) jmax=j;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
           if (j <= jmin) jmin=j;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           sum=sum+j;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           /*if (j<0) printf("j=%d num=%d \n",j,i); */        for(mi=1; mi<= wav[i]-1; mi++){
           }          for (ii=1;ii<=nlstate+ndeath;ii++)
         }            for (j=1;j<=nlstate+ndeath;j++){
         else{              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           k=k+1;            }
           if (j >= jmax) jmax=j;          for(d=0; d<dh[mi][i]; d++){
           else if (j <= jmin)jmin=j;            newm=savm;
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           sum=sum+j;            for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         jk= j/stepm;            }
         jl= j -jk*stepm;          
         ju= j -(jk+1)*stepm;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         if(jl <= -ju)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           dh[mi][i]=jk;            savm=oldm;
         else            oldm=newm;
           dh[mi][i]=jk+1;          } /* end mult */
         if(dh[mi][i]==0)        
           dh[mi][i]=1; /* At least one step */          s1=s[mw[mi][i]][i];
       }          s2=s[mw[mi+1][i]][i];
     }          if( s2 > nlstate){ 
   }            lli=log(out[s1][s2] - savm[s1][s2]);
   jmean=sum/k;          }else{
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
  }          }
 /*********** Tricode ****************************/          ipmx +=1;
 void tricode(int *Tvar, int **nbcode, int imx)          sw += weight[i];
 {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int Ndum[20],ij=1, k, j, i;  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   int cptcode=0;        } /* end of wave */
   cptcoveff=0;      } /* end of individual */
      }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   for (k=0; k<19; k++) Ndum[k]=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   for (k=1; k<=7; k++) ncodemax[k]=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
     for (i=1; i<=imx; i++) {            for (j=1;j<=nlstate+ndeath;j++){
       ij=(int)(covar[Tvar[j]][i]);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       Ndum[ij]++;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            }
       if (ij > cptcode) cptcode=ij;          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for (i=0; i<=cptcode; i++) {            for (kk=1; kk<=cptcovage;kk++) {
       if(Ndum[i]!=0) ncodemax[j]++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
     ij=1;          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for (i=1; i<=ncodemax[j]; i++) {            savm=oldm;
       for (k=0; k<=19; k++) {            oldm=newm;
         if (Ndum[k] != 0) {          } /* end mult */
           nbcode[Tvar[j]][ij]=k;        
                    s1=s[mw[mi][i]][i];
           ij++;          s2=s[mw[mi+1][i]][i];
         }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         if (ij > ncodemax[j]) break;          ipmx +=1;
       }            sw += weight[i];
     }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   }            /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
         } /* end of wave */
  for (k=0; k<19; k++) Ndum[k]=0;      } /* end of individual */
     } /* End of if */
  for (i=1; i<=ncovmodel-2; i++) {    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       ij=Tvar[i];    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       Ndum[ij]++;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     }    return -l;
   }
  ij=1;  
  for (i=1; i<=10; i++) {  /*************** log-likelihood *************/
    if((Ndum[i]!=0) && (i<=ncovcol)){  double funcone( double *x)
      Tvaraff[ij]=i;  {
      ij++;    /* Same as likeli but slower because of a lot of printf and if */
    }    int i, ii, j, k, mi, d, kk;
  }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
      double **out;
     cptcoveff=ij-1;    double lli; /* Individual log likelihood */
 }    double llt;
     int s1, s2;
 /*********** Health Expectancies ****************/    double bbh, survp;
     /*extern weight */
 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 )    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
 {    /*for(i=1;i<imx;i++) 
   /* Health expectancies */      printf(" %d\n",s[4][i]);
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;    */
   double age, agelim, hf;    cov[1]=1.;
   double ***p3mat,***varhe;  
   double **dnewm,**doldm;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   double *xp;  
   double **gp, **gm;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***gradg, ***trgradg;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int theta;      for(mi=1; mi<= wav[i]-1; mi++){
         for (ii=1;ii<=nlstate+ndeath;ii++)
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          for (j=1;j<=nlstate+ndeath;j++){
   xp=vector(1,npar);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   dnewm=matrix(1,nlstate*2,1,npar);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   doldm=matrix(1,nlstate*2,1,nlstate*2);          }
          for(d=0; d<dh[mi][i]; d++){
   fprintf(ficreseij,"# Health expectancies\n");          newm=savm;
   fprintf(ficreseij,"# Age");          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   for(i=1; i<=nlstate;i++)          for (kk=1; kk<=cptcovage;kk++) {
     for(j=1; j<=nlstate;j++)            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          }
   fprintf(ficreseij,"\n");          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   if(estepm < stepm){          savm=oldm;
     printf ("Problem %d lower than %d\n",estepm, stepm);          oldm=newm;
   }        } /* end mult */
   else  hstepm=estepm;          
   /* We compute the life expectancy from trapezoids spaced every estepm months        s1=s[mw[mi][i]][i];
    * This is mainly to measure the difference between two models: for example        s2=s[mw[mi+1][i]][i];
    * if stepm=24 months pijx are given only every 2 years and by summing them        bbh=(double)bh[mi][i]/(double)stepm; 
    * we are calculating an estimate of the Life Expectancy assuming a linear        /* bias is positive if real duration
    * progression inbetween and thus overestimating or underestimating according         * is higher than the multiple of stepm and negative otherwise.
    * to the curvature of the survival function. If, for the same date, we         */
    * estimate the model with stepm=1 month, we can keep estepm to 24 months        if( s2 > nlstate && (mle <5) ){  /* Jackson */
    * to compare the new estimate of Life expectancy with the same linear          lli=log(out[s1][s2] - savm[s1][s2]);
    * hypothesis. A more precise result, taking into account a more precise        } else if (mle==1){
    * curvature will be obtained if estepm is as small as stepm. */          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         } else if(mle==2){
   /* For example we decided to compute the life expectancy with the smallest unit */          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 */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.        } else if(mle==3){  /* exponential inter-extrapolation */
      nhstepm is the number of hstepm from age to agelim          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 */
      nstepm is the number of stepm from age to agelin.        } else if (mle==4){  /* mle=4 no inter-extrapolation */
      Look at hpijx to understand the reason of that which relies in memory size          lli=log(out[s1][s2]); /* Original formula */
      and note for a fixed period like estepm months */        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          lli=log(out[s1][s2]); /* Original formula */
      survival function given by stepm (the optimization length). Unfortunately it        } /* End of if */
      means that if the survival funtion is printed only each two years of age and if        ipmx +=1;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same        sw += weight[i];
      results. So we changed our mind and took the option of the best precision.        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   */  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        if(globpr){
           fprintf(ficresilk,"%9d %6d %1d %1d %1d %1d %3d %10.6f %6.4f\
   agelim=AGESUP;   %10.6f %10.6f %10.6f ", \
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     /* nhstepm age range expressed in number of stepm */                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */            llt +=ll[k]*gipmx/gsw;
     /* if (stepm >= YEARM) hstepm=1;*/            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          fprintf(ficresilk," %10.6f\n", -llt);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);        }
     gp=matrix(0,nhstepm,1,nlstate*2);      } /* end of wave */
     gm=matrix(0,nhstepm,1,nlstate*2);    } /* end of individual */
     for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      if(globpr==0){ /* First time we count the contributions and weights */
        gipmx=ipmx;
       gsw=sw;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    }
     return -l;
     /* Computing Variances of health expectancies */  }
   
      for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){  /*************** function likelione ***********/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       }  {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      /* This routine should help understanding what is done with 
         the selection of individuals/waves and
       cptj=0;       to check the exact contribution to the likelihood.
       for(j=1; j<= nlstate; j++){       Plotting could be done.
         for(i=1; i<=nlstate; i++){     */
           cptj=cptj+1;    int k;
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){  
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;    if(*globpri !=0){ /* Just counts and sums, no printings */
           }      strcpy(fileresilk,"ilk"); 
         }      strcat(fileresilk,fileres);
       }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
              printf("Problem with resultfile: %s\n", fileresilk);
              fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       for(i=1; i<=npar; i++)      }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      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");
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
            /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
       cptj=0;      for(k=1; k<=nlstate; k++) 
       for(j=1; j<= nlstate; j++){        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
         for(i=1;i<=nlstate;i++){      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
           cptj=cptj+1;    }
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){  
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;    *fretone=(*funcone)(p);
           }    if(*globpri !=0){
         }      fclose(ficresilk);
       }      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       for(j=1; j<= nlstate*2; j++)      fflush(fichtm); 
         for(h=0; h<=nhstepm-1; h++){    } 
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    return;
         }  }
      }  
      
 /* End theta */  /*********** Maximum Likelihood Estimation ***************/
   
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   {
      for(h=0; h<=nhstepm-1; h++)    int i,j, iter;
       for(j=1; j<=nlstate*2;j++)    double **xi;
         for(theta=1; theta <=npar; theta++)    double fret;
           trgradg[h][j][theta]=gradg[h][theta][j];    double fretone; /* Only one call to likelihood */
          /*  char filerespow[FILENAMELENGTH];*/
     xi=matrix(1,npar,1,npar);
      for(i=1;i<=nlstate*2;i++)    for (i=1;i<=npar;i++)
       for(j=1;j<=nlstate*2;j++)      for (j=1;j<=npar;j++)
         varhe[i][j][(int)age] =0.;        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
      printf("%d|",(int)age);fflush(stdout);    strcpy(filerespow,"pow"); 
      for(h=0;h<=nhstepm-1;h++){    strcat(filerespow,fileres);
       for(k=0;k<=nhstepm-1;k++){    if((ficrespow=fopen(filerespow,"w"))==NULL) {
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);      printf("Problem with resultfile: %s\n", filerespow);
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
         for(i=1;i<=nlstate*2;i++)    }
           for(j=1;j<=nlstate*2;j++)    fprintf(ficrespow,"# Powell\n# iter -2*LL");
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;    for (i=1;i<=nlstate;i++)
       }      for(j=1;j<=nlstate+ndeath;j++)
     }        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     /* Computing expectancies */    fprintf(ficrespow,"\n");
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++)    powell(p,xi,npar,ftol,&iter,&fret,func);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){  
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;    free_matrix(xi,1,npar,1,npar);
              fclose(ficrespow);
 /* 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]);*/    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         }    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   
     fprintf(ficreseij,"%3.0f",age );  }
     cptj=0;  
     for(i=1; i<=nlstate;i++)  /**** Computes Hessian and covariance matrix ***/
       for(j=1; j<=nlstate;j++){  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
         cptj++;  {
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );    double  **a,**y,*x,pd;
       }    double **hess;
     fprintf(ficreseij,"\n");    int i, j,jk;
        int *indx;
     free_matrix(gm,0,nhstepm,1,nlstate*2);  
     free_matrix(gp,0,nhstepm,1,nlstate*2);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);    void lubksb(double **a, int npar, int *indx, double b[]) ;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    void ludcmp(double **a, int npar, int *indx, double *d) ;
   }    double gompertz(double p[]);
   printf("\n");    hess=matrix(1,npar,1,npar);
   
   free_vector(xp,1,npar);    printf("\nCalculation of the hessian matrix. Wait...\n");
   free_matrix(dnewm,1,nlstate*2,1,npar);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);    for (i=1;i<=npar;i++){
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);      printf("%d",i);fflush(stdout);
 }      fprintf(ficlog,"%d",i);fflush(ficlog);
      
 /************ Variance ******************/       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
 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)      
 {      /*  printf(" %f ",p[i]);
   /* Variance of health expectancies */          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;    
   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;        if (j>i) { 
   double *xp;          printf(".%d%d",i,j);fflush(stdout);
   double **gp, **gm;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double ***gradg, ***trgradg;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double ***p3mat;          
   double age,agelim, hf;          hess[j][i]=hess[i][j];    
   int theta;          /*printf(" %lf ",hess[i][j]);*/
         }
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");      }
   fprintf(ficresvij,"# Age");    }
   for(i=1; i<=nlstate;i++)    printf("\n");
     for(j=1; j<=nlstate;j++)    fprintf(ficlog,"\n");
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);  
   fprintf(ficresvij,"\n");    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   xp=vector(1,npar);    
   dnewm=matrix(1,nlstate,1,npar);    a=matrix(1,npar,1,npar);
   doldm=matrix(1,nlstate,1,nlstate);    y=matrix(1,npar,1,npar);
      x=vector(1,npar);
   if(estepm < stepm){    indx=ivector(1,npar);
     printf ("Problem %d lower than %d\n",estepm, stepm);    for (i=1;i<=npar;i++)
   }      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   else  hstepm=estepm;      ludcmp(a,npar,indx,&pd);
   /* 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.    for (j=1;j<=npar;j++) {
      nhstepm is the number of hstepm from age to agelim      for (i=1;i<=npar;i++) x[i]=0;
      nstepm is the number of stepm from age to agelin.      x[j]=1;
      Look at hpijx to understand the reason of that which relies in memory size      lubksb(a,npar,indx,x);
      and note for a fixed period like k years */      for (i=1;i<=npar;i++){ 
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        matcov[i][j]=x[i];
      survival function given by stepm (the optimization length). Unfortunately it      }
      means that if the survival funtion is printed only each two years of age and if    }
      you sum them up and add 1 year (area under the trapezoids) you won't get the same  
      results. So we changed our mind and took the option of the best precision.    printf("\n#Hessian matrix#\n");
   */    fprintf(ficlog,"\n#Hessian matrix#\n");
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    for (i=1;i<=npar;i++) { 
   agelim = AGESUP;      for (j=1;j<=npar;j++) { 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        printf("%.3e ",hess[i][j]);
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        fprintf(ficlog,"%.3e ",hess[i][j]);
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */      }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      printf("\n");
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);      fprintf(ficlog,"\n");
     gp=matrix(0,nhstepm,1,nlstate);    }
     gm=matrix(0,nhstepm,1,nlstate);  
     /* Recompute Inverse */
     for(theta=1; theta <=npar; theta++){    for (i=1;i<=npar;i++)
       for(i=1; i<=npar; i++){ /* Computes gradient */      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    ludcmp(a,npar,indx,&pd);
       }  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      /*  printf("\n#Hessian matrix recomputed#\n");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
     for (j=1;j<=npar;j++) {
       if (popbased==1) {      for (i=1;i<=npar;i++) x[i]=0;
         for(i=1; i<=nlstate;i++)      x[j]=1;
           prlim[i][i]=probs[(int)age][i][ij];      lubksb(a,npar,indx,x);
       }      for (i=1;i<=npar;i++){ 
          y[i][j]=x[i];
       for(j=1; j<= nlstate; j++){        printf("%.3e ",y[i][j]);
         for(h=0; h<=nhstepm; h++){        fprintf(ficlog,"%.3e ",y[i][j]);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)      }
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      printf("\n");
         }      fprintf(ficlog,"\n");
       }    }
        */
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    free_matrix(a,1,npar,1,npar);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      free_matrix(y,1,npar,1,npar);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
       if (popbased==1) {    free_matrix(hess,1,npar,1,npar);
         for(i=1; i<=nlstate;i++)  
           prlim[i][i]=probs[(int)age][i][ij];  
       }  }
   
       for(j=1; j<= nlstate; j++){  /*************** hessian matrix ****************/
         for(h=0; h<=nhstepm; h++){  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  {
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    int i;
         }    int l=1, lmax=20;
       }    double k1,k2;
     double p2[NPARMAX+1];
       for(j=1; j<= nlstate; j++)    double res;
         for(h=0; h<=nhstepm; h++){    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    double fx;
         }    int k=0,kmax=10;
     } /* End theta */    double l1;
   
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    fx=func(x);
     for (i=1;i<=npar;i++) p2[i]=x[i];
     for(h=0; h<=nhstepm; h++)    for(l=0 ; l <=lmax; l++){
       for(j=1; j<=nlstate;j++)      l1=pow(10,l);
         for(theta=1; theta <=npar; theta++)      delts=delt;
           trgradg[h][j][theta]=gradg[h][theta][j];      for(k=1 ; k <kmax; k=k+1){
         delt = delta*(l1*k);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */        p2[theta]=x[theta] +delt;
     for(i=1;i<=nlstate;i++)        k1=func(p2)-fx;
       for(j=1;j<=nlstate;j++)        p2[theta]=x[theta]-delt;
         vareij[i][j][(int)age] =0.;        k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
     for(h=0;h<=nhstepm;h++){        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
       for(k=0;k<=nhstepm;k++){        
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);  #ifdef DEBUG
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         for(i=1;i<=nlstate;i++)        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
           for(j=1;j<=nlstate;j++)  #endif
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     }          k=kmax;
         }
     fprintf(ficresvij,"%.0f ",age );        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     for(i=1; i<=nlstate;i++)          k=kmax; l=lmax*10.;
       for(j=1; j<=nlstate;j++){        }
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       }          delts=delt;
     fprintf(ficresvij,"\n");        }
     free_matrix(gp,0,nhstepm,1,nlstate);      }
     free_matrix(gm,0,nhstepm,1,nlstate);    }
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    delti[theta]=delts;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    return res; 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    
   } /* End age */  }
    
   free_vector(xp,1,npar);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   free_matrix(doldm,1,nlstate,1,npar);  {
   free_matrix(dnewm,1,nlstate,1,nlstate);    int i;
     int l=1, l1, lmax=20;
 }    double k1,k2,k3,k4,res,fx;
     double p2[NPARMAX+1];
 /************ Variance of prevlim ******************/    int k;
 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)  
 {    fx=func(x);
   /* Variance of prevalence limit */    for (k=1; k<=2; k++) {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      for (i=1;i<=npar;i++) p2[i]=x[i];
   double **newm;      p2[thetai]=x[thetai]+delti[thetai]/k;
   double **dnewm,**doldm;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   int i, j, nhstepm, hstepm;      k1=func(p2)-fx;
   int k, cptcode;    
   double *xp;      p2[thetai]=x[thetai]+delti[thetai]/k;
   double *gp, *gm;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   double **gradg, **trgradg;      k2=func(p2)-fx;
   double age,agelim;    
   int theta;      p2[thetai]=x[thetai]-delti[thetai]/k;
          p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");      k3=func(p2)-fx;
   fprintf(ficresvpl,"# Age");    
   for(i=1; i<=nlstate;i++)      p2[thetai]=x[thetai]-delti[thetai]/k;
       fprintf(ficresvpl," %1d-%1d",i,i);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   fprintf(ficresvpl,"\n");      k4=func(p2)-fx;
       res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   xp=vector(1,npar);  #ifdef DEBUG
   dnewm=matrix(1,nlstate,1,npar);      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   doldm=matrix(1,nlstate,1,nlstate);      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
    #endif
   hstepm=1*YEARM; /* Every year of age */    }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    return res;
   agelim = AGESUP;  }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  /************** Inverse of matrix **************/
     if (stepm >= YEARM) hstepm=1;  void ludcmp(double **a, int n, int *indx, double *d) 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  { 
     gradg=matrix(1,npar,1,nlstate);    int i,imax,j,k; 
     gp=vector(1,nlstate);    double big,dum,sum,temp; 
     gm=vector(1,nlstate);    double *vv; 
    
     for(theta=1; theta <=npar; theta++){    vv=vector(1,n); 
       for(i=1; i<=npar; i++){ /* Computes gradient */    *d=1.0; 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    for (i=1;i<=n;i++) { 
       }      big=0.0; 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (j=1;j<=n;j++) 
       for(i=1;i<=nlstate;i++)        if ((temp=fabs(a[i][j])) > big) big=temp; 
         gp[i] = prlim[i][i];      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
          vv[i]=1.0/big; 
       for(i=1; i<=npar; i++) /* Computes gradient */    } 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    for (j=1;j<=n;j++) { 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (i=1;i<j;i++) { 
       for(i=1;i<=nlstate;i++)        sum=a[i][j]; 
         gm[i] = prlim[i][i];        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
       for(i=1;i<=nlstate;i++)      } 
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];      big=0.0; 
     } /* End theta */      for (i=j;i<=n;i++) { 
         sum=a[i][j]; 
     trgradg =matrix(1,nlstate,1,npar);        for (k=1;k<j;k++) 
           sum -= a[i][k]*a[k][j]; 
     for(j=1; j<=nlstate;j++)        a[i][j]=sum; 
       for(theta=1; theta <=npar; theta++)        if ( (dum=vv[i]*fabs(sum)) >= big) { 
         trgradg[j][theta]=gradg[theta][j];          big=dum; 
           imax=i; 
     for(i=1;i<=nlstate;i++)        } 
       varpl[i][(int)age] =0.;      } 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      if (j != imax) { 
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);        for (k=1;k<=n;k++) { 
     for(i=1;i<=nlstate;i++)          dum=a[imax][k]; 
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          a[imax][k]=a[j][k]; 
           a[j][k]=dum; 
     fprintf(ficresvpl,"%.0f ",age );        } 
     for(i=1; i<=nlstate;i++)        *d = -(*d); 
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));        vv[imax]=vv[j]; 
     fprintf(ficresvpl,"\n");      } 
     free_vector(gp,1,nlstate);      indx[j]=imax; 
     free_vector(gm,1,nlstate);      if (a[j][j] == 0.0) a[j][j]=TINY; 
     free_matrix(gradg,1,npar,1,nlstate);      if (j != n) { 
     free_matrix(trgradg,1,nlstate,1,npar);        dum=1.0/(a[j][j]); 
   } /* End age */        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       } 
   free_vector(xp,1,npar);    } 
   free_matrix(doldm,1,nlstate,1,npar);    free_vector(vv,1,n);  /* Doesn't work */
   free_matrix(dnewm,1,nlstate,1,nlstate);  ;
   } 
 }  
   void lubksb(double **a, int n, int *indx, double b[]) 
 /************ Variance of one-step probabilities  ******************/  { 
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    int i,ii=0,ip,j; 
 {    double sum; 
   int i, j,  i1, k1, l1;   
   int k2, l2, j1,  z1;    for (i=1;i<=n;i++) { 
   int k=0,l, cptcode;      ip=indx[i]; 
   int first=1;      sum=b[ip]; 
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;      b[ip]=b[i]; 
   double **dnewm,**doldm;      if (ii) 
   double *xp;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   double *gp, *gm;      else if (sum) ii=i; 
   double **gradg, **trgradg;      b[i]=sum; 
   double **mu;    } 
   double age,agelim, cov[NCOVMAX];    for (i=n;i>=1;i--) { 
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */      sum=b[i]; 
   int theta;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   char fileresprob[FILENAMELENGTH];      b[i]=sum/a[i][i]; 
   char fileresprobcov[FILENAMELENGTH];    } 
   char fileresprobcor[FILENAMELENGTH];  } 
   
   double ***varpij;  void pstamp(FILE *fichier)
   {
   strcpy(fileresprob,"prob");    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   strcat(fileresprob,fileres);  }
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  
     printf("Problem with resultfile: %s\n", fileresprob);  /************ Frequencies ********************/
   }  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
   strcpy(fileresprobcov,"probcov");  {  /* Some frequencies */
   strcat(fileresprobcov,fileres);    
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     printf("Problem with resultfile: %s\n", fileresprobcov);    int first;
   }    double ***freq; /* Frequencies */
   strcpy(fileresprobcor,"probcor");    double *pp, **prop;
   strcat(fileresprobcor,fileres);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {    char fileresp[FILENAMELENGTH];
     printf("Problem with resultfile: %s\n", fileresprobcor);    
   }    pp=vector(1,nlstate);
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    prop=matrix(1,nlstate,iagemin,iagemax+3);
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    strcpy(fileresp,"p");
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);    strcat(fileresp,fileres);
      if((ficresp=fopen(fileresp,"w"))==NULL) {
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");      printf("Problem with prevalence resultfile: %s\n", fileresp);
   fprintf(ficresprob,"# Age");      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");      exit(0);
   fprintf(ficresprobcov,"# Age");    }
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
   fprintf(ficresprobcov,"# Age");    j1=0;
     
     j=cptcoveff;
   for(i=1; i<=nlstate;i++)    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     for(j=1; j<=(nlstate+ndeath);j++){  
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    first=1;
       fprintf(ficresprobcov," p%1d-%1d ",i,j);  
       fprintf(ficresprobcor," p%1d-%1d ",i,j);    for(k1=1; k1<=j;k1++){
     }        for(i1=1; i1<=ncodemax[k1];i1++){
   fprintf(ficresprob,"\n");        j1++;
   fprintf(ficresprobcov,"\n");        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   fprintf(ficresprobcor,"\n");          scanf("%d", i);*/
   xp=vector(1,npar);        for (i=-5; i<=nlstate+ndeath; i++)  
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));            for(m=iagemin; m <= iagemax+3; m++)
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);              freq[i][jk][m]=0;
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);  
   first=1;      for (i=1; i<=nlstate; i++)  
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {        for(m=iagemin; m <= iagemax+3; m++)
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);          prop[i][m]=0;
     exit(0);        
   }        dateintsum=0;
   else{        k2cpt=0;
     fprintf(ficgp,"\n# Routine varprob");        for (i=1; i<=imx; i++) {
   }          bool=1;
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {          if  (cptcovn>0) {
     printf("Problem with html file: %s\n", optionfilehtm);            for (z1=1; z1<=cptcoveff; z1++) 
     exit(0);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   }                bool=0;
   else{          }
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");          if (bool==1){
     fprintf(fichtm,"\n<br> We have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");            for(m=firstpass; m<=lastpass; m++){
     fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix 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> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");              k2=anint[m][i]+(mint[m][i]/12.);
               /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
   }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   cov[1]=1;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   j=cptcoveff;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}                if (m<lastpass) {
   j1=0;                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   for(k1=1; k1<=1;k1++){                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     for(i1=1; i1<=ncodemax[k1];i1++){                }
     j1++;                
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     if  (cptcovn>0) {                  dateintsum=dateintsum+k2;
       fprintf(ficresprob, "\n#********** Variable ");                  k2cpt++;
       fprintf(ficresprobcov, "\n#********** Variable ");                }
       fprintf(ficgp, "\n#********** Variable ");                /*}*/
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");            }
       fprintf(ficresprobcor, "\n#********** Variable ");          }
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        }
       fprintf(ficresprob, "**********\n#");         
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       fprintf(ficresprobcov, "**********\n#");        pstamp(ficresp);
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        if  (cptcovn>0) {
       fprintf(ficgp, "**********\n#");          fprintf(ficresp, "\n#********** Variable "); 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       fprintf(ficgp, "**********\n#");          fprintf(ficresp, "**********\n#");
       for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        }
       fprintf(fichtm, "**********\n#");        for(i=1; i<=nlstate;i++) 
     }          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
            fprintf(ficresp, "\n");
       for (age=bage; age<=fage; age ++){        
         cov[2]=age;        for(i=iagemin; i <= iagemax+3; i++){
         for (k=1; k<=cptcovn;k++) {          if(i==iagemax+3){
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];            fprintf(ficlog,"Total");
         }          }else{
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];            if(first==1){
         for (k=1; k<=cptcovprod;k++)              first=0;
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];              printf("See log file for details...\n");
                    }
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));            fprintf(ficlog,"Age %d", i);
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);          }
         gp=vector(1,(nlstate)*(nlstate+ndeath));          for(jk=1; jk <=nlstate ; jk++){
         gm=vector(1,(nlstate)*(nlstate+ndeath));            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                  pp[jk] += freq[jk][m][i]; 
         for(theta=1; theta <=npar; theta++){          }
           for(i=1; i<=npar; i++)          for(jk=1; jk <=nlstate ; jk++){
             xp[i] = x[i] + (i==theta ?delti[theta]:0);            for(m=-1, pos=0; m <=0 ; m++)
                        pos += freq[jk][m][i];
           pmij(pmmij,cov,ncovmodel,xp,nlstate);            if(pp[jk]>=1.e-10){
                        if(first==1){
           k=0;              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           for(i=1; i<= (nlstate); i++){              }
             for(j=1; j<=(nlstate+ndeath);j++){              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               k=k+1;            }else{
               gp[k]=pmmij[i][j];              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(i=1; i<=npar; i++)          }
             xp[i] = x[i] - (i==theta ?delti[theta]:0);  
              for(jk=1; jk <=nlstate ; jk++){
           pmij(pmmij,cov,ncovmodel,xp,nlstate);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
           k=0;              pp[jk] += freq[jk][m][i];
           for(i=1; i<=(nlstate); i++){          }       
             for(j=1; j<=(nlstate+ndeath);j++){          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
               k=k+1;            pos += pp[jk];
               gm[k]=pmmij[i][j];            posprop += prop[jk][i];
             }          }
           }          for(jk=1; jk <=nlstate ; jk++){
                  if(pos>=1.e-5){
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)              if(first==1)
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];                  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{
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)              if(first==1)
           for(theta=1; theta <=npar; theta++)                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             trgradg[j][theta]=gradg[theta][j];              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
                    }
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);            if( i <= iagemax){
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);              if(pos>=1.e-5){
                        fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         pmij(pmmij,cov,ncovmodel,x,nlstate);                /*probs[i][jk][j1]= pp[jk]/pos;*/
                        /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
         k=0;              }
         for(i=1; i<=(nlstate); i++){              else
           for(j=1; j<=(nlstate+ndeath);j++){                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             k=k+1;            }
             mu[k][(int) age]=pmmij[i][j];          }
           }          
         }          for(jk=-1; jk <=nlstate+ndeath; jk++)
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)            for(m=-1; m <=nlstate+ndeath; m++)
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)              if(freq[jk][m][i] !=0 ) {
             varpij[i][j][(int)age] = doldm[i][j];              if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
         /*printf("\n%d ",(int)age);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){              }
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));          if(i <= iagemax)
      }*/            fprintf(ficresp,"\n");
           if(first==1)
         fprintf(ficresprob,"\n%d ",(int)age);            printf("Others in log...\n");
         fprintf(ficresprobcov,"\n%d ",(int)age);          fprintf(ficlog,"\n");
         fprintf(ficresprobcor,"\n%d ",(int)age);        }
       }
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)    }
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));    dateintmean=dateintsum/k2cpt; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){   
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);    fclose(ficresp);
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
         }    free_vector(pp,1,nlstate);
         i=0;    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
         for (k=1; k<=(nlstate);k++){    /* End of Freq */
           for (l=1; l<=(nlstate+ndeath);l++){  }
             i=i++;  
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);  /************ Prevalence ********************/
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);  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)
             for (j=1; j<=i;j++){  {  
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));       in each health status at the date of interview (if between dateprev1 and dateprev2).
             }       We still use firstpass and lastpass as another selection.
           }    */
         }/* end of loop for state */   
       } /* end of loop for age */    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/    double ***freq; /* Frequencies */
       for (k1=1; k1<=(nlstate);k1++){    double *pp, **prop;
         for (l1=1; l1<=(nlstate+ndeath);l1++){    double pos,posprop; 
           if(l1==k1) continue;    double  y2; /* in fractional years */
           i=(k1-1)*(nlstate+ndeath)+l1;    int iagemin, iagemax;
           for (k2=1; k2<=(nlstate);k2++){  
             for (l2=1; l2<=(nlstate+ndeath);l2++){    iagemin= (int) agemin;
               if(l2==k2) continue;    iagemax= (int) agemax;
               j=(k2-1)*(nlstate+ndeath)+l2;    /*pp=vector(1,nlstate);*/
               if(j<=i) continue;    prop=matrix(1,nlstate,iagemin,iagemax+3); 
               for (age=bage; age<=fage; age ++){    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
                 if ((int)age %5==0){    j1=0;
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;    
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;    j=cptcoveff;
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
                   mu1=mu[i][(int) age]/stepm*YEARM ;    
                   mu2=mu[j][(int) age]/stepm*YEARM;    for(k1=1; k1<=j;k1++){
                   /* Computing eigen value of matrix of covariance */      for(i1=1; i1<=ncodemax[k1];i1++){
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));        j1++;
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));        
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);        for (i=1; i<=nlstate; i++)  
                   /* Eigen vectors */          for(m=iagemin; m <= iagemax+3; m++)
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));            prop[i][m]=0.0;
                   v21=sqrt(1.-v11*v11);       
                   v12=-v21;        for (i=1; i<=imx; i++) { /* Each individual */
                   v22=v11;          bool=1;
                   /*printf(fignu*/          if  (cptcovn>0) {
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */            for (z1=1; z1<=cptcoveff; z1++) 
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                   if(first==1){                bool=0;
                     first=0;          } 
                     fprintf(ficgp,"\nset parametric;set nolabel");          if (bool==1) { 
                     fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%1d%1d-%1d%1d.png\">varpijgr%s%1d%1d-%1d%1d.png</A>, ",k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);                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); 
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                     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)) t \"%d\"",\                  /*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]]);*/
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);                  prop[s[m][i]][iagemax+3] += weight[i]; 
                   }else{                } 
                     first=0;              }
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);            } /* end selection of waves */
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);          }
                     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)) t \"%d\"",\        }
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \        for(i=iagemin; i <= iagemax+3; i++){  
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);          
                   }/* if first */          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
                 } /* age mod 5 */            posprop += prop[jk][i]; 
               } /* end loop age */          } 
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);  
               first=1;          for(jk=1; jk <=nlstate ; jk++){     
             } /*l12 */            if( i <=  iagemax){ 
           } /* k12 */              if(posprop>=1.e-5){ 
         } /*l1 */                probs[i][jk][j1]= prop[jk][i]/posprop;
       }/* k1 */              } 
     } /* loop covariates */            } 
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);          }/* end jk */ 
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));        }/* end i */ 
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));      } /* end i1 */
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);    } /* end k1 */
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
   }    /*free_vector(pp,1,nlstate);*/
   free_vector(xp,1,npar);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   fclose(ficresprob);  }  /* End of prevalence */
   fclose(ficresprobcov);  
   fclose(ficresprobcor);  /************* Waves Concatenation ***************/
   fclose(ficgp);  
   fclose(fichtm);  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)
 }  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        Death is a valid wave (if date is known).
 /******************* Printing html file ***********/       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
                   int lastpass, int stepm, int weightopt, char model[],\       and mw[mi+1][i]. dh depends on stepm.
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\       */
                   int popforecast, int estepm ,\  
                   double jprev1, double mprev1,double anprev1, \    int i, mi, m;
                   double jprev2, double mprev2,double anprev2){    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
   int jj1, k1, i1, cpt;       double sum=0., jmean=0.;*/
   /*char optionfilehtm[FILENAMELENGTH];*/    int first;
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {    int j, k=0,jk, ju, jl;
     printf("Problem with %s \n",optionfilehtm), exit(0);    double sum=0.;
   }    first=0;
     jmin=1e+5;
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n    jmax=-1;
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n    jmean=0.;
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n    for(i=1; i<=imx; i++){
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n      mi=0;
  - Life expectancies by age and initial health status (estepm=%2d months):      m=firstpass;
    <a href=\"e%s\">e%s</a> <br>\n</li>", \      while(s[m][i] <= nlstate){
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
           mw[++mi][i]=m;
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n        if(m >=lastpass)
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          break;
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n        else
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n          m++;
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n      }/* end while */
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n      if (s[m][i] > nlstate){
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n        mi++;     /* Death is another wave */
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);        /* if(mi==0)  never been interviewed correctly before death */
            /* Only death is a correct wave */
  if(popforecast==1) fprintf(fichtm,"\n        mw[mi][i]=m;
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n      }
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n  
         <br>",fileres,fileres,fileres,fileres);      wav[i]=mi;
  else      if(mi==0){
    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);        nbwarn++;
 fprintf(fichtm," <li>Graphs</li><p>");        if(first==0){
           printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
  m=cptcoveff;          first=1;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}        }
         if(first==1){
  jj1=0;          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
  for(k1=1; k1<=m;k1++){        }
    for(i1=1; i1<=ncodemax[k1];i1++){      } /* end mi==0 */
      jj1++;    } /* End individuals */
      if (cptcovn > 0) {  
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    for(i=1; i<=imx; i++){
        for (cpt=1; cpt<=cptcoveff;cpt++)      for(mi=1; mi<wav[i];mi++){
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);        if (stepm <=0)
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");          dh[mi][i]=1;
      }        else{
      /* Pij */          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>            if (agedc[i] < 2*AGESUP) {
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                  j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
      /* Quasi-incidences */              if(j==0) j=1;  /* Survives at least one month after exam */
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>              else if(j<0){
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                nberr++;
        /* Stable prevalence in each health state */                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]);
        for(cpt=1; cpt<nlstate;cpt++){                j=1; /* Temporary Dangerous patch */
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>                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);
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                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(cpt=1; cpt<=nlstate;cpt++) {              }
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              k=k+1;
 interval) in state (%d): v%s%d%d.png <br>              if (j >= jmax){
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                  jmax=j;
      }                ijmax=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.png <br>              if (j <= jmin){
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                jmin=j;
      }                ijmin=i;
      fprintf(fichtm,"\n<br>- Total life expectancy by age and              }
 health expectancies in states (1) and (2): e%s%d.png<br>              sum=sum+j;
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
    }              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
  }            }
 fclose(fichtm);          }
 }          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
 /******************* Gnuplot file **************/  /*        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]); */
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){  
             k=k+1;
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;            if (j >= jmax) {
   int ng;              jmax=j;
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {              ijmax=i;
     printf("Problem with file %s",optionfilegnuplot);            }
   }            else if (j <= jmin){
               jmin=j;
 #ifdef windows              ijmin=i;
     fprintf(ficgp,"cd \"%s\" \n",pathc);            }
 #endif            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
 m=pow(2,cptcoveff);            /*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){
  /* 1eme*/              nberr++;
   for (cpt=1; cpt<= nlstate ; cpt ++) {              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]);
             }
 #ifdef windows            sum=sum+j;
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          }
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);          jk= j/stepm;
 #endif          jl= j -jk*stepm;
 #ifdef unix          ju= j -(jk+1)*stepm;
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);            if(jl==0){
 #endif              dh[mi][i]=jk;
               bh[mi][i]=0;
 for (i=1; i<= nlstate ; i ++) {            }else{ /* We want a negative bias in order to only have interpolation ie
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");                    * at the price of an extra matrix product in likelihood */
   else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=jk+1;
 }              bh[mi][i]=ju;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            }
     for (i=1; i<= nlstate ; i ++) {          }else{
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            if(jl <= -ju){
   else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=jk;
 }              bh[mi][i]=jl;       /* bias is positive if real duration
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);                                   * is higher than the multiple of stepm and negative otherwise.
      for (i=1; i<= nlstate ; i ++) {                                   */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            else{
 }                dh[mi][i]=jk+1;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));              bh[mi][i]=ju;
 #ifdef unix            }
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");            if(dh[mi][i]==0){
 #endif              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);*/
   /*2 eme*/            }
           } /* end if mle */
   for (k1=1; k1<= m ; k1 ++) {        }
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);      } /* end wave */
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    }
        jmean=sum/k;
     for (i=1; i<= nlstate+1 ; i ++) {    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
       k=2*i;    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);   }
       for (j=1; j<= nlstate+1 ; j ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  /*********** Tricode ****************************/
   else fprintf(ficgp," \%%*lf (\%%*lf)");  void tricode(int *Tvar, int **nbcode, int imx)
 }    {
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    int Ndum[20],ij=1, k, j, i, maxncov=19;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    int cptcode=0;
       for (j=1; j<= nlstate+1 ; j ++) {    cptcoveff=0; 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");   
         else fprintf(ficgp," \%%*lf (\%%*lf)");    for (k=0; k<maxncov; k++) Ndum[k]=0;
 }      for (k=1; k<=7; k++) ncodemax[k]=0;
       fprintf(ficgp,"\" t\"\" w l 0,");  
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       for (j=1; j<= nlstate+1 ; j ++) {      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                                 modality*/ 
   else fprintf(ficgp," \%%*lf (\%%*lf)");        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
 }          Ndum[ij]++; /*store the modality */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
       else fprintf(ficgp,"\" t\"\" w l 0,");        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
     }                                         Tvar[j]. If V=sex and male is 0 and 
   }                                         female is 1, then  cptcode=1.*/
        }
   /*3eme*/  
       for (i=0; i<=cptcode; i++) {
   for (k1=1; k1<= m ; k1 ++) {        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
     for (cpt=1; cpt<= nlstate ; cpt ++) {      }
       k=2+nlstate*(2*cpt-2);  
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);      ij=1; 
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);      for (i=1; i<=ncodemax[j]; i++) {
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);        for (k=0; k<= maxncov; k++) {
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          if (Ndum[k] != 0) {
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            nbcode[Tvar[j]][ij]=k; 
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);            /* 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; */
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");            
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            ij++;
           }
 */          if (ij > ncodemax[j]) break; 
       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);      } 
     }  
       }  
     }   for (k=0; k< maxncov; k++) Ndum[k]=0;
   }  
     for (i=1; i<=ncovmodel-2; i++) { 
   /* CV preval stat */     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
     for (k1=1; k1<= m ; k1 ++) {     ij=Tvar[i];
     for (cpt=1; cpt<nlstate ; cpt ++) {     Ndum[ij]++;
       k=3;   }
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);  
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);   ij=1;
    for (i=1; i<= maxncov; i++) {
       for (i=1; i< nlstate ; i ++)     if((Ndum[i]!=0) && (i<=ncovcol)){
         fprintf(ficgp,"+$%d",k+i+1);       Tvaraff[ij]=i; /*For printing */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);       ij++;
           }
       l=3+(nlstate+ndeath)*cpt;   }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);   
       for (i=1; i< nlstate ; i ++) {   cptcoveff=ij-1; /*Number of simple covariates*/
         l=3+(nlstate+ndeath)*cpt;  }
         fprintf(ficgp,"+$%d",l+i+1);  
       }  /*********** Health Expectancies ****************/
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);    
     }  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   }    
    {
   /* proba elementaires */    /* Health expectancies, no variances */
    for(i=1,jk=1; i <=nlstate; i++){    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
     for(k=1; k <=(nlstate+ndeath); k++){    double age, agelim, hf;
       if (k != i) {    double ***p3mat;
         for(j=1; j <=ncovmodel; j++){    double eip;
          
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    pstamp(ficreseij);
           jk++;    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
           fprintf(ficgp,"\n");    fprintf(ficreseij,"# Age");
         }    for(i=1; i<=nlstate;i++){
       }      for(j=1; j<=nlstate;j++){
     }        fprintf(ficreseij," e%1d%1d ",i,j);
    }      }
       fprintf(ficreseij," e%1d. ",i);
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/    }
      for(jk=1; jk <=m; jk++) {    fprintf(ficreseij,"\n");
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);  
        if (ng==2)    
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");    if(estepm < stepm){
        else      printf ("Problem %d lower than %d\n",estepm, stepm);
          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);    else  hstepm=estepm;   
        i=1;    /* We compute the life expectancy from trapezoids spaced every estepm months
        for(k2=1; k2<=nlstate; k2++) {     * This is mainly to measure the difference between two models: for example
          k3=i;     * if stepm=24 months pijx are given only every 2 years and by summing them
          for(k=1; k<=(nlstate+ndeath); k++) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
            if (k != k2){     * progression in between and thus overestimating or underestimating according
              if(ng==2)     * to the curvature of the survival function. If, for the same date, we 
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
              else     * to compare the new estimate of Life expectancy with the same linear 
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);     * hypothesis. A more precise result, taking into account a more precise
              ij=1;     * curvature will be obtained if estepm is as small as stepm. */
              for(j=3; j <=ncovmodel; j++) {  
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    /* For example we decided to compute the life expectancy with the smallest unit */
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
                  ij++;       nhstepm is the number of hstepm from age to agelim 
                }       nstepm is the number of stepm from age to agelin. 
                else       Look at hpijx to understand the reason of that which relies in memory size
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);       and note for a fixed period like estepm months */
              }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
              fprintf(ficgp,")/(1");       survival function given by stepm (the optimization length). Unfortunately it
                     means that if the survival funtion is printed only each two years of age and if
              for(k1=1; k1 <=nlstate; k1++){         you sum them up and add 1 year (area under the trapezoids) you won't get the same 
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);       results. So we changed our mind and took the option of the best precision.
                ij=1;    */
                for(j=3; j <=ncovmodel; j++){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
                  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]]]);    agelim=AGESUP;
                    ij++;    /* nhstepm age range expressed in number of stepm */
                  }    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
                  else    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    /* if (stepm >= YEARM) hstepm=1;*/
                }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
                fprintf(ficgp,")");    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
              }  
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      /* Computed by stepm unit matrices, product of hstepm matrices, stored
              i=i+ncovmodel;         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
            }  
          }      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
        }   
      }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
    }  
    fclose(ficgp);      /* Computing  Variances of health expectancies */
 }  /* end gnuplot */      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          decrease memory allocation */
        printf("%d|",(int)age);fflush(stdout);
 /*************** Moving average **************/       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){      /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
   int i, cpt, cptcod;        for(j=1; j<=nlstate;j++)
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       for (i=1; i<=nlstate;i++)            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)            
           mobaverage[(int)agedeb][i][cptcod]=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]);*/
      
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){          }
       for (i=1; i<=nlstate;i++){  
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      fprintf(ficreseij,"%3.0f",age );
           for (cpt=0;cpt<=4;cpt++){      for(i=1; i<=nlstate;i++){
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];        eip=0;
           }        for(j=1; j<=nlstate;j++){
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;          eip +=eij[i][j][(int)age];
         }          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
       }        }
     }        fprintf(ficreseij,"%9.4f", eip );
          }
 }      fprintf(ficreseij,"\n");
   
     }
 /************** Forecasting ******************/    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 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){    printf("\n");
      fprintf(ficlog,"\n");
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;  
   int *popage;  }
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  
   double *popeffectif,*popcount;  void cvevsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
   double ***p3mat;  
   char fileresf[FILENAMELENGTH];  {
     /* Covariances of health expectancies eij and of total life expectancies according
  agelim=AGESUP;     to initial status i, ei. .
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    double age, agelim, hf;
      double ***p3matp, ***p3matm, ***varhe;
      double **dnewm,**doldm;
   strcpy(fileresf,"f");    double *xp, *xm;
   strcat(fileresf,fileres);    double **gp, **gm;
   if((ficresf=fopen(fileresf,"w"))==NULL) {    double ***gradg, ***trgradg;
     printf("Problem with forecast resultfile: %s\n", fileresf);    int theta;
   }  
   printf("Computing forecasting: result on file '%s' \n", fileresf);    double eip, vip;
   
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     xp=vector(1,npar);
   if (mobilav==1) {    xm=vector(1,npar);
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    dnewm=matrix(1,nlstate*nlstate,1,npar);
     movingaverage(agedeb, fage, ageminpar, mobaverage);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   }    
     pstamp(ficresstdeij);
   stepsize=(int) (stepm+YEARM-1)/YEARM;    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   if (stepm<=12) stepsize=1;    fprintf(ficresstdeij,"# Age");
      for(i=1; i<=nlstate;i++){
   agelim=AGESUP;      for(j=1; j<=nlstate;j++)
          fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   hstepm=1;      fprintf(ficresstdeij," e%1d. ",i);
   hstepm=hstepm/stepm;    }
   yp1=modf(dateintmean,&yp);    fprintf(ficresstdeij,"\n");
   anprojmean=yp;  
   yp2=modf((yp1*12),&yp);    pstamp(ficrescveij);
   mprojmean=yp;    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   yp1=modf((yp2*30.5),&yp);    fprintf(ficrescveij,"# Age");
   jprojmean=yp;    for(i=1; i<=nlstate;i++)
   if(jprojmean==0) jprojmean=1;      for(j=1; j<=nlstate;j++){
   if(mprojmean==0) jprojmean=1;        cptj= (j-1)*nlstate+i;
          for(i2=1; i2<=nlstate;i2++)
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);          for(j2=1; j2<=nlstate;j2++){
              cptj2= (j2-1)*nlstate+i2;
   for(cptcov=1;cptcov<=i2;cptcov++){            if(cptj2 <= cptj)
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
       k=k+1;          }
       fprintf(ficresf,"\n#******");      }
       for(j=1;j<=cptcoveff;j++) {    fprintf(ficrescveij,"\n");
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    
       }    if(estepm < stepm){
       fprintf(ficresf,"******\n");      printf ("Problem %d lower than %d\n",estepm, stepm);
       fprintf(ficresf,"# StartingAge FinalAge");    }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    else  hstepm=estepm;   
          /* We compute the life expectancy from trapezoids spaced every estepm months
           * This is mainly to measure the difference between two models: for example
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {     * if stepm=24 months pijx are given only every 2 years and by summing them
         fprintf(ficresf,"\n");     * we are calculating an estimate of the Life Expectancy assuming a linear 
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);       * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     * estimate the model with stepm=1 month, we can keep estepm to 24 months
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);     * to compare the new estimate of Life expectancy with the same linear 
           nhstepm = nhstepm/hstepm;     * hypothesis. A more precise result, taking into account a more precise
               * curvature will be obtained if estepm is as small as stepm. */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;    /* For example we decided to compute the life expectancy with the smallest unit */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      /* 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 
           for (h=0; h<=nhstepm; h++){       nstepm is the number of stepm from age to agelin. 
             if (h==(int) (calagedate+YEARM*cpt)) {       Look at hpijx to understand the reason of that which relies in memory size
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);       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(j=1; j<=nlstate+ndeath;j++) {       survival function given by stepm (the optimization length). Unfortunately it
               kk1=0.;kk2=0;       means that if the survival funtion is printed only each two years of age and if
               for(i=1; i<=nlstate;i++) {                     you sum them up and add 1 year (area under the trapezoids) you won't get the same 
                 if (mobilav==1)       results. So we changed our mind and took the option of the best precision.
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    */
                 else {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];  
                 }    /* If stepm=6 months */
                    /* nhstepm age range expressed in number of stepm */
               }    agelim=AGESUP;
               if (h==(int)(calagedate+12*cpt)){    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
                 fprintf(ficresf," %.3f", kk1);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
                            /* if (stepm >= YEARM) hstepm=1;*/
               }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
             }    
           }    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         }    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
       }    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     }    gp=matrix(0,nhstepm,1,nlstate*nlstate);
   }    gm=matrix(0,nhstepm,1,nlstate*nlstate);
          
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    for (age=bage; age<=fage; age ++){ 
   
   fclose(ficresf);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
 }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
 /************** 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){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
    
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      /* Computing  Variances of health expectancies */
   int *popage;      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;         decrease memory allocation */
   double *popeffectif,*popcount;      for(theta=1; theta <=npar; theta++){
   double ***p3mat,***tabpop,***tabpopprev;        for(i=1; i<=npar; i++){ 
   char filerespop[FILENAMELENGTH];          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        }
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   agelim=AGESUP;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;    
          for(j=1; j<= nlstate; j++){
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);          for(i=1; i<=nlstate; i++){
              for(h=0; h<=nhstepm-1; h++){
                gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   strcpy(filerespop,"pop");              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   strcat(filerespop,fileres);            }
   if((ficrespop=fopen(filerespop,"w"))==NULL) {          }
     printf("Problem with forecast resultfile: %s\n", filerespop);        }
   }       
   printf("Computing forecasting: result on file '%s' \n", filerespop);        for(ij=1; ij<= nlstate*nlstate; ij++)
           for(h=0; h<=nhstepm-1; h++){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
           }
   if (mobilav==1) {      }/* End theta */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      
     movingaverage(agedeb, fage, ageminpar, mobaverage);      
   }      for(h=0; h<=nhstepm-1; h++)
         for(j=1; j<=nlstate*nlstate;j++)
   stepsize=(int) (stepm+YEARM-1)/YEARM;          for(theta=1; theta <=npar; theta++)
   if (stepm<=12) stepsize=1;            trgradg[h][j][theta]=gradg[h][theta][j];
        
   agelim=AGESUP;  
         for(ij=1;ij<=nlstate*nlstate;ij++)
   hstepm=1;        for(ji=1;ji<=nlstate*nlstate;ji++)
   hstepm=hstepm/stepm;          varhe[ij][ji][(int)age] =0.;
    
   if (popforecast==1) {       printf("%d|",(int)age);fflush(stdout);
     if((ficpop=fopen(popfile,"r"))==NULL) {       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       printf("Problem with population file : %s\n",popfile);exit(0);       for(h=0;h<=nhstepm-1;h++){
     }        for(k=0;k<=nhstepm-1;k++){
     popage=ivector(0,AGESUP);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     popeffectif=vector(0,AGESUP);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
     popcount=vector(0,AGESUP);          for(ij=1;ij<=nlstate*nlstate;ij++)
                for(ji=1;ji<=nlstate*nlstate;ji++)
     i=1;                varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;        }
          }
     imx=i;      /* Computing expectancies */
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   }      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   for(cptcov=1;cptcov<=i2;cptcov++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
       k=k+1;            
       fprintf(ficrespop,"\n#******");            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
       for(j=1;j<=cptcoveff;j++) {  
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          }
       }  
       fprintf(ficrespop,"******\n");      fprintf(ficresstdeij,"%3.0f",age );
       fprintf(ficrespop,"# Age");      for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);        eip=0.;
       if (popforecast==1)  fprintf(ficrespop," [Population]");        vip=0.;
              for(j=1; j<=nlstate;j++){
       for (cpt=0; cpt<=0;cpt++) {          eip += eij[i][j][(int)age];
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);            for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
                    vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        }
           nhstepm = nhstepm/hstepm;        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
                }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficresstdeij,"\n");
           oldm=oldms;savm=savms;  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        fprintf(ficrescveij,"%3.0f",age );
              for(i=1; i<=nlstate;i++)
           for (h=0; h<=nhstepm; h++){        for(j=1; j<=nlstate;j++){
             if (h==(int) (calagedate+YEARM*cpt)) {          cptj= (j-1)*nlstate+i;
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);          for(i2=1; i2<=nlstate;i2++)
             }            for(j2=1; j2<=nlstate;j2++){
             for(j=1; j<=nlstate+ndeath;j++) {              cptj2= (j2-1)*nlstate+i2;
               kk1=0.;kk2=0;              if(cptj2 <= cptj)
               for(i=1; i<=nlstate;i++) {                              fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
                 if (mobilav==1)            }
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];        }
                 else {      fprintf(ficrescveij,"\n");
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];     
                 }    }
               }    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
               if (h==(int)(calagedate+12*cpt)){    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
                   /*fprintf(ficrespop," %.3f", kk1);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
               }    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             }    printf("\n");
             for(i=1; i<=nlstate;i++){    fprintf(ficlog,"\n");
               kk1=0.;  
                 for(j=1; j<=nlstate;j++){    free_vector(xm,1,npar);
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];    free_vector(xp,1,npar);
                 }    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
             }    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)  
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);  /************ Variance ******************/
           }  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[])
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  {
         }    /* Variance of health expectancies */
       }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
      /* double **newm;*/
   /******/    double **dnewm,**doldm;
     double **dnewmp,**doldmp;
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    int i, j, nhstepm, hstepm, h, nstepm ;
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      int k, cptcode;
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    double *xp;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    double **gp, **gm;  /* for var eij */
           nhstepm = nhstepm/hstepm;    double ***gradg, ***trgradg; /*for var eij */
              double **gradgp, **trgradgp; /* for var p point j */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double *gpp, *gmp; /* for var p point j */
           oldm=oldms;savm=savms;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double ***p3mat;
           for (h=0; h<=nhstepm; h++){    double age,agelim, hf;
             if (h==(int) (calagedate+YEARM*cpt)) {    double ***mobaverage;
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    int theta;
             }    char digit[4];
             for(j=1; j<=nlstate+ndeath;j++) {    char digitp[25];
               kk1=0.;kk2=0;  
               for(i=1; i<=nlstate;i++) {                  char fileresprobmorprev[FILENAMELENGTH];
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];      
               }    if(popbased==1){
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);      if(mobilav!=0)
             }        strcpy(digitp,"-populbased-mobilav-");
           }      else strcpy(digitp,"-populbased-nomobil-");
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    }
         }    else 
       }      strcpy(digitp,"-stablbased-");
    }  
   }    if (mobilav!=0) {
        mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   if (popforecast==1) {        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     free_ivector(popage,0,AGESUP);      }
     free_vector(popeffectif,0,AGESUP);    }
     free_vector(popcount,0,AGESUP);  
   }    strcpy(fileresprobmorprev,"prmorprev"); 
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    sprintf(digit,"%-d",ij);
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   fclose(ficrespop);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
 }    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
 /***********************************************/    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
 /**************** Main Program *****************/      printf("Problem with resultfile: %s\n", fileresprobmorprev);
 /***********************************************/      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
 int main(int argc, char *argv[])    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
 {   
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    pstamp(ficresprobmorprev);
   double agedeb, agefin,hf;    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);
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   double fret;      fprintf(ficresprobmorprev," p.%-d SE",j);
   double **xi,tmp,delta;      for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   double dum; /* Dummy variable */    }  
   double ***p3mat;    fprintf(ficresprobmorprev,"\n");
   int *indx;    fprintf(ficgp,"\n# Routine varevsij");
   char line[MAXLINE], linepar[MAXLINE];    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    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");
   int firstobs=1, lastobs=10;    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   int sdeb, sfin; /* Status at beginning and end */  /*   } */
   int c,  h , cpt,l;    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   int ju,jl, mi;    pstamp(ficresvij);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    if(popbased==1)
   int mobilav=0,popforecast=0;      fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
   int hstepm, nhstepm;    else
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
   double bage, fage, age, agelim, agebase;    for(i=1; i<=nlstate;i++)
   double ftolpl=FTOL;      for(j=1; j<=nlstate;j++)
   double **prlim;        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
   double *severity;    fprintf(ficresvij,"\n");
   double ***param; /* Matrix of parameters */  
   double  *p;    xp=vector(1,npar);
   double **matcov; /* Matrix of covariance */    dnewm=matrix(1,nlstate,1,npar);
   double ***delti3; /* Scale */    doldm=matrix(1,nlstate,1,nlstate);
   double *delti; /* Scale */    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
   double ***eij, ***vareij;    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   double **varpl; /* Variances of prevalence limits by age */  
   double *epj, vepp;    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   double kk1, kk2;    gpp=vector(nlstate+1,nlstate+ndeath);
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    gmp=vector(nlstate+1,nlstate+ndeath);
      trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
   char *alph[]={"a","a","b","c","d","e"}, str[4];    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
   char z[1]="c", occ;    else  hstepm=estepm;   
 #include <sys/time.h>    /* For example we decided to compute the life expectancy with the smallest unit */
 #include <time.h>    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];       nhstepm is the number of hstepm from age to agelim 
         nstepm is the number of stepm from age to agelin. 
   /* long total_usecs;       Look at hpijx to understand the reason of that which relies in memory size
   struct timeval start_time, end_time;       and note for a fixed period like k years */
      /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */       survival function given by stepm (the optimization length). Unfortunately it
   getcwd(pathcd, size);       means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   printf("\n%s",version);       results. So we changed our mind and took the option of the best precision.
   if(argc <=1){    */
     printf("\nEnter the parameter file name: ");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     scanf("%s",pathtot);    agelim = AGESUP;
   }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   else{      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     strcpy(pathtot,argv[1]);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   /*cygwin_split_path(pathtot,path,optionfile);      gp=matrix(0,nhstepm,1,nlstate);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      gm=matrix(0,nhstepm,1,nlstate);
   /* cutv(path,optionfile,pathtot,'\\');*/  
   
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);      for(theta=1; theta <=npar; theta++){
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   chdir(path);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   replace(pathc,path);        }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 /*-------- arguments in the command line --------*/        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   
   strcpy(fileres,"r");        if (popbased==1) {
   strcat(fileres, optionfilefiname);          if(mobilav ==0){
   strcat(fileres,".txt");    /* Other files have txt extension */            for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
   /*---------arguments file --------*/          }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
   if((ficpar=fopen(optionfile,"r"))==NULL)    {              prlim[i][i]=mobaverage[(int)age][i][ij];
     printf("Problem with optionfile %s\n",optionfile);          }
     goto end;        }
   }    
         for(j=1; j<= nlstate; j++){
   strcpy(filereso,"o");          for(h=0; h<=nhstepm; h++){
   strcat(filereso,fileres);            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
   if((ficparo=fopen(filereso,"w"))==NULL) {              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     printf("Problem with Output resultfile: %s\n", filereso);goto end;          }
   }        }
         /* This for computing probability of death (h=1 means
   /* Reads comments: lines beginning with '#' */           computed over hstepm matrices product = hstepm*stepm months) 
   while((c=getc(ficpar))=='#' && c!= EOF){           as a weighted average of prlim.
     ungetc(c,ficpar);        */
     fgets(line, MAXLINE, ficpar);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     puts(line);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
     fputs(line,ficparo);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
   }        }    
   ungetc(c,ficpar);        /* end probability of death */
   
   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(i=1; i<=npar; i++) /* Computes gradient x - delta */
   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);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   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);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
 while((c=getc(ficpar))=='#' && c!= EOF){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     ungetc(c,ficpar);   
     fgets(line, MAXLINE, ficpar);        if (popbased==1) {
     puts(line);          if(mobilav ==0){
     fputs(line,ficparo);            for(i=1; i<=nlstate;i++)
   }              prlim[i][i]=probs[(int)age][i][ij];
   ungetc(c,ficpar);          }else{ /* mobilav */ 
              for(i=1; i<=nlstate;i++)
                  prlim[i][i]=mobaverage[(int)age][i][ij];
   covar=matrix(0,NCOVMAX,1,n);          }
   cptcovn=0;        }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;  
         for(j=1; j<= nlstate; j++){
   ncovmodel=2+cptcovn;          for(h=0; h<=nhstepm; h++){
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
                gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   /* Read guess parameters */          }
   /* Reads comments: lines beginning with '#' */        }
   while((c=getc(ficpar))=='#' && c!= EOF){        /* This for computing probability of death (h=1 means
     ungetc(c,ficpar);           computed over hstepm matrices product = hstepm*stepm months) 
     fgets(line, MAXLINE, ficpar);           as a weighted average of prlim.
     puts(line);        */
     fputs(line,ficparo);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   }          for(i=1,gmp[j]=0.; i<= nlstate; i++)
   ungetc(c,ficpar);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
          }    
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        /* end probability of death */
     for(i=1; i <=nlstate; i++)  
     for(j=1; j <=nlstate+ndeath-1; j++){        for(j=1; j<= nlstate; j++) /* vareij */
       fscanf(ficpar,"%1d%1d",&i1,&j1);          for(h=0; h<=nhstepm; h++){
       fprintf(ficparo,"%1d%1d",i1,j1);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       printf("%1d%1d",i,j);          }
       for(k=1; k<=ncovmodel;k++){  
         fscanf(ficpar," %lf",&param[i][j][k]);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
         printf(" %lf",param[i][j][k]);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         fprintf(ficparo," %lf",param[i][j][k]);        }
       }  
       fscanf(ficpar,"\n");      } /* End theta */
       printf("\n");  
       fprintf(ficparo,"\n");      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     }  
        for(h=0; h<=nhstepm; h++) /* veij */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
   p=param[1][1];            trgradg[h][j][theta]=gradg[h][theta][j];
    
   /* Reads comments: lines beginning with '#' */      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   while((c=getc(ficpar))=='#' && c!= EOF){        for(theta=1; theta <=npar; theta++)
     ungetc(c,ficpar);          trgradgp[j][theta]=gradgp[theta][j];
     fgets(line, MAXLINE, ficpar);    
     puts(line);  
     fputs(line,ficparo);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   }      for(i=1;i<=nlstate;i++)
   ungetc(c,ficpar);        for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      for(h=0;h<=nhstepm;h++){
   for(i=1; i <=nlstate; i++){        for(k=0;k<=nhstepm;k++){
     for(j=1; j <=nlstate+ndeath-1; j++){          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
       fscanf(ficpar,"%1d%1d",&i1,&j1);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
       printf("%1d%1d",i,j);          for(i=1;i<=nlstate;i++)
       fprintf(ficparo,"%1d%1d",i1,j1);            for(j=1;j<=nlstate;j++)
       for(k=1; k<=ncovmodel;k++){              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         fscanf(ficpar,"%le",&delti3[i][j][k]);        }
         printf(" %le",delti3[i][j][k]);      }
         fprintf(ficparo," %le",delti3[i][j][k]);    
       }      /* pptj */
       fscanf(ficpar,"\n");      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       printf("\n");      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       fprintf(ficparo,"\n");      for(j=nlstate+1;j<=nlstate+ndeath;j++)
     }        for(i=nlstate+1;i<=nlstate+ndeath;i++)
   }          varppt[j][i]=doldmp[j][i];
   delti=delti3[1][1];      /* end ppptj */
        /*  x centered again */
   /* Reads comments: lines beginning with '#' */      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
   while((c=getc(ficpar))=='#' && c!= EOF){      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     ungetc(c,ficpar);   
     fgets(line, MAXLINE, ficpar);      if (popbased==1) {
     puts(line);        if(mobilav ==0){
     fputs(line,ficparo);          for(i=1; i<=nlstate;i++)
   }            prlim[i][i]=probs[(int)age][i][ij];
   ungetc(c,ficpar);        }else{ /* mobilav */ 
            for(i=1; i<=nlstate;i++)
   matcov=matrix(1,npar,1,npar);            prlim[i][i]=mobaverage[(int)age][i][ij];
   for(i=1; i <=npar; i++){        }
     fscanf(ficpar,"%s",&str);      }
     printf("%s",str);               
     fprintf(ficparo,"%s",str);      /* This for computing probability of death (h=1 means
     for(j=1; j <=i; j++){         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
       fscanf(ficpar," %le",&matcov[i][j]);         as a weighted average of prlim.
       printf(" %.5le",matcov[i][j]);      */
       fprintf(ficparo," %.5le",matcov[i][j]);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
     }        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     fscanf(ficpar,"\n");          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     printf("\n");      }    
     fprintf(ficparo,"\n");      /* end probability of death */
   }  
   for(i=1; i <=npar; i++)      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     for(j=i+1;j<=npar;j++)      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       matcov[i][j]=matcov[j][i];        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
            for(i=1; i<=nlstate;i++){
   printf("\n");          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
     /*-------- Rewriting paramater file ----------*/      fprintf(ficresprobmorprev,"\n");
      strcpy(rfileres,"r");    /* "Rparameterfile */  
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/      fprintf(ficresvij,"%.0f ",age );
      strcat(rfileres,".");    /* */      for(i=1; i<=nlstate;i++)
      strcat(rfileres,optionfilext);    /* Other files have txt extension */        for(j=1; j<=nlstate;j++){
     if((ficres =fopen(rfileres,"w"))==NULL) {          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       printf("Problem writing new parameter file: %s\n", fileres);goto end;        }
     }      fprintf(ficresvij,"\n");
     fprintf(ficres,"#%s\n",version);      free_matrix(gp,0,nhstepm,1,nlstate);
          free_matrix(gm,0,nhstepm,1,nlstate);
     /*-------- data file ----------*/      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
     if((fic=fopen(datafile,"r"))==NULL)    {      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       printf("Problem with datafile: %s\n", datafile);goto end;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }    } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     n= lastobs;    free_vector(gmp,nlstate+1,nlstate+ndeath);
     severity = vector(1,maxwav);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     outcome=imatrix(1,maxwav+1,1,n);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     num=ivector(1,n);    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     moisnais=vector(1,n);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     annais=vector(1,n);    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
     moisdc=vector(1,n);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
     andc=vector(1,n);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
     agedc=vector(1,n);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     cod=ivector(1,n);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     weight=vector(1,n);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     mint=matrix(1,maxwav,1,n);    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     anint=matrix(1,maxwav,1,n);    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);
     s=imatrix(1,maxwav+1,1,n);    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
     adl=imatrix(1,maxwav+1,1,n);      */
     tab=ivector(1,NCOVMAX);  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     ncodemax=ivector(1,8);    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     i=1;    free_vector(xp,1,npar);
     while (fgets(line, MAXLINE, fic) != NULL)    {    free_matrix(doldm,1,nlstate,1,nlstate);
       if ((i >= firstobs) && (i <=lastobs)) {    free_matrix(dnewm,1,nlstate,1,npar);
            free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         for (j=maxwav;j>=1;j--){    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           strcpy(line,stra);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fclose(ficresprobmorprev);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fflush(ficgp);
         }    fflush(fichtm); 
          }  /* end varevsij */
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);  /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);  {
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    double **newm;
         for (j=ncovcol;j>=1;j--){    double **dnewm,**doldm;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int i, j, nhstepm, hstepm;
         }    int k, cptcode;
         num[i]=atol(stra);    double *xp;
            double *gp, *gm;
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    double **gradg, **trgradg;
           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;}*/    double age,agelim;
     int theta;
         i=i+1;    
       }    pstamp(ficresvpl);
     }    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     /* printf("ii=%d", ij);    fprintf(ficresvpl,"# Age");
        scanf("%d",i);*/    for(i=1; i<=nlstate;i++)
   imx=i-1; /* Number of individuals */        fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   /* for (i=1; i<=imx; i++){  
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    xp=vector(1,npar);
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    dnewm=matrix(1,nlstate,1,npar);
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    doldm=matrix(1,nlstate,1,nlstate);
     }*/    
    /*  for (i=1; i<=imx; i++){    hstepm=1*YEARM; /* Every year of age */
      if (s[4][i]==9)  s[4][i]=-1;    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
      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]));}*/    agelim = AGESUP;
      for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
        nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
   /* Calculation of the number of parameter from char model*/      if (stepm >= YEARM) hstepm=1;
   Tvar=ivector(1,15);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   Tprod=ivector(1,15);      gradg=matrix(1,npar,1,nlstate);
   Tvaraff=ivector(1,15);      gp=vector(1,nlstate);
   Tvard=imatrix(1,15,1,2);      gm=vector(1,nlstate);
   Tage=ivector(1,15);        
          for(theta=1; theta <=npar; theta++){
   if (strlen(model) >1){        for(i=1; i<=npar; i++){ /* Computes gradient */
     j=0, j1=0, k1=1, k2=1;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     j=nbocc(model,'+');        }
     j1=nbocc(model,'*');        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     cptcovn=j+1;        for(i=1;i<=nlstate;i++)
     cptcovprod=j1;          gp[i] = prlim[i][i];
          
     strcpy(modelsav,model);        for(i=1; i<=npar; i++) /* Computes gradient */
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       printf("Error. Non available option model=%s ",model);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       goto end;        for(i=1;i<=nlstate;i++)
     }          gm[i] = prlim[i][i];
      
     for(i=(j+1); i>=1;i--){        for(i=1;i<=nlstate;i++)
       cutv(stra,strb,modelsav,'+');          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);      } /* End theta */
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/  
       /*scanf("%d",i);*/      trgradg =matrix(1,nlstate,1,npar);
       if (strchr(strb,'*')) {  
         cutv(strd,strc,strb,'*');      for(j=1; j<=nlstate;j++)
         if (strcmp(strc,"age")==0) {        for(theta=1; theta <=npar; theta++)
           cptcovprod--;          trgradg[j][theta]=gradg[theta][j];
           cutv(strb,stre,strd,'V');  
           Tvar[i]=atoi(stre);      for(i=1;i<=nlstate;i++)
           cptcovage++;        varpl[i][(int)age] =0.;
             Tage[cptcovage]=i;      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
             /*printf("stre=%s ", stre);*/      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
         }      for(i=1;i<=nlstate;i++)
         else if (strcmp(strd,"age")==0) {        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
           cptcovprod--;  
           cutv(strb,stre,strc,'V');      fprintf(ficresvpl,"%.0f ",age );
           Tvar[i]=atoi(stre);      for(i=1; i<=nlstate;i++)
           cptcovage++;        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
           Tage[cptcovage]=i;      fprintf(ficresvpl,"\n");
         }      free_vector(gp,1,nlstate);
         else {      free_vector(gm,1,nlstate);
           cutv(strb,stre,strc,'V');      free_matrix(gradg,1,npar,1,nlstate);
           Tvar[i]=ncovcol+k1;      free_matrix(trgradg,1,nlstate,1,npar);
           cutv(strb,strc,strd,'V');    } /* End age */
           Tprod[k1]=i;  
           Tvard[k1][1]=atoi(strc);    free_vector(xp,1,npar);
           Tvard[k1][2]=atoi(stre);    free_matrix(doldm,1,nlstate,1,npar);
           Tvar[cptcovn+k2]=Tvard[k1][1];    free_matrix(dnewm,1,nlstate,1,nlstate);
           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++;  /************ Variance of one-step probabilities  ******************/
           k2=k2+2;  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
         }  {
       }    int i, j=0,  i1, k1, l1, t, tj;
       else {    int k2, l2, j1,  z1;
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    int k=0,l, cptcode;
        /*  scanf("%d",i);*/    int first=1, first1;
       cutv(strd,strc,strb,'V');    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
       Tvar[i]=atoi(strc);    double **dnewm,**doldm;
       }    double *xp;
       strcpy(modelsav,stra);      double *gp, *gm;
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    double **gradg, **trgradg;
         scanf("%d",i);*/    double **mu;
     }    double age,agelim, cov[NCOVMAX];
 }    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
      int theta;
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    char fileresprob[FILENAMELENGTH];
   printf("cptcovprod=%d ", cptcovprod);    char fileresprobcov[FILENAMELENGTH];
   scanf("%d ",i);*/    char fileresprobcor[FILENAMELENGTH];
     fclose(fic);  
     double ***varpij;
     /*  if(mle==1){*/  
     if (weightopt != 1) { /* Maximisation without weights*/    strcpy(fileresprob,"prob"); 
       for(i=1;i<=n;i++) weight[i]=1.0;    strcat(fileresprob,fileres);
     }    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     /*-calculation of age at interview from date of interview and age at death -*/      printf("Problem with resultfile: %s\n", fileresprob);
     agev=matrix(1,maxwav,1,imx);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     for (i=1; i<=imx; i++) {    strcpy(fileresprobcov,"probcov"); 
       for(m=2; (m<= maxwav); m++) {    strcat(fileresprobcov,fileres);
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
          anint[m][i]=9999;      printf("Problem with resultfile: %s\n", fileresprobcov);
          s[m][i]=-1;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
        }    }
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;    strcpy(fileresprobcor,"probcor"); 
       }    strcat(fileresprobcor,fileres);
     }    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
     for (i=1; i<=imx; i++)  {      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    }
       for(m=1; (m<= maxwav); m++){    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
         if(s[m][i] >0){    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           if (s[m][i] >= nlstate+1) {    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
             if(agedc[i]>0)    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
               if(moisdc[i]!=99 && andc[i]!=9999)    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
                 agev[m][i]=agedc[i];    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/    pstamp(ficresprob);
            else {    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
               if (andc[i]!=9999){    fprintf(ficresprob,"# Age");
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    pstamp(ficresprobcov);
               agev[m][i]=-1;    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
               }    fprintf(ficresprobcov,"# Age");
             }    pstamp(ficresprobcor);
           }    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
           else if(s[m][i] !=9){ /* Should no more exist */    fprintf(ficresprobcor,"# Age");
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);  
             if(mint[m][i]==99 || anint[m][i]==9999)  
               agev[m][i]=1;    for(i=1; i<=nlstate;i++)
             else if(agev[m][i] <agemin){      for(j=1; j<=(nlstate+ndeath);j++){
               agemin=agev[m][i];        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/        fprintf(ficresprobcov," p%1d-%1d ",i,j);
             }        fprintf(ficresprobcor," p%1d-%1d ",i,j);
             else if(agev[m][i] >agemax){      }  
               agemax=agev[m][i];   /* fprintf(ficresprob,"\n");
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    fprintf(ficresprobcov,"\n");
             }    fprintf(ficresprobcor,"\n");
             /*agev[m][i]=anint[m][i]-annais[i];*/   */
             /*   agev[m][i] = age[i]+2*m;*/   xp=vector(1,npar);
           }    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           else { /* =9 */    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
             agev[m][i]=1;    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
             s[m][i]=-1;    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
           }    first=1;
         }    fprintf(ficgp,"\n# Routine varprob");
         else /*= 0 Unknown */    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
           agev[m][i]=1;    fprintf(fichtm,"\n");
       }  
        fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     }    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     for (i=1; i<=imx; i++)  {    file %s<br>\n",optionfilehtmcov);
       for(m=1; (m<= maxwav); m++){    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
         if (s[m][i] > (nlstate+ndeath)) {  and drawn. It helps understanding how is the covariance between two incidences.\
           printf("Error: Wrong value in nlstate or ndeath\n");     They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
           goto end;    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
         }  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
       }  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
     }  standard deviations wide on each axis. <br>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
     free_vector(severity,1,maxwav);  
     free_imatrix(outcome,1,maxwav+1,1,n);    cov[1]=1;
     free_vector(moisnais,1,n);    tj=cptcoveff;
     free_vector(annais,1,n);    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     /* free_matrix(mint,1,maxwav,1,n);    j1=0;
        free_matrix(anint,1,maxwav,1,n);*/    for(t=1; t<=tj;t++){
     free_vector(moisdc,1,n);      for(i1=1; i1<=ncodemax[t];i1++){ 
     free_vector(andc,1,n);        j1++;
         if  (cptcovn>0) {
              fprintf(ficresprob, "\n#********** Variable "); 
     wav=ivector(1,imx);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          fprintf(ficresprob, "**********\n#\n");
     mw=imatrix(1,lastpass-firstpass+1,1,imx);          fprintf(ficresprobcov, "\n#********** Variable "); 
              for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     /* Concatenates waves */          fprintf(ficresprobcov, "**********\n#\n");
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);          
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       Tcode=ivector(1,100);          fprintf(ficgp, "**********\n#\n");
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);          
       ncodemax[1]=1;          
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          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]]);
    codtab=imatrix(1,100,1,10);          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
    h=0;          
    m=pow(2,cptcoveff);          fprintf(ficresprobcor, "\n#********** Variable ");    
            for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    for(k=1;k<=cptcoveff; k++){          fprintf(ficresprobcor, "**********\n#");    
      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++){        for (age=bage; age<=fage; age ++){ 
            h++;          cov[2]=age;
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;          for (k=1; k<=cptcovn;k++) {
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[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]]];
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);          
       codtab[1][2]=1;codtab[2][2]=2; */          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
    /* for(i=1; i <=m ;i++){          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
       for(k=1; k <=cptcovn; k++){          gp=vector(1,(nlstate)*(nlstate+ndeath));
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);          gm=vector(1,(nlstate)*(nlstate+ndeath));
       }      
       printf("\n");          for(theta=1; theta <=npar; theta++){
       }            for(i=1; i<=npar; i++)
       scanf("%d",i);*/              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
                
    /* Calculates basic frequencies. Computes observed prevalence at single age            pmij(pmmij,cov,ncovmodel,xp,nlstate);
        and prints on file fileres'p'. */            
             k=0;
                for(i=1; i<= (nlstate); i++){
                  for(j=1; j<=(nlstate+ndeath);j++){
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                k=k+1;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                gp[k]=pmmij[i][j];
     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(i=1; i<=npar; i++)
     /* For Powell, parameters are in a vector p[] starting at p[1]              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
        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) */            pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
     if(mle==1){            for(i=1; i<=(nlstate); i++){
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);              for(j=1; j<=(nlstate+ndeath);j++){
     }                k=k+1;
                    gm[k]=pmmij[i][j];
     /*--------- 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);            }
         
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
    jk=1;              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
    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++){          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
      for(k=1; k <=(nlstate+ndeath); k++){            for(theta=1; theta <=npar; theta++)
        if (k != i)              trgradg[j][theta]=gradg[theta][j];
          {          
            printf("%d%d ",i,k);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
            fprintf(ficres,"%1d%1d ",i,k);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
            for(j=1; j <=ncovmodel; j++){          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
              printf("%f ",p[jk]);          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
              fprintf(ficres,"%f ",p[jk]);          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
              jk++;          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
            }  
            printf("\n");          pmij(pmmij,cov,ncovmodel,x,nlstate);
            fprintf(ficres,"\n");          
          }          k=0;
      }          for(i=1; i<=(nlstate); i++){
    }            for(j=1; j<=(nlstate+ndeath);j++){
  if(mle==1){              k=k+1;
     /* Computing hessian and covariance matrix */              mu[k][(int) age]=pmmij[i][j];
     ftolhess=ftol; /* Usually correct */            }
     hesscov(matcov, p, npar, delti, ftolhess, func);          }
  }          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
     printf("# Scales (for hessian or gradient estimation)\n");              varpij[i][j][(int)age] = doldm[i][j];
      for(i=1,jk=1; i <=nlstate; i++){  
       for(j=1; j <=nlstate+ndeath; j++){          /*printf("\n%d ",(int)age);
         if (j!=i) {            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
           fprintf(ficres,"%1d%1d",i,j);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           printf("%1d%1d",i,j);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           for(k=1; k<=ncovmodel;k++){            }*/
             printf(" %.5e",delti[jk]);  
             fprintf(ficres," %.5e",delti[jk]);          fprintf(ficresprob,"\n%d ",(int)age);
             jk++;          fprintf(ficresprobcov,"\n%d ",(int)age);
           }          fprintf(ficresprobcor,"\n%d ",(int)age);
           printf("\n");  
           fprintf(ficres,"\n");          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
         }            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
       }          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
      }            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
                fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
     k=1;          }
     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");          i=0;
     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");          for (k=1; k<=(nlstate);k++){
     for(i=1;i<=npar;i++){            for (l=1; l<=(nlstate+ndeath);l++){ 
       /*  if (k>nlstate) k=1;              i=i++;
       i1=(i-1)/(ncovmodel*nlstate)+1;              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
       printf("%s%d%d",alph[k],i1,tab[i]);*/              for (j=1; j<=i;j++){
       fprintf(ficres,"%3d",i);                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
       printf("%3d",i);                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
       for(j=1; j<=i;j++){              }
         fprintf(ficres," %.5e",matcov[i][j]);            }
         printf(" %.5e",matcov[i][j]);          }/* end of loop for state */
       }        } /* end of loop for age */
       fprintf(ficres,"\n");  
       printf("\n");        /* Confidence intervalle of pij  */
       k++;        /*
     }          fprintf(ficgp,"\nset noparametric;unset label");
              fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
     while((c=getc(ficpar))=='#' && c!= EOF){          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
       ungetc(c,ficpar);          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);
       fgets(line, MAXLINE, ficpar);          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
       puts(line);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
       fputs(line,ficparo);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
     }        */
     ungetc(c,ficpar);  
     estepm=0;        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);        first1=1;
     if (estepm==0 || estepm < stepm) estepm=stepm;        for (k2=1; k2<=(nlstate);k2++){
     if (fage <= 2) {          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
       bage = ageminpar;            if(l2==k2) continue;
       fage = agemaxpar;            j=(k2-1)*(nlstate+ndeath)+l2;
     }            for (k1=1; k1<=(nlstate);k1++){
                  for (l1=1; l1<=(nlstate+ndeath);l1++){ 
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");                if(l1==k1) continue;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);                i=(k1-1)*(nlstate+ndeath)+l1;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);                if(i<=j) continue;
                  for (age=bage; age<=fage; age ++){ 
     while((c=getc(ficpar))=='#' && c!= EOF){                  if ((int)age %5==0){
     ungetc(c,ficpar);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
     fgets(line, MAXLINE, ficpar);                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
     puts(line);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
     fputs(line,ficparo);                    mu1=mu[i][(int) age]/stepm*YEARM ;
   }                    mu2=mu[j][(int) age]/stepm*YEARM;
   ungetc(c,ficpar);                    c12=cv12/sqrt(v1*v2);
                      /* Computing eigen value of matrix of covariance */
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                    /* Eigen vectors */
                          v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
   while((c=getc(ficpar))=='#' && c!= EOF){                    /*v21=sqrt(1.-v11*v11); *//* error */
     ungetc(c,ficpar);                    v21=(lc1-v1)/cv12*v11;
     fgets(line, MAXLINE, ficpar);                    v12=-v21;
     puts(line);                    v22=v11;
     fputs(line,ficparo);                    tnalp=v21/v11;
   }                    if(first1==1){
   ungetc(c,ficpar);                      first1=0;
                        printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
    dateprev1=anprev1+mprev1/12.+jprev1/365.;                    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);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;                    /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
   fscanf(ficpar,"pop_based=%d\n",&popbased);                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
   fprintf(ficparo,"pop_based=%d\n",popbased);                      if(first==1){
   fprintf(ficres,"pop_based=%d\n",popbased);                        first=0;
                        fprintf(ficgp,"\nset parametric;unset label");
   while((c=getc(ficpar))=='#' && c!= EOF){                      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);
     ungetc(c,ficpar);                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
     fgets(line, MAXLINE, ficpar);                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
     puts(line);   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
     fputs(line,ficparo);  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
   }                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
   ungetc(c,ficpar);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   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);                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
 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(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
 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);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
 while((c=getc(ficpar))=='#' && c!= EOF){                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
     ungetc(c,ficpar);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
     fgets(line, MAXLINE, ficpar);                    }else{
     puts(line);                      first=0;
     fputs(line,ficparo);                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
   }                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
   ungetc(c,ficpar);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
   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 first */
                   } /* age mod 5 */
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
 /*------------ gnuplot -------------*/                first=1;
   strcpy(optionfilegnuplot,optionfilefiname);              } /*l12 */
   strcat(optionfilegnuplot,".gp");            } /* k12 */
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {          } /*l1 */
     printf("Problem with file %s",optionfilegnuplot);        }/* k1 */
   }      } /* loop covariates */
   fclose(ficgp);    }
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
 /*--------- index.htm --------*/    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   strcpy(optionfilehtm,optionfile);    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   strcat(optionfilehtm,".htm");    free_vector(xp,1,npar);
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    fclose(ficresprob);
     printf("Problem with %s \n",optionfilehtm), exit(0);    fclose(ficresprobcov);
   }    fclose(ficresprobcor);
     fflush(ficgp);
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    fflush(fichtmcov);
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n  }
 \n  
 Total number of observations=%d <br>\n  
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n  /******************* Printing html file ***********/
 <hr  size=\"2\" color=\"#EC5E5E\">  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
  <ul><li>Parameter files<br>\n                    int lastpass, int stepm, int weightopt, char model[],\
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
  - Gnuplot file name: <a href=\"%s\">%s</a><br></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);                    int popforecast, int estepm ,\
   fclose(fichtm);                    double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);    int jj1, k1, i1, cpt;
    
 /*------------ free_vector  -------------*/     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
  chdir(path);     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
    </ul>");
  free_ivector(wav,1,imx);     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);               jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
  free_ivector(num,1,n);     fprintf(fichtm,"\
  free_vector(agedc,1,n);   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
  /*free_matrix(covar,1,NCOVMAX,1,n);*/             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
  fclose(ficparo);     fprintf(fichtm,"\
  fclose(ficres);   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
   /*--------------- Prevalence limit --------------*/   - (a) Life expectancies by health status at initial age, (b) health expectancies by health status at initial age:  ei., eij (estepm=%2d months): \
       <a href=\"%s\">%s</a> <br>\n</li>",
   strcpy(filerespl,"pl");             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   strcat(filerespl,fileres);  
   if((ficrespl=fopen(filerespl,"w"))==NULL) {  
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   }  
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);   m=cptcoveff;
   fprintf(ficrespl,"#Prevalence limit\n");   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   fprintf(ficrespl,"#Age ");  
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);   jj1=0;
   fprintf(ficrespl,"\n");   for(k1=1; k1<=m;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
   prlim=matrix(1,nlstate,1,nlstate);       jj1++;
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       if (cptcovn > 0) {
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         for (cpt=1; cpt<=cptcoveff;cpt++) 
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
   k=0;       }
   agebase=ageminpar;       /* Pij */
   agelim=agemaxpar;       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   ftolpl=1.e-10;  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
   i1=cptcoveff;       /* Quasi-incidences */
   if (cptcovn < 1){i1=1;}       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   for(cptcov=1;cptcov<=i1;cptcov++){  <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){         /* Period (stable) prevalence in each health state */
         k=k+1;         for(cpt=1; cpt<nlstate;cpt++){
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
         fprintf(ficrespl,"\n#******");  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
         for(j=1;j<=cptcoveff;j++)         }
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       for(cpt=1; cpt<=nlstate;cpt++) {
         fprintf(ficrespl,"******\n");          fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
          <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
         for (age=agebase; age<=agelim; age++){       }
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);     } /* end i1 */
           fprintf(ficrespl,"%.0f",age );   }/* End k1 */
           for(i=1; i<=nlstate;i++)   fprintf(fichtm,"</ul>");
           fprintf(ficrespl," %.5f", prlim[i][i]);  
           fprintf(ficrespl,"\n");  
         }   fprintf(fichtm,"\
       }  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
     }   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   fclose(ficrespl);  
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   /*------------- h Pij x at various ages ------------*/           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
     fprintf(fichtm,"\
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   if((ficrespij=fopen(filerespij,"w"))==NULL) {           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  
   }   fprintf(fichtm,"\
   printf("Computing pij: result on file '%s' \n", filerespij);   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
             subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
   stepsize=(int) (stepm+YEARM-1)/YEARM;   fprintf(fichtm,"\
   /*if (stepm<=24) stepsize=2;*/   - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
   agelim=AGESUP;             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
   hstepm=stepsize*YEARM; /* Every year of age */   fprintf(fichtm,"\
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */   - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
       <a href=\"%s\">%s</a> <br>\n</li>",
   k=0;             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
   for(cptcov=1;cptcov<=i1;cptcov++){   fprintf(fichtm,"\
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), eij are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences (i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
       k=k+1;           estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
         fprintf(ficrespij,"\n#****** ");   fprintf(fichtm,"\
         for(j=1;j<=cptcoveff;j++)   - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors: <a href=\"%s\">%s</a> <br>\n",
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);           subdirf2(fileres,"t"),subdirf2(fileres,"t"));
         fprintf(ficrespij,"******\n");   fprintf(fichtm,"\
           - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */           subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  /*  if(popforecast==1) fprintf(fichtm,"\n */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
           oldm=oldms;savm=savms;  /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    /*      <br>",fileres,fileres,fileres,fileres); */
           fprintf(ficrespij,"# Age");  /*  else  */
           for(i=1; i<=nlstate;i++)  /*    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(j=1; j<=nlstate+ndeath;j++)   fflush(fichtm);
               fprintf(ficrespij," %1d-%1d",i,j);   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
           fprintf(ficrespij,"\n");  
            for (h=0; h<=nhstepm; h++){   m=cptcoveff;
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
             for(i=1; i<=nlstate;i++)  
               for(j=1; j<=nlstate+ndeath;j++)   jj1=0;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);   for(k1=1; k1<=m;k1++){
             fprintf(ficrespij,"\n");     for(i1=1; i1<=ncodemax[k1];i1++){
              }       jj1++;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       if (cptcovn > 0) {
           fprintf(ficrespij,"\n");         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
         }         for (cpt=1; cpt<=cptcoveff;cpt++) 
     }           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   }         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);       for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   fclose(ficrespij);  prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
   /*---------- Forecasting ------------------*/       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   if((stepm == 1) && (strcmp(model,".")==0)){  health expectancies in states (1) and (2): %s%d.png<br>\
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);     } /* end i1 */
   }   }/* End k1 */
   else{   fprintf(fichtm,"</ul>");
     erreur=108;   fflush(fichtm);
     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);  }
   }  
    /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   /*---------- Health expectancies and variances ------------*/  
     char dirfileres[132],optfileres[132];
   strcpy(filerest,"t");    int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
   strcat(filerest,fileres);    int ng;
   if((ficrest=fopen(filerest,"w"))==NULL) {  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  /*     printf("Problem with file %s",optionfilegnuplot); */
   }  /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   printf("Computing Total LEs with variances: file '%s' \n", filerest);  /*   } */
   
     /*#ifdef windows */
   strcpy(filerese,"e");    fprintf(ficgp,"cd \"%s\" \n",pathc);
   strcat(filerese,fileres);      /*#endif */
   if((ficreseij=fopen(filerese,"w"))==NULL) {    m=pow(2,cptcoveff);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);  
   }    strcpy(dirfileres,optionfilefiname);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    strcpy(optfileres,"vpl");
    /* 1eme*/
  strcpy(fileresv,"v");    for (cpt=1; cpt<= nlstate ; cpt ++) {
   strcat(fileresv,fileres);     for (k1=1; k1<= m ; k1 ++) {
   if((ficresvij=fopen(fileresv,"w"))==NULL) {       fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);       fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
   }       fprintf(ficgp,"set xlabel \"Age\" \n\
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);  set ylabel \"Probability\" \n\
   calagedate=-1;  set ter png small\n\
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  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);
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){       for (i=1; i<= nlstate ; i ++) {
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
       k=k+1;         else fprintf(ficgp," \%%*lf (\%%*lf)");
       fprintf(ficrest,"\n#****** ");       }
       for(j=1;j<=cptcoveff;j++)       fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       for (i=1; i<= nlstate ; i ++) {
       fprintf(ficrest,"******\n");         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
       fprintf(ficreseij,"\n#****** ");       } 
       for(j=1;j<=cptcoveff;j++)       fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       for (i=1; i<= nlstate ; i ++) {
       fprintf(ficreseij,"******\n");         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
       fprintf(ficresvij,"\n#****** ");       }  
       for(j=1;j<=cptcoveff;j++)       fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     }
       fprintf(ficresvij,"******\n");    }
     /*2 eme*/
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    
       oldm=oldms;savm=savms;    for (k1=1; k1<= m ; k1 ++) { 
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);        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);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      
       oldm=oldms;savm=savms;      for (i=1; i<= nlstate+1 ; i ++) {
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);        k=2*i;
            fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
            if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          else fprintf(ficgp," \%%*lf (\%%*lf)");
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);        }   
       fprintf(ficrest,"\n");        if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
       epj=vector(1,nlstate+1);        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
       for(age=bage; age <=fage ;age++){        for (j=1; j<= nlstate+1 ; j ++) {
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
         if (popbased==1) {          else fprintf(ficgp," \%%*lf (\%%*lf)");
           for(i=1; i<=nlstate;i++)        }   
             prlim[i][i]=probs[(int)age][i][k];        fprintf(ficgp,"\" t\"\" w l 0,");
         }        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
                for (j=1; j<= nlstate+1 ; j ++) {
         fprintf(ficrest," %4.0f",age);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){          else fprintf(ficgp," \%%*lf (\%%*lf)");
           for(i=1, epj[j]=0.;i <=nlstate;i++) {        }   
             epj[j] += prlim[i][i]*eij[i][j][(int)age];        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/        else fprintf(ficgp,"\" t\"\" w l 0,");
           }      }
           epj[nlstate+1] +=epj[j];    }
         }    
     /*3eme*/
         for(i=1, vepp=0.;i <=nlstate;i++)    
           for(j=1;j <=nlstate;j++)    for (k1=1; k1<= m ; k1 ++) { 
             vepp += vareij[i][j][(int)age];      for (cpt=1; cpt<= nlstate ; cpt ++) {
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));        /*       k=2+nlstate*(2*cpt-2); */
         for(j=1;j <=nlstate;j++){        k=2+(nlstate+1)*(cpt-1);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         }        fprintf(ficgp,"set ter png small\n\
         fprintf(ficrest,"\n");  set size 0.65,0.65\n\
       }  plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
     }        /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
   }          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
 free_matrix(mint,1,maxwav,1,n);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);          fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
     free_vector(weight,1,n);          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
   fclose(ficreseij);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
   fclose(ficresvij);          
   fclose(ficrest);        */
   fclose(ficpar);        for (i=1; i< nlstate ; i ++) {
   free_vector(epj,1,nlstate+1);          fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
            /*      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);*/
   /*------- Variance limit prevalence------*/            
         } 
   strcpy(fileresvpl,"vpl");        fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
   strcat(fileresvpl,fileres);      }
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    }
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    
     exit(0);    /* CV preval stable (period) */
   }    for (k1=1; k1<= m ; k1 ++) { 
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);      for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
   k=0;        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
   for(cptcov=1;cptcov<=i1;cptcov++){        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  set ter png small\nset size 0.65,0.65\n\
       k=k+1;  unset log y\n\
       fprintf(ficresvpl,"\n#****** ");  plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
       for(j=1;j<=cptcoveff;j++)        
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for (i=1; i< nlstate ; i ++)
       fprintf(ficresvpl,"******\n");          fprintf(ficgp,"+$%d",k+i+1);
              fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
       varpl=matrix(1,nlstate,(int) bage, (int) fage);        
       oldm=oldms;savm=savms;        l=3+(nlstate+ndeath)*cpt;
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);        fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
     }        for (i=1; i< nlstate ; i ++) {
  }          l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
   fclose(ficresvpl);        }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
   /*---------- End : free ----------------*/      } 
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    }  
      
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    /* proba elementaires */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    for(i=1,jk=1; i <=nlstate; i++){
        for(k=1; k <=(nlstate+ndeath); k++){
          if (k != i) {
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);          for(j=1; j <=ncovmodel; j++){
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);            fprintf(ficgp,"p%d=%f ",jk,p[jk]);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);            jk++; 
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);            fprintf(ficgp,"\n");
            }
   free_matrix(matcov,1,npar,1,npar);        }
   free_vector(delti,1,npar);      }
   free_matrix(agev,1,maxwav,1,imx);     }
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
   fprintf(fichtm,"\n</body>");       for(jk=1; jk <=m; jk++) {
   fclose(fichtm);         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
   fclose(ficgp);         if (ng==2)
             fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
   if(erreur >0)           fprintf(ficgp,"\nset title \"Probability\"\n");
     printf("End of Imach with error or warning %d\n",erreur);         fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
   else   printf("End of Imach\n");         i=1;
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */         for(k2=1; k2<=nlstate; k2++) {
             k3=i;
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/           for(k=1; k<=(nlstate+ndeath); k++) {
   /*printf("Total time was %d uSec.\n", total_usecs);*/             if (k != k2){
   /*------ End -----------*/               if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
  end:                 fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
 #ifdef windows               ij=1;
   /* chdir(pathcd);*/               for(j=3; j <=ncovmodel; j++) {
 #endif                 if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
  /*system("wgnuplot graph.plt");*/                   fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
  /*system("../gp37mgw/wgnuplot graph.plt");*/                   ij++;
  /*system("cd ../gp37mgw");*/                 }
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/                 else
  strcpy(plotcmd,GNUPLOTPROGRAM);                   fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
  strcat(plotcmd," ");               }
  strcat(plotcmd,optionfilegnuplot);               fprintf(ficgp,")/(1");
  system(plotcmd);               
                for(k1=1; k1 <=nlstate; k1++){   
 #ifdef windows                 fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
   while (z[0] != 'q') {                 ij=1;
     /* chdir(path); */                 for(j=3; j <=ncovmodel; j++){
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");                   if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
     scanf("%s",z);                     fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
     if (z[0] == 'c') system("./imach");                     ij++;
     else if (z[0] == 'e') system(optionfilehtm);                   }
     else if (z[0] == 'g') system(plotcmd);                   else
     else if (z[0] == 'q') exit(0);                     fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
   }                 }
 #endif                 fprintf(ficgp,")");
 }               }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  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]; 
     char **bp, *tok, *val; /* pathtot */
     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  *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: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Un peu sale */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem with datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %d %s for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
           exit(1);
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           exit(1);
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         exit(1);
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line,j);
         exit(1);
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       lval=strtol(strb,&endptr,10); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%d' at line number %ld %s for individual %d\nShould be a weight.  Exiting.\n",lval, i,line,linei);
         exit(1);
       }
       weight[i]=(double)(lval); 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a value of the %d covar (meaning 0 for the reference or 1. IMaCh does not build design variables, do it your self).  Exiting.\n",lval,linei, i,line,j);
           exit(1);
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       } 
       lstra=strlen(stra);
       
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
     fclose(fic);
     /* 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);*/
   
       /*  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\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\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,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*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  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (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*/
       pstamp(ficrespij);
       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 Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: 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(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       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#****** ");
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\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, strstart);  
           cvevsij(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);
           }
   
           pstamp(ficrest);
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state ( 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(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (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(prlim,1,nlstate,1,nlstate);
       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);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     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);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",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.1.48  
changed lines
  Added in v.1.117


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