Diff for /imach/src/imach.c between versions 1.38 and 1.123

version 1.38, 2002/04/03 12:19:36 version 1.123, 2006/03/20 10:52:43
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.123  2006/03/20 10:52:43  brouard
      * imach.c (Module): <title> changed, corresponds to .htm file
   This program computes Healthy Life Expectancies from    name. <head> headers where missing.
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a  
   first survey ("cross") where individuals from different ages are    * imach.c (Module): Weights can have a decimal point as for
   interviewed on their health status or degree of disability (in the    English (a comma might work with a correct LC_NUMERIC environment,
   case of a health survey which is our main interest) -2- at least a    otherwise the weight is truncated).
   second wave of interviews ("longitudinal") which measure each change    Modification of warning when the covariates values are not 0 or
   (if any) in individual health status.  Health expectancies are    1.
   computed from the time spent in each health state according to a    Version 0.98g
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.122  2006/03/20 09:45:41  brouard
   simplest model is the multinomial logistic model where pij is the    (Module): Weights can have a decimal point as for
   probabibility to be observed in state j at the second wave    English (a comma might work with a correct LC_NUMERIC environment,
   conditional to be observed in state i at the first wave. Therefore    otherwise the weight is truncated).
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Modification of warning when the covariates values are not 0 or
   'age' is age and 'sex' is a covariate. If you want to have a more    1.
   complex model than "constant and age", you should modify the program    Version 0.98g
   where the markup *Covariates have to be included here again* invites  
   you to do it.  More covariates you add, slower the    Revision 1.121  2006/03/16 17:45:01  lievre
   convergence.    * imach.c (Module): Comments concerning covariates added
   
   The advantage of this computer programme, compared to a simple    * imach.c (Module): refinements in the computation of lli if
   multinomial logistic model, is clear when the delay between waves is not    status=-2 in order to have more reliable computation if stepm is
   identical for each individual. Also, if a individual missed an    not 1 month. Version 0.98f
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.120  2006/03/16 15:10:38  lievre
     (Module): refinements in the computation of lli if
   hPijx is the probability to be observed in state i at age x+h    status=-2 in order to have more reliable computation if stepm is
   conditional to the observed state i at age x. The delay 'h' can be    not 1 month. Version 0.98f
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.119  2006/03/15 17:42:26  brouard
   semester or year) is model as a multinomial logistic.  The hPx    (Module): Bug if status = -2, the loglikelihood was
   matrix is simply the matrix product of nh*stepm elementary matrices    computed as likelihood omitting the logarithm. Version O.98e
   and the contribution of each individual to the likelihood is simply  
   hPijx.    Revision 1.118  2006/03/14 18:20:07  brouard
     (Module): varevsij Comments added explaining the second
   Also this programme outputs the covariance matrix of the parameters but also    table of variances if popbased=1 .
   of the life expectancies. It also computes the prevalence limits.    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
      (Module): Function pstamp added
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    (Module): Version 0.98d
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.117  2006/03/14 17:16:22  brouard
   from the European Union.    (Module): varevsij Comments added explaining the second
   It is copyrighted identically to a GNU software product, ie programme and    table of variances if popbased=1 .
   software can be distributed freely for non commercial use. Latest version    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   can be accessed at http://euroreves.ined.fr/imach .    (Module): Function pstamp added
   **********************************************************************/    (Module): Version 0.98d
    
 #include <math.h>    Revision 1.116  2006/03/06 10:29:27  brouard
 #include <stdio.h>    (Module): Variance-covariance wrong links and
 #include <stdlib.h>    varian-covariance of ej. is needed (Saito).
 #include <unistd.h>  
     Revision 1.115  2006/02/27 12:17:45  brouard
 #define MAXLINE 256    (Module): One freematrix added in mlikeli! 0.98c
 #define GNUPLOTPROGRAM "wgnuplot"  
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    Revision 1.114  2006/02/26 12:57:58  brouard
 #define FILENAMELENGTH 80    (Module): Some improvements in processing parameter
 /*#define DEBUG*/    filename with strsep.
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.113  2006/02/24 14:20:24  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    (Module): Memory leaks checks with valgrind and:
     datafile was not closed, some imatrix were not freed and on matrix
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    allocation too.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.112  2006/01/30 09:55:26  brouard
 #define NINTERVMAX 8    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.111  2006/01/25 20:38:18  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): Lots of cleaning and bugs added (Gompertz)
 #define MAXN 20000    (Module): Comments can be added in data file. Missing date values
 #define YEARM 12. /* Number of months per year */    can be a simple dot '.'.
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
   
 int erreur; /* Error number */    Revision 1.109  2006/01/24 19:37:15  brouard
 int nvar;    (Module): Comments (lines starting with a #) are allowed in data.
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.108  2006/01/19 18:05:42  lievre
 int nlstate=2; /* Number of live states */    Gnuplot problem appeared...
 int ndeath=1; /* Number of dead states */    To be fixed
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.107  2006/01/19 16:20:37  brouard
     Test existence of gnuplot in imach path
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.106  2006/01/19 13:24:36  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    Some cleaning and links added in html output
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.105  2006/01/05 20:23:19  lievre
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    *** empty log message ***
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.104  2005/09/30 16:11:43  lievre
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    (Module): sump fixed, loop imx fixed, and simplifications.
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    (Module): If the status is missing at the last wave but we know
 FILE *ficgp,*ficresprob,*ficpop;    that the person is alive, then we can code his/her status as -2
 FILE *ficreseij;    (instead of missing=-1 in earlier versions) and his/her
   char filerese[FILENAMELENGTH];    contributions to the likelihood is 1 - Prob of dying from last
  FILE  *ficresvij;    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   char fileresv[FILENAMELENGTH];    the healthy state at last known wave). Version is 0.98
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.103  2005/09/30 15:54:49  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.102  2004/09/15 17:31:30  brouard
 #define FTOL 1.0e-10    Add the possibility to read data file including tab characters.
   
 #define NRANSI    Revision 1.101  2004/09/15 10:38:38  brouard
 #define ITMAX 200    Fix on curr_time
   
 #define TOL 2.0e-4    Revision 1.100  2004/07/12 18:29:06  brouard
     Add version for Mac OS X. Just define UNIX in Makefile
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10    Revision 1.99  2004/06/05 08:57:40  brouard
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    *** empty log message ***
   
 #define GOLD 1.618034    Revision 1.98  2004/05/16 15:05:56  brouard
 #define GLIMIT 100.0    New version 0.97 . First attempt to estimate force of mortality
 #define TINY 1.0e-20    directly from the data i.e. without the need of knowing the health
     state at each age, but using a Gompertz model: log u =a + b*age .
 static double maxarg1,maxarg2;    This is the basic analysis of mortality and should be done before any
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    other analysis, in order to test if the mortality estimated from the
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    cross-longitudinal survey is different from the mortality estimated
      from other sources like vital statistic data.
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    The same imach parameter file can be used but the option for mle should be -3.
   
 static double sqrarg;    Agnès, who wrote this part of the code, tried to keep most of the
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    former routines in order to include the new code within the former code.
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     The output is very simple: only an estimate of the intercept and of
 int imx;    the slope with 95% confident intervals.
 int stepm;  
 /* Stepm, step in month: minimum step interpolation*/    Current limitations:
     A) Even if you enter covariates, i.e. with the
 int estepm;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    B) There is no computation of Life Expectancy nor Life Table.
   
 int m,nb;    Revision 1.97  2004/02/20 13:25:42  lievre
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Version 0.96d. Population forecasting command line is (temporarily)
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    suppressed.
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.96  2003/07/15 15:38:55  brouard
     * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 double *weight;    rewritten within the same printf. Workaround: many printfs.
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.95  2003/07/08 07:54:34  brouard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    * imach.c (Repository):
     (Repository): Using imachwizard code to output a more meaningful covariance
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    matrix (cov(a12,c31) instead of numbers.
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.94  2003/06/27 13:00:02  brouard
 /**************** split *************************/    Just cleaning
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.93  2003/06/25 16:33:55  brouard
    char *s;                             /* pointer */    (Module): On windows (cygwin) function asctime_r doesn't
    int  l1, l2;                         /* length counters */    exist so I changed back to asctime which exists.
     (Module): Version 0.96b
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.92  2003/06/25 16:30:45  brouard
 #ifdef windows    (Module): On windows (cygwin) function asctime_r doesn't
    s = strrchr( path, '\\' );           /* find last / */    exist so I changed back to asctime which exists.
 #else  
    s = strrchr( path, '/' );            /* find last / */    Revision 1.91  2003/06/25 15:30:29  brouard
 #endif    * imach.c (Repository): Duplicated warning errors corrected.
    if ( s == NULL ) {                   /* no directory, so use current */    (Repository): Elapsed time after each iteration is now output. It
 #if     defined(__bsd__)                /* get current working directory */    helps to forecast when convergence will be reached. Elapsed time
       extern char       *getwd( );    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
       if ( getwd( dirc ) == NULL ) {  
 #else    Revision 1.90  2003/06/24 12:34:15  brouard
       extern char       *getcwd( );    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    of the covariance matrix to be input.
 #endif  
          return( GLOCK_ERROR_GETCWD );    Revision 1.89  2003/06/24 12:30:52  brouard
       }    (Module): Some bugs corrected for windows. Also, when
       strcpy( name, path );             /* we've got it */    mle=-1 a template is output in file "or"mypar.txt with the design
    } else {                             /* strip direcotry from path */    of the covariance matrix to be input.
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.88  2003/06/23 17:54:56  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    * 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.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.87  2003/06/18 12:26:01  brouard
       dirc[l1-l2] = 0;                  /* add zero */    Version 0.96
    }  
    l1 = strlen( dirc );                 /* length of directory */    Revision 1.86  2003/06/17 20:04:08  brouard
 #ifdef windows    (Module): Change position of html and gnuplot routines and added
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    routine fileappend.
 #else  
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    Revision 1.85  2003/06/17 13:12:43  brouard
 #endif    * imach.c (Repository): Check when date of death was earlier that
    s = strrchr( name, '.' );            /* find last / */    current date of interview. It may happen when the death was just
    s++;    prior to the death. In this case, dh was negative and likelihood
    strcpy(ext,s);                       /* save extension */    was wrong (infinity). We still send an "Error" but patch by
    l1= strlen( name);    assuming that the date of death was just one stepm after the
    l2= strlen( s)+1;    interview.
    strncpy( finame, name, l1-l2);    (Repository): Because some people have very long ID (first column)
    finame[l1-l2]= 0;    we changed int to long in num[] and we added a new lvector for
    return( 0 );                         /* we're done */    memory allocation. But we also truncated to 8 characters (left
 }    truncation)
     (Repository): No more line truncation errors.
   
 /******************************************/    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 void replace(char *s, char*t)    place. It differs from routine "prevalence" which may be called
 {    many times. Probs is memory consuming and must be used with
   int i;    parcimony.
   int lg=20;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   i=0;  
   lg=strlen(t);    Revision 1.83  2003/06/10 13:39:11  lievre
   for(i=0; i<= lg; i++) {    *** empty log message ***
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.82  2003/06/05 15:57:20  brouard
   }    Add log in  imach.c and  fullversion number is now printed.
 }  
   */
 int nbocc(char *s, char occ)  /*
 {     Interpolated Markov Chain
   int i,j=0;  
   int lg=20;    Short summary of the programme:
   i=0;    
   lg=strlen(s);    This program computes Healthy Life Expectancies from
   for(i=0; i<= lg; i++) {    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   if  (s[i] == occ ) j++;    first survey ("cross") where individuals from different ages are
   }    interviewed on their health status or degree of disability (in the
   return j;    case of a health survey which is our main interest) -2- at least a
 }    second wave of interviews ("longitudinal") which measure each change
     (if any) in individual health status.  Health expectancies are
 void cutv(char *u,char *v, char*t, char occ)    computed from the time spent in each health state according to a
 {    model. More health states you consider, more time is necessary to reach the
   int i,lg,j,p=0;    Maximum Likelihood of the parameters involved in the model.  The
   i=0;    simplest model is the multinomial logistic model where pij is the
   for(j=0; j<=strlen(t)-1; j++) {    probability to be observed in state j at the second wave
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    conditional to be observed in state i at the first wave. Therefore
   }    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
     'age' is age and 'sex' is a covariate. If you want to have a more
   lg=strlen(t);    complex model than "constant and age", you should modify the program
   for(j=0; j<p; j++) {    where the markup *Covariates have to be included here again* invites
     (u[j] = t[j]);    you to do it.  More covariates you add, slower the
   }    convergence.
      u[p]='\0';  
     The advantage of this computer programme, compared to a simple
    for(j=0; j<= lg; j++) {    multinomial logistic model, is clear when the delay between waves is not
     if (j>=(p+1))(v[j-p-1] = t[j]);    identical for each individual. Also, if a individual missed an
   }    intermediate interview, the information is lost, but taken into
 }    account using an interpolation or extrapolation.  
   
 /********************** nrerror ********************/    hPijx is the probability to be observed in state i at age x+h
     conditional to the observed state i at age x. The delay 'h' can be
 void nrerror(char error_text[])    split into an exact number (nh*stepm) of unobserved intermediate
 {    states. This elementary transition (by month, quarter,
   fprintf(stderr,"ERREUR ...\n");    semester or year) is modelled as a multinomial logistic.  The hPx
   fprintf(stderr,"%s\n",error_text);    matrix is simply the matrix product of nh*stepm elementary matrices
   exit(1);    and the contribution of each individual to the likelihood is simply
 }    hPijx.
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    Also this programme outputs the covariance matrix of the parameters but also
 {    of the life expectancies. It also computes the period (stable) prevalence. 
   double *v;    
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   if (!v) nrerror("allocation failure in vector");             Institut national d'études démographiques, Paris.
   return v-nl+NR_END;    This software have been partly granted by Euro-REVES, a concerted action
 }    from the European Union.
     It is copyrighted identically to a GNU software product, ie programme and
 /************************ free vector ******************/    software can be distributed freely for non commercial use. Latest version
 void free_vector(double*v, int nl, int nh)    can be accessed at http://euroreves.ined.fr/imach .
 {  
   free((FREE_ARG)(v+nl-NR_END));    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
     
 /************************ivector *******************************/    **********************************************************************/
 int *ivector(long nl,long nh)  /*
 {    main
   int *v;    read parameterfile
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    read datafile
   if (!v) nrerror("allocation failure in ivector");    concatwav
   return v-nl+NR_END;    freqsummary
 }    if (mle >= 1)
       mlikeli
 /******************free ivector **************************/    print results files
 void free_ivector(int *v, long nl, long nh)    if mle==1 
 {       computes hessian
   free((FREE_ARG)(v+nl-NR_END));    read end of parameter file: agemin, agemax, bage, fage, estepm
 }        begin-prev-date,...
     open gnuplot file
 /******************* imatrix *******************************/    open html file
 int **imatrix(long nrl, long nrh, long ncl, long nch)    period (stable) prevalence
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */     for age prevalim()
 {    h Pij x
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    variance of p varprob
   int **m;    forecasting if prevfcast==1 prevforecast call prevalence()
      health expectancies
   /* allocate pointers to rows */    Variance-covariance of DFLE
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    prevalence()
   if (!m) nrerror("allocation failure 1 in matrix()");     movingaverage()
   m += NR_END;    varevsij() 
   m -= nrl;    if popbased==1 varevsij(,popbased)
      total life expectancies
      Variance of period (stable) prevalence
   /* allocate rows and set pointers to them */   end
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  
     
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  #include <math.h>
    #include <stdio.h>
   /* return pointer to array of pointers to rows */  #include <stdlib.h>
   return m;  #include <string.h>
 }  #include <unistd.h>
   
 /****************** free_imatrix *************************/  #include <limits.h>
 void free_imatrix(m,nrl,nrh,ncl,nch)  #include <sys/types.h>
       int **m;  #include <sys/stat.h>
       long nch,ncl,nrh,nrl;  #include <errno.h>
      /* free an int matrix allocated by imatrix() */  extern int errno;
 {  
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  /* #include <sys/time.h> */
   free((FREE_ARG) (m+nrl-NR_END));  #include <time.h>
 }  #include "timeval.h"
   
 /******************* matrix *******************************/  /* #include <libintl.h> */
 double **matrix(long nrl, long nrh, long ncl, long nch)  /* #define _(String) gettext (String) */
 {  
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  #define MAXLINE 256
   double **m;  
   #define GNUPLOTPROGRAM "gnuplot"
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   if (!m) nrerror("allocation failure 1 in matrix()");  #define FILENAMELENGTH 132
   m += NR_END;  
   m -= nrl;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   m[nrl] += NR_END;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   m[nrl] -= ncl;  
   #define NINTERVMAX 8
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   return m;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 }  #define NCOVMAX 8 /* Maximum number of covariates */
   #define MAXN 20000
 /*************************free matrix ************************/  #define YEARM 12. /* Number of months per year */
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #define AGESUP 130
 {  #define AGEBASE 40
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   free((FREE_ARG)(m+nrl-NR_END));  #ifdef UNIX
 }  #define DIRSEPARATOR '/'
   #define CHARSEPARATOR "/"
 /******************* ma3x *******************************/  #define ODIRSEPARATOR '\\'
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #else
 {  #define DIRSEPARATOR '\\'
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define CHARSEPARATOR "\\"
   double ***m;  #define ODIRSEPARATOR '/'
   #endif
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  /* $Id$ */
   m += NR_END;  /* $State$ */
   m -= nrl;  
   char version[]="Imach version 0.98g, March 2006, INED-EUROREVES-Institut de longevite ";
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  char fullversion[]="$Revision$ $Date$"; 
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  char strstart[80];
   m[nrl] += NR_END;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   m[nrl] -= ncl;  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   int nvar;
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int npar=NPARMAX;
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  int nlstate=2; /* Number of live states */
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  int ndeath=1; /* Number of dead states */
   m[nrl][ncl] += NR_END;  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   m[nrl][ncl] -= nll;  int popbased=0;
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  int *wav; /* Number of waves for this individuual 0 is possible */
    int maxwav; /* Maxim number of waves */
   for (i=nrl+1; i<=nrh; i++) {  int jmin, jmax; /* min, max spacing between 2 waves */
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
     for (j=ncl+1; j<=nch; j++)  int gipmx, gsw; /* Global variables on the number of contributions 
       m[i][j]=m[i][j-1]+nlay;                     to the likelihood and the sum of weights (done by funcone)*/
   }  int mle, weightopt;
   return m;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 }  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
 /*************************free ma3x ************************/             * wave mi and wave mi+1 is not an exact multiple of stepm. */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  double jmean; /* Mean space between 2 waves */
 {  double **oldm, **newm, **savm; /* Working pointers to matrices */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   free((FREE_ARG)(m+nrl-NR_END));  FILE *ficlog, *ficrespow;
 }  int globpr; /* Global variable for printing or not */
   double fretone; /* Only one call to likelihood */
 /***************** f1dim *************************/  long ipmx; /* Number of contributions */
 extern int ncom;  double sw; /* Sum of weights */
 extern double *pcom,*xicom;  char filerespow[FILENAMELENGTH];
 extern double (*nrfunc)(double []);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
    FILE *ficresilk;
 double f1dim(double x)  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 {  FILE *ficresprobmorprev;
   int j;  FILE *fichtm, *fichtmcov; /* Html File */
   double f;  FILE *ficreseij;
   double *xt;  char filerese[FILENAMELENGTH];
    FILE *ficresstdeij;
   xt=vector(1,ncom);  char fileresstde[FILENAMELENGTH];
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  FILE *ficrescveij;
   f=(*nrfunc)(xt);  char filerescve[FILENAMELENGTH];
   free_vector(xt,1,ncom);  FILE  *ficresvij;
   return f;  char fileresv[FILENAMELENGTH];
 }  FILE  *ficresvpl;
   char fileresvpl[FILENAMELENGTH];
 /*****************brent *************************/  char title[MAXLINE];
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 {  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   int iter;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   double a,b,d,etemp;  char command[FILENAMELENGTH];
   double fu,fv,fw,fx;  int  outcmd=0;
   double ftemp;  
   double p,q,r,tol1,tol2,u,v,w,x,xm;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   double e=0.0;  
    char filelog[FILENAMELENGTH]; /* Log file */
   a=(ax < cx ? ax : cx);  char filerest[FILENAMELENGTH];
   b=(ax > cx ? ax : cx);  char fileregp[FILENAMELENGTH];
   x=w=v=bx;  char popfile[FILENAMELENGTH];
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
     xm=0.5*(a+b);  
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  struct timezone tzp;
     printf(".");fflush(stdout);  extern int gettimeofday();
 #ifdef DEBUG  struct tm tmg, tm, tmf, *gmtime(), *localtime();
     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);  long time_value;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  extern long time();
 #endif  char strcurr[80], strfor[80];
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;  char *endptr;
       return fx;  long lval;
     }  double dval;
     ftemp=fu;  
     if (fabs(e) > tol1) {  #define NR_END 1
       r=(x-w)*(fx-fv);  #define FREE_ARG char*
       q=(x-v)*(fx-fw);  #define FTOL 1.0e-10
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  #define NRANSI 
       if (q > 0.0) p = -p;  #define ITMAX 200 
       q=fabs(q);  
       etemp=e;  #define TOL 2.0e-4 
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #define CGOLD 0.3819660 
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define ZEPS 1.0e-10 
       else {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
         d=p/q;  
         u=x+d;  #define GOLD 1.618034 
         if (u-a < tol2 || b-u < tol2)  #define GLIMIT 100.0 
           d=SIGN(tol1,xm-x);  #define TINY 1.0e-20 
       }  
     } else {  static double maxarg1,maxarg2;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
     }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    
     fu=(*f)(u);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
     if (fu <= fx) {  #define rint(a) floor(a+0.5)
       if (u >= x) a=x; else b=x;  
       SHFT(v,w,x,u)  static double sqrarg;
         SHFT(fv,fw,fx,fu)  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
         } else {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
           if (u < x) a=u; else b=u;  int agegomp= AGEGOMP;
           if (fu <= fw || w == x) {  
             v=w;  int imx; 
             w=u;  int stepm=1;
             fv=fw;  /* Stepm, step in month: minimum step interpolation*/
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {  int estepm;
             v=u;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
             fv=fu;  
           }  int m,nb;
         }  long *num;
   }  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   nrerror("Too many iterations in brent");  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   *xmin=x;  double **pmmij, ***probs;
   return fx;  double *ageexmed,*agecens;
 }  double dateintmean=0;
   
 /****************** mnbrak ***********************/  double *weight;
   int **s; /* Status */
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  double *agedc, **covar, idx;
             double (*func)(double))  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 {  double *lsurv, *lpop, *tpop;
   double ulim,u,r,q, dum;  
   double fu;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
    double ftolhess; /* Tolerance for computing hessian */
   *fa=(*func)(*ax);  
   *fb=(*func)(*bx);  /**************** split *************************/
   if (*fb > *fa) {  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     SHFT(dum,*ax,*bx,dum)  {
       SHFT(dum,*fb,*fa,dum)    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       }       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   *cx=(*bx)+GOLD*(*bx-*ax);    */ 
   *fc=(*func)(*cx);    char  *ss;                            /* pointer */
   while (*fb > *fc) {    int   l1, l2;                         /* length counters */
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);    l1 = strlen(path );                   /* length of path */
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     ulim=(*bx)+GLIMIT*(*cx-*bx);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     if ((*bx-u)*(u-*cx) > 0.0) {      strcpy( name, path );               /* we got the fullname name because no directory */
       fu=(*func)(u);      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     } else if ((*cx-u)*(u-ulim) > 0.0) {        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       fu=(*func)(u);      /* get current working directory */
       if (fu < *fc) {      /*    extern  char* getcwd ( char *buf , int len);*/
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
           SHFT(*fb,*fc,fu,(*func)(u))        return( GLOCK_ERROR_GETCWD );
           }      }
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {      /* got dirc from getcwd*/
       u=ulim;      printf(" DIRC = %s \n",dirc);
       fu=(*func)(u);    } else {                              /* strip direcotry from path */
     } else {      ss++;                               /* after this, the filename */
       u=(*cx)+GOLD*(*cx-*bx);      l2 = strlen( ss );                  /* length of filename */
       fu=(*func)(u);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     }      strcpy( name, ss );         /* save file name */
     SHFT(*ax,*bx,*cx,u)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       SHFT(*fa,*fb,*fc,fu)      dirc[l1-l2] = 0;                    /* add zero */
       }      printf(" DIRC2 = %s \n",dirc);
 }    }
     /* We add a separator at the end of dirc if not exists */
 /*************** linmin ************************/    l1 = strlen( dirc );                  /* length of directory */
     if( dirc[l1-1] != DIRSEPARATOR ){
 int ncom;      dirc[l1] =  DIRSEPARATOR;
 double *pcom,*xicom;      dirc[l1+1] = 0; 
 double (*nrfunc)(double []);      printf(" DIRC3 = %s \n",dirc);
      }
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    ss = strrchr( name, '.' );            /* find last / */
 {    if (ss >0){
   double brent(double ax, double bx, double cx,      ss++;
                double (*f)(double), double tol, double *xmin);      strcpy(ext,ss);                     /* save extension */
   double f1dim(double x);      l1= strlen( name);
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,      l2= strlen(ss)+1;
               double *fc, double (*func)(double));      strncpy( finame, name, l1-l2);
   int j;      finame[l1-l2]= 0;
   double xx,xmin,bx,ax;    }
   double fx,fb,fa;  
      return( 0 );                          /* we're done */
   ncom=n;  }
   pcom=vector(1,n);  
   xicom=vector(1,n);  
   nrfunc=func;  /******************************************/
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  void replace_back_to_slash(char *s, char*t)
     xicom[j]=xi[j];  {
   }    int i;
   ax=0.0;    int lg=0;
   xx=1.0;    i=0;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    lg=strlen(t);
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    for(i=0; i<= lg; i++) {
 #ifdef DEBUG      (s[i] = t[i]);
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);      if (t[i]== '\\') s[i]='/';
 #endif    }
   for (j=1;j<=n;j++) {  }
     xi[j] *= xmin;  
     p[j] += xi[j];  int nbocc(char *s, char occ)
   }  {
   free_vector(xicom,1,n);    int i,j=0;
   free_vector(pcom,1,n);    int lg=20;
 }    i=0;
     lg=strlen(s);
 /*************** powell ************************/    for(i=0; i<= lg; i++) {
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    if  (s[i] == occ ) j++;
             double (*func)(double []))    }
 {    return j;
   void linmin(double p[], double xi[], int n, double *fret,  }
               double (*func)(double []));  
   int i,ibig,j;  void cutv(char *u,char *v, char*t, char occ)
   double del,t,*pt,*ptt,*xit;  {
   double fp,fptt;    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
   double *xits;       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
   pt=vector(1,n);       gives u="abcedf" and v="ghi2j" */
   ptt=vector(1,n);    int i,lg,j,p=0;
   xit=vector(1,n);    i=0;
   xits=vector(1,n);    for(j=0; j<=strlen(t)-1; j++) {
   *fret=(*func)(p);      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
   for (j=1;j<=n;j++) pt[j]=p[j];    }
   for (*iter=1;;++(*iter)) {  
     fp=(*fret);    lg=strlen(t);
     ibig=0;    for(j=0; j<p; j++) {
     del=0.0;      (u[j] = t[j]);
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    }
     for (i=1;i<=n;i++)       u[p]='\0';
       printf(" %d %.12f",i, p[i]);  
     printf("\n");     for(j=0; j<= lg; j++) {
     for (i=1;i<=n;i++) {      if (j>=(p+1))(v[j-p-1] = t[j]);
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    }
       fptt=(*fret);  }
 #ifdef DEBUG  
       printf("fret=%lf \n",*fret);  /********************** nrerror ********************/
 #endif  
       printf("%d",i);fflush(stdout);  void nrerror(char error_text[])
       linmin(p,xit,n,fret,func);  {
       if (fabs(fptt-(*fret)) > del) {    fprintf(stderr,"ERREUR ...\n");
         del=fabs(fptt-(*fret));    fprintf(stderr,"%s\n",error_text);
         ibig=i;    exit(EXIT_FAILURE);
       }  }
 #ifdef DEBUG  /*********************** vector *******************/
       printf("%d %.12e",i,(*fret));  double *vector(int nl, int nh)
       for (j=1;j<=n;j++) {  {
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    double *v;
         printf(" x(%d)=%.12e",j,xit[j]);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       }    if (!v) nrerror("allocation failure in vector");
       for(j=1;j<=n;j++)    return v-nl+NR_END;
         printf(" p=%.12e",p[j]);  }
       printf("\n");  
 #endif  /************************ free vector ******************/
     }  void free_vector(double*v, int nl, int nh)
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  {
 #ifdef DEBUG    free((FREE_ARG)(v+nl-NR_END));
       int k[2],l;  }
       k[0]=1;  
       k[1]=-1;  /************************ivector *******************************/
       printf("Max: %.12e",(*func)(p));  int *ivector(long nl,long nh)
       for (j=1;j<=n;j++)  {
         printf(" %.12e",p[j]);    int *v;
       printf("\n");    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       for(l=0;l<=1;l++) {    if (!v) nrerror("allocation failure in ivector");
         for (j=1;j<=n;j++) {    return v-nl+NR_END;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  }
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  
         }  /******************free ivector **************************/
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  void free_ivector(int *v, long nl, long nh)
       }  {
 #endif    free((FREE_ARG)(v+nl-NR_END));
   }
   
       free_vector(xit,1,n);  /************************lvector *******************************/
       free_vector(xits,1,n);  long *lvector(long nl,long nh)
       free_vector(ptt,1,n);  {
       free_vector(pt,1,n);    long *v;
       return;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     }    if (!v) nrerror("allocation failure in ivector");
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    return v-nl+NR_END;
     for (j=1;j<=n;j++) {  }
       ptt[j]=2.0*p[j]-pt[j];  
       xit[j]=p[j]-pt[j];  /******************free lvector **************************/
       pt[j]=p[j];  void free_lvector(long *v, long nl, long nh)
     }  {
     fptt=(*func)(ptt);    free((FREE_ARG)(v+nl-NR_END));
     if (fptt < fp) {  }
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  
       if (t < 0.0) {  /******************* imatrix *******************************/
         linmin(p,xit,n,fret,func);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         for (j=1;j<=n;j++) {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
           xi[j][ibig]=xi[j][n];  { 
           xi[j][n]=xit[j];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         }    int **m; 
 #ifdef DEBUG    
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    /* allocate pointers to rows */ 
         for(j=1;j<=n;j++)    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
           printf(" %.12e",xit[j]);    if (!m) nrerror("allocation failure 1 in matrix()"); 
         printf("\n");    m += NR_END; 
 #endif    m -= nrl; 
       }    
     }    
   }    /* allocate rows and set pointers to them */ 
 }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 /**** Prevalence limit ****************/    m[nrl] += NR_END; 
     m[nrl] -= ncl; 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    
 {    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    
      matrix by transitions matrix until convergence is reached */    /* return pointer to array of pointers to rows */ 
     return m; 
   int i, ii,j,k;  } 
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();  /****************** free_imatrix *************************/
   double **out, cov[NCOVMAX], **pmij();  void free_imatrix(m,nrl,nrh,ncl,nch)
   double **newm;        int **m;
   double agefin, delaymax=50 ; /* Max number of years to converge */        long nch,ncl,nrh,nrl; 
        /* free an int matrix allocated by imatrix() */ 
   for (ii=1;ii<=nlstate+ndeath;ii++)  { 
     for (j=1;j<=nlstate+ndeath;j++){    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    free((FREE_ARG) (m+nrl-NR_END)); 
     }  } 
   
    cov[1]=1.;  /******************* matrix *******************************/
    double **matrix(long nrl, long nrh, long ncl, long nch)
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  {
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     newm=savm;    double **m;
     /* Covariates have to be included here again */  
      cov[2]=agefin;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      if (!m) nrerror("allocation failure 1 in matrix()");
       for (k=1; k<=cptcovn;k++) {    m += NR_END;
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    m -= nrl;
         /*      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]]);*/  
       }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for (k=1; k<=cptcovprod;k++)    m[nrl] += NR_END;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    m[nrl] -= ncl;
   
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    return m;
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);     */
   }
     savm=oldm;  
     oldm=newm;  /*************************free matrix ************************/
     maxmax=0.;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     for(j=1;j<=nlstate;j++){  {
       min=1.;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       max=0.;    free((FREE_ARG)(m+nrl-NR_END));
       for(i=1; i<=nlstate; i++) {  }
         sumnew=0;  
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /******************* ma3x *******************************/
         prlim[i][j]= newm[i][j]/(1-sumnew);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
         max=FMAX(max,prlim[i][j]);  {
         min=FMIN(min,prlim[i][j]);    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       }    double ***m;
       maxmin=max-min;  
       maxmax=FMAX(maxmax,maxmin);    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     }    if (!m) nrerror("allocation failure 1 in matrix()");
     if(maxmax < ftolpl){    m += NR_END;
       return prlim;    m -= nrl;
     }  
   }    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
 /*************** transition probabilities ***************/    m[nrl] -= ncl;
   
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
 {  
   double s1, s2;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   /*double t34;*/    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   int i,j,j1, nc, ii, jj;    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
     for(i=1; i<= nlstate; i++){    for (j=ncl+1; j<=nch; j++) 
     for(j=1; j<i;j++){      m[nrl][j]=m[nrl][j-1]+nlay;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    
         /*s2 += param[i][j][nc]*cov[nc];*/    for (i=nrl+1; i<=nrh; i++) {
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/      for (j=ncl+1; j<=nch; j++) 
       }        m[i][j]=m[i][j-1]+nlay;
       ps[i][j]=s2;    }
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    return m; 
     }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     for(j=i+1; j<=nlstate+ndeath;j++){             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       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 ma3x ************************/
       ps[i][j]=s2;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     }  {
   }    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     /*ps[3][2]=1;*/    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     free((FREE_ARG)(m+nrl-NR_END));
   for(i=1; i<= nlstate; i++){  }
      s1=0;  
     for(j=1; j<i; j++)  /*************** function subdirf ***********/
       s1+=exp(ps[i][j]);  char *subdirf(char fileres[])
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       s1+=exp(ps[i][j]);    /* Caution optionfilefiname is hidden */
     ps[i][i]=1./(s1+1.);    strcpy(tmpout,optionfilefiname);
     for(j=1; j<i; j++)    strcat(tmpout,"/"); /* Add to the right */
       ps[i][j]= exp(ps[i][j])*ps[i][i];    strcat(tmpout,fileres);
     for(j=i+1; j<=nlstate+ndeath; j++)    return tmpout;
       ps[i][j]= exp(ps[i][j])*ps[i][i];  }
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  
   } /* end i */  /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  {
     for(jj=1; jj<= nlstate+ndeath; jj++){    
       ps[ii][jj]=0;    /* Caution optionfilefiname is hidden */
       ps[ii][ii]=1;    strcpy(tmpout,optionfilefiname);
     }    strcat(tmpout,"/");
   }    strcat(tmpout,preop);
     strcat(tmpout,fileres);
     return tmpout;
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /*************** function subdirf3 ***********/
    }  char *subdirf3(char fileres[], char *preop, char *preop2)
     printf("\n ");  {
     }    
     printf("\n ");printf("%lf ",cov[2]);*/    /* Caution optionfilefiname is hidden */
 /*    strcpy(tmpout,optionfilefiname);
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    strcat(tmpout,"/");
   goto end;*/    strcat(tmpout,preop);
     return ps;    strcat(tmpout,preop2);
 }    strcat(tmpout,fileres);
     return tmpout;
 /**************** Product of 2 matrices ******************/  }
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  /***************** f1dim *************************/
 {  extern int ncom; 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  extern double *pcom,*xicom;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  extern double (*nrfunc)(double []); 
   /* in, b, out are matrice of pointers which should have been initialized   
      before: only the contents of out is modified. The function returns  double f1dim(double x) 
      a pointer to pointers identical to out */  { 
   long i, j, k;    int j; 
   for(i=nrl; i<= nrh; i++)    double f;
     for(k=ncolol; k<=ncoloh; k++)    double *xt; 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)   
         out[i][k] +=in[i][j]*b[j][k];    xt=vector(1,ncom); 
     for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   return out;    f=(*nrfunc)(xt); 
 }    free_vector(xt,1,ncom); 
     return f; 
   } 
 /************* Higher Matrix Product ***************/  
   /*****************brent *************************/
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
 {  { 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    int iter; 
      duration (i.e. until    double a,b,d,etemp;
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    double fu,fv,fw,fx;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    double ftemp;
      (typically every 2 years instead of every month which is too big).    double p,q,r,tol1,tol2,u,v,w,x,xm; 
      Model is determined by parameters x and covariates have to be    double e=0.0; 
      included manually here.   
     a=(ax < cx ? ax : cx); 
      */    b=(ax > cx ? ax : cx); 
     x=w=v=bx; 
   int i, j, d, h, k;    fw=fv=fx=(*f)(x); 
   double **out, cov[NCOVMAX];    for (iter=1;iter<=ITMAX;iter++) { 
   double **newm;      xm=0.5*(a+b); 
       tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   /* Hstepm could be zero and should return the unit matrix */      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   for (i=1;i<=nlstate+ndeath;i++)      printf(".");fflush(stdout);
     for (j=1;j<=nlstate+ndeath;j++){      fprintf(ficlog,".");fflush(ficlog);
       oldm[i][j]=(i==j ? 1.0 : 0.0);  #ifdef DEBUG
       po[i][j][0]=(i==j ? 1.0 : 0.0);      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);
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   for(h=1; h <=nhstepm; h++){  #endif
     for(d=1; d <=hstepm; d++){      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
       newm=savm;        *xmin=x; 
       /* Covariates have to be included here again */        return fx; 
       cov[1]=1.;      } 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      ftemp=fu;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      if (fabs(e) > tol1) { 
       for (k=1; k<=cptcovage;k++)        r=(x-w)*(fx-fv); 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];        q=(x-v)*(fx-fw); 
       for (k=1; k<=cptcovprod;k++)        p=(x-v)*q-(x-w)*r; 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        q=2.0*(q-r); 
         if (q > 0.0) p = -p; 
         q=fabs(q); 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/        etemp=e; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/        e=d; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       savm=oldm;        else { 
       oldm=newm;          d=p/q; 
     }          u=x+d; 
     for(i=1; i<=nlstate+ndeath; i++)          if (u-a < tol2 || b-u < tol2) 
       for(j=1;j<=nlstate+ndeath;j++) {            d=SIGN(tol1,xm-x); 
         po[i][j][h]=newm[i][j];        } 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      } else { 
          */        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       }      } 
   } /* end h */      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   return po;      fu=(*f)(u); 
 }      if (fu <= fx) { 
         if (u >= x) a=x; else b=x; 
         SHFT(v,w,x,u) 
 /*************** log-likelihood *************/          SHFT(fv,fw,fx,fu) 
 double func( double *x)          } else { 
 {            if (u < x) a=u; else b=u; 
   int i, ii, j, k, mi, d, kk;            if (fu <= fw || w == x) { 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];              v=w; 
   double **out;              w=u; 
   double sw; /* Sum of weights */              fv=fw; 
   double lli; /* Individual log likelihood */              fw=fu; 
   long ipmx;            } else if (fu <= fv || v == x || v == w) { 
   /*extern weight */              v=u; 
   /* We are differentiating ll according to initial status */              fv=fu; 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/            } 
   /*for(i=1;i<imx;i++)          } 
     printf(" %d\n",s[4][i]);    } 
   */    nrerror("Too many iterations in brent"); 
   cov[1]=1.;    *xmin=x; 
     return fx; 
   for(k=1; k<=nlstate; k++) ll[k]=0.;  } 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){  
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  /****************** mnbrak ***********************/
     for(mi=1; mi<= wav[i]-1; mi++){  
       for (ii=1;ii<=nlstate+ndeath;ii++)  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);              double (*func)(double)) 
       for(d=0; d<dh[mi][i]; d++){  { 
         newm=savm;    double ulim,u,r,q, dum;
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    double fu; 
         for (kk=1; kk<=cptcovage;kk++) {   
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    *fa=(*func)(*ax); 
         }    *fb=(*func)(*bx); 
            if (*fb > *fa) { 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      SHFT(dum,*ax,*bx,dum) 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        SHFT(dum,*fb,*fa,dum) 
         savm=oldm;        } 
         oldm=newm;    *cx=(*bx)+GOLD*(*bx-*ax); 
            *fc=(*func)(*cx); 
            while (*fb > *fc) { 
       } /* end mult */      r=(*bx-*ax)*(*fb-*fc); 
            q=(*bx-*cx)*(*fb-*fa); 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       ipmx +=1;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       sw += weight[i];      if ((*bx-u)*(u-*cx) > 0.0) { 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        fu=(*func)(u); 
     } /* end of wave */      } else if ((*cx-u)*(u-ulim) > 0.0) { 
   } /* end of individual */        fu=(*func)(u); 
         if (fu < *fc) { 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */            SHFT(*fb,*fc,fu,(*func)(u)) 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */            } 
   return -l;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
 }        u=ulim; 
         fu=(*func)(u); 
       } else { 
 /*********** Maximum Likelihood Estimation ***************/        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      } 
 {      SHFT(*ax,*bx,*cx,u) 
   int i,j, iter;        SHFT(*fa,*fb,*fc,fu) 
   double **xi,*delti;        } 
   double fret;  } 
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)  /*************** linmin ************************/
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);  int ncom; 
   printf("Powell\n");  double *pcom,*xicom;
   powell(p,xi,npar,ftol,&iter,&fret,func);  double (*nrfunc)(double []); 
    
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));  { 
     double brent(double ax, double bx, double cx, 
 }                 double (*f)(double), double tol, double *xmin); 
     double f1dim(double x); 
 /**** Computes Hessian and covariance matrix ***/    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))                double *fc, double (*func)(double)); 
 {    int j; 
   double  **a,**y,*x,pd;    double xx,xmin,bx,ax; 
   double **hess;    double fx,fb,fa;
   int i, j,jk;   
   int *indx;    ncom=n; 
     pcom=vector(1,n); 
   double hessii(double p[], double delta, int theta, double delti[]);    xicom=vector(1,n); 
   double hessij(double p[], double delti[], int i, int j);    nrfunc=func; 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    for (j=1;j<=n;j++) { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;      pcom[j]=p[j]; 
       xicom[j]=xi[j]; 
   hess=matrix(1,npar,1,npar);    } 
     ax=0.0; 
   printf("\nCalculation of the hessian matrix. Wait...\n");    xx=1.0; 
   for (i=1;i<=npar;i++){    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     printf("%d",i);fflush(stdout);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     hess[i][i]=hessii(p,ftolhess,i,delti);  #ifdef DEBUG
     /*printf(" %f ",p[i]);*/    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     /*printf(" %lf ",hess[i][i]);*/    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   }  #endif
      for (j=1;j<=n;j++) { 
   for (i=1;i<=npar;i++) {      xi[j] *= xmin; 
     for (j=1;j<=npar;j++)  {      p[j] += xi[j]; 
       if (j>i) {    } 
         printf(".%d%d",i,j);fflush(stdout);    free_vector(xicom,1,n); 
         hess[i][j]=hessij(p,delti,i,j);    free_vector(pcom,1,n); 
         hess[j][i]=hess[i][j];      } 
         /*printf(" %lf ",hess[i][j]);*/  
       }  char *asc_diff_time(long time_sec, char ascdiff[])
     }  {
   }    long sec_left, days, hours, minutes;
   printf("\n");    days = (time_sec) / (60*60*24);
     sec_left = (time_sec) % (60*60*24);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    hours = (sec_left) / (60*60) ;
      sec_left = (sec_left) %(60*60);
   a=matrix(1,npar,1,npar);    minutes = (sec_left) /60;
   y=matrix(1,npar,1,npar);    sec_left = (sec_left) % (60);
   x=vector(1,npar);    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   indx=ivector(1,npar);    return ascdiff;
   for (i=1;i<=npar;i++)  }
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  
   ludcmp(a,npar,indx,&pd);  /*************** powell ************************/
   void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   for (j=1;j<=npar;j++) {              double (*func)(double [])) 
     for (i=1;i<=npar;i++) x[i]=0;  { 
     x[j]=1;    void linmin(double p[], double xi[], int n, double *fret, 
     lubksb(a,npar,indx,x);                double (*func)(double [])); 
     for (i=1;i<=npar;i++){    int i,ibig,j; 
       matcov[i][j]=x[i];    double del,t,*pt,*ptt,*xit;
     }    double fp,fptt;
   }    double *xits;
     int niterf, itmp;
   printf("\n#Hessian matrix#\n");  
   for (i=1;i<=npar;i++) {    pt=vector(1,n); 
     for (j=1;j<=npar;j++) {    ptt=vector(1,n); 
       printf("%.3e ",hess[i][j]);    xit=vector(1,n); 
     }    xits=vector(1,n); 
     printf("\n");    *fret=(*func)(p); 
   }    for (j=1;j<=n;j++) pt[j]=p[j]; 
     for (*iter=1;;++(*iter)) { 
   /* Recompute Inverse */      fp=(*fret); 
   for (i=1;i<=npar;i++)      ibig=0; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      del=0.0; 
   ludcmp(a,npar,indx,&pd);      last_time=curr_time;
       (void) gettimeofday(&curr_time,&tzp);
   /*  printf("\n#Hessian matrix recomputed#\n");      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);
   for (j=1;j<=npar;j++) {      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
     for (i=1;i<=npar;i++) x[i]=0;      */
     x[j]=1;     for (i=1;i<=n;i++) {
     lubksb(a,npar,indx,x);        printf(" %d %.12f",i, p[i]);
     for (i=1;i<=npar;i++){        fprintf(ficlog," %d %.12lf",i, p[i]);
       y[i][j]=x[i];        fprintf(ficrespow," %.12lf", p[i]);
       printf("%.3e ",y[i][j]);      }
     }      printf("\n");
     printf("\n");      fprintf(ficlog,"\n");
   }      fprintf(ficrespow,"\n");fflush(ficrespow);
   */      if(*iter <=3){
         tm = *localtime(&curr_time.tv_sec);
   free_matrix(a,1,npar,1,npar);        strcpy(strcurr,asctime(&tm));
   free_matrix(y,1,npar,1,npar);  /*       asctime_r(&tm,strcurr); */
   free_vector(x,1,npar);        forecast_time=curr_time; 
   free_ivector(indx,1,npar);        itmp = strlen(strcurr);
   free_matrix(hess,1,npar,1,npar);        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);
         for(niterf=10;niterf<=30;niterf+=10){
 /*************** hessian matrix ****************/          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
 double hessii( double x[], double delta, int theta, double delti[])          tmf = *localtime(&forecast_time.tv_sec);
 {  /*      asctime_r(&tmf,strfor); */
   int i;          strcpy(strfor,asctime(&tmf));
   int l=1, lmax=20;          itmp = strlen(strfor);
   double k1,k2;          if(strfor[itmp-1]=='\n')
   double p2[NPARMAX+1];          strfor[itmp-1]='\0';
   double res;          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);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   double fx;        }
   int k=0,kmax=10;      }
   double l1;      for (i=1;i<=n;i++) { 
         for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   fx=func(x);        fptt=(*fret); 
   for (i=1;i<=npar;i++) p2[i]=x[i];  #ifdef DEBUG
   for(l=0 ; l <=lmax; l++){        printf("fret=%lf \n",*fret);
     l1=pow(10,l);        fprintf(ficlog,"fret=%lf \n",*fret);
     delts=delt;  #endif
     for(k=1 ; k <kmax; k=k+1){        printf("%d",i);fflush(stdout);
       delt = delta*(l1*k);        fprintf(ficlog,"%d",i);fflush(ficlog);
       p2[theta]=x[theta] +delt;        linmin(p,xit,n,fret,func); 
       k1=func(p2)-fx;        if (fabs(fptt-(*fret)) > del) { 
       p2[theta]=x[theta]-delt;          del=fabs(fptt-(*fret)); 
       k2=func(p2)-fx;          ibig=i; 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        } 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  #ifdef DEBUG
              printf("%d %.12e",i,(*fret));
 #ifdef DEBUG        fprintf(ficlog,"%d %.12e",i,(*fret));
       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 (j=1;j<=n;j++) {
 #endif          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          printf(" x(%d)=%.12e",j,xit[j]);
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         k=kmax;        }
       }        for(j=1;j<=n;j++) {
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */          printf(" p=%.12e",p[j]);
         k=kmax; l=lmax*10.;          fprintf(ficlog," p=%.12e",p[j]);
       }        }
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        printf("\n");
         delts=delt;        fprintf(ficlog,"\n");
       }  #endif
     }      } 
   }      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   delti[theta]=delts;  #ifdef DEBUG
   return res;        int k[2],l;
          k[0]=1;
 }        k[1]=-1;
         printf("Max: %.12e",(*func)(p));
 double hessij( double x[], double delti[], int thetai,int thetaj)        fprintf(ficlog,"Max: %.12e",(*func)(p));
 {        for (j=1;j<=n;j++) {
   int i;          printf(" %.12e",p[j]);
   int l=1, l1, lmax=20;          fprintf(ficlog," %.12e",p[j]);
   double k1,k2,k3,k4,res,fx;        }
   double p2[NPARMAX+1];        printf("\n");
   int k;        fprintf(ficlog,"\n");
         for(l=0;l<=1;l++) {
   fx=func(x);          for (j=1;j<=n;j++) {
   for (k=1; k<=2; k++) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     for (i=1;i<=npar;i++) p2[i]=x[i];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     p2[thetai]=x[thetai]+delti[thetai]/k;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          }
     k1=func(p2)-fx;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
            fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     p2[thetai]=x[thetai]+delti[thetai]/k;        }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  #endif
     k2=func(p2)-fx;  
    
     p2[thetai]=x[thetai]-delti[thetai]/k;        free_vector(xit,1,n); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        free_vector(xits,1,n); 
     k3=func(p2)-fx;        free_vector(ptt,1,n); 
          free_vector(pt,1,n); 
     p2[thetai]=x[thetai]-delti[thetai]/k;        return; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      } 
     k4=func(p2)-fx;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      for (j=1;j<=n;j++) { 
 #ifdef DEBUG        ptt[j]=2.0*p[j]-pt[j]; 
     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);        xit[j]=p[j]-pt[j]; 
 #endif        pt[j]=p[j]; 
   }      } 
   return res;      fptt=(*func)(ptt); 
 }      if (fptt < fp) { 
         t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
 /************** Inverse of matrix **************/        if (t < 0.0) { 
 void ludcmp(double **a, int n, int *indx, double *d)          linmin(p,xit,n,fret,func); 
 {          for (j=1;j<=n;j++) { 
   int i,imax,j,k;            xi[j][ibig]=xi[j][n]; 
   double big,dum,sum,temp;            xi[j][n]=xit[j]; 
   double *vv;          }
    #ifdef DEBUG
   vv=vector(1,n);          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   *d=1.0;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   for (i=1;i<=n;i++) {          for(j=1;j<=n;j++){
     big=0.0;            printf(" %.12e",xit[j]);
     for (j=1;j<=n;j++)            fprintf(ficlog," %.12e",xit[j]);
       if ((temp=fabs(a[i][j])) > big) big=temp;          }
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          printf("\n");
     vv[i]=1.0/big;          fprintf(ficlog,"\n");
   }  #endif
   for (j=1;j<=n;j++) {        }
     for (i=1;i<j;i++) {      } 
       sum=a[i][j];    } 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  } 
       a[i][j]=sum;  
     }  /**** Prevalence limit (stable or period prevalence)  ****************/
     big=0.0;  
     for (i=j;i<=n;i++) {  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       sum=a[i][j];  {
       for (k=1;k<j;k++)    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
         sum -= a[i][k]*a[k][j];       matrix by transitions matrix until convergence is reached */
       a[i][j]=sum;  
       if ( (dum=vv[i]*fabs(sum)) >= big) {    int i, ii,j,k;
         big=dum;    double min, max, maxmin, maxmax,sumnew=0.;
         imax=i;    double **matprod2();
       }    double **out, cov[NCOVMAX], **pmij();
     }    double **newm;
     if (j != imax) {    double agefin, delaymax=50 ; /* Max number of years to converge */
       for (k=1;k<=n;k++) {  
         dum=a[imax][k];    for (ii=1;ii<=nlstate+ndeath;ii++)
         a[imax][k]=a[j][k];      for (j=1;j<=nlstate+ndeath;j++){
         a[j][k]=dum;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       }      }
       *d = -(*d);  
       vv[imax]=vv[j];     cov[1]=1.;
     }   
     indx[j]=imax;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     if (a[j][j] == 0.0) a[j][j]=TINY;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     if (j != n) {      newm=savm;
       dum=1.0/(a[j][j]);      /* Covariates have to be included here again */
       for (i=j+1;i<=n;i++) a[i][j] *= dum;       cov[2]=agefin;
     }    
   }        for (k=1; k<=cptcovn;k++) {
   free_vector(vv,1,n);  /* Doesn't work */          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
 ;          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
 }        }
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 void lubksb(double **a, int n, int *indx, double b[])        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]]];
   int i,ii=0,ip,j;  
   double sum;        /*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]);*/
   for (i=1;i<=n;i++) {        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
     ip=indx[i];      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
     sum=b[ip];  
     b[ip]=b[i];      savm=oldm;
     if (ii)      oldm=newm;
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];      maxmax=0.;
     else if (sum) ii=i;      for(j=1;j<=nlstate;j++){
     b[i]=sum;        min=1.;
   }        max=0.;
   for (i=n;i>=1;i--) {        for(i=1; i<=nlstate; i++) {
     sum=b[i];          sumnew=0;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     b[i]=sum/a[i][i];          prlim[i][j]= newm[i][j]/(1-sumnew);
   }          max=FMAX(max,prlim[i][j]);
 }          min=FMIN(min,prlim[i][j]);
         }
 /************ Frequencies ********************/        maxmin=max-min;
 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)        maxmax=FMAX(maxmax,maxmin);
 {  /* Some frequencies */      }
        if(maxmax < ftolpl){
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;        return prlim;
   double ***freq; /* Frequencies */      }
   double *pp;    }
   double pos, k2, dateintsum=0,k2cpt=0;  }
   FILE *ficresp;  
   char fileresp[FILENAMELENGTH];  /*************** transition probabilities ***************/ 
    
   pp=vector(1,nlstate);  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  {
   strcpy(fileresp,"p");    double s1, s2;
   strcat(fileresp,fileres);    /*double t34;*/
   if((ficresp=fopen(fileresp,"w"))==NULL) {    int i,j,j1, nc, ii, jj;
     printf("Problem with prevalence resultfile: %s\n", fileresp);  
     exit(0);      for(i=1; i<= nlstate; i++){
   }        for(j=1; j<i;j++){
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   j1=0;            /*s2 += param[i][j][nc]*cov[nc];*/
              s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   j=cptcoveff;  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          }
            ps[i][j]=s2;
   for(k1=1; k1<=j;k1++){  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
     for(i1=1; i1<=ncodemax[k1];i1++){        }
       j1++;        for(j=i+1; j<=nlstate+ndeath;j++){
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
         scanf("%d", i);*/            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
       for (i=-1; i<=nlstate+ndeath; i++)    /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
         for (jk=-1; jk<=nlstate+ndeath; jk++)            }
           for(m=agemin; m <= agemax+3; m++)          ps[i][j]=s2;
             freq[i][jk][m]=0;        }
            }
       dateintsum=0;      /*ps[3][2]=1;*/
       k2cpt=0;      
       for (i=1; i<=imx; i++) {      for(i=1; i<= nlstate; i++){
         bool=1;        s1=0;
         if  (cptcovn>0) {        for(j=1; j<i; j++)
           for (z1=1; z1<=cptcoveff; z1++)          s1+=exp(ps[i][j]);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        for(j=i+1; j<=nlstate+ndeath; j++)
               bool=0;          s1+=exp(ps[i][j]);
         }        ps[i][i]=1./(s1+1.);
         if (bool==1) {        for(j=1; j<i; j++)
           for(m=firstpass; m<=lastpass; m++){          ps[i][j]= exp(ps[i][j])*ps[i][i];
             k2=anint[m][i]+(mint[m][i]/12.);        for(j=i+1; j<=nlstate+ndeath; j++)
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
               if(agev[m][i]==0) agev[m][i]=agemax+1;        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
               if(agev[m][i]==1) agev[m][i]=agemax+2;      } /* end i */
               if (m<lastpass) {      
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        for(jj=1; jj<= nlstate+ndeath; jj++){
               }          ps[ii][jj]=0;
                        ps[ii][ii]=1;
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        }
                 dateintsum=dateintsum+k2;      }
                 k2cpt++;      
               }  
             }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
           }  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
         }  /*         printf("ddd %lf ",ps[ii][jj]); */
       }  /*       } */
          /*       printf("\n "); */
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  /*        } */
   /*        printf("\n ");printf("%lf ",cov[2]); */
       if  (cptcovn>0) {         /*
         fprintf(ficresp, "\n#********** Variable ");        for(i=1; i<= npar; i++) printf("%f ",x[i]);
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        goto end;*/
         fprintf(ficresp, "**********\n#");      return ps;
       }  }
       for(i=1; i<=nlstate;i++)  
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  /**************** Product of 2 matrices ******************/
       fprintf(ficresp, "\n");  
        double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       for(i=(int)agemin; i <= (int)agemax+3; i++){  {
         if(i==(int)agemax+3)    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
           printf("Total");       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
         else    /* in, b, out are matrice of pointers which should have been initialized 
           printf("Age %d", i);       before: only the contents of out is modified. The function returns
         for(jk=1; jk <=nlstate ; jk++){       a pointer to pointers identical to out */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    long i, j, k;
             pp[jk] += freq[jk][m][i];    for(i=nrl; i<= nrh; i++)
         }      for(k=ncolol; k<=ncoloh; k++)
         for(jk=1; jk <=nlstate ; jk++){        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           for(m=-1, pos=0; m <=0 ; m++)          out[i][k] +=in[i][j]*b[j][k];
             pos += freq[jk][m][i];  
           if(pp[jk]>=1.e-10)    return out;
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  }
           else  
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  
         }  /************* Higher Matrix Product ***************/
   
         for(jk=1; jk <=nlstate ; jk++){  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  {
             pp[jk] += freq[jk][m][i];    /* Computes the transition matrix starting at age 'age' over 
         }       'nhstepm*hstepm*stepm' months (i.e. until
        age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
         for(jk=1,pos=0; jk <=nlstate ; jk++)       nhstepm*hstepm matrices. 
           pos += pp[jk];       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         for(jk=1; jk <=nlstate ; jk++){       (typically every 2 years instead of every month which is too big 
           if(pos>=1.e-5)       for the memory).
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);       Model is determined by parameters x and covariates have to be 
           else       included manually here. 
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  
           if( i <= (int) agemax){       */
             if(pos>=1.e-5){  
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    int i, j, d, h, k;
               probs[i][jk][j1]= pp[jk]/pos;    double **out, cov[NCOVMAX];
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/    double **newm;
             }  
             else    /* Hstepm could be zero and should return the unit matrix */
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    for (i=1;i<=nlstate+ndeath;i++)
           }      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);
         for(jk=-1; jk <=nlstate+ndeath; jk++)      }
           for(m=-1; m <=nlstate+ndeath; m++)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    for(h=1; h <=nhstepm; h++){
         if(i <= (int) agemax)      for(d=1; d <=hstepm; d++){
           fprintf(ficresp,"\n");        newm=savm;
         printf("\n");        /* Covariates have to be included here again */
       }        cov[1]=1.;
     }        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   }        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   dateintmean=dateintsum/k2cpt;        for (k=1; k<=cptcovage;k++)
            cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   fclose(ficresp);        for (k=1; k<=cptcovprod;k++)
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   free_vector(pp,1,nlstate);  
    
   /* End of Freq */        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
 }        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
 /************ Prevalence ********************/                     pmij(pmmij,cov,ncovmodel,x,nlstate));
 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)        savm=oldm;
 {  /* Some frequencies */        oldm=newm;
        }
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      for(i=1; i<=nlstate+ndeath; i++)
   double ***freq; /* Frequencies */        for(j=1;j<=nlstate+ndeath;j++) {
   double *pp;          po[i][j][h]=newm[i][j];
   double pos, k2;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
            */
   pp=vector(1,nlstate);        }
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    } /* end h */
      return po;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  }
   j1=0;  
    
   j=cptcoveff;  /*************** log-likelihood *************/
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  double func( double *x)
    {
  for(k1=1; k1<=j;k1++){    int i, ii, j, k, mi, d, kk;
     for(i1=1; i1<=ncodemax[k1];i1++){    double l, ll[NLSTATEMAX], cov[NCOVMAX];
       j1++;    double **out;
      double sw; /* Sum of weights */
       for (i=-1; i<=nlstate+ndeath; i++)      double lli; /* Individual log likelihood */
         for (jk=-1; jk<=nlstate+ndeath; jk++)      int s1, s2;
           for(m=agemin; m <= agemax+3; m++)    double bbh, survp;
             freq[i][jk][m]=0;    long ipmx;
          /*extern weight */
       for (i=1; i<=imx; i++) {    /* We are differentiating ll according to initial status */
         bool=1;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         if  (cptcovn>0) {    /*for(i=1;i<imx;i++) 
           for (z1=1; z1<=cptcoveff; z1++)      printf(" %d\n",s[4][i]);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])    */
               bool=0;    cov[1]=1.;
         }  
         if (bool==1) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
           for(m=firstpass; m<=lastpass; m++){  
             k2=anint[m][i]+(mint[m][i]/12.);    if(mle==1){
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
               if(agev[m][i]==0) agev[m][i]=agemax+1;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
               if(agev[m][i]==1) agev[m][i]=agemax+2;        for(mi=1; mi<= wav[i]-1; mi++){
               if (m<lastpass) freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          for (ii=1;ii<=nlstate+ndeath;ii++)
               /* freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];  */            for (j=1;j<=nlstate+ndeath;j++){
             }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            }
       }          for(d=0; d<dh[mi][i]; d++){
         for(i=(int)agemin; i <= (int)agemax+3; i++){            newm=savm;
           for(jk=1; jk <=nlstate ; jk++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)            for (kk=1; kk<=cptcovage;kk++) {
               pp[jk] += freq[jk][m][i];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }            }
           for(jk=1; jk <=nlstate ; jk++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             for(m=-1, pos=0; m <=0 ; m++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             pos += freq[jk][m][i];            savm=oldm;
         }            oldm=newm;
                  } /* end mult */
          for(jk=1; jk <=nlstate ; jk++){        
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
              pp[jk] += freq[jk][m][i];          /* 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 
                     * (in months) between two waves is not a multiple of stepm, we rounded to 
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];           * the nearest (and in case of equal distance, to the lowest) interval but now
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
          for(jk=1; jk <=nlstate ; jk++){                     * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
            if( i <= (int) agemax){           * probability in order to take into account the bias as a fraction of the way
              if(pos>=1.e-5){           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
                probs[i][jk][j1]= pp[jk]/pos;           * -stepm/2 to stepm/2 .
              }           * For stepm=1 the results are the same as for previous versions of Imach.
            }           * For stepm > 1 the results are less biased than in previous versions. 
          }           */
                    s1=s[mw[mi][i]][i];
         }          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
   }          /* bias bh is positive if real duration
             * is higher than the multiple of stepm and negative otherwise.
             */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   free_vector(pp,1,nlstate);          if( s2 > nlstate){ 
              /* i.e. if s2 is a death state and if the date of death is known 
 }  /* End of Freq */               then the contribution to the likelihood is the probability to 
                die between last step unit time and current  step unit time, 
 /************* Waves Concatenation ***************/               which is also equal to probability to die before dh 
                minus probability to die before dh-stepm . 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)               In version up to 0.92 likelihood was computed
 {          as if date of death was unknown. Death was treated as any other
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          health state: the date of the interview describes the actual state
      Death is a valid wave (if date is known).          and not the date of a change in health state. The former idea was
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          to consider that at each interview the state was recorded
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          (healthy, disable or death) and IMaCh was corrected; but when we
      and mw[mi+1][i]. dh depends on stepm.          introduced the exact date of death then we should have modified
      */          the contribution of an exact death to the likelihood. This new
           contribution is smaller and very dependent of the step unit
   int i, mi, m;          stepm. It is no more the probability to die between last interview
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          and month of death but the probability to survive from last
      double sum=0., jmean=0.;*/          interview up to one month before death multiplied by the
           probability to die within a month. Thanks to Chris
   int j, k=0,jk, ju, jl;          Jackson for correcting this bug.  Former versions increased
   double sum=0.;          mortality artificially. The bad side is that we add another loop
   jmin=1e+5;          which slows down the processing. The difference can be up to 10%
   jmax=-1;          lower mortality.
   jmean=0.;            */
   for(i=1; i<=imx; i++){            lli=log(out[s1][s2] - savm[s1][s2]);
     mi=0;  
     m=firstpass;  
     while(s[m][i] <= nlstate){          } else if  (s2==-2) {
       if(s[m][i]>=1)            for (j=1,survp=0. ; j<=nlstate; j++) 
         mw[++mi][i]=m;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       if(m >=lastpass)            /*survp += out[s1][j]; */
         break;            lli= log(survp);
       else          }
         m++;          
     }/* end while */          else if  (s2==-4) { 
     if (s[m][i] > nlstate){            for (j=3,survp=0. ; j<=nlstate; j++)  
       mi++;     /* Death is another wave */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       /* if(mi==0)  never been interviewed correctly before death */            lli= log(survp); 
          /* Only death is a correct wave */          } 
       mw[mi][i]=m;  
     }          else if  (s2==-5) { 
             for (j=1,survp=0. ; j<=2; j++)  
     wav[i]=mi;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     if(mi==0)            lli= log(survp); 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          } 
   }          
           else{
   for(i=1; i<=imx; i++){            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     for(mi=1; mi<wav[i];mi++){            /*  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 (stepm <=0)          } 
         dh[mi][i]=1;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       else{          /*if(lli ==000.0)*/
         if (s[mw[mi+1][i]][i] > nlstate) {          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
           if (agedc[i] < 2*AGESUP) {          ipmx +=1;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          sw += weight[i];
           if(j==0) j=1;  /* Survives at least one month after exam */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           k=k+1;        } /* end of wave */
           if (j >= jmax) jmax=j;      } /* end of individual */
           if (j <= jmin) jmin=j;    }  else if(mle==2){
           sum=sum+j;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           /*if (j<0) printf("j=%d num=%d \n",j,i); */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           }        for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
         else{            for (j=1;j<=nlstate+ndeath;j++){
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           k=k+1;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           if (j >= jmax) jmax=j;            }
           else if (j <= jmin)jmin=j;          for(d=0; d<=dh[mi][i]; d++){
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */            newm=savm;
           sum=sum+j;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         }            for (kk=1; kk<=cptcovage;kk++) {
         jk= j/stepm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         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];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
   }          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 */
   jmean=sum/k;          ipmx +=1;
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          sw += weight[i];
  }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 /*********** Tricode ****************************/        } /* end of wave */
 void tricode(int *Tvar, int **nbcode, int imx)      } /* end of individual */
 {    }  else if(mle==3){  /* exponential inter-extrapolation */
   int Ndum[20],ij=1, k, j, i;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   int cptcode=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   cptcoveff=0;        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
   for (k=0; k<19; k++) Ndum[k]=0;            for (j=1;j<=nlstate+ndeath;j++){
   for (k=1; k<=7; k++) ncodemax[k]=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {            }
     for (i=1; i<=imx; i++) {          for(d=0; d<dh[mi][i]; d++){
       ij=(int)(covar[Tvar[j]][i]);            newm=savm;
       Ndum[ij]++;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            for (kk=1; kk<=cptcovage;kk++) {
       if (ij > cptcode) cptcode=ij;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for (i=0; i<=cptcode; i++) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       if(Ndum[i]!=0) ncodemax[j]++;            savm=oldm;
     }            oldm=newm;
     ij=1;          } /* end mult */
         
           s1=s[mw[mi][i]][i];
     for (i=1; i<=ncodemax[j]; i++) {          s2=s[mw[mi+1][i]][i];
       for (k=0; k<=19; k++) {          bbh=(double)bh[mi][i]/(double)stepm; 
         if (Ndum[k] != 0) {          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 */
           nbcode[Tvar[j]][ij]=k;          ipmx +=1;
           /*     printf("nbcodeaaaaaaaaaaa=%d Tvar[j]=%d ij=%d j=%d",nbcode[Tvar[j]][ij],Tvar[j],ij,j);*/          sw += weight[i];
           ij++;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }        } /* end of wave */
         if (ij > ncodemax[j]) break;      } /* end of individual */
       }      }else if (mle==4){  /* ml=4 no inter-extrapolation */
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   }          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
  for (k=0; k<19; k++) Ndum[k]=0;          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
  for (i=1; i<=ncovmodel-2; i++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       ij=Tvar[i];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       Ndum[ij]++;            }
     }          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
  ij=1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
  for (i=1; i<=10; i++) {            for (kk=1; kk<=cptcovage;kk++) {
    if((Ndum[i]!=0) && (i<=ncovcol)){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      Tvaraff[ij]=i;            }
      ij++;          
    }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
              savm=oldm;
     cptcoveff=ij-1;            oldm=newm;
 }          } /* end mult */
         
 /*********** Health Expectancies ****************/          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm)          if( s2 > nlstate){ 
 {            lli=log(out[s1][s2] - savm[s1][s2]);
   /* Health expectancies */          }else{
   int i, j, nhstepm, hstepm, h, nstepm;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   double age, agelim, hf;          }
   double ***p3mat;          ipmx +=1;
            sw += weight[i];
   fprintf(ficreseij,"# Health expectancies\n");          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fprintf(ficreseij,"# Age");  /*      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]); */
   for(i=1; i<=nlstate;i++)        } /* end of wave */
     for(j=1; j<=nlstate;j++)      } /* end of individual */
       fprintf(ficreseij," %1d-%1d",i,j);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   fprintf(ficreseij,"\n");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   if(estepm < stepm){        for(mi=1; mi<= wav[i]-1; mi++){
     printf ("Problem %d lower than %d\n",estepm, stepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
   }            for (j=1;j<=nlstate+ndeath;j++){
   else  hstepm=estepm;                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* We compute the life expectancy from trapezoids spaced every estepm months              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    * This is mainly to measure the difference between two models: for example            }
    * if stepm=24 months pijx are given only every 2 years and by summing them          for(d=0; d<dh[mi][i]; d++){
    * we are calculating an estimate of the Life Expectancy assuming a linear            newm=savm;
    * progression inbetween and thus overestimating or underestimating according            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
    * to the curvature of the survival function. If, for the same date, we            for (kk=1; kk<=cptcovage;kk++) {
    * estimate the model with stepm=1 month, we can keep estepm to 24 months              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
    * to compare the new estimate of Life expectancy with the same linear            }
    * hypothesis. A more precise result, taking into account a more precise          
    * curvature will be obtained if estepm is as small as stepm. */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* For example we decided to compute the life expectancy with the smallest unit */            savm=oldm;
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            oldm=newm;
      nhstepm is the number of hstepm from age to agelim          } /* end mult */
      nstepm is the number of stepm from age to agelin.        
      Look at hpijx to understand the reason of that which relies in memory size          s1=s[mw[mi][i]][i];
      and note for a fixed period like estepm months */          s2=s[mw[mi+1][i]][i];
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
      survival function given by stepm (the optimization length). Unfortunately it          ipmx +=1;
      means that if the survival funtion is printed only each two years of age and if          sw += weight[i];
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      results. So we changed our mind and took the option of the best precision.          /*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 */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */      } /* end of individual */
     } /* End of if */
   agelim=AGESUP;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     /* nhstepm age range expressed in number of stepm */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     nstepm=(int) rint((agelim-age)*YEARM/stepm);    return -l;
     /* 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 */  /*************** log-likelihood *************/
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  double funcone( double *x)
     /* Computed by stepm unit matrices, product of hstepm matrices, stored  {
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    /* Same as likeli but slower because of a lot of printf and if */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      int i, ii, j, k, mi, d, kk;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     for(i=1; i<=nlstate;i++)    double **out;
       for(j=1; j<=nlstate;j++)    double lli; /* Individual log likelihood */
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){    double llt;
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;    int s1, s2;
           /* 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]);*/    double bbh, survp;
         }    /*extern weight */
     fprintf(ficreseij,"%3.0f",age );    /* We are differentiating ll according to initial status */
     for(i=1; i<=nlstate;i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       for(j=1; j<=nlstate;j++){    /*for(i=1;i<imx;i++) 
         fprintf(ficreseij," %9.4f", eij[i][j][(int)age]);      printf(" %d\n",s[4][i]);
       }    */
     fprintf(ficreseij,"\n");    cov[1]=1.;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
   }    for(k=1; k<=nlstate; k++) ll[k]=0.;
 }  
     for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 /************ Variance ******************/      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)      for(mi=1; mi<= wav[i]-1; mi++){
 {        for (ii=1;ii<=nlstate+ndeath;ii++)
   /* Variance of health expectancies */          for (j=1;j<=nlstate+ndeath;j++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **newm;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **dnewm,**doldm;          }
   int i, j, nhstepm, hstepm, h, nstepm ;        for(d=0; d<dh[mi][i]; d++){
   int k, cptcode;          newm=savm;
   double *xp;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double **gp, **gm;          for (kk=1; kk<=cptcovage;kk++) {
   double ***gradg, ***trgradg;            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double ***p3mat;          }
   double age,agelim, hf;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int theta;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           savm=oldm;
    fprintf(ficresvij,"# Covariances of life expectancies\n");          oldm=newm;
   fprintf(ficresvij,"# Age");        } /* end mult */
   for(i=1; i<=nlstate;i++)        
     for(j=1; j<=nlstate;j++)        s1=s[mw[mi][i]][i];
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        s2=s[mw[mi+1][i]][i];
   fprintf(ficresvij,"\n");        bbh=(double)bh[mi][i]/(double)stepm; 
         /* bias is positive if real duration
   xp=vector(1,npar);         * is higher than the multiple of stepm and negative otherwise.
   dnewm=matrix(1,nlstate,1,npar);         */
   doldm=matrix(1,nlstate,1,nlstate);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
            lli=log(out[s1][s2] - savm[s1][s2]);
   if(estepm < stepm){        } else if  (s2==-2) {
     printf ("Problem %d lower than %d\n",estepm, stepm);          for (j=1,survp=0. ; j<=nlstate; j++) 
   }            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   else  hstepm=estepm;            lli= log(survp);
   /* For example we decided to compute the life expectancy with the smallest unit */        }else if (mle==1){
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
      nhstepm is the number of hstepm from age to agelim        } else if(mle==2){
      nstepm is the number of stepm from age to agelin.          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 */
      Look at hpijx to understand the reason of that which relies in memory size        } else if(mle==3){  /* exponential inter-extrapolation */
      and note for a fixed period like k years */          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 */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        } else if (mle==4){  /* mle=4 no inter-extrapolation */
      survival function given by stepm (the optimization length). Unfortunately it          lli=log(out[s1][s2]); /* Original formula */
      means that if the survival funtion is printed only each two years of age and if        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          lli=log(out[s1][s2]); /* Original formula */
      results. So we changed our mind and took the option of the best precision.        } /* End of if */
   */        ipmx +=1;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        sw += weight[i];
   agelim = AGESUP;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  /*       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]); */
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        if(globpr){
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);   %11.6f %11.6f %11.6f ", \
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     gp=matrix(0,nhstepm,1,nlstate);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
     gm=matrix(0,nhstepm,1,nlstate);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
             llt +=ll[k]*gipmx/gsw;
     for(theta=1; theta <=npar; theta++){            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
       for(i=1; i<=npar; i++){ /* Computes gradient */          }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          fprintf(ficresilk," %10.6f\n", -llt);
       }        }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        } /* end of wave */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    } /* end of individual */
     for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       if (popbased==1) {    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         for(i=1; i<=nlstate;i++)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
           prlim[i][i]=probs[(int)age][i][ij];    if(globpr==0){ /* First time we count the contributions and weights */
       }      gipmx=ipmx;
        gsw=sw;
       for(j=1; j<= nlstate; j++){    }
         for(h=0; h<=nhstepm; h++){    return -l;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)  }
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];  
         }  
       }  /*************** function likelione ***********/
      void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       for(i=1; i<=npar; i++) /* Computes gradient */  {
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    /* This routine should help understanding what is done with 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);         the selection of individuals/waves and
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);       to check the exact contribution to the likelihood.
         Plotting could be done.
       if (popbased==1) {     */
         for(i=1; i<=nlstate;i++)    int k;
           prlim[i][i]=probs[(int)age][i][ij];  
       }    if(*globpri !=0){ /* Just counts and sums, no printings */
       strcpy(fileresilk,"ilk"); 
       for(j=1; j<= nlstate; j++){      strcat(fileresilk,fileres);
         for(h=0; h<=nhstepm; h++){      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        printf("Problem with resultfile: %s\n", fileresilk);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
         }      }
       }      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
       fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       for(j=1; j<= nlstate; j++)      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
         for(h=0; h<=nhstepm; h++){      for(k=1; k<=nlstate; k++) 
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
         }      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     } /* End theta */    }
   
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    *fretone=(*funcone)(p);
     if(*globpri !=0){
     for(h=0; h<=nhstepm; h++)      fclose(ficresilk);
       for(j=1; j<=nlstate;j++)      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
         for(theta=1; theta <=npar; theta++)      fflush(fichtm); 
           trgradg[h][j][theta]=gradg[h][theta][j];    } 
     return;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */  }
     for(i=1;i<=nlstate;i++)  
       for(j=1;j<=nlstate;j++)  
         vareij[i][j][(int)age] =0.;  /*********** Maximum Likelihood Estimation ***************/
   
     for(h=0;h<=nhstepm;h++){  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       for(k=0;k<=nhstepm;k++){  {
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    int i,j, iter;
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    double **xi;
         for(i=1;i<=nlstate;i++)    double fret;
           for(j=1;j<=nlstate;j++)    double fretone; /* Only one call to likelihood */
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    /*  char filerespow[FILENAMELENGTH];*/
       }    xi=matrix(1,npar,1,npar);
     }    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++)
     fprintf(ficresvij,"%.0f ",age );        xi[i][j]=(i==j ? 1.0 : 0.0);
     for(i=1; i<=nlstate;i++)    printf("Powell\n");  fprintf(ficlog,"Powell\n");
       for(j=1; j<=nlstate;j++){    strcpy(filerespow,"pow"); 
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    strcat(filerespow,fileres);
       }    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     fprintf(ficresvij,"\n");      printf("Problem with resultfile: %s\n", filerespow);
     free_matrix(gp,0,nhstepm,1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     free_matrix(gm,0,nhstepm,1,nlstate);    }
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    for (i=1;i<=nlstate;i++)
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(j=1;j<=nlstate+ndeath;j++)
   } /* End age */        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
      fprintf(ficrespow,"\n");
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    powell(p,xi,npar,ftol,&iter,&fret,func);
   free_matrix(dnewm,1,nlstate,1,nlstate);  
     free_matrix(xi,1,npar,1,npar);
 }    fclose(ficrespow);
     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
 /************ Variance of prevlim ******************/    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
 {  
   /* Variance of prevalence limit */  }
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  
   double **newm;  /**** Computes Hessian and covariance matrix ***/
   double **dnewm,**doldm;  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   int i, j, nhstepm, hstepm;  {
   int k, cptcode;    double  **a,**y,*x,pd;
   double *xp;    double **hess;
   double *gp, *gm;    int i, j,jk;
   double **gradg, **trgradg;    int *indx;
   double age,agelim;  
   int theta;    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
        double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");    void lubksb(double **a, int npar, int *indx, double b[]) ;
   fprintf(ficresvpl,"# Age");    void ludcmp(double **a, int npar, int *indx, double *d) ;
   for(i=1; i<=nlstate;i++)    double gompertz(double p[]);
       fprintf(ficresvpl," %1d-%1d",i,i);    hess=matrix(1,npar,1,npar);
   fprintf(ficresvpl,"\n");  
     printf("\nCalculation of the hessian matrix. Wait...\n");
   xp=vector(1,npar);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   dnewm=matrix(1,nlstate,1,npar);    for (i=1;i<=npar;i++){
   doldm=matrix(1,nlstate,1,nlstate);      printf("%d",i);fflush(stdout);
        fprintf(ficlog,"%d",i);fflush(ficlog);
   hstepm=1*YEARM; /* Every year of age */     
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   agelim = AGESUP;      
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      /*  printf(" %f ",p[i]);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     if (stepm >= YEARM) hstepm=1;    }
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    
     gradg=matrix(1,npar,1,nlstate);    for (i=1;i<=npar;i++) {
     gp=vector(1,nlstate);      for (j=1;j<=npar;j++)  {
     gm=vector(1,nlstate);        if (j>i) { 
           printf(".%d%d",i,j);fflush(stdout);
     for(theta=1; theta <=npar; theta++){          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
       for(i=1; i<=npar; i++){ /* Computes gradient */          hess[i][j]=hessij(p,delti,i,j,func,npar);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          
       }          hess[j][i]=hess[i][j];    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          /*printf(" %lf ",hess[i][j]);*/
       for(i=1;i<=nlstate;i++)        }
         gp[i] = prlim[i][i];      }
        }
       for(i=1; i<=npar; i++) /* Computes gradient */    printf("\n");
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    fprintf(ficlog,"\n");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
         gm[i] = prlim[i][i];    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     
       for(i=1;i<=nlstate;i++)    a=matrix(1,npar,1,npar);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    y=matrix(1,npar,1,npar);
     } /* End theta */    x=vector(1,npar);
     indx=ivector(1,npar);
     trgradg =matrix(1,nlstate,1,npar);    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     for(j=1; j<=nlstate;j++)    ludcmp(a,npar,indx,&pd);
       for(theta=1; theta <=npar; theta++)  
         trgradg[j][theta]=gradg[theta][j];    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
     for(i=1;i<=nlstate;i++)      x[j]=1;
       varpl[i][(int)age] =0.;      lubksb(a,npar,indx,x);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      for (i=1;i<=npar;i++){ 
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);        matcov[i][j]=x[i];
     for(i=1;i<=nlstate;i++)      }
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    }
   
     fprintf(ficresvpl,"%.0f ",age );    printf("\n#Hessian matrix#\n");
     for(i=1; i<=nlstate;i++)    fprintf(ficlog,"\n#Hessian matrix#\n");
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    for (i=1;i<=npar;i++) { 
     fprintf(ficresvpl,"\n");      for (j=1;j<=npar;j++) { 
     free_vector(gp,1,nlstate);        printf("%.3e ",hess[i][j]);
     free_vector(gm,1,nlstate);        fprintf(ficlog,"%.3e ",hess[i][j]);
     free_matrix(gradg,1,npar,1,nlstate);      }
     free_matrix(trgradg,1,nlstate,1,npar);      printf("\n");
   } /* End age */      fprintf(ficlog,"\n");
     }
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    /* Recompute Inverse */
   free_matrix(dnewm,1,nlstate,1,nlstate);    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
 }    ludcmp(a,npar,indx,&pd);
   
 /************ Variance of one-step probabilities  ******************/    /*  printf("\n#Hessian matrix recomputed#\n");
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)  
 {    for (j=1;j<=npar;j++) {
   int i, j;      for (i=1;i<=npar;i++) x[i]=0;
   int k=0, cptcode;      x[j]=1;
   double **dnewm,**doldm;      lubksb(a,npar,indx,x);
   double *xp;      for (i=1;i<=npar;i++){ 
   double *gp, *gm;        y[i][j]=x[i];
   double **gradg, **trgradg;        printf("%.3e ",y[i][j]);
   double age,agelim, cov[NCOVMAX];        fprintf(ficlog,"%.3e ",y[i][j]);
   int theta;      }
   char fileresprob[FILENAMELENGTH];      printf("\n");
       fprintf(ficlog,"\n");
   strcpy(fileresprob,"prob");    }
   strcat(fileresprob,fileres);    */
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  
     printf("Problem with resultfile: %s\n", fileresprob);    free_matrix(a,1,npar,1,npar);
   }    free_matrix(y,1,npar,1,npar);
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
   xp=vector(1,npar);  
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));  }
    
   cov[1]=1;  /*************** hessian matrix ****************/
   for (age=bage; age<=fage; age ++){  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     cov[2]=age;  {
     gradg=matrix(1,npar,1,9);    int i;
     trgradg=matrix(1,9,1,npar);    int l=1, lmax=20;
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    double k1,k2;
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    double p2[NPARMAX+1];
        double res;
     for(theta=1; theta <=npar; theta++){    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       for(i=1; i<=npar; i++)    double fx;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    int k=0,kmax=10;
          double l1;
       pmij(pmmij,cov,ncovmodel,xp,nlstate);  
        fx=func(x);
       k=0;    for (i=1;i<=npar;i++) p2[i]=x[i];
       for(i=1; i<= (nlstate+ndeath); i++){    for(l=0 ; l <=lmax; l++){
         for(j=1; j<=(nlstate+ndeath);j++){      l1=pow(10,l);
            k=k+1;      delts=delt;
           gp[k]=pmmij[i][j];      for(k=1 ; k <kmax; k=k+1){
         }        delt = delta*(l1*k);
       }        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;
       for(i=1; i<=npar; i++)        p2[theta]=x[theta]-delt;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        k2=func(p2)-fx;
            /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
       pmij(pmmij,cov,ncovmodel,xp,nlstate);        
       k=0;  #ifdef DEBUG
       for(i=1; i<=(nlstate+ndeath); i++){        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         for(j=1; j<=(nlstate+ndeath);j++){        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);
           k=k+1;  #endif
           gm[k]=pmmij[i][j];        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       }          k=kmax;
              }
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];            k=kmax; l=lmax*10.;
     }        }
         else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)          delts=delt;
       for(theta=1; theta <=npar; theta++)        }
       trgradg[j][theta]=gradg[theta][j];      }
      }
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    delti[theta]=delts;
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    return res; 
     
      pmij(pmmij,cov,ncovmodel,x,nlstate);  }
   
      k=0;  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
      for(i=1; i<=(nlstate+ndeath); i++){  {
        for(j=1; j<=(nlstate+ndeath);j++){    int i;
          k=k+1;    int l=1, l1, lmax=20;
          gm[k]=pmmij[i][j];    double k1,k2,k3,k4,res,fx;
         }    double p2[NPARMAX+1];
      }    int k;
        
      /*printf("\n%d ",(int)age);    fx=func(x);
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    for (k=1; k<=2; k++) {
              for (i=1;i<=npar;i++) p2[i]=x[i];
       p2[thetai]=x[thetai]+delti[thetai]/k;
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
      }*/      k1=func(p2)-fx;
     
   fprintf(ficresprob,"\n%d ",(int)age);      p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      k2=func(p2)-fx;
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);    
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      p2[thetai]=x[thetai]-delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k3=func(p2)-fx;
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));      p2[thetai]=x[thetai]-delti[thetai]/k;
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      k4=func(p2)-fx;
 }      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
  free_vector(xp,1,npar);  #ifdef DEBUG
 fclose(ficresprob);      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
       fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
 }  #endif
     }
 /******************* Printing html file ***********/    return res;
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \  }
  int lastpass, int stepm, int weightopt, char model[],\  
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \  /************** Inverse of matrix **************/
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\  void ludcmp(double **a, int n, int *indx, double *d) 
  char version[], int popforecast, int estepm ){  { 
   int jj1, k1, i1, cpt;    int i,imax,j,k; 
   FILE *fichtm;    double big,dum,sum,temp; 
   /*char optionfilehtm[FILENAMELENGTH];*/    double *vv; 
    
   strcpy(optionfilehtm,optionfile);    vv=vector(1,n); 
   strcat(optionfilehtm,".htm");    *d=1.0; 
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    for (i=1;i<=n;i++) { 
     printf("Problem with %s \n",optionfilehtm), exit(0);      big=0.0; 
   }      for (j=1;j<=n;j++) 
         if ((temp=fabs(a[i][j])) > big) big=temp; 
  fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n      vv[i]=1.0/big; 
 \n    } 
 Total number of observations=%d <br>\n    for (j=1;j<=n;j++) { 
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n      for (i=1;i<j;i++) { 
 <hr  size=\"2\" color=\"#EC5E5E\">        sum=a[i][j]; 
  <ul><li>Outputs files<br>\n        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n        a[i][j]=sum; 
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n      } 
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n      big=0.0; 
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n      for (i=j;i<=n;i++) { 
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n        sum=a[i][j]; 
  - Life expectancies by age and initial health status (estepm=%2d months): <a href=\"e%s\">e%s</a> <br>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot,fileres,fileres,fileres,fileres,fileres,fileres,estepm,fileres,fileres);        for (k=1;k<j;k++) 
           sum -= a[i][k]*a[k][j]; 
  fprintf(fichtm,"\n        a[i][j]=sum; 
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n        if ( (dum=vv[i]*fabs(sum)) >= big) { 
  - Variances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n          big=dum; 
  - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>\n          imax=i; 
  - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);        } 
       } 
  if(popforecast==1) fprintf(fichtm,"\n      if (j != imax) { 
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n        for (k=1;k<=n;k++) { 
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n          dum=a[imax][k]; 
         <br>",fileres,fileres,fileres,fileres);          a[imax][k]=a[j][k]; 
  else          a[j][k]=dum; 
    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);        } 
 fprintf(fichtm," <li>Graphs</li><p>");        *d = -(*d); 
         vv[imax]=vv[j]; 
  m=cptcoveff;      } 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      indx[j]=imax; 
       if (a[j][j] == 0.0) a[j][j]=TINY; 
  jj1=0;      if (j != n) { 
  for(k1=1; k1<=m;k1++){        dum=1.0/(a[j][j]); 
    for(i1=1; i1<=ncodemax[k1];i1++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
        jj1++;      } 
        if (cptcovn > 0) {    } 
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    free_vector(vv,1,n);  /* Doesn't work */
          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\">");  
        }  void lubksb(double **a, int n, int *indx, double b[]) 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>  { 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        int i,ii=0,ip,j; 
        for(cpt=1; cpt<nlstate;cpt++){    double sum; 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>   
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    for (i=1;i<=n;i++) { 
        }      ip=indx[i]; 
     for(cpt=1; cpt<=nlstate;cpt++) {      sum=b[ip]; 
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      b[ip]=b[i]; 
 interval) in state (%d): v%s%d%d.gif <br>      if (ii) 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
      }      else if (sum) ii=i; 
      for(cpt=1; cpt<=nlstate;cpt++) {      b[i]=sum; 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    } 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    for (i=n;i>=1;i--) { 
      }      sum=b[i]; 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
 health expectancies in states (1) and (2): e%s%d.gif<br>      b[i]=sum/a[i][i]; 
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);    } 
 fprintf(fichtm,"\n</body>");  } 
    }  
    }  void pstamp(FILE *fichier)
 fclose(fichtm);  {
 }    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   }
 /******************* Gnuplot file **************/  
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){  /************ 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[])
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;  {  /* Some frequencies */
     
   strcpy(optionfilegnuplot,optionfilefiname);    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
   strcat(optionfilegnuplot,".gp.txt");    int first;
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {    double ***freq; /* Frequencies */
     printf("Problem with file %s",optionfilegnuplot);    double *pp, **prop;
   }    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     char fileresp[FILENAMELENGTH];
 #ifdef windows    
     fprintf(ficgp,"cd \"%s\" \n",pathc);    pp=vector(1,nlstate);
 #endif    prop=matrix(1,nlstate,iagemin,iagemax+3);
 m=pow(2,cptcoveff);    strcpy(fileresp,"p");
      strcat(fileresp,fileres);
  /* 1eme*/    if((ficresp=fopen(fileresp,"w"))==NULL) {
   for (cpt=1; cpt<= nlstate ; cpt ++) {      printf("Problem with prevalence resultfile: %s\n", fileresp);
    for (k1=1; k1<= m ; k1 ++) {      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
       exit(0);
 #ifdef windows    }
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
 #endif    j1=0;
 #ifdef unix    
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);    j=cptcoveff;
 #endif    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   
 for (i=1; i<= nlstate ; i ++) {    first=1;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for(k1=1; k1<=j;k1++){
 }      for(i1=1; i1<=ncodemax[k1];i1++){
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);        j1++;
     for (i=1; i<= nlstate ; i ++) {        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          scanf("%d", i);*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");        for (i=-5; i<=nlstate+ndeath; i++)  
 }          for (jk=-5; jk<=nlstate+ndeath; jk++)  
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            for(m=iagemin; m <= iagemax+3; m++)
      for (i=1; i<= nlstate ; i ++) {              freq[i][jk][m]=0;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");      for (i=1; i<=nlstate; i++)  
 }          for(m=iagemin; m <= iagemax+3; m++)
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          prop[i][m]=0;
 #ifdef unix        
 fprintf(ficgp,"\nset ter gif small size 400,300");        dateintsum=0;
 #endif        k2cpt=0;
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        for (i=1; i<=imx; i++) {
    }          bool=1;
   }          if  (cptcovn>0) {
   /*2 eme*/            for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   for (k1=1; k1<= m ; k1 ++) {                bool=0;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",ageminpar,fage);          }
              if (bool==1){
     for (i=1; i<= nlstate+1 ; i ++) {            for(m=firstpass; m<=lastpass; m++){
       k=2*i;              k2=anint[m][i]+(mint[m][i]/12.);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
       for (j=1; j<= nlstate+1 ; j ++) {                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   else fprintf(ficgp," \%%*lf (\%%*lf)");                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
 }                  if (m<lastpass) {
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);                }
       for (j=1; j<= nlstate+1 ; j ++) {                
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
         else fprintf(ficgp," \%%*lf (\%%*lf)");                  dateintsum=dateintsum+k2;
 }                    k2cpt++;
       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<= nlstate+1 ; j ++) {            }
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          }
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }           
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       else fprintf(ficgp,"\" t\"\" w l 0,");        pstamp(ficresp);
     }        if  (cptcovn>0) {
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);          fprintf(ficresp, "\n#********** Variable "); 
   }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresp, "**********\n#");
   /*3eme*/        }
         for(i=1; i<=nlstate;i++) 
   for (k1=1; k1<= m ; k1 ++) {          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
     for (cpt=1; cpt<= nlstate ; cpt ++) {        fprintf(ficresp, "\n");
       k=2+nlstate*(cpt-1);        
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);        for(i=iagemin; i <= iagemax+3; i++){
       for (i=1; i< nlstate ; i ++) {          if(i==iagemax+3){
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);            fprintf(ficlog,"Total");
       }          }else{
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            if(first==1){
     }              first=0;
     }              printf("See log file for details...\n");
              }
   /* CV preval stat */            fprintf(ficlog,"Age %d", i);
     for (k1=1; k1<= m ; k1 ++) {          }
     for (cpt=1; cpt<nlstate ; cpt ++) {          for(jk=1; jk <=nlstate ; jk++){
       k=3;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);              pp[jk] += freq[jk][m][i]; 
           }
       for (i=1; i< nlstate ; i ++)          for(jk=1; jk <=nlstate ; jk++){
         fprintf(ficgp,"+$%d",k+i+1);            for(m=-1, pos=0; m <=0 ; m++)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);              pos += freq[jk][m][i];
                  if(pp[jk]>=1.e-10){
       l=3+(nlstate+ndeath)*cpt;              if(first==1){
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       for (i=1; i< nlstate ; i ++) {              }
         l=3+(nlstate+ndeath)*cpt;              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
         fprintf(ficgp,"+$%d",l+i+1);            }else{
       }              if(first==1)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                  printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     }            }
   }            }
    
   /* proba elementaires */          for(jk=1; jk <=nlstate ; jk++){
    for(i=1,jk=1; i <=nlstate; i++){            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     for(k=1; k <=(nlstate+ndeath); k++){              pp[jk] += freq[jk][m][i];
       if (k != i) {          }       
         for(j=1; j <=ncovmodel; j++){          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
                    pos += pp[jk];
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);            posprop += prop[jk][i];
           jk++;          }
           fprintf(ficgp,"\n");          for(jk=1; jk <=nlstate ; jk++){
         }            if(pos>=1.e-5){
       }              if(first==1)
     }                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     }              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
     for(jk=1; jk <=m; jk++) {              if(first==1)
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
    i=1;              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
    for(k2=1; k2<=nlstate; k2++) {            }
      k3=i;            if( i <= iagemax){
      for(k=1; k<=(nlstate+ndeath); k++) {              if(pos>=1.e-5){
        if (k != k2){                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);                /*probs[i][jk][j1]= pp[jk]/pos;*/
 ij=1;                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
         for(j=3; j <=ncovmodel; j++) {              }
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {              else
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             ij++;            }
           }          }
           else          
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          for(jk=-1; jk <=nlstate+ndeath; jk++)
         }            for(m=-1; m <=nlstate+ndeath; m++)
           fprintf(ficgp,")/(1");              if(freq[jk][m][i] !=0 ) {
                      if(first==1)
         for(k1=1; k1 <=nlstate; k1++){                  printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 ij=1;              }
           for(j=3; j <=ncovmodel; j++){          if(i <= iagemax)
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {            fprintf(ficresp,"\n");
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          if(first==1)
             ij++;            printf("Others in log...\n");
           }          fprintf(ficlog,"\n");
           else        }
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      }
           }    }
           fprintf(ficgp,")");    dateintmean=dateintsum/k2cpt; 
         }   
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    fclose(ficresp);
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
         i=i+ncovmodel;    free_vector(pp,1,nlstate);
        }    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
      }    /* End of Freq */
    }  }
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);  
    }  /************ Prevalence ********************/
      void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   fclose(ficgp);  {  
 }  /* end gnuplot */    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
        in each health status at the date of interview (if between dateprev1 and dateprev2).
        We still use firstpass and lastpass as another selection.
 /*************** Moving average **************/    */
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){   
     int i, m, jk, k1, i1, j1, bool, z1,z2,j;
   int i, cpt, cptcod;    double ***freq; /* Frequencies */
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)    double *pp, **prop;
       for (i=1; i<=nlstate;i++)    double pos,posprop; 
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    double  y2; /* in fractional years */
           mobaverage[(int)agedeb][i][cptcod]=0.;    int iagemin, iagemax;
      
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){    iagemin= (int) agemin;
       for (i=1; i<=nlstate;i++){    iagemax= (int) agemax;
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    /*pp=vector(1,nlstate);*/
           for (cpt=0;cpt<=4;cpt++){    prop=matrix(1,nlstate,iagemin,iagemax+3); 
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
           }    j1=0;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;    
         }    j=cptcoveff;
       }    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     }    
        for(k1=1; k1<=j;k1++){
 }      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
         
 /************** Forecasting ******************/        for (i=1; i<=nlstate; i++)  
 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){          for(m=iagemin; m <= iagemax+3; m++)
              prop[i][m]=0.0;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;       
   int *popage;        for (i=1; i<=imx; i++) { /* Each individual */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;          bool=1;
   double *popeffectif,*popcount;          if  (cptcovn>0) {
   double ***p3mat;            for (z1=1; z1<=cptcoveff; z1++) 
   char fileresf[FILENAMELENGTH];              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
  agelim=AGESUP;          } 
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;          if (bool==1) { 
             for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
                if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                  if(agev[m][i]==0) agev[m][i]=iagemax+1;
   strcpy(fileresf,"f");                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   strcat(fileresf,fileres);                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); 
   if((ficresf=fopen(fileresf,"w"))==NULL) {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     printf("Problem with forecast resultfile: %s\n", fileresf);                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
   }                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   printf("Computing forecasting: result on file '%s' \n", fileresf);                  prop[s[m][i]][iagemax+3] += weight[i]; 
                 } 
   if (cptcoveff==0) ncodemax[cptcoveff]=1;              }
             } /* end selection of waves */
   if (mobilav==1) {          }
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        }
     movingaverage(agedeb, fage, ageminpar, mobaverage);        for(i=iagemin; i <= iagemax+3; i++){  
   }          
           for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
   stepsize=(int) (stepm+YEARM-1)/YEARM;            posprop += prop[jk][i]; 
   if (stepm<=12) stepsize=1;          } 
    
   agelim=AGESUP;          for(jk=1; jk <=nlstate ; jk++){     
              if( i <=  iagemax){ 
   hstepm=1;              if(posprop>=1.e-5){ 
   hstepm=hstepm/stepm;                probs[i][jk][j1]= prop[jk][i]/posprop;
   yp1=modf(dateintmean,&yp);              } 
   anprojmean=yp;            } 
   yp2=modf((yp1*12),&yp);          }/* end jk */ 
   mprojmean=yp;        }/* end i */ 
   yp1=modf((yp2*30.5),&yp);      } /* end i1 */
   jprojmean=yp;    } /* end k1 */
   if(jprojmean==0) jprojmean=1;    
   if(mprojmean==0) jprojmean=1;    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
      /*free_vector(pp,1,nlstate);*/
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
    }  /* End of prevalence */
   for(cptcov=1;cptcov<=i2;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  /************* Waves Concatenation ***************/
       k=k+1;  
       fprintf(ficresf,"\n#******");  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)
       for(j=1;j<=cptcoveff;j++) {  {
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       }       Death is a valid wave (if date is known).
       fprintf(ficresf,"******\n");       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       fprintf(ficresf,"# StartingAge FinalAge");       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);       and mw[mi+1][i]. dh depends on stepm.
             */
        
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {    int i, mi, m;
         fprintf(ficresf,"\n");    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);         double sum=0., jmean=0.;*/
     int first;
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    int j, k=0,jk, ju, jl;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    double sum=0.;
           nhstepm = nhstepm/hstepm;    first=0;
              jmin=1e+5;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    jmax=-1;
           oldm=oldms;savm=savms;    jmean=0.;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      for(i=1; i<=imx; i++){
              mi=0;
           for (h=0; h<=nhstepm; h++){      m=firstpass;
             if (h==(int) (calagedate+YEARM*cpt)) {      while(s[m][i] <= nlstate){
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
             }          mw[++mi][i]=m;
             for(j=1; j<=nlstate+ndeath;j++) {        if(m >=lastpass)
               kk1=0.;kk2=0;          break;
               for(i=1; i<=nlstate;i++) {                      else
                 if (mobilav==1)          m++;
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      }/* end while */
                 else {      if (s[m][i] > nlstate){
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];        mi++;     /* Death is another wave */
                 }        /* if(mi==0)  never been interviewed correctly before death */
                           /* Only death is a correct wave */
               }        mw[mi][i]=m;
               if (h==(int)(calagedate+12*cpt)){      }
                 fprintf(ficresf," %.3f", kk1);  
                              wav[i]=mi;
               }      if(mi==0){
             }        nbwarn++;
           }        if(first==0){
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
         }          first=1;
       }        }
     }        if(first==1){
   }          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
                }
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      } /* end mi==0 */
     } /* End individuals */
   fclose(ficresf);  
 }    for(i=1; i<=imx; i++){
 /************** Forecasting ******************/      for(mi=1; mi<wav[i];mi++){
 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){        if (stepm <=0)
            dh[mi][i]=1;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;        else{
   int *popage;          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;            if (agedc[i] < 2*AGESUP) {
   double *popeffectif,*popcount;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   double ***p3mat,***tabpop,***tabpopprev;              if(j==0) j=1;  /* Survives at least one month after exam */
   char filerespop[FILENAMELENGTH];              else if(j<0){
                 nberr++;
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                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]);
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                j=1; /* Temporary Dangerous patch */
   agelim=AGESUP;                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);
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;                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);
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              }
                k=k+1;
                if (j >= jmax){
   strcpy(filerespop,"pop");                jmax=j;
   strcat(filerespop,fileres);                ijmax=i;
   if((ficrespop=fopen(filerespop,"w"))==NULL) {              }
     printf("Problem with forecast resultfile: %s\n", filerespop);              if (j <= jmin){
   }                jmin=j;
   printf("Computing forecasting: result on file '%s' \n", filerespop);                ijmin=i;
               }
   if (cptcoveff==0) ncodemax[cptcoveff]=1;              sum=sum+j;
               /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   if (mobilav==1) {              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            }
     movingaverage(agedeb, fage, ageminpar, mobaverage);          }
   }          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   stepsize=(int) (stepm+YEARM-1)/YEARM;  /*        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]); */
   if (stepm<=12) stepsize=1;  
              k=k+1;
   agelim=AGESUP;            if (j >= jmax) {
                jmax=j;
   hstepm=1;              ijmax=i;
   hstepm=hstepm/stepm;            }
              else if (j <= jmin){
   if (popforecast==1) {              jmin=j;
     if((ficpop=fopen(popfile,"r"))==NULL) {              ijmin=i;
       printf("Problem with population file : %s\n",popfile);exit(0);            }
     }            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     popage=ivector(0,AGESUP);            /*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]);*/
     popeffectif=vector(0,AGESUP);            if(j<0){
     popcount=vector(0,AGESUP);              nberr++;
                  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]);
     i=1;                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]);
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;            }
                sum=sum+j;
     imx=i;          }
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];          jk= j/stepm;
   }          jl= j -jk*stepm;
           ju= j -(jk+1)*stepm;
   for(cptcov=1;cptcov<=i2;cptcov++){          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            if(jl==0){
       k=k+1;              dh[mi][i]=jk;
       fprintf(ficrespop,"\n#******");              bh[mi][i]=0;
       for(j=1;j<=cptcoveff;j++) {            }else{ /* We want a negative bias in order to only have interpolation ie
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    * at the price of an extra matrix product in likelihood */
       }              dh[mi][i]=jk+1;
       fprintf(ficrespop,"******\n");              bh[mi][i]=ju;
       fprintf(ficrespop,"# Age");            }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);          }else{
       if (popforecast==1)  fprintf(ficrespop," [Population]");            if(jl <= -ju){
                    dh[mi][i]=jk;
       for (cpt=0; cpt<=0;cpt++) {              bh[mi][i]=jl;       /* bias is positive if real duration
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);                                     * is higher than the multiple of stepm and negative otherwise.
                                           */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){            }
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            else{
           nhstepm = nhstepm/hstepm;              dh[mi][i]=jk+1;
                        bh[mi][i]=ju;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            }
           oldm=oldms;savm=savms;            if(dh[mi][i]==0){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                dh[mi][i]=1; /* At least one step */
                      bh[mi][i]=ju; /* At least one step */
           for (h=0; h<=nhstepm; h++){              /*  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);*/
             if (h==(int) (calagedate+YEARM*cpt)) {            }
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);          } /* end if mle */
             }        }
             for(j=1; j<=nlstate+ndeath;j++) {      } /* end wave */
               kk1=0.;kk2=0;    }
               for(i=1; i<=nlstate;i++) {                  jmean=sum/k;
                 if (mobilav==1)    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);
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    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);
                 else {   }
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];  
                 }  /*********** Tricode ****************************/
               }  void tricode(int *Tvar, int **nbcode, int imx)
               if (h==(int)(calagedate+12*cpt)){  {
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    
                   /*fprintf(ficrespop," %.3f", kk1);    int Ndum[20],ij=1, k, j, i, maxncov=19;
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/    int cptcode=0;
               }    cptcoveff=0; 
             }   
             for(i=1; i<=nlstate;i++){    for (k=0; k<maxncov; k++) Ndum[k]=0;
               kk1=0.;    for (k=1; k<=7; k++) ncodemax[k]=0;
                 for(j=1; j<=nlstate;j++){  
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
                 }      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];                                 modality*/ 
             }        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
         Ndum[ij]++; /*store the modality */
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
           }                                         Tvar[j]. If V=sex and male is 0 and 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                                         female is 1, then  cptcode=1.*/
         }      }
       }  
        for (i=0; i<=cptcode; i++) {
   /******/        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<=(anpyram1-anpyram);cpt++) {  
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        ij=1; 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      for (i=1; i<=ncodemax[j]; i++) {
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        for (k=0; k<= maxncov; k++) {
           nhstepm = nhstepm/hstepm;          if (Ndum[k] != 0) {
                      nbcode[Tvar[j]][ij]=k; 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            /* 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; */
           oldm=oldms;savm=savms;            
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              ij++;
           for (h=0; h<=nhstepm; h++){          }
             if (h==(int) (calagedate+YEARM*cpt)) {          if (ij > ncodemax[j]) break; 
               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++) {                 for (k=0; k< maxncov; k++) Ndum[k]=0;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];      
               }   for (i=1; i<=ncovmodel-2; i++) { 
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
             }     ij=Tvar[i];
           }     Ndum[ij]++;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);   }
         }  
       }   ij=1;
    }   for (i=1; i<= maxncov; i++) {
   }     if((Ndum[i]!=0) && (i<=ncovcol)){
         Tvaraff[ij]=i; /*For printing */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);       ij++;
      }
   if (popforecast==1) {   }
     free_ivector(popage,0,AGESUP);   
     free_vector(popeffectif,0,AGESUP);   cptcoveff=ij-1; /*Number of simple covariates*/
     free_vector(popcount,0,AGESUP);  }
   }  
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  /*********** Health Expectancies ****************/
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   fclose(ficrespop);  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[] )
 }  
   {
 /***********************************************/    /* Health expectancies, no variances */
 /**************** Main Program *****************/    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
 /***********************************************/    double age, agelim, hf;
     double ***p3mat;
 int main(int argc, char *argv[])    double eip;
 {  
     pstamp(ficreseij);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   double agedeb, agefin,hf;    fprintf(ficreseij,"# Age");
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;    for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++){
   double fret;        fprintf(ficreseij," e%1d%1d ",i,j);
   double **xi,tmp,delta;      }
       fprintf(ficreseij," e%1d. ",i);
   double dum; /* Dummy variable */    }
   double ***p3mat;    fprintf(ficreseij,"\n");
   int *indx;  
   char line[MAXLINE], linepar[MAXLINE];    
   char title[MAXLINE];    if(estepm < stepm){
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];      printf ("Problem %d lower than %d\n",estepm, stepm);
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    }
      else  hstepm=estepm;   
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
   char filerest[FILENAMELENGTH];     * if stepm=24 months pijx are given only every 2 years and by summing them
   char fileregp[FILENAMELENGTH];     * we are calculating an estimate of the Life Expectancy assuming a linear 
   char popfile[FILENAMELENGTH];     * progression in between and thus overestimating or underestimating according
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];     * to the curvature of the survival function. If, for the same date, we 
   int firstobs=1, lastobs=10;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   int sdeb, sfin; /* Status at beginning and end */     * to compare the new estimate of Life expectancy with the same linear 
   int c,  h , cpt,l;     * hypothesis. A more precise result, taking into account a more precise
   int ju,jl, mi;     * curvature will be obtained if estepm is as small as stepm. */
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;  
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    /* For example we decided to compute the life expectancy with the smallest unit */
   int mobilav=0,popforecast=0;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   int hstepm, nhstepm;       nhstepm is the number of hstepm from age to agelim 
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1;       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   double bage, fage, age, agelim, agebase;       and note for a fixed period like estepm months */
   double ftolpl=FTOL;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   double **prlim;       survival function given by stepm (the optimization length). Unfortunately it
   double *severity;       means that if the survival funtion is printed only each two years of age and if
   double ***param; /* Matrix of parameters */       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   double  *p;       results. So we changed our mind and took the option of the best precision.
   double **matcov; /* Matrix of covariance */    */
   double ***delti3; /* Scale */    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   double *delti; /* Scale */  
   double ***eij, ***vareij;    agelim=AGESUP;
   double **varpl; /* Variances of prevalence limits by age */    /* nhstepm age range expressed in number of stepm */
   double *epj, vepp;    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
   double kk1, kk2;    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    /* if (stepm >= YEARM) hstepm=1;*/
      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   char version[80]="Imach version 0.8b, March 2002, INED-EUROREVES ";  
   char *alph[]={"a","a","b","c","d","e"}, str[4];    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepm matrices, stored
          in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   char z[1]="c", occ;      
 #include <sys/time.h>      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
 #include <time.h>      
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
        
   /* long total_usecs;      printf("%d|",(int)age);fflush(stdout);
   struct timeval start_time, end_time;      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      /* Computing expectancies */
   getcwd(pathcd, size);      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   printf("\n%s",version);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   if(argc <=1){            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     printf("\nEnter the parameter file name: ");            
     scanf("%s",pathtot);            /* 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]);*/
   }  
   else{          }
     strcpy(pathtot,argv[1]);  
   }      fprintf(ficreseij,"%3.0f",age );
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      for(i=1; i<=nlstate;i++){
   /*cygwin_split_path(pathtot,path,optionfile);        eip=0;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/        for(j=1; j<=nlstate;j++){
   /* cutv(path,optionfile,pathtot,'\\');*/          eip +=eij[i][j][(int)age];
           fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);        }
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);        fprintf(ficreseij,"%9.4f", eip );
   chdir(path);      }
   replace(pathc,path);      fprintf(ficreseij,"\n");
       
 /*-------- arguments in the command line --------*/    }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   strcpy(fileres,"r");    printf("\n");
   strcat(fileres, optionfilefiname);    fprintf(ficlog,"\n");
   strcat(fileres,".txt");    /* Other files have txt extension */    
   }
   /*---------arguments file --------*/  
   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[] )
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  
     printf("Problem with optionfile %s\n",optionfile);  {
     goto end;    /* Covariances of health expectancies eij and of total life expectancies according
   }     to initial status i, ei. .
     */
   strcpy(filereso,"o");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   strcat(filereso,fileres);    double age, agelim, hf;
   if((ficparo=fopen(filereso,"w"))==NULL) {    double ***p3matp, ***p3matm, ***varhe;
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    double **dnewm,**doldm;
   }    double *xp, *xm;
     double **gp, **gm;
   /* Reads comments: lines beginning with '#' */    double ***gradg, ***trgradg;
   while((c=getc(ficpar))=='#' && c!= EOF){    int theta;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    double eip, vip;
     puts(line);  
     fputs(line,ficparo);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   }    xp=vector(1,npar);
   ungetc(c,ficpar);    xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
   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);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   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);    pstamp(ficresstdeij);
 while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
     ungetc(c,ficpar);    fprintf(ficresstdeij,"# Age");
     fgets(line, MAXLINE, ficpar);    for(i=1; i<=nlstate;i++){
     puts(line);      for(j=1; j<=nlstate;j++)
     fputs(line,ficparo);        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   }      fprintf(ficresstdeij," e%1d. ",i);
   ungetc(c,ficpar);    }
      fprintf(ficresstdeij,"\n");
      
   covar=matrix(0,NCOVMAX,1,n);    pstamp(ficrescveij);
   cptcovn=0;    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    fprintf(ficrescveij,"# Age");
     for(i=1; i<=nlstate;i++)
   ncovmodel=2+cptcovn;      for(j=1; j<=nlstate;j++){
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */        cptj= (j-1)*nlstate+i;
          for(i2=1; i2<=nlstate;i2++)
   /* Read guess parameters */          for(j2=1; j2<=nlstate;j2++){
   /* Reads comments: lines beginning with '#' */            cptj2= (j2-1)*nlstate+i2;
   while((c=getc(ficpar))=='#' && c!= EOF){            if(cptj2 <= cptj)
     ungetc(c,ficpar);              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
     fgets(line, MAXLINE, ficpar);          }
     puts(line);      }
     fputs(line,ficparo);    fprintf(ficrescveij,"\n");
   }    
   ungetc(c,ficpar);    if(estepm < stepm){
        printf ("Problem %d lower than %d\n",estepm, stepm);
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    }
     for(i=1; i <=nlstate; i++)    else  hstepm=estepm;   
     for(j=1; j <=nlstate+ndeath-1; j++){    /* We compute the life expectancy from trapezoids spaced every estepm months
       fscanf(ficpar,"%1d%1d",&i1,&j1);     * This is mainly to measure the difference between two models: for example
       fprintf(ficparo,"%1d%1d",i1,j1);     * if stepm=24 months pijx are given only every 2 years and by summing them
       printf("%1d%1d",i,j);     * we are calculating an estimate of the Life Expectancy assuming a linear 
       for(k=1; k<=ncovmodel;k++){     * progression in between and thus overestimating or underestimating according
         fscanf(ficpar," %lf",&param[i][j][k]);     * to the curvature of the survival function. If, for the same date, we 
         printf(" %lf",param[i][j][k]);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
         fprintf(ficparo," %lf",param[i][j][k]);     * to compare the new estimate of Life expectancy with the same linear 
       }     * hypothesis. A more precise result, taking into account a more precise
       fscanf(ficpar,"\n");     * curvature will be obtained if estepm is as small as stepm. */
       printf("\n");  
       fprintf(ficparo,"\n");    /* For example we decided to compute the life expectancy with the smallest unit */
     }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         nhstepm is the number of hstepm from age to agelim 
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   p=param[1][1];       and note for a fixed period like estepm months */
      /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   /* Reads comments: lines beginning with '#' */       survival function given by stepm (the optimization length). Unfortunately it
   while((c=getc(ficpar))=='#' && c!= EOF){       means that if the survival funtion is printed only each two years of age and if
     ungetc(c,ficpar);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     fgets(line, MAXLINE, ficpar);       results. So we changed our mind and took the option of the best precision.
     puts(line);    */
     fputs(line,ficparo);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   }  
   ungetc(c,ficpar);    /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    agelim=AGESUP;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
   for(i=1; i <=nlstate; i++){    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     for(j=1; j <=nlstate+ndeath-1; j++){    /* if (stepm >= YEARM) hstepm=1;*/
       fscanf(ficpar,"%1d%1d",&i1,&j1);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       printf("%1d%1d",i,j);    
       fprintf(ficparo,"%1d%1d",i1,j1);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       for(k=1; k<=ncovmodel;k++){    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fscanf(ficpar,"%le",&delti3[i][j][k]);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
         printf(" %le",delti3[i][j][k]);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
         fprintf(ficparo," %le",delti3[i][j][k]);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
       }    gm=matrix(0,nhstepm,1,nlstate*nlstate);
       fscanf(ficpar,"\n");  
       printf("\n");    for (age=bage; age<=fage; age ++){ 
       fprintf(ficparo,"\n");  
     }      /* Computed by stepm unit matrices, product of hstepm matrices, stored
   }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   delti=delti3[1][1];   
        hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Computing  Variances of health expectancies */
     ungetc(c,ficpar);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
     fgets(line, MAXLINE, ficpar);         decrease memory allocation */
     puts(line);      for(theta=1; theta <=npar; theta++){
     fputs(line,ficparo);        for(i=1; i<=npar; i++){ 
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   ungetc(c,ficpar);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
          }
   matcov=matrix(1,npar,1,npar);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   for(i=1; i <=npar; i++){        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     fscanf(ficpar,"%s",&str);    
     printf("%s",str);        for(j=1; j<= nlstate; j++){
     fprintf(ficparo,"%s",str);          for(i=1; i<=nlstate; i++){
     for(j=1; j <=i; j++){            for(h=0; h<=nhstepm-1; h++){
       fscanf(ficpar," %le",&matcov[i][j]);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
       printf(" %.5le",matcov[i][j]);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
       fprintf(ficparo," %.5le",matcov[i][j]);            }
     }          }
     fscanf(ficpar,"\n");        }
     printf("\n");       
     fprintf(ficparo,"\n");        for(ij=1; ij<= nlstate*nlstate; ij++)
   }          for(h=0; h<=nhstepm-1; h++){
   for(i=1; i <=npar; i++)            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
     for(j=i+1;j<=npar;j++)          }
       matcov[i][j]=matcov[j][i];      }/* End theta */
          
   printf("\n");      
       for(h=0; h<=nhstepm-1; h++)
         for(j=1; j<=nlstate*nlstate;j++)
     /*-------- Rewriting paramater file ----------*/          for(theta=1; theta <=npar; theta++)
      strcpy(rfileres,"r");    /* "Rparameterfile */            trgradg[h][j][theta]=gradg[h][theta][j];
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/      
      strcat(rfileres,".");    /* */  
      strcat(rfileres,optionfilext);    /* Other files have txt extension */       for(ij=1;ij<=nlstate*nlstate;ij++)
     if((ficres =fopen(rfileres,"w"))==NULL) {        for(ji=1;ji<=nlstate*nlstate;ji++)
       printf("Problem writing new parameter file: %s\n", fileres);goto end;          varhe[ij][ji][(int)age] =0.;
     }  
     fprintf(ficres,"#%s\n",version);       printf("%d|",(int)age);fflush(stdout);
           fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     /*-------- data file ----------*/       for(h=0;h<=nhstepm-1;h++){
     if((fic=fopen(datafile,"r"))==NULL)    {        for(k=0;k<=nhstepm-1;k++){
       printf("Problem with datafile: %s\n", datafile);goto end;          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     }          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(ij=1;ij<=nlstate*nlstate;ij++)
     n= lastobs;            for(ji=1;ji<=nlstate*nlstate;ji++)
     severity = vector(1,maxwav);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     outcome=imatrix(1,maxwav+1,1,n);        }
     num=ivector(1,n);      }
     moisnais=vector(1,n);      /* Computing expectancies */
     annais=vector(1,n);      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     moisdc=vector(1,n);      for(i=1; i<=nlstate;i++)
     andc=vector(1,n);        for(j=1; j<=nlstate;j++)
     agedc=vector(1,n);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     cod=ivector(1,n);            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     weight=vector(1,n);            
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */            /* 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]);*/
     mint=matrix(1,maxwav,1,n);  
     anint=matrix(1,maxwav,1,n);          }
     s=imatrix(1,maxwav+1,1,n);  
     adl=imatrix(1,maxwav+1,1,n);          fprintf(ficresstdeij,"%3.0f",age );
     tab=ivector(1,NCOVMAX);      for(i=1; i<=nlstate;i++){
     ncodemax=ivector(1,8);        eip=0.;
         vip=0.;
     i=1;        for(j=1; j<=nlstate;j++){
     while (fgets(line, MAXLINE, fic) != NULL)    {          eip += eij[i][j][(int)age];
       if ((i >= firstobs) && (i <=lastobs)) {          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 (j=maxwav;j>=1;j--){          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        }
           strcpy(line,stra);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      }
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      fprintf(ficresstdeij,"\n");
         }  
              fprintf(ficrescveij,"%3.0f",age );
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);      for(i=1; i<=nlstate;i++)
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);          for(i2=1; i2<=nlstate;i2++)
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);            for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);              if(cptj2 <= cptj)
         for (j=ncovcol;j>=1;j--){                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);            }
         }        }
         num[i]=atol(stra);      fprintf(ficrescveij,"\n");
             
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    }
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
         i=i+1;    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       }    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     }    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     /* printf("ii=%d", ij);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        scanf("%d",i);*/    printf("\n");
   imx=i-1; /* Number of individuals */    fprintf(ficlog,"\n");
   
   /* for (i=1; i<=imx; i++){    free_vector(xm,1,npar);
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    free_vector(xp,1,npar);
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     }*/    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
    }
   /* for (i=1; i<=imx; i++){  
      if (s[4][i]==9)  s[4][i]=-1;  /************ Variance ******************/
      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]));}  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[])
   */  {
      /* Variance of health expectancies */
   /* Calculation of the number of parameter from char model*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   Tvar=ivector(1,15);    /* double **newm;*/
   Tprod=ivector(1,15);    double **dnewm,**doldm;
   Tvaraff=ivector(1,15);    double **dnewmp,**doldmp;
   Tvard=imatrix(1,15,1,2);    int i, j, nhstepm, hstepm, h, nstepm ;
   Tage=ivector(1,15);          int k, cptcode;
        double *xp;
   if (strlen(model) >1){    double **gp, **gm;  /* for var eij */
     j=0, j1=0, k1=1, k2=1;    double ***gradg, ***trgradg; /*for var eij */
     j=nbocc(model,'+');    double **gradgp, **trgradgp; /* for var p point j */
     j1=nbocc(model,'*');    double *gpp, *gmp; /* for var p point j */
     cptcovn=j+1;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     cptcovprod=j1;    double ***p3mat;
        double age,agelim, hf;
     strcpy(modelsav,model);    double ***mobaverage;
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    int theta;
       printf("Error. Non available option model=%s ",model);    char digit[4];
       goto end;    char digitp[25];
     }  
        char fileresprobmorprev[FILENAMELENGTH];
     for(i=(j+1); i>=1;i--){  
       cutv(stra,strb,modelsav,'+');    if(popbased==1){
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);      if(mobilav!=0)
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        strcpy(digitp,"-populbased-mobilav-");
       /*scanf("%d",i);*/      else strcpy(digitp,"-populbased-nomobil-");
       if (strchr(strb,'*')) {    }
         cutv(strd,strc,strb,'*');    else 
         if (strcmp(strc,"age")==0) {      strcpy(digitp,"-stablbased-");
           cptcovprod--;  
           cutv(strb,stre,strd,'V');    if (mobilav!=0) {
           Tvar[i]=atoi(stre);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           cptcovage++;      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
             Tage[cptcovage]=i;        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
             /*printf("stre=%s ", stre);*/        printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }      }
         else if (strcmp(strd,"age")==0) {    }
           cptcovprod--;  
           cutv(strb,stre,strc,'V');    strcpy(fileresprobmorprev,"prmorprev"); 
           Tvar[i]=atoi(stre);    sprintf(digit,"%-d",ij);
           cptcovage++;    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
           Tage[cptcovage]=i;    strcat(fileresprobmorprev,digit); /* Tvar to be done */
         }    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
         else {    strcat(fileresprobmorprev,fileres);
           cutv(strb,stre,strc,'V');    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
           Tvar[i]=ncovcol+k1;      printf("Problem with resultfile: %s\n", fileresprobmorprev);
           cutv(strb,strc,strd,'V');      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           Tprod[k1]=i;    }
           Tvard[k1][1]=atoi(strc);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           Tvard[k1][2]=atoi(stre);   
           Tvar[cptcovn+k2]=Tvard[k1][1];    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    pstamp(ficresprobmorprev);
           for (k=1; k<=lastobs;k++)    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);
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           k1++;    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           k2=k2+2;      fprintf(ficresprobmorprev," p.%-d SE",j);
         }      for(i=1; i<=nlstate;i++)
       }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
       else {    }  
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    fprintf(ficresprobmorprev,"\n");
        /*  scanf("%d",i);*/    fprintf(ficgp,"\n# Routine varevsij");
       cutv(strd,strc,strb,'V');    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
       Tvar[i]=atoi(strc);    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
       }    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       strcpy(modelsav,stra);    /*   } */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         scanf("%d",i);*/    pstamp(ficresvij);
     }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
 }    if(popbased==1)
        fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    else
   printf("cptcovprod=%d ", cptcovprod);      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   scanf("%d ",i);*/    fprintf(ficresvij,"# Age");
     fclose(fic);    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
     /*  if(mle==1){*/        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     if (weightopt != 1) { /* Maximisation without weights*/    fprintf(ficresvij,"\n");
       for(i=1;i<=n;i++) weight[i]=1.0;  
     }    xp=vector(1,npar);
     /*-calculation of age at interview from date of interview and age at death -*/    dnewm=matrix(1,nlstate,1,npar);
     agev=matrix(1,maxwav,1,imx);    doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     for (i=1; i<=imx; i++) {    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       for(m=2; (m<= maxwav); m++) {  
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
          anint[m][i]=9999;    gpp=vector(nlstate+1,nlstate+ndeath);
          s[m][i]=-1;    gmp=vector(nlstate+1,nlstate+ndeath);
        }    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;    
       }    if(estepm < stepm){
     }      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     for (i=1; i<=imx; i++)  {    else  hstepm=estepm;   
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    /* For example we decided to compute the life expectancy with the smallest unit */
       for(m=1; (m<= maxwav); m++){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         if(s[m][i] >0){       nhstepm is the number of hstepm from age to agelim 
           if (s[m][i] >= nlstate+1) {       nstepm is the number of stepm from age to agelin. 
             if(agedc[i]>0)       Look at hpijx to understand the reason of that which relies in memory size
               if(moisdc[i]!=99 && andc[i]!=9999)       and note for a fixed period like k years */
                 agev[m][i]=agedc[i];    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/       survival function given by stepm (the optimization length). Unfortunately it
            else {       means that if the survival funtion is printed every two years of age and if
               if (andc[i]!=9999){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);       results. So we changed our mind and took the option of the best precision.
               agev[m][i]=-1;    */
               }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
             }    agelim = AGESUP;
           }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
           else if(s[m][i] !=9){ /* Should no more exist */      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
             if(mint[m][i]==99 || anint[m][i]==9999)      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
               agev[m][i]=1;      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
             else if(agev[m][i] <agemin){      gp=matrix(0,nhstepm,1,nlstate);
               agemin=agev[m][i];      gm=matrix(0,nhstepm,1,nlstate);
               /*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){      for(theta=1; theta <=npar; theta++){
               agemax=agev[m][i];        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/          xp[i] = x[i] + (i==theta ?delti[theta]:0);
             }        }
             /*agev[m][i]=anint[m][i]-annais[i];*/        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             /*   agev[m][i] = age[i]+2*m;*/        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           }  
           else { /* =9 */        if (popbased==1) {
             agev[m][i]=1;          if(mobilav ==0){
             s[m][i]=-1;            for(i=1; i<=nlstate;i++)
           }              prlim[i][i]=probs[(int)age][i][ij];
         }          }else{ /* mobilav */ 
         else /*= 0 Unknown */            for(i=1; i<=nlstate;i++)
           agev[m][i]=1;              prlim[i][i]=mobaverage[(int)age][i][ij];
       }          }
            }
     }    
     for (i=1; i<=imx; i++)  {        for(j=1; j<= nlstate; j++){
       for(m=1; (m<= maxwav); m++){          for(h=0; h<=nhstepm; h++){
         if (s[m][i] > (nlstate+ndeath)) {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           printf("Error: Wrong value in nlstate or ndeath\n");                gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           goto end;          }
         }        }
       }        /* This for computing probability of death (h=1 means
     }           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);        */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
     free_vector(severity,1,maxwav);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
     free_imatrix(outcome,1,maxwav+1,1,n);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
     free_vector(moisnais,1,n);        }    
     free_vector(annais,1,n);        /* end probability of death */
     /* free_matrix(mint,1,maxwav,1,n);  
        free_matrix(anint,1,maxwav,1,n);*/        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
     free_vector(moisdc,1,n);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     free_vector(andc,1,n);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       
     wav=ivector(1,imx);        if (popbased==1) {
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          if(mobilav ==0){
     mw=imatrix(1,lastpass-firstpass+1,1,imx);            for(i=1; i<=nlstate;i++)
                  prlim[i][i]=probs[(int)age][i][ij];
     /* Concatenates waves */          }else{ /* mobilav */ 
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);            for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
       Tcode=ivector(1,100);        }
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);  
       ncodemax[1]=1;        for(j=1; j<= nlstate; j++){
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          for(h=0; h<=nhstepm; h++){
                  for(i=1, gm[h][j]=0.;i<=nlstate;i++)
    codtab=imatrix(1,100,1,10);              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
    h=0;          }
    m=pow(2,cptcoveff);        }
          /* This for computing probability of death (h=1 means
    for(k=1;k<=cptcoveff; k++){           computed over hstepm matrices product = hstepm*stepm months) 
      for(i=1; i <=(m/pow(2,k));i++){           as a weighted average of prlim.
        for(j=1; j <= ncodemax[k]; j++){        */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){        for(j=nlstate+1;j<=nlstate+ndeath;j++){
            h++;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;           gmp[j] += prlim[i][i]*p3mat[i][j][1];
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/        }    
          }        /* end probability of death */
        }  
      }        for(j=1; j<= nlstate; j++) /* vareij */
    }          for(h=0; h<=nhstepm; h++){
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       codtab[1][2]=1;codtab[2][2]=2; */          }
    /* for(i=1; i <=m ;i++){  
       for(k=1; k <=cptcovn; k++){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
       }        }
       printf("\n");  
       }      } /* End theta */
       scanf("%d",i);*/  
          trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
    /* Calculates basic frequencies. Computes observed prevalence at single age  
        and prints on file fileres'p'. */      for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
              for(theta=1; theta <=npar; theta++)
                trgradg[h][j][theta]=gradg[h][theta][j];
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(theta=1; theta <=npar; theta++)
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          trgradgp[j][theta]=gradgp[theta][j];
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    
        
     /* For Powell, parameters are in a vector p[] starting at p[1]      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */      for(i=1;i<=nlstate;i++)
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */        for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
     if(mle==1){  
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      for(h=0;h<=nhstepm;h++){
     }        for(k=0;k<=nhstepm;k++){
              matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
     /*--------- results files --------------*/          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
     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;i++)
              for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
    jk=1;        }
    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++){      /* pptj */
      for(k=1; k <=(nlstate+ndeath); k++){      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
        if (k != i)      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
          {      for(j=nlstate+1;j<=nlstate+ndeath;j++)
            printf("%d%d ",i,k);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
            fprintf(ficres,"%1d%1d ",i,k);          varppt[j][i]=doldmp[j][i];
            for(j=1; j <=ncovmodel; j++){      /* end ppptj */
              printf("%f ",p[jk]);      /*  x centered again */
              fprintf(ficres,"%f ",p[jk]);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
              jk++;      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
            }   
            printf("\n");      if (popbased==1) {
            fprintf(ficres,"\n");        if(mobilav ==0){
          }          for(i=1; i<=nlstate;i++)
      }            prlim[i][i]=probs[(int)age][i][ij];
    }        }else{ /* mobilav */ 
  if(mle==1){          for(i=1; i<=nlstate;i++)
     /* Computing hessian and covariance matrix */            prlim[i][i]=mobaverage[(int)age][i][ij];
     ftolhess=ftol; /* Usually correct */        }
     hesscov(matcov, p, npar, delti, ftolhess, func);      }
  }               
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");      /* This for computing probability of death (h=1 means
     printf("# Scales (for hessian or gradient estimation)\n");         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
      for(i=1,jk=1; i <=nlstate; i++){         as a weighted average of prlim.
       for(j=1; j <=nlstate+ndeath; j++){      */
         if (j!=i) {      for(j=nlstate+1;j<=nlstate+ndeath;j++){
           fprintf(ficres,"%1d%1d",i,j);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           printf("%1d%1d",i,j);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
           for(k=1; k<=ncovmodel;k++){      }    
             printf(" %.5e",delti[jk]);      /* end probability of death */
             fprintf(ficres," %.5e",delti[jk]);  
             jk++;      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
           }      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           printf("\n");        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
           fprintf(ficres,"\n");        for(i=1; i<=nlstate;i++){
         }          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
       }        }
      }      } 
          fprintf(ficresprobmorprev,"\n");
     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");      fprintf(ficresvij,"%.0f ",age );
     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(i=1; i<=nlstate;i++)
     for(i=1;i<=npar;i++){        for(j=1; j<=nlstate;j++){
       /*  if (k>nlstate) k=1;          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       i1=(i-1)/(ncovmodel*nlstate)+1;        }
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);      fprintf(ficresvij,"\n");
       printf("%s%d%d",alph[k],i1,tab[i]);*/      free_matrix(gp,0,nhstepm,1,nlstate);
       fprintf(ficres,"%3d",i);      free_matrix(gm,0,nhstepm,1,nlstate);
       printf("%3d",i);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       for(j=1; j<=i;j++){      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
         fprintf(ficres," %.5e",matcov[i][j]);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         printf(" %.5e",matcov[i][j]);    } /* End age */
       }    free_vector(gpp,nlstate+1,nlstate+ndeath);
       fprintf(ficres,"\n");    free_vector(gmp,nlstate+1,nlstate+ndeath);
       printf("\n");    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
       k++;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     }    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
        /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
       ungetc(c,ficpar);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
       fgets(line, MAXLINE, ficpar);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
       puts(line);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
       fputs(line,ficparo);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     }    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     ungetc(c,ficpar);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     estepm=0;    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    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);
     if (estepm==0 || estepm < stepm) estepm=stepm;    /*  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);
     if (fage <= 2) {  */
       bage = ageminpar;  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
       fage = agemaxpar;    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     }  
        free_vector(xp,1,npar);
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    free_matrix(doldm,1,nlstate,1,nlstate);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    free_matrix(dnewm,1,nlstate,1,npar);
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
      free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     ungetc(c,ficpar);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fgets(line, MAXLINE, ficpar);    fclose(ficresprobmorprev);
     puts(line);    fflush(ficgp);
     fputs(line,ficparo);    fflush(fichtm); 
   }  }  /* end varevsij */
   ungetc(c,ficpar);  
    /************ Variance of prevlim ******************/
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);  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[])
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  {
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    /* Variance of prevalence limit */
          /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   while((c=getc(ficpar))=='#' && c!= EOF){    double **newm;
     ungetc(c,ficpar);    double **dnewm,**doldm;
     fgets(line, MAXLINE, ficpar);    int i, j, nhstepm, hstepm;
     puts(line);    int k, cptcode;
     fputs(line,ficparo);    double *xp;
   }    double *gp, *gm;
   ungetc(c,ficpar);    double **gradg, **trgradg;
      double age,agelim;
     int theta;
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
   fscanf(ficpar,"pop_based=%d\n",&popbased);    fprintf(ficresvpl,"# Age");
   fprintf(ficparo,"pop_based=%d\n",popbased);      for(i=1; i<=nlstate;i++)
   fprintf(ficres,"pop_based=%d\n",popbased);          fprintf(ficresvpl," %1d-%1d",i,i);
      fprintf(ficresvpl,"\n");
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    xp=vector(1,npar);
     fgets(line, MAXLINE, ficpar);    dnewm=matrix(1,nlstate,1,npar);
     puts(line);    doldm=matrix(1,nlstate,1,nlstate);
     fputs(line,ficparo);    
   }    hstepm=1*YEARM; /* Every year of age */
   ungetc(c,ficpar);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
   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);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
 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);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
 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);      if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
 while((c=getc(ficpar))=='#' && c!= EOF){      gp=vector(1,nlstate);
     ungetc(c,ficpar);      gm=vector(1,nlstate);
     fgets(line, MAXLINE, ficpar);  
     puts(line);      for(theta=1; theta <=npar; theta++){
     fputs(line,ficparo);        for(i=1; i<=npar; i++){ /* Computes gradient */
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   ungetc(c,ficpar);        }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);        for(i=1;i<=nlstate;i++)
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);          gp[i] = prlim[i][i];
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      
         for(i=1; i<=npar; i++) /* Computes gradient */
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
 /*------------ gnuplot -------------*/        for(i=1;i<=nlstate;i++)
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);          gm[i] = prlim[i][i];
    
 /*------------ free_vector  -------------*/        for(i=1;i<=nlstate;i++)
  chdir(path);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
        } /* End theta */
  free_ivector(wav,1,imx);  
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      trgradg =matrix(1,nlstate,1,npar);
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);    
  free_ivector(num,1,n);      for(j=1; j<=nlstate;j++)
  free_vector(agedc,1,n);        for(theta=1; theta <=npar; theta++)
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          trgradg[j][theta]=gradg[theta][j];
  fclose(ficparo);  
  fclose(ficres);      for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
 /*--------- index.htm --------*/      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);      for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
    
   /*--------------- Prevalence limit --------------*/      fprintf(ficresvpl,"%.0f ",age );
        for(i=1; i<=nlstate;i++)
   strcpy(filerespl,"pl");        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
   strcat(filerespl,fileres);      fprintf(ficresvpl,"\n");
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      free_vector(gp,1,nlstate);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      free_vector(gm,1,nlstate);
   }      free_matrix(gradg,1,npar,1,nlstate);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);      free_matrix(trgradg,1,nlstate,1,npar);
   fprintf(ficrespl,"#Prevalence limit\n");    } /* End age */
   fprintf(ficrespl,"#Age ");  
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    free_vector(xp,1,npar);
   fprintf(ficrespl,"\n");    free_matrix(doldm,1,nlstate,1,npar);
      free_matrix(dnewm,1,nlstate,1,nlstate);
   prlim=matrix(1,nlstate,1,nlstate);  
   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 */  /************ Variance of one-step probabilities  ******************/
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  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[])
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  {
   k=0;    int i, j=0,  i1, k1, l1, t, tj;
   agebase=ageminpar;    int k2, l2, j1,  z1;
   agelim=agemaxpar;    int k=0,l, cptcode;
   ftolpl=1.e-10;    int first=1, first1;
   i1=cptcoveff;    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
   if (cptcovn < 1){i1=1;}    double **dnewm,**doldm;
     double *xp;
   for(cptcov=1;cptcov<=i1;cptcov++){    double *gp, *gm;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double **gradg, **trgradg;
         k=k+1;    double **mu;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    double age,agelim, cov[NCOVMAX];
         fprintf(ficrespl,"\n#******");    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
         for(j=1;j<=cptcoveff;j++)    int theta;
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    char fileresprob[FILENAMELENGTH];
         fprintf(ficrespl,"******\n");    char fileresprobcov[FILENAMELENGTH];
            char fileresprobcor[FILENAMELENGTH];
         for (age=agebase; age<=agelim; age++){  
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    double ***varpij;
           fprintf(ficrespl,"%.0f",age );  
           for(i=1; i<=nlstate;i++)    strcpy(fileresprob,"prob"); 
           fprintf(ficrespl," %.5f", prlim[i][i]);    strcat(fileresprob,fileres);
           fprintf(ficrespl,"\n");    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
         }      printf("Problem with resultfile: %s\n", fileresprob);
       }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }    }
   fclose(ficrespl);    strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
   /*------------- h Pij x at various ages ------------*/    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprobcov);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    }
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    strcpy(fileresprobcor,"probcor"); 
   }    strcat(fileresprobcor,fileres);
   printf("Computing pij: result on file '%s' \n", filerespij);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprobcor);
   stepsize=(int) (stepm+YEARM-1)/YEARM;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   /*if (stepm<=24) stepsize=2;*/    }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   agelim=AGESUP;    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   hstepm=stepsize*YEARM; /* Every year of age */    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
      printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   k=0;    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   for(cptcov=1;cptcov<=i1;cptcov++){    pstamp(ficresprob);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
       k=k+1;    fprintf(ficresprob,"# Age");
         fprintf(ficrespij,"\n#****** ");    pstamp(ficresprobcov);
         for(j=1;j<=cptcoveff;j++)    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficresprobcov,"# Age");
         fprintf(ficrespij,"******\n");    pstamp(ficresprobcor);
            fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    fprintf(ficresprobcor,"# Age");
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(i=1; i<=nlstate;i++)
           oldm=oldms;savm=savms;      for(j=1; j<=(nlstate+ndeath);j++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          fprintf(ficresprob," p%1d-%1d (SE)",i,j);
           fprintf(ficrespij,"# Age");        fprintf(ficresprobcov," p%1d-%1d ",i,j);
           for(i=1; i<=nlstate;i++)        fprintf(ficresprobcor," p%1d-%1d ",i,j);
             for(j=1; j<=nlstate+ndeath;j++)      }  
               fprintf(ficrespij," %1d-%1d",i,j);   /* fprintf(ficresprob,"\n");
           fprintf(ficrespij,"\n");    fprintf(ficresprobcov,"\n");
           for (h=0; h<=nhstepm; h++){    fprintf(ficresprobcor,"\n");
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );   */
             for(i=1; i<=nlstate;i++)   xp=vector(1,npar);
               for(j=1; j<=nlstate+ndeath;j++)    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
             fprintf(ficrespij,"\n");    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
           }    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    first=1;
           fprintf(ficrespij,"\n");    fprintf(ficgp,"\n# Routine varprob");
         }    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     }    fprintf(fichtm,"\n");
   }  
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
   fclose(ficrespij);    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
   /*---------- Forecasting ------------------*/    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   if((stepm == 1) && (strcmp(model,".")==0)){  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);  standard deviations wide on each axis. <br>\
     free_matrix(mint,1,maxwav,1,n);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
     free_vector(weight,1,n);}  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   else{  
     erreur=108;    cov[1]=1;
     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);    tj=cptcoveff;
   }    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
      j1=0;
     for(t=1; t<=tj;t++){
   /*---------- Health expectancies and variances ------------*/      for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
   strcpy(filerest,"t");        if  (cptcovn>0) {
   strcat(filerest,fileres);          fprintf(ficresprob, "\n#********** Variable "); 
   if((ficrest=fopen(filerest,"w"))==NULL) {          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;          fprintf(ficresprob, "**********\n#\n");
   }          fprintf(ficresprobcov, "\n#********** Variable "); 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
   strcpy(filerese,"e");          fprintf(ficgp, "\n#********** Variable "); 
   strcat(filerese,fileres);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   if((ficreseij=fopen(filerese,"w"))==NULL) {          fprintf(ficgp, "**********\n#\n");
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          
   }          
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);          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]]);
  strcpy(fileresv,"v");          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   strcat(fileresv,fileres);          
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          fprintf(ficresprobcor, "\n#********** Variable ");    
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   }          fprintf(ficresprobcor, "**********\n#");    
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);        }
         
   k=0;        for (age=bage; age<=fage; age ++){ 
   for(cptcov=1;cptcov<=i1;cptcov++){          cov[2]=age;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for (k=1; k<=cptcovn;k++) {
       k=k+1;            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
       fprintf(ficrest,"\n#****** ");          }
       for(j=1;j<=cptcoveff;j++)          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          for (k=1; k<=cptcovprod;k++)
       fprintf(ficrest,"******\n");            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
       fprintf(ficreseij,"\n#****** ");          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
       for(j=1;j<=cptcoveff;j++)          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          gp=vector(1,(nlstate)*(nlstate+ndeath));
       fprintf(ficreseij,"******\n");          gm=vector(1,(nlstate)*(nlstate+ndeath));
       
       fprintf(ficresvij,"\n#****** ");          for(theta=1; theta <=npar; theta++){
       for(j=1;j<=cptcoveff;j++)            for(i=1; i<=npar; i++)
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
       fprintf(ficresvij,"******\n");            
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            
       oldm=oldms;savm=savms;            k=0;
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm);              for(i=1; i<= (nlstate); i++){
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);              for(j=1; j<=(nlstate+ndeath);j++){
       oldm=oldms;savm=savms;                k=k+1;
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);                gp[k]=pmmij[i][j];
                  }
             }
              
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");            for(i=1; i<=npar; i++)
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       fprintf(ficrest,"\n");      
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
       epj=vector(1,nlstate+1);            k=0;
       for(age=bage; age <=fage ;age++){            for(i=1; i<=(nlstate); i++){
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);              for(j=1; j<=(nlstate+ndeath);j++){
         if (popbased==1) {                k=k+1;
           for(i=1; i<=nlstate;i++)                gm[k]=pmmij[i][j];
             prlim[i][i]=probs[(int)age][i][k];              }
         }            }
               
         fprintf(ficrest," %4.0f",age);            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           for(i=1, epj[j]=0.;i <=nlstate;i++) {          }
             epj[j] += prlim[i][i]*eij[i][j][(int)age];  
           }          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
           epj[nlstate+1] +=epj[j];            for(theta=1; theta <=npar; theta++)
         }              trgradg[j][theta]=gradg[theta][j];
         for(i=1, vepp=0.;i <=nlstate;i++)          
           for(j=1;j <=nlstate;j++)          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
             vepp += vareij[i][j][(int)age];          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
         for(j=1;j <=nlstate;j++){          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         }          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         fprintf(ficrest,"\n");  
       }          pmij(pmmij,cov,ncovmodel,x,nlstate);
     }          
   }          k=0;
           for(i=1; i<=(nlstate); i++){
   fclose(ficreseij);            for(j=1; j<=(nlstate+ndeath);j++){
   fclose(ficresvij);              k=k+1;
   fclose(ficrest);              mu[k][(int) age]=pmmij[i][j];
   fclose(ficpar);            }
   free_vector(epj,1,nlstate+1);          }
            for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
   /*------- Variance limit prevalence------*/              for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   strcpy(fileresvpl,"vpl");  
   strcat(fileresvpl,fileres);          /*printf("\n%d ",(int)age);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     exit(0);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   }            }*/
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);  
           fprintf(ficresprob,"\n%d ",(int)age);
   k=0;          fprintf(ficresprobcov,"\n%d ",(int)age);
   for(cptcov=1;cptcov<=i1;cptcov++){          fprintf(ficresprobcor,"\n%d ",(int)age);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
       fprintf(ficresvpl,"\n#****** ");            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
       for(j=1;j<=cptcoveff;j++)          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
       fprintf(ficresvpl,"******\n");            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
                }
       varpl=matrix(1,nlstate,(int) bage, (int) fage);          i=0;
       oldm=oldms;savm=savms;          for (k=1; k<=(nlstate);k++){
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);            for (l=1; l<=(nlstate+ndeath);l++){ 
     }              i=i++;
  }              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
   fclose(ficresvpl);              for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
   /*---------- End : free ----------------*/                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);              }
              }
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);          }/* end of loop for state */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);        } /* end of loop for age */
    
          /* Confidence intervalle of pij  */
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        /*
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset noparametric;unset label");
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
            fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
   free_matrix(matcov,1,npar,1,npar);          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
   free_vector(delti,1,npar);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   free_matrix(agev,1,maxwav,1,imx);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        */
   
   if(erreur >0)        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
     printf("End of Imach with error or warning %d\n",erreur);        first1=1;
   else   printf("End of Imach\n");        for (k2=1; k2<=(nlstate);k2++){
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
              if(l2==k2) continue;
   /* 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);*/            j=(k2-1)*(nlstate+ndeath)+l2;
   /*printf("Total time was %d uSec.\n", total_usecs);*/            for (k1=1; k1<=(nlstate);k1++){
   /*------ End -----------*/              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
  end:                if(i<=j) continue;
 #ifdef windows                for (age=bage; age<=fage; age ++){ 
   /* chdir(pathcd);*/                  if ((int)age %5==0){
 #endif                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
  /*system("wgnuplot graph.plt");*/                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
  /*system("../gp37mgw/wgnuplot graph.plt");*/                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
  /*system("cd ../gp37mgw");*/                    mu1=mu[i][(int) age]/stepm*YEARM ;
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/                    mu2=mu[j][(int) age]/stepm*YEARM;
  strcpy(plotcmd,GNUPLOTPROGRAM);                    c12=cv12/sqrt(v1*v2);
  strcat(plotcmd," ");                    /* Computing eigen value of matrix of covariance */
  strcat(plotcmd,optionfilegnuplot);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
  system(plotcmd);                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
 #ifdef windows                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
   while (z[0] != 'q') {                    /*v21=sqrt(1.-v11*v11); *//* error */
     /* chdir(path); */                    v21=(lc1-v1)/cv12*v11;
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");                    v12=-v21;
     scanf("%s",z);                    v22=v11;
     if (z[0] == 'c') system("./imach");                    tnalp=v21/v11;
     else if (z[0] == 'e') system(optionfilehtm);                    if(first1==1){
     else if (z[0] == 'g') system(plotcmd);                      first1=0;
     else if (z[0] == 'q') exit(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);
   }                    }
 #endif                    fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
 }                    /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, (b) health expectancies by health status at initial age:  ei., eij . If one or more covariate are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           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);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of 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>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (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>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - 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",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - 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",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+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);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     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; /* Dirty */
       }
     }
     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); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     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);
       goto end;
       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 \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\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 while opening datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem while opening 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;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         exit(1);
       }
       weight[i]=dval; 
       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 for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    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,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><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",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><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",\
             optionfilehtm,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,pathcd); /* 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,pathcd); /* 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\n# Age ( 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>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*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);
     }
   }
   
   
   

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changed lines
  Added in v.1.123


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