Diff for /imach/src/imach.c between versions 1.21 and 1.129

version 1.21, 2002/02/21 18:42:24 version 1.129, 2007/08/31 13:49:27
Line 1 Line 1
      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.129  2007/08/31 13:49:27  lievre
   individuals from different ages are interviewed on their health status    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.128  2006/06/30 13:02:05  brouard
   Health expectancies are computed from the transistions observed between    (Module): Clarifications on computing e.j
   waves and are computed for each degree of severity of disability (number  
   of life states). More degrees you consider, more time is necessary to    Revision 1.127  2006/04/28 18:11:50  brouard
   reach the Maximum Likelihood of the parameters involved in the model.    (Module): Yes the sum of survivors was wrong since
   The simplest model is the multinomial logistic model where pij is    imach-114 because nhstepm was no more computed in the age
   the probabibility to be observed in state j at the second wave conditional    loop. Now we define nhstepma in the age loop.
   to be observed in state i at the first wave. Therefore the model is:    (Module): In order to speed up (in case of numerous covariates) we
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    compute health expectancies (without variances) in a first step
   is a covariate. If you want to have a more complex model than "constant and    and then all the health expectancies with variances or standard
   age", you should modify the program where the markup    deviation (needs data from the Hessian matrices) which slows the
     *Covariates have to be included here again* invites you to do it.    computation.
   More covariates you add, less is the speed of the convergence.    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
   The advantage that this computer programme claims, comes from that if the  
   delay between waves is not identical for each individual, or if some    Revision 1.126  2006/04/28 17:23:28  brouard
   individual missed an interview, the information is not rounded or lost, but    (Module): Yes the sum of survivors was wrong since
   taken into account using an interpolation or extrapolation.    imach-114 because nhstepm was no more computed in the age
   hPijx is the probability to be    loop. Now we define nhstepma in the age loop.
   observed in state i at age x+h conditional to the observed state i at age    Version 0.98h
   x. The delay 'h' can be split into an exact number (nh*stepm) of  
   unobserved intermediate  states. This elementary transition (by month or    Revision 1.125  2006/04/04 15:20:31  lievre
   quarter trimester, semester or year) is model as a multinomial logistic.    Errors in calculation of health expectancies. Age was not initialized.
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Forecasting file added.
   and the contribution of each individual to the likelihood is simply hPijx.  
     Revision 1.124  2006/03/22 17:13:53  lievre
   Also this programme outputs the covariance matrix of the parameters but also    Parameters are printed with %lf instead of %f (more numbers after the comma).
   of the life expectancies. It also computes the prevalence limits.    The log-likelihood is printed in the log file
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.123  2006/03/20 10:52:43  brouard
            Institut national d'études démographiques, Paris.    * imach.c (Module): <title> changed, corresponds to .htm file
   This software have been partly granted by Euro-REVES, a concerted action    name. <head> headers where missing.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    * imach.c (Module): Weights can have a decimal point as for
   software can be distributed freely for non commercial use. Latest version    English (a comma might work with a correct LC_NUMERIC environment,
   can be accessed at http://euroreves.ined.fr/imach .    otherwise the weight is truncated).
   **********************************************************************/    Modification of warning when the covariates values are not 0 or
      1.
 #include <math.h>    Version 0.98g
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.122  2006/03/20 09:45:41  brouard
 #include <unistd.h>    (Module): Weights can have a decimal point as for
     English (a comma might work with a correct LC_NUMERIC environment,
 #define MAXLINE 256    otherwise the weight is truncated).
 #define FILENAMELENGTH 80    Modification of warning when the covariates values are not 0 or
 /*#define DEBUG*/    1.
 #define windows    Version 0.98g
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */  
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    Revision 1.121  2006/03/16 17:45:01  lievre
     * imach.c (Module): Comments concerning covariates added
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    * imach.c (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
 #define NINTERVMAX 8    not 1 month. Version 0.98f
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.120  2006/03/16 15:10:38  lievre
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): refinements in the computation of lli if
 #define MAXN 20000    status=-2 in order to have more reliable computation if stepm is
 #define YEARM 12. /* Number of months per year */    not 1 month. Version 0.98f
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.119  2006/03/15 17:42:26  brouard
     (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 int erreur; /* Error number */  
 int nvar;    Revision 1.118  2006/03/14 18:20:07  brouard
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    (Module): varevsij Comments added explaining the second
 int npar=NPARMAX;    table of variances if popbased=1 .
 int nlstate=2; /* Number of live states */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 int ndeath=1; /* Number of dead states */    (Module): Function pstamp added
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    (Module): Version 0.98d
 int popbased=0;  
     Revision 1.117  2006/03/14 17:16:22  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): varevsij Comments added explaining the second
 int maxwav; /* Maxim number of waves */    table of variances if popbased=1 .
 int jmin, jmax; /* min, max spacing between 2 waves */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 int mle, weightopt;    (Module): Function pstamp added
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): Version 0.98d
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.116  2006/03/06 10:29:27  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Variance-covariance wrong links and
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    varian-covariance of ej. is needed (Saito).
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;  
 FILE *ficgp, *fichtm,*ficresprob,*ficpop;    Revision 1.115  2006/02/27 12:17:45  brouard
 FILE *ficreseij;    (Module): One freematrix added in mlikeli! 0.98c
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.114  2006/02/26 12:57:58  brouard
   char fileresv[FILENAMELENGTH];    (Module): Some improvements in processing parameter
  FILE  *ficresvpl;    filename with strsep.
   char fileresvpl[FILENAMELENGTH];  
     Revision 1.113  2006/02/24 14:20:24  brouard
 #define NR_END 1    (Module): Memory leaks checks with valgrind and:
 #define FREE_ARG char*    datafile was not closed, some imatrix were not freed and on matrix
 #define FTOL 1.0e-10    allocation too.
   
 #define NRANSI    Revision 1.112  2006/01/30 09:55:26  brouard
 #define ITMAX 200    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   
 #define TOL 2.0e-4    Revision 1.111  2006/01/25 20:38:18  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 #define CGOLD 0.3819660    (Module): Comments can be added in data file. Missing date values
 #define ZEPS 1.0e-10    can be a simple dot '.'.
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     Revision 1.110  2006/01/25 00:51:50  brouard
 #define GOLD 1.618034    (Module): Lots of cleaning and bugs added (Gompertz)
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.109  2006/01/24 19:37:15  brouard
     (Module): Comments (lines starting with a #) are allowed in data.
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.108  2006/01/19 18:05:42  lievre
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Gnuplot problem appeared...
      To be fixed
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.107  2006/01/19 16:20:37  brouard
     Test existence of gnuplot in imach path
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.106  2006/01/19 13:24:36  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Some cleaning and links added in html output
   
 int imx;    Revision 1.105  2006/01/05 20:23:19  lievre
 int stepm;    *** empty log message ***
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.104  2005/09/30 16:11:43  lievre
 int m,nb;    (Module): sump fixed, loop imx fixed, and simplifications.
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    (Module): If the status is missing at the last wave but we know
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    that the person is alive, then we can code his/her status as -2
 double **pmmij, ***probs, ***mobaverage;    (instead of missing=-1 in earlier versions) and his/her
 double dateintmean=0;    contributions to the likelihood is 1 - Prob of dying from last
     health status (= 1-p13= p11+p12 in the easiest case of somebody in
 double *weight;    the healthy state at last known wave). Version is 0.98
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.103  2005/09/30 15:54:49  lievre
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    (Module): sump fixed, loop imx fixed, and simplifications.
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Revision 1.102  2004/09/15 17:31:30  brouard
 double ftolhess; /* Tolerance for computing hessian */    Add the possibility to read data file including tab characters.
   
 /**************** split *************************/    Revision 1.101  2004/09/15 10:38:38  brouard
 static  int split( char *path, char *dirc, char *name )    Fix on curr_time
 {  
    char *s;                             /* pointer */    Revision 1.100  2004/07/12 18:29:06  brouard
    int  l1, l2;                         /* length counters */    Add version for Mac OS X. Just define UNIX in Makefile
   
    l1 = strlen( path );                 /* length of path */    Revision 1.99  2004/06/05 08:57:40  brouard
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    *** empty log message ***
    s = strrchr( path, '\\' );           /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.98  2004/05/16 15:05:56  brouard
 #if     defined(__bsd__)                /* get current working directory */    New version 0.97 . First attempt to estimate force of mortality
       extern char       *getwd( );    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 .
       if ( getwd( dirc ) == NULL ) {    This is the basic analysis of mortality and should be done before any
 #else    other analysis, in order to test if the mortality estimated from the
       extern char       *getcwd( );    cross-longitudinal survey is different from the mortality estimated
     from other sources like vital statistic data.
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    The same imach parameter file can be used but the option for mle should be -3.
          return( GLOCK_ERROR_GETCWD );  
       }    Agnès, who wrote this part of the code, tried to keep most of the
       strcpy( name, path );             /* we've got it */    former routines in order to include the new code within the former code.
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */    The output is very simple: only an estimate of the intercept and of
       l2 = strlen( s );                 /* length of filename */    the slope with 95% confident intervals.
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );  
       strcpy( name, s );                /* save file name */    Current limitations:
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    A) Even if you enter covariates, i.e. with the
       dirc[l1-l2] = 0;                  /* add zero */    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
    }    B) There is no computation of Life Expectancy nor Life Table.
    l1 = strlen( dirc );                 /* length of directory */  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    Revision 1.97  2004/02/20 13:25:42  lievre
    return( 0 );                         /* we're done */    Version 0.96d. Population forecasting command line is (temporarily)
 }    suppressed.
   
     Revision 1.96  2003/07/15 15:38:55  brouard
 /******************************************/    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
     rewritten within the same printf. Workaround: many printfs.
 void replace(char *s, char*t)  
 {    Revision 1.95  2003/07/08 07:54:34  brouard
   int i;    * imach.c (Repository):
   int lg=20;    (Repository): Using imachwizard code to output a more meaningful covariance
   i=0;    matrix (cov(a12,c31) instead of numbers.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.94  2003/06/27 13:00:02  brouard
     (s[i] = t[i]);    Just cleaning
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.93  2003/06/25 16:33:55  brouard
 }    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
 int nbocc(char *s, char occ)    (Module): Version 0.96b
 {  
   int i,j=0;    Revision 1.92  2003/06/25 16:30:45  brouard
   int lg=20;    (Module): On windows (cygwin) function asctime_r doesn't
   i=0;    exist so I changed back to asctime which exists.
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {    Revision 1.91  2003/06/25 15:30:29  brouard
   if  (s[i] == occ ) j++;    * imach.c (Repository): Duplicated warning errors corrected.
   }    (Repository): Elapsed time after each iteration is now output. It
   return j;    helps to forecast when convergence will be reached. Elapsed time
 }    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
 void cutv(char *u,char *v, char*t, char occ)  
 {    Revision 1.90  2003/06/24 12:34:15  brouard
   int i,lg,j,p=0;    (Module): Some bugs corrected for windows. Also, when
   i=0;    mle=-1 a template is output in file "or"mypar.txt with the design
   for(j=0; j<=strlen(t)-1; j++) {    of the covariance matrix to be input.
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  
   }    Revision 1.89  2003/06/24 12:30:52  brouard
     (Module): Some bugs corrected for windows. Also, when
   lg=strlen(t);    mle=-1 a template is output in file "or"mypar.txt with the design
   for(j=0; j<p; j++) {    of the covariance matrix to be input.
     (u[j] = t[j]);  
   }    Revision 1.88  2003/06/23 17:54:56  brouard
      u[p]='\0';    * 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.
   
    for(j=0; j<= lg; j++) {    Revision 1.87  2003/06/18 12:26:01  brouard
     if (j>=(p+1))(v[j-p-1] = t[j]);    Version 0.96
   }  
 }    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 /********************** nrerror ********************/    routine fileappend.
   
 void nrerror(char error_text[])    Revision 1.85  2003/06/17 13:12:43  brouard
 {    * imach.c (Repository): Check when date of death was earlier that
   fprintf(stderr,"ERREUR ...\n");    current date of interview. It may happen when the death was just
   fprintf(stderr,"%s\n",error_text);    prior to the death. In this case, dh was negative and likelihood
   exit(1);    was wrong (infinity). We still send an "Error" but patch by
 }    assuming that the date of death was just one stepm after the
 /*********************** vector *******************/    interview.
 double *vector(int nl, int nh)    (Repository): Because some people have very long ID (first column)
 {    we changed int to long in num[] and we added a new lvector for
   double *v;    memory allocation. But we also truncated to 8 characters (left
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    truncation)
   if (!v) nrerror("allocation failure in vector");    (Repository): No more line truncation errors.
   return v-nl+NR_END;  
 }    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 /************************ free vector ******************/    place. It differs from routine "prevalence" which may be called
 void free_vector(double*v, int nl, int nh)    many times. Probs is memory consuming and must be used with
 {    parcimony.
   free((FREE_ARG)(v+nl-NR_END));    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 }  
     Revision 1.83  2003/06/10 13:39:11  lievre
 /************************ivector *******************************/    *** empty log message ***
 int *ivector(long nl,long nh)  
 {    Revision 1.82  2003/06/05 15:57:20  brouard
   int *v;    Add log in  imach.c and  fullversion number is now printed.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");  */
   return v-nl+NR_END;  /*
 }     Interpolated Markov Chain
   
 /******************free ivector **************************/    Short summary of the programme:
 void free_ivector(int *v, long nl, long nh)    
 {    This program computes Healthy Life Expectancies from
   free((FREE_ARG)(v+nl-NR_END));    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 }    first survey ("cross") where individuals from different ages are
     interviewed on their health status or degree of disability (in the
 /******************* imatrix *******************************/    case of a health survey which is our main interest) -2- at least a
 int **imatrix(long nrl, long nrh, long ncl, long nch)    second wave of interviews ("longitudinal") which measure each change
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    (if any) in individual health status.  Health expectancies are
 {    computed from the time spent in each health state according to a
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    model. More health states you consider, more time is necessary to reach the
   int **m;    Maximum Likelihood of the parameters involved in the model.  The
      simplest model is the multinomial logistic model where pij is the
   /* allocate pointers to rows */    probability to be observed in state j at the second wave
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    conditional to be observed in state i at the first wave. Therefore
   if (!m) nrerror("allocation failure 1 in matrix()");    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   m += NR_END;    'age' is age and 'sex' is a covariate. If you want to have a more
   m -= nrl;    complex model than "constant and age", you should modify the program
      where the markup *Covariates have to be included here again* invites
      you to do it.  More covariates you add, slower the
   /* allocate rows and set pointers to them */    convergence.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    The advantage of this computer programme, compared to a simple
   m[nrl] += NR_END;    multinomial logistic model, is clear when the delay between waves is not
   m[nrl] -= ncl;    identical for each individual. Also, if a individual missed an
      intermediate interview, the information is lost, but taken into
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    account using an interpolation or extrapolation.  
    
   /* return pointer to array of pointers to rows */    hPijx is the probability to be observed in state i at age x+h
   return m;    conditional to the observed state i at age x. The delay 'h' can be
 }    split into an exact number (nh*stepm) of unobserved intermediate
     states. This elementary transition (by month, quarter,
 /****************** free_imatrix *************************/    semester or year) is modelled as a multinomial logistic.  The hPx
 void free_imatrix(m,nrl,nrh,ncl,nch)    matrix is simply the matrix product of nh*stepm elementary matrices
       int **m;    and the contribution of each individual to the likelihood is simply
       long nch,ncl,nrh,nrl;    hPijx.
      /* free an int matrix allocated by imatrix() */  
 {    Also this programme outputs the covariance matrix of the parameters but also
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    of the life expectancies. It also computes the period (stable) prevalence. 
   free((FREE_ARG) (m+nrl-NR_END));    
 }    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
              Institut national d'études démographiques, Paris.
 /******************* matrix *******************************/    This software have been partly granted by Euro-REVES, a concerted action
 double **matrix(long nrl, long nrh, long ncl, long nch)    from the European Union.
 {    It is copyrighted identically to a GNU software product, ie programme and
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    software can be distributed freely for non commercial use. Latest version
   double **m;    can be accessed at http://euroreves.ined.fr/imach .
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   if (!m) nrerror("allocation failure 1 in matrix()");    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   m += NR_END;    
   m -= nrl;    **********************************************************************/
   /*
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    main
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    read parameterfile
   m[nrl] += NR_END;    read datafile
   m[nrl] -= ncl;    concatwav
     freqsummary
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    if (mle >= 1)
   return m;      mlikeli
 }    print results files
     if mle==1 
 /*************************free matrix ************************/       computes hessian
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    read end of parameter file: agemin, agemax, bage, fage, estepm
 {        begin-prev-date,...
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    open gnuplot file
   free((FREE_ARG)(m+nrl-NR_END));    open html file
 }    period (stable) prevalence
      for age prevalim()
 /******************* ma3x *******************************/    h Pij x
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    variance of p varprob
 {    forecasting if prevfcast==1 prevforecast call prevalence()
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    health expectancies
   double ***m;    Variance-covariance of DFLE
     prevalence()
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));     movingaverage()
   if (!m) nrerror("allocation failure 1 in matrix()");    varevsij() 
   m += NR_END;    if popbased==1 varevsij(,popbased)
   m -= nrl;    total life expectancies
     Variance of period (stable) prevalence
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));   end
   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>
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #include <stdio.h>
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #include <stdlib.h>
   m[nrl][ncl] += NR_END;  #include <string.h>
   m[nrl][ncl] -= nll;  #include <unistd.h>
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  #include <limits.h>
    #include <sys/types.h>
   for (i=nrl+1; i<=nrh; i++) {  #include <sys/stat.h>
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #include <errno.h>
     for (j=ncl+1; j<=nch; j++)  extern int errno;
       m[i][j]=m[i][j-1]+nlay;  
   }  /* #include <sys/time.h> */
   return m;  #include <time.h>
 }  #include "timeval.h"
   
 /*************************free ma3x ************************/  /* #include <libintl.h> */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  /* #define _(String) gettext (String) */
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #define MAXLINE 256
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define GNUPLOTPROGRAM "gnuplot"
 }  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
 /***************** f1dim *************************/  
 extern int ncom;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 extern double *pcom,*xicom;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 extern double (*nrfunc)(double []);  
    #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 double f1dim(double x)  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 {  
   int j;  #define NINTERVMAX 8
   double f;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   double *xt;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
    #define NCOVMAX 8 /* Maximum number of covariates */
   xt=vector(1,ncom);  #define MAXN 20000
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define YEARM 12. /* Number of months per year */
   f=(*nrfunc)(xt);  #define AGESUP 130
   free_vector(xt,1,ncom);  #define AGEBASE 40
   return f;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 }  #ifdef UNIX
   #define DIRSEPARATOR '/'
 /*****************brent *************************/  #define CHARSEPARATOR "/"
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #define ODIRSEPARATOR '\\'
 {  #else
   int iter;  #define DIRSEPARATOR '\\'
   double a,b,d,etemp;  #define CHARSEPARATOR "\\"
   double fu,fv,fw,fx;  #define ODIRSEPARATOR '/'
   double ftemp;  #endif
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;  /* $Id$ */
    /* $State$ */
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  char version[]="Imach version 0.98i, June 2006, INED-EUROREVES-Institut de longevite ";
   x=w=v=bx;  char fullversion[]="$Revision$ $Date$"; 
   fw=fv=fx=(*f)(x);  char strstart[80];
   for (iter=1;iter<=ITMAX;iter++) {  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     xm=0.5*(a+b);  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  int nvar;
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
     printf(".");fflush(stdout);  int npar=NPARMAX;
 #ifdef DEBUG  int nlstate=2; /* Number of live states */
     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);  int ndeath=1; /* Number of dead states */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #endif  int popbased=0;
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;  int *wav; /* Number of waves for this individuual 0 is possible */
       return fx;  int maxwav; /* Maxim number of waves */
     }  int jmin, jmax; /* min, max spacing between 2 waves */
     ftemp=fu;  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
     if (fabs(e) > tol1) {  int gipmx, gsw; /* Global variables on the number of contributions 
       r=(x-w)*(fx-fv);                     to the likelihood and the sum of weights (done by funcone)*/
       q=(x-v)*(fx-fw);  int mle, weightopt;
       p=(x-v)*q-(x-w)*r;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       q=2.0*(q-r);  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       if (q > 0.0) p = -p;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       q=fabs(q);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       etemp=e;  double jmean; /* Mean space between 2 waves */
       e=d;  double **oldm, **newm, **savm; /* Working pointers to matrices */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
       else {  FILE *ficlog, *ficrespow;
         d=p/q;  int globpr; /* Global variable for printing or not */
         u=x+d;  double fretone; /* Only one call to likelihood */
         if (u-a < tol2 || b-u < tol2)  long ipmx; /* Number of contributions */
           d=SIGN(tol1,xm-x);  double sw; /* Sum of weights */
       }  char filerespow[FILENAMELENGTH];
     } else {  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  FILE *ficresilk;
     }  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  FILE *ficresprobmorprev;
     fu=(*f)(u);  FILE *fichtm, *fichtmcov; /* Html File */
     if (fu <= fx) {  FILE *ficreseij;
       if (u >= x) a=x; else b=x;  char filerese[FILENAMELENGTH];
       SHFT(v,w,x,u)  FILE *ficresstdeij;
         SHFT(fv,fw,fx,fu)  char fileresstde[FILENAMELENGTH];
         } else {  FILE *ficrescveij;
           if (u < x) a=u; else b=u;  char filerescve[FILENAMELENGTH];
           if (fu <= fw || w == x) {  FILE  *ficresvij;
             v=w;  char fileresv[FILENAMELENGTH];
             w=u;  FILE  *ficresvpl;
             fv=fw;  char fileresvpl[FILENAMELENGTH];
             fw=fu;  char title[MAXLINE];
           } else if (fu <= fv || v == x || v == w) {  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
             v=u;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
             fv=fu;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
           }  char command[FILENAMELENGTH];
         }  int  outcmd=0;
   }  
   nrerror("Too many iterations in brent");  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   *xmin=x;  
   return fx;  char filelog[FILENAMELENGTH]; /* Log file */
 }  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 /****************** mnbrak ***********************/  char popfile[FILENAMELENGTH];
   
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
             double (*func)(double))  
 {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   double ulim,u,r,q, dum;  struct timezone tzp;
   double fu;  extern int gettimeofday();
    struct tm tmg, tm, tmf, *gmtime(), *localtime();
   *fa=(*func)(*ax);  long time_value;
   *fb=(*func)(*bx);  extern long time();
   if (*fb > *fa) {  char strcurr[80], strfor[80];
     SHFT(dum,*ax,*bx,dum)  
       SHFT(dum,*fb,*fa,dum)  char *endptr;
       }  long lval;
   *cx=(*bx)+GOLD*(*bx-*ax);  double dval;
   *fc=(*func)(*cx);  
   while (*fb > *fc) {  #define NR_END 1
     r=(*bx-*ax)*(*fb-*fc);  #define FREE_ARG char*
     q=(*bx-*cx)*(*fb-*fa);  #define FTOL 1.0e-10
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #define NRANSI 
     ulim=(*bx)+GLIMIT*(*cx-*bx);  #define ITMAX 200 
     if ((*bx-u)*(u-*cx) > 0.0) {  
       fu=(*func)(u);  #define TOL 2.0e-4 
     } else if ((*cx-u)*(u-ulim) > 0.0) {  
       fu=(*func)(u);  #define CGOLD 0.3819660 
       if (fu < *fc) {  #define ZEPS 1.0e-10 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  #define GOLD 1.618034 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  #define GLIMIT 100.0 
       u=ulim;  #define TINY 1.0e-20 
       fu=(*func)(u);  
     } else {  static double maxarg1,maxarg2;
       u=(*cx)+GOLD*(*cx-*bx);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       fu=(*func)(u);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     }    
     SHFT(*ax,*bx,*cx,u)  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
       SHFT(*fa,*fb,*fc,fu)  #define rint(a) floor(a+0.5)
       }  
 }  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 /*************** linmin ************************/  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   int agegomp= AGEGOMP;
 int ncom;  
 double *pcom,*xicom;  int imx; 
 double (*nrfunc)(double []);  int stepm=1;
    /* Stepm, step in month: minimum step interpolation*/
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  int estepm;
   double brent(double ax, double bx, double cx,  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
                double (*f)(double), double tol, double *xmin);  
   double f1dim(double x);  int m,nb;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  long *num;
               double *fc, double (*func)(double));  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   int j;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double xx,xmin,bx,ax;  double **pmmij, ***probs;
   double fx,fb,fa;  double *ageexmed,*agecens;
    double dateintmean=0;
   ncom=n;  
   pcom=vector(1,n);  double *weight;
   xicom=vector(1,n);  int **s; /* Status */
   nrfunc=func;  double *agedc, **covar, idx;
   for (j=1;j<=n;j++) {  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
     pcom[j]=p[j];  double *lsurv, *lpop, *tpop;
     xicom[j]=xi[j];  
   }  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   ax=0.0;  double ftolhess; /* Tolerance for computing hessian */
   xx=1.0;  
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  /**************** split *************************/
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 #ifdef DEBUG  {
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
 #endif       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   for (j=1;j<=n;j++) {    */ 
     xi[j] *= xmin;    char  *ss;                            /* pointer */
     p[j] += xi[j];    int   l1, l2;                         /* length counters */
   }  
   free_vector(xicom,1,n);    l1 = strlen(path );                   /* length of path */
   free_vector(pcom,1,n);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 }    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     if ( ss == NULL ) {                   /* no directory, so determine current directory */
 /*************** powell ************************/      strcpy( name, path );               /* we got the fullname name because no directory */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
             double (*func)(double []))        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
 {      /* get current working directory */
   void linmin(double p[], double xi[], int n, double *fret,      /*    extern  char* getcwd ( char *buf , int len);*/
               double (*func)(double []));      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   int i,ibig,j;        return( GLOCK_ERROR_GETCWD );
   double del,t,*pt,*ptt,*xit;      }
   double fp,fptt;      /* got dirc from getcwd*/
   double *xits;      printf(" DIRC = %s \n",dirc);
   pt=vector(1,n);    } else {                              /* strip direcotry from path */
   ptt=vector(1,n);      ss++;                               /* after this, the filename */
   xit=vector(1,n);      l2 = strlen( ss );                  /* length of filename */
   xits=vector(1,n);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   *fret=(*func)(p);      strcpy( name, ss );         /* save file name */
   for (j=1;j<=n;j++) pt[j]=p[j];      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   for (*iter=1;;++(*iter)) {      dirc[l1-l2] = 0;                    /* add zero */
     fp=(*fret);      printf(" DIRC2 = %s \n",dirc);
     ibig=0;    }
     del=0.0;    /* We add a separator at the end of dirc if not exists */
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    l1 = strlen( dirc );                  /* length of directory */
     for (i=1;i<=n;i++)    if( dirc[l1-1] != DIRSEPARATOR ){
       printf(" %d %.12f",i, p[i]);      dirc[l1] =  DIRSEPARATOR;
     printf("\n");      dirc[l1+1] = 0; 
     for (i=1;i<=n;i++) {      printf(" DIRC3 = %s \n",dirc);
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    }
       fptt=(*fret);    ss = strrchr( name, '.' );            /* find last / */
 #ifdef DEBUG    if (ss >0){
       printf("fret=%lf \n",*fret);      ss++;
 #endif      strcpy(ext,ss);                     /* save extension */
       printf("%d",i);fflush(stdout);      l1= strlen( name);
       linmin(p,xit,n,fret,func);      l2= strlen(ss)+1;
       if (fabs(fptt-(*fret)) > del) {      strncpy( finame, name, l1-l2);
         del=fabs(fptt-(*fret));      finame[l1-l2]= 0;
         ibig=i;    }
       }  
 #ifdef DEBUG    return( 0 );                          /* we're done */
       printf("%d %.12e",i,(*fret));  }
       for (j=1;j<=n;j++) {  
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  
         printf(" x(%d)=%.12e",j,xit[j]);  /******************************************/
       }  
       for(j=1;j<=n;j++)  void replace_back_to_slash(char *s, char*t)
         printf(" p=%.12e",p[j]);  {
       printf("\n");    int i;
 #endif    int lg=0;
     }    i=0;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    lg=strlen(t);
 #ifdef DEBUG    for(i=0; i<= lg; i++) {
       int k[2],l;      (s[i] = t[i]);
       k[0]=1;      if (t[i]== '\\') s[i]='/';
       k[1]=-1;    }
       printf("Max: %.12e",(*func)(p));  }
       for (j=1;j<=n;j++)  
         printf(" %.12e",p[j]);  int nbocc(char *s, char occ)
       printf("\n");  {
       for(l=0;l<=1;l++) {    int i,j=0;
         for (j=1;j<=n;j++) {    int lg=20;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    i=0;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    lg=strlen(s);
         }    for(i=0; i<= lg; i++) {
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    if  (s[i] == occ ) j++;
       }    }
 #endif    return j;
   }
   
       free_vector(xit,1,n);  void cutv(char *u,char *v, char*t, char occ)
       free_vector(xits,1,n);  {
       free_vector(ptt,1,n);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
       free_vector(pt,1,n);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       return;       gives u="abcedf" and v="ghi2j" */
     }    int i,lg,j,p=0;
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    i=0;
     for (j=1;j<=n;j++) {    for(j=0; j<=strlen(t)-1; j++) {
       ptt[j]=2.0*p[j]-pt[j];      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
       xit[j]=p[j]-pt[j];    }
       pt[j]=p[j];  
     }    lg=strlen(t);
     fptt=(*func)(ptt);    for(j=0; j<p; j++) {
     if (fptt < fp) {      (u[j] = t[j]);
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    }
       if (t < 0.0) {       u[p]='\0';
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {     for(j=0; j<= lg; j++) {
           xi[j][ibig]=xi[j][n];      if (j>=(p+1))(v[j-p-1] = t[j]);
           xi[j][n]=xit[j];    }
         }  }
 #ifdef DEBUG  
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  /********************** nrerror ********************/
         for(j=1;j<=n;j++)  
           printf(" %.12e",xit[j]);  void nrerror(char error_text[])
         printf("\n");  {
 #endif    fprintf(stderr,"ERREUR ...\n");
       }    fprintf(stderr,"%s\n",error_text);
     }    exit(EXIT_FAILURE);
   }  }
 }  /*********************** vector *******************/
   double *vector(int nl, int nh)
 /**** Prevalence limit ****************/  {
     double *v;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 {    if (!v) nrerror("allocation failure in vector");
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    return v-nl+NR_END;
      matrix by transitions matrix until convergence is reached */  }
   
   int i, ii,j,k;  /************************ free vector ******************/
   double min, max, maxmin, maxmax,sumnew=0.;  void free_vector(double*v, int nl, int nh)
   double **matprod2();  {
   double **out, cov[NCOVMAX], **pmij();    free((FREE_ARG)(v+nl-NR_END));
   double **newm;  }
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /************************ivector *******************************/
   for (ii=1;ii<=nlstate+ndeath;ii++)  int *ivector(long nl,long nh)
     for (j=1;j<=nlstate+ndeath;j++){  {
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    int *v;
     }    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
    cov[1]=1.;    return v-nl+NR_END;
    }
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  /******************free ivector **************************/
     newm=savm;  void free_ivector(int *v, long nl, long nh)
     /* Covariates have to be included here again */  {
      cov[2]=agefin;    free((FREE_ARG)(v+nl-NR_END));
    }
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /************************lvector *******************************/
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/  long *lvector(long nl,long nh)
       }  {
       for (k=1; k<=cptcovage;k++)    long *v;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       for (k=1; k<=cptcovprod;k++)    if (!v) nrerror("allocation failure in ivector");
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    return v-nl+NR_END;
   }
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /******************free lvector **************************/
   void free_lvector(long *v, long nl, long nh)
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  {
     free((FREE_ARG)(v+nl-NR_END));
     savm=oldm;  }
     oldm=newm;  
     maxmax=0.;  /******************* imatrix *******************************/
     for(j=1;j<=nlstate;j++){  int **imatrix(long nrl, long nrh, long ncl, long nch) 
       min=1.;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       max=0.;  { 
       for(i=1; i<=nlstate; i++) {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         sumnew=0;    int **m; 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    
         prlim[i][j]= newm[i][j]/(1-sumnew);    /* allocate pointers to rows */ 
         max=FMAX(max,prlim[i][j]);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
         min=FMIN(min,prlim[i][j]);    if (!m) nrerror("allocation failure 1 in matrix()"); 
       }    m += NR_END; 
       maxmin=max-min;    m -= nrl; 
       maxmax=FMAX(maxmax,maxmin);    
     }    
     if(maxmax < ftolpl){    /* allocate rows and set pointers to them */ 
       return prlim;    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; 
     
 /*************** transition probabilities ***************/    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    /* return pointer to array of pointers to rows */ 
 {    return m; 
   double s1, s2;  } 
   /*double t34;*/  
   int i,j,j1, nc, ii, jj;  /****************** free_imatrix *************************/
   void free_imatrix(m,nrl,nrh,ncl,nch)
     for(i=1; i<= nlstate; i++){        int **m;
     for(j=1; j<i;j++){        long nch,ncl,nrh,nrl; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){       /* free an int matrix allocated by imatrix() */ 
         /*s2 += param[i][j][nc]*cov[nc];*/  { 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    free((FREE_ARG) (m+nrl-NR_END)); 
       }  } 
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  /******************* matrix *******************************/
     }  double **matrix(long nrl, long nrh, long ncl, long nch)
     for(j=i+1; j<=nlstate+ndeath;j++){  {
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    double **m;
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       ps[i][j]=(s2);    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
   }    m -= nrl;
     /*ps[3][2]=1;*/  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   for(i=1; i<= nlstate; i++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
      s1=0;    m[nrl] += NR_END;
     for(j=1; j<i; j++)    m[nrl] -= ncl;
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       s1+=exp(ps[i][j]);    return m;
     ps[i][i]=1./(s1+1.);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
     for(j=1; j<i; j++)     */
       ps[i][j]= exp(ps[i][j])*ps[i][i];  }
     for(j=i+1; j<=nlstate+ndeath; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];  /*************************free matrix ************************/
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   } /* end i */  {
     free((FREE_ARG)(m[nrl]+ncl-NR_END));
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    free((FREE_ARG)(m+nrl-NR_END));
     for(jj=1; jj<= nlstate+ndeath; jj++){  }
       ps[ii][jj]=0;  
       ps[ii][ii]=1;  /******************* ma3x *******************************/
     }  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   }  {
     long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     double ***m;
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      printf("%lf ",ps[ii][jj]);    if (!m) nrerror("allocation failure 1 in matrix()");
    }    m += NR_END;
     printf("\n ");    m -= nrl;
     }  
     printf("\n ");printf("%lf ",cov[2]);*/    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 /*    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    m[nrl] += NR_END;
   goto end;*/    m[nrl] -= ncl;
     return ps;  
 }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   
 /**************** Product of 2 matrices ******************/    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    m[nrl][ncl] += NR_END;
 {    m[nrl][ncl] -= nll;
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    for (j=ncl+1; j<=nch; j++) 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */      m[nrl][j]=m[nrl][j-1]+nlay;
   /* in, b, out are matrice of pointers which should have been initialized    
      before: only the contents of out is modified. The function returns    for (i=nrl+1; i<=nrh; i++) {
      a pointer to pointers identical to out */      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   long i, j, k;      for (j=ncl+1; j<=nch; j++) 
   for(i=nrl; i<= nrh; i++)        m[i][j]=m[i][j-1]+nlay;
     for(k=ncolol; k<=ncoloh; k++)    }
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    return m; 
         out[i][k] +=in[i][j]*b[j][k];    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
              &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   return out;    */
 }  }
   
   /*************************free ma3x ************************/
 /************* Higher Matrix Product ***************/  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   {
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
 {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    free((FREE_ARG)(m+nrl-NR_END));
      duration (i.e. until  }
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  /*************** function subdirf ***********/
      (typically every 2 years instead of every month which is too big).  char *subdirf(char fileres[])
      Model is determined by parameters x and covariates have to be  {
      included manually here.    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
      */    strcat(tmpout,"/"); /* Add to the right */
     strcat(tmpout,fileres);
   int i, j, d, h, k;    return tmpout;
   double **out, cov[NCOVMAX];  }
   double **newm;  
   /*************** function subdirf2 ***********/
   /* Hstepm could be zero and should return the unit matrix */  char *subdirf2(char fileres[], char *preop)
   for (i=1;i<=nlstate+ndeath;i++)  {
     for (j=1;j<=nlstate+ndeath;j++){    
       oldm[i][j]=(i==j ? 1.0 : 0.0);    /* Caution optionfilefiname is hidden */
       po[i][j][0]=(i==j ? 1.0 : 0.0);    strcpy(tmpout,optionfilefiname);
     }    strcat(tmpout,"/");
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    strcat(tmpout,preop);
   for(h=1; h <=nhstepm; h++){    strcat(tmpout,fileres);
     for(d=1; d <=hstepm; d++){    return tmpout;
       newm=savm;  }
       /* Covariates have to be included here again */  
       cov[1]=1.;  /*************** function subdirf3 ***********/
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  char *subdirf3(char fileres[], char *preop, char *preop2)
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  {
       for (k=1; k<=cptcovage;k++)    
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    /* Caution optionfilefiname is hidden */
       for (k=1; k<=cptcovprod;k++)    strcpy(tmpout,optionfilefiname);
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    strcat(tmpout,"/");
     strcat(tmpout,preop);
     strcat(tmpout,preop2);
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    strcat(tmpout,fileres);
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    return tmpout;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  }
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  
       savm=oldm;  /***************** f1dim *************************/
       oldm=newm;  extern int ncom; 
     }  extern double *pcom,*xicom;
     for(i=1; i<=nlstate+ndeath; i++)  extern double (*nrfunc)(double []); 
       for(j=1;j<=nlstate+ndeath;j++) {   
         po[i][j][h]=newm[i][j];  double f1dim(double x) 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  { 
          */    int j; 
       }    double f;
   } /* end h */    double *xt; 
   return po;   
 }    xt=vector(1,ncom); 
     for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
 /*************** log-likelihood *************/    free_vector(xt,1,ncom); 
 double func( double *x)    return f; 
 {  } 
   int i, ii, j, k, mi, d, kk;  
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  /*****************brent *************************/
   double **out;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   double sw; /* Sum of weights */  { 
   double lli; /* Individual log likelihood */    int iter; 
   long ipmx;    double a,b,d,etemp;
   /*extern weight */    double fu,fv,fw,fx;
   /* We are differentiating ll according to initial status */    double ftemp;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   /*for(i=1;i<imx;i++)    double e=0.0; 
     printf(" %d\n",s[4][i]);   
   */    a=(ax < cx ? ax : cx); 
   cov[1]=1.;    b=(ax > cx ? ax : cx); 
     x=w=v=bx; 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    fw=fv=fx=(*f)(x); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    for (iter=1;iter<=ITMAX;iter++) { 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];      xm=0.5*(a+b); 
     for(mi=1; mi<= wav[i]-1; mi++){      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       for (ii=1;ii<=nlstate+ndeath;ii++)      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      printf(".");fflush(stdout);
       for(d=0; d<dh[mi][i]; d++){      fprintf(ficlog,".");fflush(ficlog);
         newm=savm;  #ifdef DEBUG
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      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);
         for (kk=1; kk<=cptcovage;kk++) {      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);
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
         }  #endif
              if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,        *xmin=x; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        return fx; 
         savm=oldm;      } 
         oldm=newm;      ftemp=fu;
              if (fabs(e) > tol1) { 
                r=(x-w)*(fx-fv); 
       } /* end mult */        q=(x-v)*(fx-fw); 
              p=(x-v)*q-(x-w)*r; 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);        q=2.0*(q-r); 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        if (q > 0.0) p = -p; 
       ipmx +=1;        q=fabs(q); 
       sw += weight[i];        etemp=e; 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        e=d; 
     } /* end of wave */        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   } /* end of individual */          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         else { 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];          d=p/q; 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */          u=x+d; 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */          if (u-a < tol2 || b-u < tol2) 
   return -l;            d=SIGN(tol1,xm-x); 
 }        } 
       } else { 
         d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
 /*********** Maximum Likelihood Estimation ***************/      } 
       u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))      fu=(*f)(u); 
 {      if (fu <= fx) { 
   int i,j, iter;        if (u >= x) a=x; else b=x; 
   double **xi,*delti;        SHFT(v,w,x,u) 
   double fret;          SHFT(fv,fw,fx,fu) 
   xi=matrix(1,npar,1,npar);          } else { 
   for (i=1;i<=npar;i++)            if (u < x) a=u; else b=u; 
     for (j=1;j<=npar;j++)            if (fu <= fw || w == x) { 
       xi[i][j]=(i==j ? 1.0 : 0.0);              v=w; 
   printf("Powell\n");              w=u; 
   powell(p,xi,npar,ftol,&iter,&fret,func);              fv=fw; 
               fw=fu; 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));            } else if (fu <= fv || v == x || v == w) { 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));              v=u; 
               fv=fu; 
 }            } 
           } 
 /**** Computes Hessian and covariance matrix ***/    } 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    nrerror("Too many iterations in brent"); 
 {    *xmin=x; 
   double  **a,**y,*x,pd;    return fx; 
   double **hess;  } 
   int i, j,jk;  
   int *indx;  /****************** mnbrak ***********************/
   
   double hessii(double p[], double delta, int theta, double delti[]);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   double hessij(double p[], double delti[], int i, int j);              double (*func)(double)) 
   void lubksb(double **a, int npar, int *indx, double b[]) ;  { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;    double ulim,u,r,q, dum;
     double fu; 
   hess=matrix(1,npar,1,npar);   
     *fa=(*func)(*ax); 
   printf("\nCalculation of the hessian matrix. Wait...\n");    *fb=(*func)(*bx); 
   for (i=1;i<=npar;i++){    if (*fb > *fa) { 
     printf("%d",i);fflush(stdout);      SHFT(dum,*ax,*bx,dum) 
     hess[i][i]=hessii(p,ftolhess,i,delti);        SHFT(dum,*fb,*fa,dum) 
     /*printf(" %f ",p[i]);*/        } 
     /*printf(" %lf ",hess[i][i]);*/    *cx=(*bx)+GOLD*(*bx-*ax); 
   }    *fc=(*func)(*cx); 
      while (*fb > *fc) { 
   for (i=1;i<=npar;i++) {      r=(*bx-*ax)*(*fb-*fc); 
     for (j=1;j<=npar;j++)  {      q=(*bx-*cx)*(*fb-*fa); 
       if (j>i) {      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
         printf(".%d%d",i,j);fflush(stdout);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
         hess[i][j]=hessij(p,delti,i,j);      ulim=(*bx)+GLIMIT*(*cx-*bx); 
         hess[j][i]=hess[i][j];          if ((*bx-u)*(u-*cx) > 0.0) { 
         /*printf(" %lf ",hess[i][j]);*/        fu=(*func)(u); 
       }      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     }        fu=(*func)(u); 
   }        if (fu < *fc) { 
   printf("\n");          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");            } 
        } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   a=matrix(1,npar,1,npar);        u=ulim; 
   y=matrix(1,npar,1,npar);        fu=(*func)(u); 
   x=vector(1,npar);      } else { 
   indx=ivector(1,npar);        u=(*cx)+GOLD*(*cx-*bx); 
   for (i=1;i<=npar;i++)        fu=(*func)(u); 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      } 
   ludcmp(a,npar,indx,&pd);      SHFT(*ax,*bx,*cx,u) 
         SHFT(*fa,*fb,*fc,fu) 
   for (j=1;j<=npar;j++) {        } 
     for (i=1;i<=npar;i++) x[i]=0;  } 
     x[j]=1;  
     lubksb(a,npar,indx,x);  /*************** linmin ************************/
     for (i=1;i<=npar;i++){  
       matcov[i][j]=x[i];  int ncom; 
     }  double *pcom,*xicom;
   }  double (*nrfunc)(double []); 
    
   printf("\n#Hessian matrix#\n");  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for (i=1;i<=npar;i++) {  { 
     for (j=1;j<=npar;j++) {    double brent(double ax, double bx, double cx, 
       printf("%.3e ",hess[i][j]);                 double (*f)(double), double tol, double *xmin); 
     }    double f1dim(double x); 
     printf("\n");    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   }                double *fc, double (*func)(double)); 
     int j; 
   /* Recompute Inverse */    double xx,xmin,bx,ax; 
   for (i=1;i<=npar;i++)    double fx,fb,fa;
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];   
   ludcmp(a,npar,indx,&pd);    ncom=n; 
     pcom=vector(1,n); 
   /*  printf("\n#Hessian matrix recomputed#\n");    xicom=vector(1,n); 
     nrfunc=func; 
   for (j=1;j<=npar;j++) {    for (j=1;j<=n;j++) { 
     for (i=1;i<=npar;i++) x[i]=0;      pcom[j]=p[j]; 
     x[j]=1;      xicom[j]=xi[j]; 
     lubksb(a,npar,indx,x);    } 
     for (i=1;i<=npar;i++){    ax=0.0; 
       y[i][j]=x[i];    xx=1.0; 
       printf("%.3e ",y[i][j]);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     }    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     printf("\n");  #ifdef DEBUG
   }    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   */    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
   free_matrix(a,1,npar,1,npar);    for (j=1;j<=n;j++) { 
   free_matrix(y,1,npar,1,npar);      xi[j] *= xmin; 
   free_vector(x,1,npar);      p[j] += xi[j]; 
   free_ivector(indx,1,npar);    } 
   free_matrix(hess,1,npar,1,npar);    free_vector(xicom,1,n); 
     free_vector(pcom,1,n); 
   } 
 }  
   char *asc_diff_time(long time_sec, char ascdiff[])
 /*************** hessian matrix ****************/  {
 double hessii( double x[], double delta, int theta, double delti[])    long sec_left, days, hours, minutes;
 {    days = (time_sec) / (60*60*24);
   int i;    sec_left = (time_sec) % (60*60*24);
   int l=1, lmax=20;    hours = (sec_left) / (60*60) ;
   double k1,k2;    sec_left = (sec_left) %(60*60);
   double p2[NPARMAX+1];    minutes = (sec_left) /60;
   double res;    sec_left = (sec_left) % (60);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   double fx;    return ascdiff;
   int k=0,kmax=10;  }
   double l1;  
   /*************** powell ************************/
   fx=func(x);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   for (i=1;i<=npar;i++) p2[i]=x[i];              double (*func)(double [])) 
   for(l=0 ; l <=lmax; l++){  { 
     l1=pow(10,l);    void linmin(double p[], double xi[], int n, double *fret, 
     delts=delt;                double (*func)(double [])); 
     for(k=1 ; k <kmax; k=k+1){    int i,ibig,j; 
       delt = delta*(l1*k);    double del,t,*pt,*ptt,*xit;
       p2[theta]=x[theta] +delt;    double fp,fptt;
       k1=func(p2)-fx;    double *xits;
       p2[theta]=x[theta]-delt;    int niterf, itmp;
       k2=func(p2)-fx;  
       /*res= (k1-2.0*fx+k2)/delt/delt; */    pt=vector(1,n); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    ptt=vector(1,n); 
          xit=vector(1,n); 
 #ifdef DEBUG    xits=vector(1,n); 
       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);    *fret=(*func)(p); 
 #endif    for (j=1;j<=n;j++) pt[j]=p[j]; 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    for (*iter=1;;++(*iter)) { 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){      fp=(*fret); 
         k=kmax;      ibig=0; 
       }      del=0.0; 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */      last_time=curr_time;
         k=kmax; l=lmax*10.;      (void) gettimeofday(&curr_time,&tzp);
       }      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){      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); fflush(ficlog);
         delts=delt;  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       }     for (i=1;i<=n;i++) {
     }        printf(" %d %.12f",i, p[i]);
   }        fprintf(ficlog," %d %.12lf",i, p[i]);
   delti[theta]=delts;        fprintf(ficrespow," %.12lf", p[i]);
   return res;      }
        printf("\n");
 }      fprintf(ficlog,"\n");
       fprintf(ficrespow,"\n");fflush(ficrespow);
 double hessij( double x[], double delti[], int thetai,int thetaj)      if(*iter <=3){
 {        tm = *localtime(&curr_time.tv_sec);
   int i;        strcpy(strcurr,asctime(&tm));
   int l=1, l1, lmax=20;  /*       asctime_r(&tm,strcurr); */
   double k1,k2,k3,k4,res,fx;        forecast_time=curr_time; 
   double p2[NPARMAX+1];        itmp = strlen(strcurr);
   int k;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
           strcurr[itmp-1]='\0';
   fx=func(x);        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   for (k=1; k<=2; k++) {        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     for (i=1;i<=npar;i++) p2[i]=x[i];        for(niterf=10;niterf<=30;niterf+=10){
     p2[thetai]=x[thetai]+delti[thetai]/k;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          tmf = *localtime(&forecast_time.tv_sec);
     k1=func(p2)-fx;  /*      asctime_r(&tmf,strfor); */
            strcpy(strfor,asctime(&tmf));
     p2[thetai]=x[thetai]+delti[thetai]/k;          itmp = strlen(strfor);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          if(strfor[itmp-1]=='\n')
     k2=func(p2)-fx;          strfor[itmp-1]='\0';
            printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
     p2[thetai]=x[thetai]-delti[thetai]/k;          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);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        }
     k3=func(p2)-fx;      }
        for (i=1;i<=n;i++) { 
     p2[thetai]=x[thetai]-delti[thetai]/k;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        fptt=(*fret); 
     k4=func(p2)-fx;  #ifdef DEBUG
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        printf("fret=%lf \n",*fret);
 #ifdef DEBUG        fprintf(ficlog,"fret=%lf \n",*fret);
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);  #endif
 #endif        printf("%d",i);fflush(stdout);
   }        fprintf(ficlog,"%d",i);fflush(ficlog);
   return res;        linmin(p,xit,n,fret,func); 
 }        if (fabs(fptt-(*fret)) > del) { 
           del=fabs(fptt-(*fret)); 
 /************** Inverse of matrix **************/          ibig=i; 
 void ludcmp(double **a, int n, int *indx, double *d)        } 
 {  #ifdef DEBUG
   int i,imax,j,k;        printf("%d %.12e",i,(*fret));
   double big,dum,sum,temp;        fprintf(ficlog,"%d %.12e",i,(*fret));
   double *vv;        for (j=1;j<=n;j++) {
            xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   vv=vector(1,n);          printf(" x(%d)=%.12e",j,xit[j]);
   *d=1.0;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   for (i=1;i<=n;i++) {        }
     big=0.0;        for(j=1;j<=n;j++) {
     for (j=1;j<=n;j++)          printf(" p=%.12e",p[j]);
       if ((temp=fabs(a[i][j])) > big) big=temp;          fprintf(ficlog," p=%.12e",p[j]);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");        }
     vv[i]=1.0/big;        printf("\n");
   }        fprintf(ficlog,"\n");
   for (j=1;j<=n;j++) {  #endif
     for (i=1;i<j;i++) {      } 
       sum=a[i][j];      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  #ifdef DEBUG
       a[i][j]=sum;        int k[2],l;
     }        k[0]=1;
     big=0.0;        k[1]=-1;
     for (i=j;i<=n;i++) {        printf("Max: %.12e",(*func)(p));
       sum=a[i][j];        fprintf(ficlog,"Max: %.12e",(*func)(p));
       for (k=1;k<j;k++)        for (j=1;j<=n;j++) {
         sum -= a[i][k]*a[k][j];          printf(" %.12e",p[j]);
       a[i][j]=sum;          fprintf(ficlog," %.12e",p[j]);
       if ( (dum=vv[i]*fabs(sum)) >= big) {        }
         big=dum;        printf("\n");
         imax=i;        fprintf(ficlog,"\n");
       }        for(l=0;l<=1;l++) {
     }          for (j=1;j<=n;j++) {
     if (j != imax) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
       for (k=1;k<=n;k++) {            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
         dum=a[imax][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]);
         a[imax][k]=a[j][k];          }
         a[j][k]=dum;          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)));
       *d = -(*d);        }
       vv[imax]=vv[j];  #endif
     }  
     indx[j]=imax;  
     if (a[j][j] == 0.0) a[j][j]=TINY;        free_vector(xit,1,n); 
     if (j != n) {        free_vector(xits,1,n); 
       dum=1.0/(a[j][j]);        free_vector(ptt,1,n); 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        free_vector(pt,1,n); 
     }        return; 
   }      } 
   free_vector(vv,1,n);  /* Doesn't work */      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
 ;      for (j=1;j<=n;j++) { 
 }        ptt[j]=2.0*p[j]-pt[j]; 
         xit[j]=p[j]-pt[j]; 
 void lubksb(double **a, int n, int *indx, double b[])        pt[j]=p[j]; 
 {      } 
   int i,ii=0,ip,j;      fptt=(*func)(ptt); 
   double sum;      if (fptt < fp) { 
          t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
   for (i=1;i<=n;i++) {        if (t < 0.0) { 
     ip=indx[i];          linmin(p,xit,n,fret,func); 
     sum=b[ip];          for (j=1;j<=n;j++) { 
     b[ip]=b[i];            xi[j][ibig]=xi[j][n]; 
     if (ii)            xi[j][n]=xit[j]; 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          }
     else if (sum) ii=i;  #ifdef DEBUG
     b[i]=sum;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   for (i=n;i>=1;i--) {          for(j=1;j<=n;j++){
     sum=b[i];            printf(" %.12e",xit[j]);
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];            fprintf(ficlog," %.12e",xit[j]);
     b[i]=sum/a[i][i];          }
   }          printf("\n");
 }          fprintf(ficlog,"\n");
   #endif
 /************ Frequencies ********************/        }
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2)      } 
 {  /* Some frequencies */    } 
    } 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  
   double ***freq; /* Frequencies */  /**** Prevalence limit (stable or period prevalence)  ****************/
   double *pp;  
   double pos, k2, dateintsum=0,k2cpt=0;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   FILE *ficresp;  {
   char fileresp[FILENAMELENGTH];    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
        matrix by transitions matrix until convergence is reached */
   pp=vector(1,nlstate);  
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    int i, ii,j,k;
   strcpy(fileresp,"p");    double min, max, maxmin, maxmax,sumnew=0.;
   strcat(fileresp,fileres);    double **matprod2();
   if((ficresp=fopen(fileresp,"w"))==NULL) {    double **out, cov[NCOVMAX], **pmij();
     printf("Problem with prevalence resultfile: %s\n", fileresp);    double **newm;
     exit(0);    double agefin, delaymax=50 ; /* Max number of years to converge */
   }  
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    for (ii=1;ii<=nlstate+ndeath;ii++)
   j1=0;      for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   j=cptcoveff;      }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  
      cov[1]=1.;
   for(k1=1; k1<=j;k1++){   
    for(i1=1; i1<=ncodemax[k1];i1++){   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
        j1++;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      newm=savm;
          scanf("%d", i);*/      /* Covariates have to be included here again */
         for (i=-1; i<=nlstate+ndeath; i++)         cov[2]=agefin;
          for (jk=-1; jk<=nlstate+ndeath; jk++)      
            for(m=agemin; m <= agemax+3; m++)        for (k=1; k<=cptcovn;k++) {
              freq[i][jk][m]=0;          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]]);*/
         dateintsum=0;        }
         k2cpt=0;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
        for (i=1; i<=imx; i++) {        for (k=1; k<=cptcovprod;k++)
          bool=1;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
          if  (cptcovn>0) {  
            for (z1=1; z1<=cptcoveff; z1++)        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
                bool=0;        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
          }      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
          if (bool==1) {  
            for(m=firstpass; m<=lastpass; m++){      savm=oldm;
              k2=anint[m][i]+(mint[m][i]/12.);      oldm=newm;
              if ((k2>=dateprev1) && (k2<=dateprev2)) {      maxmax=0.;
                if(agev[m][i]==0) agev[m][i]=agemax+1;      for(j=1;j<=nlstate;j++){
                if(agev[m][i]==1) agev[m][i]=agemax+2;        min=1.;
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        max=0.;
                freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        for(i=1; i<=nlstate; i++) {
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {          sumnew=0;
                  dateintsum=dateintsum+k2;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
                  k2cpt++;          prlim[i][j]= newm[i][j]/(1-sumnew);
                }          max=FMAX(max,prlim[i][j]);
           min=FMIN(min,prlim[i][j]);
              }        }
            }        maxmin=max-min;
          }        maxmax=FMAX(maxmax,maxmin);
        }      }
         if  (cptcovn>0) {      if(maxmax < ftolpl){
          fprintf(ficresp, "\n#********** Variable ");        return prlim;
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      }
        fprintf(ficresp, "**********\n#");    }
         }  }
        for(i=1; i<=nlstate;i++)  
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  /*************** transition probabilities ***************/ 
        fprintf(ficresp, "\n");  
          double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   for(i=(int)agemin; i <= (int)agemax+3; i++){  {
     if(i==(int)agemax+3)    double s1, s2;
       printf("Total");    /*double t34;*/
     else    int i,j,j1, nc, ii, jj;
       printf("Age %d", i);  
     for(jk=1; jk <=nlstate ; jk++){      for(i=1; i<= nlstate; i++){
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        for(j=1; j<i;j++){
         pp[jk] += freq[jk][m][i];          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     }            /*s2 += param[i][j][nc]*cov[nc];*/
     for(jk=1; jk <=nlstate ; jk++){            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
       for(m=-1, pos=0; m <=0 ; m++)  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
         pos += freq[jk][m][i];          }
       if(pp[jk]>=1.e-10)          ps[i][j]=s2;
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
       else        }
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        for(j=i+1; j<=nlstate+ndeath;j++){
     }          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];
      for(jk=1; jk <=nlstate ; jk++){  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          }
         pp[jk] += freq[jk][m][i];          ps[i][j]=s2;
      }        }
       }
     for(jk=1,pos=0; jk <=nlstate ; jk++)      /*ps[3][2]=1;*/
       pos += pp[jk];      
     for(jk=1; jk <=nlstate ; jk++){      for(i=1; i<= nlstate; i++){
       if(pos>=1.e-5)        s1=0;
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        for(j=1; j<i; j++)
       else          s1+=exp(ps[i][j]);
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        for(j=i+1; j<=nlstate+ndeath; j++)
       if( i <= (int) agemax){          s1+=exp(ps[i][j]);
         if(pos>=1.e-5){        ps[i][i]=1./(s1+1.);
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        for(j=1; j<i; j++)
           probs[i][jk][j1]= pp[jk]/pos;          ps[i][j]= exp(ps[i][j])*ps[i][i];
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/        for(j=i+1; j<=nlstate+ndeath; j++)
         }          ps[i][j]= exp(ps[i][j])*ps[i][i];
       else        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      } /* end i */
       }      
     }      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     for(jk=-1; jk <=nlstate+ndeath; jk++)        for(jj=1; jj<= nlstate+ndeath; jj++){
       for(m=-1; m <=nlstate+ndeath; m++)          ps[ii][jj]=0;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          ps[ii][ii]=1;
     if(i <= (int) agemax)        }
       fprintf(ficresp,"\n");      }
     printf("\n");      
     }  
     }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
  }  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   dateintmean=dateintsum/k2cpt;  /*         printf("ddd %lf ",ps[ii][jj]); */
    /*       } */
   fclose(ficresp);  /*       printf("\n "); */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  /*        } */
   free_vector(pp,1,nlstate);  /*        printf("\n ");printf("%lf ",cov[2]); */
          /*
   /* End of Freq */        for(i=1; i<= npar; i++) printf("%f ",x[i]);
 }        goto end;*/
       return ps;
 /************ Prevalence ********************/  }
 void prevalence(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 calagedate)  
 {  /* Some frequencies */  /**************** Product of 2 matrices ******************/
    
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   double ***freq; /* Frequencies */  {
   double *pp;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   double pos, k2;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     /* in, b, out are matrice of pointers which should have been initialized 
   pp=vector(1,nlstate);       before: only the contents of out is modified. The function returns
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);       a pointer to pointers identical to out */
      long i, j, k;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    for(i=nrl; i<= nrh; i++)
   j1=0;      for(k=ncolol; k<=ncoloh; k++)
          for(j=ncl,out[i][k]=0.; j<=nch; j++)
   j=cptcoveff;          out[i][k] +=in[i][j]*b[j][k];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  
      return out;
  for(k1=1; k1<=j;k1++){  }
     for(i1=1; i1<=ncodemax[k1];i1++){  
       j1++;  
    /************* Higher Matrix Product ***************/
       for (i=-1; i<=nlstate+ndeath; i++)    
         for (jk=-1; jk<=nlstate+ndeath; 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=agemin; m <= agemax+3; m++)  {
             freq[i][jk][m]=0;    /* Computes the transition matrix starting at age 'age' over 
             'nhstepm*hstepm*stepm' months (i.e. until
       for (i=1; i<=imx; i++) {       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
         bool=1;       nhstepm*hstepm matrices. 
         if  (cptcovn>0) {       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
           for (z1=1; z1<=cptcoveff; z1++)       (typically every 2 years instead of every month which is too big 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])       for the memory).
               bool=0;       Model is determined by parameters x and covariates have to be 
         }       included manually here. 
         if (bool==1) {  
           for(m=firstpass; m<=lastpass; m++){       */
             k2=anint[m][i]+(mint[m][i]/12.);  
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    int i, j, d, h, k;
               if(agev[m][i]==0) agev[m][i]=agemax+1;    double **out, cov[NCOVMAX];
               if(agev[m][i]==1) agev[m][i]=agemax+2;    double **newm;
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];  
               freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];      /* Hstepm could be zero and should return the unit matrix */
             }    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(i=(int)agemin; i <= (int)agemax+3; i++){    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           for(jk=1; jk <=nlstate ; jk++){    for(h=1; h <=nhstepm; h++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for(d=1; d <=hstepm; d++){
               pp[jk] += freq[jk][m][i];        newm=savm;
           }        /* Covariates have to be included here again */
           for(jk=1; jk <=nlstate ; jk++){        cov[1]=1.;
             for(m=-1, pos=0; m <=0 ; m++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
             pos += freq[jk][m][i];        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         }        for (k=1; k<=cptcovage;k++)
                  cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
          for(jk=1; jk <=nlstate ; jk++){        for (k=1; k<=cptcovprod;k++)
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
              pp[jk] += freq[jk][m][i];  
          }  
                  /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        /*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, 
          for(jk=1; jk <=nlstate ; jk++){                               pmij(pmmij,cov,ncovmodel,x,nlstate));
            if( i <= (int) agemax){        savm=oldm;
              if(pos>=1.e-5){        oldm=newm;
                probs[i][jk][j1]= pp[jk]/pos;      }
              }      for(i=1; i<=nlstate+ndeath; i++)
            }        for(j=1;j<=nlstate+ndeath;j++) {
          }          po[i][j][h]=newm[i][j];
                    /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
         }        }
     }      /*printf("h=%d ",h);*/
   }    } /* end h */
    /*     printf("\n H=%d \n",h); */
      return po;
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  }
   free_vector(pp,1,nlstate);  
    
 }  /* End of Freq */  /*************** log-likelihood *************/
   double func( double *x)
 /************* Waves Concatenation ***************/  {
     int i, ii, j, k, mi, d, kk;
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    double l, ll[NLSTATEMAX], cov[NCOVMAX];
 {    double **out;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    double sw; /* Sum of weights */
      Death is a valid wave (if date is known).    double lli; /* Individual log likelihood */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    int s1, s2;
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    double bbh, survp;
      and mw[mi+1][i]. dh depends on stepm.    long ipmx;
      */    /*extern weight */
     /* We are differentiating ll according to initial status */
   int i, mi, m;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    /*for(i=1;i<imx;i++) 
      double sum=0., jmean=0.;*/      printf(" %d\n",s[4][i]);
     */
   int j, k=0,jk, ju, jl;    cov[1]=1.;
   double sum=0.;  
   jmin=1e+5;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   jmax=-1;  
   jmean=0.;    if(mle==1){
   for(i=1; i<=imx; i++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     mi=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     m=firstpass;        for(mi=1; mi<= wav[i]-1; mi++){
     while(s[m][i] <= nlstate){          for (ii=1;ii<=nlstate+ndeath;ii++)
       if(s[m][i]>=1)            for (j=1;j<=nlstate+ndeath;j++){
         mw[++mi][i]=m;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       if(m >=lastpass)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         break;            }
       else          for(d=0; d<dh[mi][i]; d++){
         m++;            newm=savm;
     }/* end while */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     if (s[m][i] > nlstate){            for (kk=1; kk<=cptcovage;kk++) {
       mi++;     /* Death is another wave */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       /* if(mi==0)  never been interviewed correctly before death */            }
          /* Only death is a correct wave */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       mw[mi][i]=m;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     }            savm=oldm;
             oldm=newm;
     wav[i]=mi;          } /* end mult */
     if(mi==0)        
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   }          /* But now since version 0.9 we anticipate for bias at large stepm.
            * If stepm is larger than one month (smallest stepm) and if the exact delay 
   for(i=1; i<=imx; i++){           * (in months) between two waves is not a multiple of stepm, we rounded to 
     for(mi=1; mi<wav[i];mi++){           * the nearest (and in case of equal distance, to the lowest) interval but now
       if (stepm <=0)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         dh[mi][i]=1;           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
       else{           * probability in order to take into account the bias as a fraction of the way
         if (s[mw[mi+1][i]][i] > nlstate) {           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
           if (agedc[i] < 2*AGESUP) {           * -stepm/2 to stepm/2 .
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);           * For stepm=1 the results are the same as for previous versions of Imach.
           if(j==0) j=1;  /* Survives at least one month after exam */           * For stepm > 1 the results are less biased than in previous versions. 
           k=k+1;           */
           if (j >= jmax) jmax=j;          s1=s[mw[mi][i]][i];
           if (j <= jmin) jmin=j;          s2=s[mw[mi+1][i]][i];
           sum=sum+j;          bbh=(double)bh[mi][i]/(double)stepm; 
           /* if (j<10) printf("j=%d num=%d ",j,i); */          /* bias bh is positive if real duration
           }           * is higher than the multiple of stepm and negative otherwise.
         }           */
         else{          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          if( s2 > nlstate){ 
           k=k+1;            /* i.e. if s2 is a death state and if the date of death is known 
           if (j >= jmax) jmax=j;               then the contribution to the likelihood is the probability to 
           else if (j <= jmin)jmin=j;               die between last step unit time and current  step unit time, 
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */               which is also equal to probability to die before dh 
           sum=sum+j;               minus probability to die before dh-stepm . 
         }               In version up to 0.92 likelihood was computed
         jk= j/stepm;          as if date of death was unknown. Death was treated as any other
         jl= j -jk*stepm;          health state: the date of the interview describes the actual state
         ju= j -(jk+1)*stepm;          and not the date of a change in health state. The former idea was
         if(jl <= -ju)          to consider that at each interview the state was recorded
           dh[mi][i]=jk;          (healthy, disable or death) and IMaCh was corrected; but when we
         else          introduced the exact date of death then we should have modified
           dh[mi][i]=jk+1;          the contribution of an exact death to the likelihood. This new
         if(dh[mi][i]==0)          contribution is smaller and very dependent of the step unit
           dh[mi][i]=1; /* At least one step */          stepm. It is no more the probability to die between last interview
       }          and month of death but the probability to survive from last
     }          interview up to one month before death multiplied by the
   }          probability to die within a month. Thanks to Chris
   jmean=sum/k;          Jackson for correcting this bug.  Former versions increased
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          mortality artificially. The bad side is that we add another loop
  }          which slows down the processing. The difference can be up to 10%
 /*********** Tricode ****************************/          lower mortality.
 void tricode(int *Tvar, int **nbcode, int imx)            */
 {            lli=log(out[s1][s2] - savm[s1][s2]);
   int Ndum[20],ij=1, k, j, i;  
   int cptcode=0;  
   cptcoveff=0;          } else if  (s2==-2) {
              for (j=1,survp=0. ; j<=nlstate; j++) 
   for (k=0; k<19; k++) Ndum[k]=0;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   for (k=1; k<=7; k++) ncodemax[k]=0;            /*survp += out[s1][j]; */
             lli= log(survp);
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          }
     for (i=1; i<=imx; i++) {          
       ij=(int)(covar[Tvar[j]][i]);          else if  (s2==-4) { 
       Ndum[ij]++;            for (j=3,survp=0. ; j<=nlstate; j++)  
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       if (ij > cptcode) cptcode=ij;            lli= log(survp); 
     }          } 
   
     for (i=0; i<=cptcode; i++) {          else if  (s2==-5) { 
       if(Ndum[i]!=0) ncodemax[j]++;            for (j=1,survp=0. ; j<=2; j++)  
     }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     ij=1;            lli= log(survp); 
           } 
           
     for (i=1; i<=ncodemax[j]; i++) {          else{
       for (k=0; k<=19; k++) {            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         if (Ndum[k] != 0) {            /*  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 */
           nbcode[Tvar[j]][ij]=k;          } 
           ij++;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         }          /*if(lli ==000.0)*/
         if (ij > ncodemax[j]) break;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       }            ipmx +=1;
     }          sw += weight[i];
   }            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
  for (k=0; k<19; k++) Ndum[k]=0;      } /* end of individual */
     }  else if(mle==2){
  for (i=1; i<=ncovmodel-2; i++) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       ij=Tvar[i];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       Ndum[ij]++;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
  ij=1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  for (i=1; i<=10; i++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    if((Ndum[i]!=0) && (i<=ncov)){            }
      Tvaraff[ij]=i;          for(d=0; d<=dh[mi][i]; d++){
      ij++;            newm=savm;
    }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
  }            for (kk=1; kk<=cptcovage;kk++) {
                cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     cptcoveff=ij-1;            }
 }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 /*********** Health Expectancies ****************/            savm=oldm;
             oldm=newm;
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          } /* end mult */
 {        
   /* Health expectancies */          s1=s[mw[mi][i]][i];
   int i, j, nhstepm, hstepm, h;          s2=s[mw[mi+1][i]][i];
   double age, agelim,hf;          bbh=(double)bh[mi][i]/(double)stepm; 
   double ***p3mat;          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 */
            ipmx +=1;
   fprintf(ficreseij,"# Health expectancies\n");          sw += weight[i];
   fprintf(ficreseij,"# Age");          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   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 if(mle==3){  /* exponential inter-extrapolation */
   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];
   hstepm=1*YEARM; /*  Every j years of age (in month) */        for(mi=1; mi<= wav[i]-1; mi++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
   agelim=AGESUP;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* nhstepm age range expressed in number of stepm */            }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          for(d=0; d<dh[mi][i]; d++){
     /* Typically if 20 years = 20*12/6=40 stepm */            newm=savm;
     if (stepm >= YEARM) hstepm=1;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */            for (kk=1; kk<=cptcovage;kk++) {
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            }
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
             oldm=newm;
     for(i=1; i<=nlstate;i++)          } /* end mult */
       for(j=1; j<=nlstate;j++)        
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){          s1=s[mw[mi][i]][i];
           eij[i][j][(int)age] +=p3mat[i][j][h];          s2=s[mw[mi+1][i]][i];
         }          bbh=(double)bh[mi][i]/(double)stepm; 
              lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
     hf=1;          ipmx +=1;
     if (stepm >= YEARM) hf=stepm/YEARM;          sw += weight[i];
     fprintf(ficreseij,"%.0f",age );          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for(i=1; i<=nlstate;i++)        } /* end of wave */
       for(j=1; j<=nlstate;j++){      } /* end of individual */
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
       }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     fprintf(ficreseij,"\n");        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(mi=1; mi<= wav[i]-1; mi++){
   }          for (ii=1;ii<=nlstate+ndeath;ii++)
 }            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /************ Variance ******************/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)            }
 {          for(d=0; d<dh[mi][i]; d++){
   /* Variance of health expectancies */            newm=savm;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double **newm;            for (kk=1; kk<=cptcovage;kk++) {
   double **dnewm,**doldm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int i, j, nhstepm, hstepm, h;            }
   int k, cptcode;          
   double *xp;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double **gp, **gm;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double ***gradg, ***trgradg;            savm=oldm;
   double ***p3mat;            oldm=newm;
   double age,agelim;          } /* end mult */
   int theta;        
           s1=s[mw[mi][i]][i];
    fprintf(ficresvij,"# Covariances of life expectancies\n");          s2=s[mw[mi+1][i]][i];
   fprintf(ficresvij,"# Age");          if( s2 > nlstate){ 
   for(i=1; i<=nlstate;i++)            lli=log(out[s1][s2] - savm[s1][s2]);
     for(j=1; j<=nlstate;j++)          }else{
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   fprintf(ficresvij,"\n");          }
           ipmx +=1;
   xp=vector(1,npar);          sw += weight[i];
   dnewm=matrix(1,nlstate,1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   doldm=matrix(1,nlstate,1,nlstate);  /*      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=1*YEARM; /* Every year of age */      } /* end of individual */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   agelim = AGESUP;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        for(mi=1; mi<= wav[i]-1; mi++){
     if (stepm >= YEARM) hstepm=1;          for (ii=1;ii<=nlstate+ndeath;ii++)
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            for (j=1;j<=nlstate+ndeath;j++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     gp=matrix(0,nhstepm,1,nlstate);            }
     gm=matrix(0,nhstepm,1,nlstate);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
     for(theta=1; theta <=npar; theta++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(i=1; i<=npar; i++){ /* Computes gradient */            for (kk=1; kk<=cptcovage;kk++) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       if (popbased==1) {            savm=oldm;
         for(i=1; i<=nlstate;i++)            oldm=newm;
           prlim[i][i]=probs[(int)age][i][ij];          } /* end mult */
       }        
                s1=s[mw[mi][i]][i];
       for(j=1; j<= nlstate; j++){          s2=s[mw[mi+1][i]][i];
         for(h=0; h<=nhstepm; h++){          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          ipmx +=1;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          sw += weight[i];
         }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
            } /* end of wave */
       for(i=1; i<=npar; i++) /* Computes gradient */      } /* end of individual */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    } /* End of if */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       if (popbased==1) {    return -l;
         for(i=1; i<=nlstate;i++)  }
           prlim[i][i]=probs[(int)age][i][ij];  
       }  /*************** log-likelihood *************/
   double funcone( double *x)
       for(j=1; j<= nlstate; j++){  {
         for(h=0; h<=nhstepm; h++){    /* Same as likeli but slower because of a lot of printf and if */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    int i, ii, j, k, mi, d, kk;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    double l, ll[NLSTATEMAX], cov[NCOVMAX];
         }    double **out;
       }    double lli; /* Individual log likelihood */
     double llt;
       for(j=1; j<= nlstate; j++)    int s1, s2;
         for(h=0; h<=nhstepm; h++){    double bbh, survp;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    /*extern weight */
         }    /* We are differentiating ll according to initial status */
     } /* End theta */    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     /*for(i=1;i<imx;i++) 
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);      printf(" %d\n",s[4][i]);
     */
     for(h=0; h<=nhstepm; h++)    cov[1]=1.;
       for(j=1; j<=nlstate;j++)  
         for(theta=1; theta <=npar; theta++)    for(k=1; k<=nlstate; k++) ll[k]=0.;
           trgradg[h][j][theta]=gradg[h][theta][j];  
     for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(i=1;i<=nlstate;i++)      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1;j<=nlstate;j++)      for(mi=1; mi<= wav[i]-1; mi++){
         vareij[i][j][(int)age] =0.;        for (ii=1;ii<=nlstate+ndeath;ii++)
     for(h=0;h<=nhstepm;h++){          for (j=1;j<=nlstate+ndeath;j++){
       for(k=0;k<=nhstepm;k++){            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          }
         for(i=1;i<=nlstate;i++)        for(d=0; d<dh[mi][i]; d++){
           for(j=1;j<=nlstate;j++)          newm=savm;
             vareij[i][j][(int)age] += doldm[i][j];          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }          for (kk=1; kk<=cptcovage;kk++) {
     }            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     h=1;          }
     if (stepm >= YEARM) h=stepm/YEARM;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     fprintf(ficresvij,"%.0f ",age );                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(i=1; i<=nlstate;i++)          savm=oldm;
       for(j=1; j<=nlstate;j++){          oldm=newm;
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);        } /* end mult */
       }        
     fprintf(ficresvij,"\n");        s1=s[mw[mi][i]][i];
     free_matrix(gp,0,nhstepm,1,nlstate);        s2=s[mw[mi+1][i]][i];
     free_matrix(gm,0,nhstepm,1,nlstate);        bbh=(double)bh[mi][i]/(double)stepm; 
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        /* bias is positive if real duration
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);         * is higher than the multiple of stepm and negative otherwise.
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         */
   } /* End age */        if( s2 > nlstate && (mle <5) ){  /* Jackson */
            lli=log(out[s1][s2] - savm[s1][s2]);
   free_vector(xp,1,npar);        } else if  (s2==-2) {
   free_matrix(doldm,1,nlstate,1,npar);          for (j=1,survp=0. ; j<=nlstate; j++) 
   free_matrix(dnewm,1,nlstate,1,nlstate);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           lli= log(survp);
 }        }else if (mle==1){
           lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 /************ Variance of prevlim ******************/        } else if(mle==2){
 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)          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
 {        } else if(mle==3){  /* exponential inter-extrapolation */
   /* Variance of prevalence limit */          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   double **newm;          lli=log(out[s1][s2]); /* Original formula */
   double **dnewm,**doldm;        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   int i, j, nhstepm, hstepm;          lli=log(out[s1][s2]); /* Original formula */
   int k, cptcode;        } /* End of if */
   double *xp;        ipmx +=1;
   double *gp, *gm;        sw += weight[i];
   double **gradg, **trgradg;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double age,agelim;  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   int theta;        if(globpr){
              fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");   %11.6f %11.6f %11.6f ", \
   fprintf(ficresvpl,"# Age");                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
   for(i=1; i<=nlstate;i++)                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       fprintf(ficresvpl," %1d-%1d",i,i);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   fprintf(ficresvpl,"\n");            llt +=ll[k]*gipmx/gsw;
             fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   xp=vector(1,npar);          }
   dnewm=matrix(1,nlstate,1,npar);          fprintf(ficresilk," %10.6f\n", -llt);
   doldm=matrix(1,nlstate,1,nlstate);        }
        } /* end of wave */
   hstepm=1*YEARM; /* Every year of age */    } /* end of individual */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   agelim = AGESUP;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    if(globpr==0){ /* First time we count the contributions and weights */
     if (stepm >= YEARM) hstepm=1;      gipmx=ipmx;
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      gsw=sw;
     gradg=matrix(1,npar,1,nlstate);    }
     gp=vector(1,nlstate);    return -l;
     gm=vector(1,nlstate);  }
   
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */  /*************** function likelione ***********/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       }  {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    /* This routine should help understanding what is done with 
       for(i=1;i<=nlstate;i++)       the selection of individuals/waves and
         gp[i] = prlim[i][i];       to check the exact contribution to the likelihood.
           Plotting could be done.
       for(i=1; i<=npar; i++) /* Computes gradient */     */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    int k;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)    if(*globpri !=0){ /* Just counts and sums, no printings */
         gm[i] = prlim[i][i];      strcpy(fileresilk,"ilk"); 
       strcat(fileresilk,fileres);
       for(i=1;i<=nlstate;i++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        printf("Problem with resultfile: %s\n", fileresilk);
     } /* End theta */        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
     trgradg =matrix(1,nlstate,1,npar);      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(theta=1; theta <=npar; theta++)      for(k=1; k<=nlstate; k++) 
         trgradg[j][theta]=gradg[theta][j];        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     for(i=1;i<=nlstate;i++)    }
       varpl[i][(int)age] =0.;  
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    *fretone=(*funcone)(p);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    if(*globpri !=0){
     for(i=1;i<=nlstate;i++)      fclose(ficresilk);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       fflush(fichtm); 
     fprintf(ficresvpl,"%.0f ",age );    } 
     for(i=1; i<=nlstate;i++)    return;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));  }
     fprintf(ficresvpl,"\n");  
     free_vector(gp,1,nlstate);  
     free_vector(gm,1,nlstate);  /*********** Maximum Likelihood Estimation ***************/
     free_matrix(gradg,1,npar,1,nlstate);  
     free_matrix(trgradg,1,nlstate,1,npar);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   } /* End age */  {
     int i,j, iter;
   free_vector(xp,1,npar);    double **xi;
   free_matrix(doldm,1,nlstate,1,npar);    double fret;
   free_matrix(dnewm,1,nlstate,1,nlstate);    double fretone; /* Only one call to likelihood */
     /*  char filerespow[FILENAMELENGTH];*/
 }    xi=matrix(1,npar,1,npar);
     for (i=1;i<=npar;i++)
 /************ Variance of one-step probabilities  ******************/      for (j=1;j<=npar;j++)
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)        xi[i][j]=(i==j ? 1.0 : 0.0);
 {    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   int i, j;    strcpy(filerespow,"pow"); 
   int k=0, cptcode;    strcat(filerespow,fileres);
   double **dnewm,**doldm;    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   double *xp;      printf("Problem with resultfile: %s\n", filerespow);
   double *gp, *gm;      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   double **gradg, **trgradg;    }
   double age,agelim, cov[NCOVMAX];    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   int theta;    for (i=1;i<=nlstate;i++)
   char fileresprob[FILENAMELENGTH];      for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   strcpy(fileresprob,"prob");    fprintf(ficrespow,"\n");
   strcat(fileresprob,fileres);  
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    powell(p,xi,npar,ftol,&iter,&fret,func);
     printf("Problem with resultfile: %s\n", fileresprob);  
   }    free_matrix(xi,1,npar,1,npar);
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);    fclose(ficrespow);
      printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   xp=vector(1,npar);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));  }
    
   cov[1]=1;  /**** Computes Hessian and covariance matrix ***/
   for (age=bage; age<=fage; age ++){  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     cov[2]=age;  {
     gradg=matrix(1,npar,1,9);    double  **a,**y,*x,pd;
     trgradg=matrix(1,9,1,npar);    double **hess;
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    int i, j,jk;
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    int *indx;
      
     for(theta=1; theta <=npar; theta++){    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(i=1; i<=npar; i++)    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    void lubksb(double **a, int npar, int *indx, double b[]) ;
          void ludcmp(double **a, int npar, int *indx, double *d) ;
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    double gompertz(double p[]);
        hess=matrix(1,npar,1,npar);
       k=0;  
       for(i=1; i<= (nlstate+ndeath); i++){    printf("\nCalculation of the hessian matrix. Wait...\n");
         for(j=1; j<=(nlstate+ndeath);j++){    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
            k=k+1;    for (i=1;i<=npar;i++){
           gp[k]=pmmij[i][j];      printf("%d",i);fflush(stdout);
         }      fprintf(ficlog,"%d",i);fflush(ficlog);
       }     
        hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
       for(i=1; i<=npar; i++)      
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      /*  printf(" %f ",p[i]);
              printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    
       k=0;    for (i=1;i<=npar;i++) {
       for(i=1; i<=(nlstate+ndeath); i++){      for (j=1;j<=npar;j++)  {
         for(j=1; j<=(nlstate+ndeath);j++){        if (j>i) { 
           k=k+1;          printf(".%d%d",i,j);fflush(stdout);
           gm[k]=pmmij[i][j];          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
         }          hess[i][j]=hessij(p,delti,i,j,func,npar);
       }          
                hess[j][i]=hess[i][j];    
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)          /*printf(" %lf ",hess[i][j]);*/
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];          }
     }      }
     }
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    printf("\n");
       for(theta=1; theta <=npar; theta++)    fprintf(ficlog,"\n");
       trgradg[j][theta]=gradg[theta][j];  
      printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    
     a=matrix(1,npar,1,npar);
      pmij(pmmij,cov,ncovmodel,x,nlstate);    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
      k=0;    indx=ivector(1,npar);
      for(i=1; i<=(nlstate+ndeath); i++){    for (i=1;i<=npar;i++)
        for(j=1; j<=(nlstate+ndeath);j++){      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
          k=k+1;    ludcmp(a,npar,indx,&pd);
          gm[k]=pmmij[i][j];  
         }    for (j=1;j<=npar;j++) {
      }      for (i=1;i<=npar;i++) x[i]=0;
            x[j]=1;
      /*printf("\n%d ",(int)age);      lubksb(a,npar,indx,x);
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      for (i=1;i<=npar;i++){ 
                matcov[i][j]=x[i];
       }
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    }
      }*/  
     printf("\n#Hessian matrix#\n");
   fprintf(ficresprob,"\n%d ",(int)age);    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      for (j=1;j<=npar;j++) { 
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        printf("%.3e ",hess[i][j]);
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        fprintf(ficlog,"%.3e ",hess[i][j]);
   }      }
       printf("\n");
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));      fprintf(ficlog,"\n");
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    }
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    /* Recompute Inverse */
 }    for (i=1;i<=npar;i++)
  free_vector(xp,1,npar);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
 fclose(ficresprob);    ludcmp(a,npar,indx,&pd);
  exit(0);  
 }    /*  printf("\n#Hessian matrix recomputed#\n");
   
 /***********************************************/    for (j=1;j<=npar;j++) {
 /**************** Main Program *****************/      for (i=1;i<=npar;i++) x[i]=0;
 /***********************************************/      x[j]=1;
       lubksb(a,npar,indx,x);
 /*int main(int argc, char *argv[])*/      for (i=1;i<=npar;i++){ 
 int main()        y[i][j]=x[i];
 {        printf("%.3e ",y[i][j]);
         fprintf(ficlog,"%.3e ",y[i][j]);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      }
   double agedeb, agefin,hf;      printf("\n");
   double agemin=1.e20, agemax=-1.e20;      fprintf(ficlog,"\n");
     }
   double fret;    */
   double **xi,tmp,delta;  
     free_matrix(a,1,npar,1,npar);
   double dum; /* Dummy variable */    free_matrix(y,1,npar,1,npar);
   double ***p3mat;    free_vector(x,1,npar);
   int *indx;    free_ivector(indx,1,npar);
   char line[MAXLINE], linepar[MAXLINE];    free_matrix(hess,1,npar,1,npar);
   char title[MAXLINE];  
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];  }
   char filerest[FILENAMELENGTH];  
   char fileregp[FILENAMELENGTH];  /*************** hessian matrix ****************/
   char popfile[FILENAMELENGTH];  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];  {
   int firstobs=1, lastobs=10;    int i;
   int sdeb, sfin; /* Status at beginning and end */    int l=1, lmax=20;
   int c,  h , cpt,l;    double k1,k2;
   int ju,jl, mi;    double p2[NPARMAX+1];
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    double res;
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   int mobilav=0,popforecast=0;    double fx;
   int hstepm, nhstepm;    int k=0,kmax=10;
   int *popage;/*boolprev=0 if date and zero if wave*/    double l1;
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2;  
     fx=func(x);
   double bage, fage, age, agelim, agebase;    for (i=1;i<=npar;i++) p2[i]=x[i];
   double ftolpl=FTOL;    for(l=0 ; l <=lmax; l++){
   double **prlim;      l1=pow(10,l);
   double *severity;      delts=delt;
   double ***param; /* Matrix of parameters */      for(k=1 ; k <kmax; k=k+1){
   double  *p;        delt = delta*(l1*k);
   double **matcov; /* Matrix of covariance */        p2[theta]=x[theta] +delt;
   double ***delti3; /* Scale */        k1=func(p2)-fx;
   double *delti; /* Scale */        p2[theta]=x[theta]-delt;
   double ***eij, ***vareij;        k2=func(p2)-fx;
   double **varpl; /* Variances of prevalence limits by age */        /*res= (k1-2.0*fx+k2)/delt/delt; */
   double *epj, vepp;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   double kk1, kk2;        
   double *popeffectif,*popcount;  #ifdef DEBUG
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,jprojmean,mprojmean,anprojmean, calagedate;        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   double yp,yp1,yp2;        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   #endif
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   char *alph[]={"a","a","b","c","d","e"}, str[4];        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
         }
   char z[1]="c", occ;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
 #include <sys/time.h>          k=kmax; l=lmax*10.;
 #include <time.h>        }
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            delts=delt;
   /* long total_usecs;        }
   struct timeval start_time, end_time;      }
      }
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    delti[theta]=delts;
     return res; 
     
   printf("\nIMACH, Version 0.7");  }
   printf("\nEnter the parameter file name: ");  
   double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
 #ifdef windows  {
   scanf("%s",pathtot);    int i;
   getcwd(pathcd, size);    int l=1, l1, lmax=20;
   /*cygwin_split_path(pathtot,path,optionfile);    double k1,k2,k3,k4,res,fx;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    double p2[NPARMAX+1];
   /* cutv(path,optionfile,pathtot,'\\');*/    int k;
   
 split(pathtot, path,optionfile);    fx=func(x);
   chdir(path);    for (k=1; k<=2; k++) {
   replace(pathc,path);      for (i=1;i<=npar;i++) p2[i]=x[i];
 #endif      p2[thetai]=x[thetai]+delti[thetai]/k;
 #ifdef unix      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   scanf("%s",optionfile);      k1=func(p2)-fx;
 #endif    
       p2[thetai]=x[thetai]+delti[thetai]/k;
 /*-------- arguments in the command line --------*/      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k2=func(p2)-fx;
   strcpy(fileres,"r");    
   strcat(fileres, optionfile);      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   /*---------arguments file --------*/      k3=func(p2)-fx;
     
   if((ficpar=fopen(optionfile,"r"))==NULL)    {      p2[thetai]=x[thetai]-delti[thetai]/k;
     printf("Problem with optionfile %s\n",optionfile);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     goto end;      k4=func(p2)-fx;
   }      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   #ifdef DEBUG
   strcpy(filereso,"o");      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);
   strcat(filereso,fileres);      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);
   if((ficparo=fopen(filereso,"w"))==NULL) {  #endif
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    }
   }    return res;
   }
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){  /************** Inverse of matrix **************/
     ungetc(c,ficpar);  void ludcmp(double **a, int n, int *indx, double *d) 
     fgets(line, MAXLINE, ficpar);  { 
     puts(line);    int i,imax,j,k; 
     fputs(line,ficparo);    double big,dum,sum,temp; 
   }    double *vv; 
   ungetc(c,ficpar);   
     vv=vector(1,n); 
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    *d=1.0; 
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);    for (i=1;i<=n;i++) { 
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);      big=0.0; 
 while((c=getc(ficpar))=='#' && c!= EOF){      for (j=1;j<=n;j++) 
     ungetc(c,ficpar);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     fgets(line, MAXLINE, ficpar);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     puts(line);      vv[i]=1.0/big; 
     fputs(line,ficparo);    } 
   }    for (j=1;j<=n;j++) { 
   ungetc(c,ficpar);      for (i=1;i<j;i++) { 
          sum=a[i][j]; 
            for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   covar=matrix(0,NCOVMAX,1,n);        a[i][j]=sum; 
   cptcovn=0;      } 
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      big=0.0; 
       for (i=j;i<=n;i++) { 
   ncovmodel=2+cptcovn;        sum=a[i][j]; 
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */        for (k=1;k<j;k++) 
            sum -= a[i][k]*a[k][j]; 
   /* Read guess parameters */        a[i][j]=sum; 
   /* Reads comments: lines beginning with '#' */        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   while((c=getc(ficpar))=='#' && c!= EOF){          big=dum; 
     ungetc(c,ficpar);          imax=i; 
     fgets(line, MAXLINE, ficpar);        } 
     puts(line);      } 
     fputs(line,ficparo);      if (j != imax) { 
   }        for (k=1;k<=n;k++) { 
   ungetc(c,ficpar);          dum=a[imax][k]; 
            a[imax][k]=a[j][k]; 
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          a[j][k]=dum; 
     for(i=1; i <=nlstate; i++)        } 
     for(j=1; j <=nlstate+ndeath-1; j++){        *d = -(*d); 
       fscanf(ficpar,"%1d%1d",&i1,&j1);        vv[imax]=vv[j]; 
       fprintf(ficparo,"%1d%1d",i1,j1);      } 
       printf("%1d%1d",i,j);      indx[j]=imax; 
       for(k=1; k<=ncovmodel;k++){      if (a[j][j] == 0.0) a[j][j]=TINY; 
         fscanf(ficpar," %lf",&param[i][j][k]);      if (j != n) { 
         printf(" %lf",param[i][j][k]);        dum=1.0/(a[j][j]); 
         fprintf(ficparo," %lf",param[i][j][k]);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       }      } 
       fscanf(ficpar,"\n");    } 
       printf("\n");    free_vector(vv,1,n);  /* Doesn't work */
       fprintf(ficparo,"\n");  ;
     }  } 
    
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  void lubksb(double **a, int n, int *indx, double b[]) 
   { 
   p=param[1][1];    int i,ii=0,ip,j; 
      double sum; 
   /* Reads comments: lines beginning with '#' */   
   while((c=getc(ficpar))=='#' && c!= EOF){    for (i=1;i<=n;i++) { 
     ungetc(c,ficpar);      ip=indx[i]; 
     fgets(line, MAXLINE, ficpar);      sum=b[ip]; 
     puts(line);      b[ip]=b[i]; 
     fputs(line,ficparo);      if (ii) 
   }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   ungetc(c,ficpar);      else if (sum) ii=i; 
       b[i]=sum; 
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    } 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    for (i=n;i>=1;i--) { 
   for(i=1; i <=nlstate; i++){      sum=b[i]; 
     for(j=1; j <=nlstate+ndeath-1; j++){      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);      b[i]=sum/a[i][i]; 
       printf("%1d%1d",i,j);    } 
       fprintf(ficparo,"%1d%1d",i1,j1);  } 
       for(k=1; k<=ncovmodel;k++){  
         fscanf(ficpar,"%le",&delti3[i][j][k]);  void pstamp(FILE *fichier)
         printf(" %le",delti3[i][j][k]);  {
         fprintf(ficparo," %le",delti3[i][j][k]);    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
       }  }
       fscanf(ficpar,"\n");  
       printf("\n");  /************ Frequencies ********************/
       fprintf(ficparo,"\n");  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
     }  {  /* Some frequencies */
   }    
   delti=delti3[1][1];    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
      int first;
   /* Reads comments: lines beginning with '#' */    double ***freq; /* Frequencies */
   while((c=getc(ficpar))=='#' && c!= EOF){    double *pp, **prop;
     ungetc(c,ficpar);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     fgets(line, MAXLINE, ficpar);    char fileresp[FILENAMELENGTH];
     puts(line);    
     fputs(line,ficparo);    pp=vector(1,nlstate);
   }    prop=matrix(1,nlstate,iagemin,iagemax+3);
   ungetc(c,ficpar);    strcpy(fileresp,"p");
      strcat(fileresp,fileres);
   matcov=matrix(1,npar,1,npar);    if((ficresp=fopen(fileresp,"w"))==NULL) {
   for(i=1; i <=npar; i++){      printf("Problem with prevalence resultfile: %s\n", fileresp);
     fscanf(ficpar,"%s",&str);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     printf("%s",str);      exit(0);
     fprintf(ficparo,"%s",str);    }
     for(j=1; j <=i; j++){    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
       fscanf(ficpar," %le",&matcov[i][j]);    j1=0;
       printf(" %.5le",matcov[i][j]);    
       fprintf(ficparo," %.5le",matcov[i][j]);    j=cptcoveff;
     }    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     fscanf(ficpar,"\n");  
     printf("\n");    first=1;
     fprintf(ficparo,"\n");  
   }    for(k1=1; k1<=j;k1++){
   for(i=1; i <=npar; i++)      for(i1=1; i1<=ncodemax[k1];i1++){
     for(j=i+1;j<=npar;j++)        j1++;
       matcov[i][j]=matcov[j][i];        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
              scanf("%d", i);*/
   printf("\n");        for (i=-5; i<=nlstate+ndeath; i++)  
           for (jk=-5; jk<=nlstate+ndeath; jk++)  
             for(m=iagemin; m <= iagemax+3; m++)
     /*-------- data file ----------*/              freq[i][jk][m]=0;
     if((ficres =fopen(fileres,"w"))==NULL) {  
       printf("Problem with resultfile: %s\n", fileres);goto end;      for (i=1; i<=nlstate; i++)  
     }        for(m=iagemin; m <= iagemax+3; m++)
     fprintf(ficres,"#%s\n",version);          prop[i][m]=0;
            
     if((fic=fopen(datafile,"r"))==NULL)    {        dateintsum=0;
       printf("Problem with datafile: %s\n", datafile);goto end;        k2cpt=0;
     }        for (i=1; i<=imx; i++) {
           bool=1;
     n= lastobs;          if  (cptcovn>0) {
     severity = vector(1,maxwav);            for (z1=1; z1<=cptcoveff; z1++) 
     outcome=imatrix(1,maxwav+1,1,n);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     num=ivector(1,n);                bool=0;
     moisnais=vector(1,n);          }
     annais=vector(1,n);          if (bool==1){
     moisdc=vector(1,n);            for(m=firstpass; m<=lastpass; m++){
     andc=vector(1,n);              k2=anint[m][i]+(mint[m][i]/12.);
     agedc=vector(1,n);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     cod=ivector(1,n);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     weight=vector(1,n);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     mint=matrix(1,maxwav,1,n);                if (m<lastpass) {
     anint=matrix(1,maxwav,1,n);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     s=imatrix(1,maxwav+1,1,n);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     adl=imatrix(1,maxwav+1,1,n);                    }
     tab=ivector(1,NCOVMAX);                
     ncodemax=ivector(1,8);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                   dateintsum=dateintsum+k2;
     i=1;                  k2cpt++;
     while (fgets(line, MAXLINE, fic) != NULL)    {                }
       if ((i >= firstobs) && (i <=lastobs)) {                /*}*/
                    }
         for (j=maxwav;j>=1;j--){          }
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        }
           strcpy(line,stra);         
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        pstamp(ficresp);
         }        if  (cptcovn>0) {
                  fprintf(ficresp, "\n#********** Variable "); 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          fprintf(ficresp, "**********\n#");
         }
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);        for(i=1; i<=nlstate;i++) 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        
         for (j=ncov;j>=1;j--){        for(i=iagemin; i <= iagemax+3; i++){
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);          if(i==iagemax+3){
         }            fprintf(ficlog,"Total");
         num[i]=atol(stra);          }else{
                    if(first==1){
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){              first=0;
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/              printf("See log file for details...\n");
             }
         i=i+1;            fprintf(ficlog,"Age %d", i);
       }          }
     }          for(jk=1; jk <=nlstate ; jk++){
     /* printf("ii=%d", ij);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
        scanf("%d",i);*/              pp[jk] += freq[jk][m][i]; 
   imx=i-1; /* Number of individuals */          }
           for(jk=1; jk <=nlstate ; jk++){
   /* for (i=1; i<=imx; i++){            for(m=-1, pos=0; m <=0 ; m++)
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;              pos += freq[jk][m][i];
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;            if(pp[jk]>=1.e-10){
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;              if(first==1){
     }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               }
     for (i=1; i<=imx; i++)              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     if (covar[1][i]==0) printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/            }else{
               if(first==1)
   /* Calculation of the number of parameter from char model*/                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   Tvar=ivector(1,15);              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   Tprod=ivector(1,15);            }
   Tvaraff=ivector(1,15);          }
   Tvard=imatrix(1,15,1,2);  
   Tage=ivector(1,15);                for(jk=1; jk <=nlstate ; jk++){
                for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   if (strlen(model) >1){              pp[jk] += freq[jk][m][i];
     j=0, j1=0, k1=1, k2=1;          }       
     j=nbocc(model,'+');          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     j1=nbocc(model,'*');            pos += pp[jk];
     cptcovn=j+1;            posprop += prop[jk][i];
     cptcovprod=j1;          }
              for(jk=1; jk <=nlstate ; jk++){
                if(pos>=1.e-5){
     strcpy(modelsav,model);              if(first==1)
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       printf("Error. Non available option model=%s ",model);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       goto end;            }else{
     }              if(first==1)
                    printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     for(i=(j+1); i>=1;i--){              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       cutv(stra,strb,modelsav,'+');            }
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);            if( i <= iagemax){
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/              if(pos>=1.e-5){
       /*scanf("%d",i);*/                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
       if (strchr(strb,'*')) {                /*probs[i][jk][j1]= pp[jk]/pos;*/
         cutv(strd,strc,strb,'*');                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
         if (strcmp(strc,"age")==0) {              }
           cptcovprod--;              else
           cutv(strb,stre,strd,'V');                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
           Tvar[i]=atoi(stre);            }
           cptcovage++;          }
             Tage[cptcovage]=i;          
             /*printf("stre=%s ", stre);*/          for(jk=-1; jk <=nlstate+ndeath; jk++)
         }            for(m=-1; m <=nlstate+ndeath; m++)
         else if (strcmp(strd,"age")==0) {              if(freq[jk][m][i] !=0 ) {
           cptcovprod--;              if(first==1)
           cutv(strb,stre,strc,'V');                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
           Tvar[i]=atoi(stre);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
           cptcovage++;              }
           Tage[cptcovage]=i;          if(i <= iagemax)
         }            fprintf(ficresp,"\n");
         else {          if(first==1)
           cutv(strb,stre,strc,'V');            printf("Others in log...\n");
           Tvar[i]=ncov+k1;          fprintf(ficlog,"\n");
           cutv(strb,strc,strd,'V');        }
           Tprod[k1]=i;      }
           Tvard[k1][1]=atoi(strc);    }
           Tvard[k1][2]=atoi(stre);    dateintmean=dateintsum/k2cpt; 
           Tvar[cptcovn+k2]=Tvard[k1][1];   
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    fclose(ficresp);
           for (k=1; k<=lastobs;k++)    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    free_vector(pp,1,nlstate);
           k1++;    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
           k2=k2+2;    /* End of Freq */
         }  }
       }  
       else {  /************ Prevalence ********************/
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/  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)
        /*  scanf("%d",i);*/  {  
       cutv(strd,strc,strb,'V');    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
       Tvar[i]=atoi(strc);       in each health status at the date of interview (if between dateprev1 and dateprev2).
       }       We still use firstpass and lastpass as another selection.
       strcpy(modelsav,stra);      */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);   
         scanf("%d",i);*/    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
     }    double ***freq; /* Frequencies */
 }    double *pp, **prop;
      double pos,posprop; 
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    double  y2; /* in fractional years */
   printf("cptcovprod=%d ", cptcovprod);    int iagemin, iagemax;
   scanf("%d ",i);*/  
     fclose(fic);    iagemin= (int) agemin;
     iagemax= (int) agemax;
     /*  if(mle==1){*/    /*pp=vector(1,nlstate);*/
     if (weightopt != 1) { /* Maximisation without weights*/    prop=matrix(1,nlstate,iagemin,iagemax+3); 
       for(i=1;i<=n;i++) weight[i]=1.0;    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     }    j1=0;
     /*-calculation of age at interview from date of interview and age at death -*/    
     agev=matrix(1,maxwav,1,imx);    j=cptcoveff;
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
    for (i=1; i<=imx; i++)    
      for(m=2; (m<= maxwav); m++)    for(k1=1; k1<=j;k1++){
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){      for(i1=1; i1<=ncodemax[k1];i1++){
          anint[m][i]=9999;        j1++;
          s[m][i]=-1;        
        }        for (i=1; i<=nlstate; i++)  
              for(m=iagemin; m <= iagemax+3; m++)
     for (i=1; i<=imx; i++)  {            prop[i][m]=0.0;
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);       
       for(m=1; (m<= maxwav); m++){        for (i=1; i<=imx; i++) { /* Each individual */
         if(s[m][i] >0){          bool=1;
           if (s[m][i] == nlstate+1) {          if  (cptcovn>0) {
             if(agedc[i]>0)            for (z1=1; z1<=cptcoveff; z1++) 
               if(moisdc[i]!=99 && andc[i]!=9999)              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
               agev[m][i]=agedc[i];                bool=0;
             else {          } 
               if (andc[i]!=9999){          if (bool==1) { 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
               agev[m][i]=-1;              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;
           }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
           else if(s[m][i] !=9){ /* Should no more exist */                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); 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
             if(mint[m][i]==99 || anint[m][i]==9999)                  /*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]]);*/
               agev[m][i]=1;                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
             else if(agev[m][i] <agemin){                  prop[s[m][i]][iagemax+3] += weight[i]; 
               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);*/              }
             }            } /* end selection of waves */
             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);*/        for(i=iagemin; i <= iagemax+3; i++){  
             }          
             /*agev[m][i]=anint[m][i]-annais[i];*/          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             /*   agev[m][i] = age[i]+2*m;*/            posprop += prop[jk][i]; 
           }          } 
           else { /* =9 */  
             agev[m][i]=1;          for(jk=1; jk <=nlstate ; jk++){     
             s[m][i]=-1;            if( i <=  iagemax){ 
           }              if(posprop>=1.e-5){ 
         }                probs[i][jk][j1]= prop[jk][i]/posprop;
         else /*= 0 Unknown */              } else
           agev[m][i]=1;                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
       }            } 
              }/* end jk */ 
     }        }/* end i */ 
     for (i=1; i<=imx; i++)  {      } /* end i1 */
       for(m=1; (m<= maxwav); m++){    } /* end k1 */
         if (s[m][i] > (nlstate+ndeath)) {    
           printf("Error: Wrong value in nlstate or ndeath\n");      /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
           goto end;    /*free_vector(pp,1,nlstate);*/
         }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
       }  }  /* End of prevalence */
     }  
   /************* Waves Concatenation ***************/
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  
   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)
     free_vector(severity,1,maxwav);  {
     free_imatrix(outcome,1,maxwav+1,1,n);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
     free_vector(moisnais,1,n);       Death is a valid wave (if date is known).
     free_vector(annais,1,n);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     /* free_matrix(mint,1,maxwav,1,n);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
        free_matrix(anint,1,maxwav,1,n);*/       and mw[mi+1][i]. dh depends on stepm.
     free_vector(moisdc,1,n);       */
     free_vector(andc,1,n);  
     int i, mi, m;
        /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     wav=ivector(1,imx);       double sum=0., jmean=0.;*/
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    int first;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    int j, k=0,jk, ju, jl;
        double sum=0.;
     /* Concatenates waves */    first=0;
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    jmin=1e+5;
     jmax=-1;
     jmean=0.;
       Tcode=ivector(1,100);    for(i=1; i<=imx; i++){
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);      mi=0;
       ncodemax[1]=1;      m=firstpass;
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      while(s[m][i] <= nlstate){
              if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
    codtab=imatrix(1,100,1,10);          mw[++mi][i]=m;
    h=0;        if(m >=lastpass)
    m=pow(2,cptcoveff);          break;
          else
    for(k=1;k<=cptcoveff; k++){          m++;
      for(i=1; i <=(m/pow(2,k));i++){      }/* end while */
        for(j=1; j <= ncodemax[k]; j++){      if (s[m][i] > nlstate){
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){        mi++;     /* Death is another wave */
            h++;        /* if(mi==0)  never been interviewed correctly before death */
            if (h>m) h=1;codtab[h][k]=j;           /* Only death is a correct wave */
          }        mw[mi][i]=m;
        }      }
      }  
    }      wav[i]=mi;
          if(mi==0){
    /* Calculates basic frequencies. Computes observed prevalence at single age        nbwarn++;
        and prints on file fileres'p'. */        if(first==0){
           printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
              first=1;
            }
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        if(first==1){
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        }
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      } /* end mi==0 */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    } /* End individuals */
        
     /* For Powell, parameters are in a vector p[] starting at p[1]    for(i=1; i<=imx; i++){
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */      for(mi=1; mi<wav[i];mi++){
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */        if (stepm <=0)
           dh[mi][i]=1;
     if(mle==1){        else{
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     }            if (agedc[i] < 2*AGESUP) {
                  j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     /*--------- results files --------------*/              if(j==0) j=1;  /* Survives at least one month after exam */
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);              else if(j<0){
                  nberr++;
                 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]);
    jk=1;                j=1; /* Temporary Dangerous patch */
    fprintf(ficres,"# Parameters\n");                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
    printf("# Parameters\n");                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]);
    for(i=1,jk=1; i <=nlstate; i++){                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
      for(k=1; k <=(nlstate+ndeath); k++){              }
        if (k != i)              k=k+1;
          {              if (j >= jmax){
            printf("%d%d ",i,k);                jmax=j;
            fprintf(ficres,"%1d%1d ",i,k);                ijmax=i;
            for(j=1; j <=ncovmodel; j++){              }
              printf("%f ",p[jk]);              if (j <= jmin){
              fprintf(ficres,"%f ",p[jk]);                jmin=j;
              jk++;                ijmin=i;
            }              }
            printf("\n");              sum=sum+j;
            fprintf(ficres,"\n");              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
          }              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
      }            }
    }          }
  if(mle==1){          else{
     /* Computing hessian and covariance matrix */            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     ftolhess=ftol; /* Usually correct */  /*        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]); */
     hesscov(matcov, p, npar, delti, ftolhess, func);  
  }            k=k+1;
     fprintf(ficres,"# Scales\n");            if (j >= jmax) {
     printf("# Scales\n");              jmax=j;
      for(i=1,jk=1; i <=nlstate; i++){              ijmax=i;
       for(j=1; j <=nlstate+ndeath; j++){            }
         if (j!=i) {            else if (j <= jmin){
           fprintf(ficres,"%1d%1d",i,j);              jmin=j;
           printf("%1d%1d",i,j);              ijmin=i;
           for(k=1; k<=ncovmodel;k++){            }
             printf(" %.5e",delti[jk]);            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             fprintf(ficres," %.5e",delti[jk]);            /*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]);*/
             jk++;            if(j<0){
           }              nberr++;
           printf("\n");              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]);
           fprintf(ficres,"\n");              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]);
         }            }
       }            sum=sum+j;
      }          }
              jk= j/stepm;
     k=1;          jl= j -jk*stepm;
     fprintf(ficres,"# Covariance\n");          ju= j -(jk+1)*stepm;
     printf("# Covariance\n");          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
     for(i=1;i<=npar;i++){            if(jl==0){
       /*  if (k>nlstate) k=1;              dh[mi][i]=jk;
       i1=(i-1)/(ncovmodel*nlstate)+1;              bh[mi][i]=0;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);            }else{ /* We want a negative bias in order to only have interpolation ie
       printf("%s%d%d",alph[k],i1,tab[i]);*/                    * at the price of an extra matrix product in likelihood */
       fprintf(ficres,"%3d",i);              dh[mi][i]=jk+1;
       printf("%3d",i);              bh[mi][i]=ju;
       for(j=1; j<=i;j++){            }
         fprintf(ficres," %.5e",matcov[i][j]);          }else{
         printf(" %.5e",matcov[i][j]);            if(jl <= -ju){
       }              dh[mi][i]=jk;
       fprintf(ficres,"\n");              bh[mi][i]=jl;       /* bias is positive if real duration
       printf("\n");                                   * is higher than the multiple of stepm and negative otherwise.
       k++;                                   */
     }            }
                else{
     while((c=getc(ficpar))=='#' && c!= EOF){              dh[mi][i]=jk+1;
       ungetc(c,ficpar);              bh[mi][i]=ju;
       fgets(line, MAXLINE, ficpar);            }
       puts(line);            if(dh[mi][i]==0){
       fputs(line,ficparo);              dh[mi][i]=1; /* At least one step */
     }              bh[mi][i]=ju; /* At least one step */
     ungetc(c,ficpar);              /*  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);*/
              }
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);          } /* end if mle */
            }
     if (fage <= 2) {      } /* end wave */
       bage = agemin;    }
       fage = agemax;    jmean=sum/k;
     }    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);
     fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
     fprintf(ficres,"# agemin agemax for life expectancy.\n");   }
   
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  /*********** Tricode ****************************/
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  void tricode(int *Tvar, int **nbcode, int imx)
    {
     while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);    int Ndum[20],ij=1, k, j, i, maxncov=19;
     fgets(line, MAXLINE, ficpar);    int cptcode=0;
     puts(line);    cptcoveff=0; 
     fputs(line,ficparo);   
   }    for (k=0; k<maxncov; k++) Ndum[k]=0;
   ungetc(c,ficpar);    for (k=1; k<=7; k++) ncodemax[k]=0;
    
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mob_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);                                 modality*/ 
              ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
   while((c=getc(ficpar))=='#' && c!= EOF){        Ndum[ij]++; /*store the modality */
     ungetc(c,ficpar);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     fgets(line, MAXLINE, ficpar);        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
     puts(line);                                         Tvar[j]. If V=sex and male is 0 and 
     fputs(line,ficparo);                                         female is 1, then  cptcode=1.*/
   }      }
   ungetc(c,ficpar);  
        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 */
    dateprev1=anprev1+mprev1/12.+jprev1/365.;      }
    dateprev2=anprev2+mprev2/12.+jprev2/365.;  
       ij=1; 
   fscanf(ficpar,"pop_based=%d\n",&popbased);      for (i=1; i<=ncodemax[j]; i++) {
    fprintf(ficparo,"pop_based=%d\n",popbased);          for (k=0; k<= maxncov; k++) {
    fprintf(ficres,"pop_based=%d\n",popbased);            if (Ndum[k] != 0) {
             nbcode[Tvar[j]][ij]=k; 
   while((c=getc(ficpar))=='#' && c!= EOF){            /* 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; */
     ungetc(c,ficpar);            
     fgets(line, MAXLINE, ficpar);            ij++;
     puts(line);          }
     fputs(line,ficparo);          if (ij > ncodemax[j]) break; 
   }        }  
   ungetc(c,ficpar);      } 
   fscanf(ficpar,"popforecast=%d popfile=%s starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf\n",&popforecast,popfile,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2);    }  
 fprintf(ficparo,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);  
 fprintf(ficres,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);   for (k=0; k< maxncov; k++) Ndum[k]=0;
   
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2);   for (i=1; i<=ncovmodel-2; i++) { 
      /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
  /*------------ gnuplot -------------*/     ij=Tvar[i];
 chdir(pathcd);     Ndum[ij]++;
   if((ficgp=fopen("graph.plt","w"))==NULL) {   }
     printf("Problem with file graph.gp");goto end;  
   }   ij=1;
 #ifdef windows   for (i=1; i<= maxncov; i++) {
   fprintf(ficgp,"cd \"%s\" \n",pathc);     if((Ndum[i]!=0) && (i<=ncovcol)){
 #endif       Tvaraff[ij]=i; /*For printing */
 m=pow(2,cptcoveff);       ij++;
       }
  /* 1eme*/   }
   for (cpt=1; cpt<= nlstate ; cpt ++) {   
    for (k1=1; k1<= m ; k1 ++) {   cptcoveff=ij-1; /*Number of simple covariates*/
   }
 #ifdef windows  
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);  /*********** Health Expectancies ****************/
 #endif  
 #ifdef unix  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);  
 #endif  {
     /* Health expectancies, no variances */
 for (i=1; i<= nlstate ; i ++) {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    int nhstepma, nstepma; /* Decreasing with age */
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double age, agelim, hf;
 }    double ***p3mat;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    double eip;
     for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    pstamp(ficreseij);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
 }    fprintf(ficreseij,"# Age");
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    for(i=1; i<=nlstate;i++){
      for (i=1; i<= nlstate ; i ++) {      for(j=1; j<=nlstate;j++){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        fprintf(ficreseij," e%1d%1d ",i,j);
   else fprintf(ficgp," \%%*lf (\%%*lf)");      }
 }        fprintf(ficreseij," e%1d. ",i);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    }
 #ifdef unix    fprintf(ficreseij,"\n");
 fprintf(ficgp,"\nset ter gif small size 400,300");  
 #endif    
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    if(estepm < stepm){
    }      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
   /*2 eme*/    else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
   for (k1=1; k1<= m ; k1 ++) {     * This is mainly to measure the difference between two models: for example
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);     * if stepm=24 months pijx are given only every 2 years and by summing them
         * we are calculating an estimate of the Life Expectancy assuming a linear 
     for (i=1; i<= nlstate+1 ; i ++) {     * progression in between and thus overestimating or underestimating according
       k=2*i;     * to the curvature of the survival function. If, for the same date, we 
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       for (j=1; j<= nlstate+1 ; j ++) {     * to compare the new estimate of Life expectancy with the same linear 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");     * hypothesis. A more precise result, taking into account a more precise
   else fprintf(ficgp," \%%*lf (\%%*lf)");     * curvature will be obtained if estepm is as small as stepm. */
 }    
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    /* For example we decided to compute the life expectancy with the smallest unit */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);       nhstepm is the number of hstepm from age to agelim 
       for (j=1; j<= nlstate+1 ; j ++) {       nstepm is the number of stepm from age to agelin. 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       Look at hpijx to understand the reason of that which relies in memory size
         else fprintf(ficgp," \%%*lf (\%%*lf)");       and note for a fixed period like estepm months */
 }      /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fprintf(ficgp,"\" t\"\" w l 0,");       survival function given by stepm (the optimization length). Unfortunately it
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);       means that if the survival funtion is printed only each two years of age and if
       for (j=1; j<= nlstate+1 ; j ++) {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       results. So we changed our mind and took the option of the best precision.
   else fprintf(ficgp," \%%*lf (\%%*lf)");    */
 }      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  
       else fprintf(ficgp,"\" t\"\" w l 0,");    agelim=AGESUP;
     }    /* If stepm=6 months */
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
   }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
        
   /*3eme*/  /* nhstepm age range expressed in number of stepm */
     nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   for (k1=1; k1<= m ; k1 ++) {    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     for (cpt=1; cpt<= nlstate ; cpt ++) {    /* if (stepm >= YEARM) hstepm=1;*/
       k=2+nlstate*(cpt-1);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       for (i=1; i< nlstate ; i ++) {  
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);    for (age=bage; age<=fage; age ++){ 
       }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     }      /* if (stepm >= YEARM) hstepm=1;*/
   }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
    
   /* CV preval stat */      /* If stepm=6 months */
   for (k1=1; k1<= m ; k1 ++) {      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     for (cpt=1; cpt<nlstate ; cpt ++) {         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       k=3;      
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for (i=1; i< nlstate ; i ++)      
         fprintf(ficgp,"+$%d",k+i+1);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);      
            printf("%d|",(int)age);fflush(stdout);
       l=3+(nlstate+ndeath)*cpt;      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);      
       for (i=1; i< nlstate ; i ++) {      /* Computing expectancies */
         l=3+(nlstate+ndeath)*cpt;      for(i=1; i<=nlstate;i++)
         fprintf(ficgp,"+$%d",l+i+1);        for(j=1; j<=nlstate;j++)
       }          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);              eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            
     }            /* 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]);*/
   }    
           }
   /* proba elementaires */  
    for(i=1,jk=1; i <=nlstate; i++){      fprintf(ficreseij,"%3.0f",age );
     for(k=1; k <=(nlstate+ndeath); k++){      for(i=1; i<=nlstate;i++){
       if (k != i) {        eip=0;
         for(j=1; j <=ncovmodel; j++){        for(j=1; j<=nlstate;j++){
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/          eip +=eij[i][j][(int)age];
           /*fprintf(ficgp,"%s",alph[1]);*/          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);        }
           jk++;        fprintf(ficreseij,"%9.4f", eip );
           fprintf(ficgp,"\n");      }
         }      fprintf(ficreseij,"\n");
       }      
     }    }
     }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
   for(jk=1; jk <=m; jk++) {    fprintf(ficlog,"\n");
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);    
    i=1;  }
    for(k2=1; k2<=nlstate; k2++) {  
      k3=i;  void cvevsij(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[] )
      for(k=1; k<=(nlstate+ndeath); k++) {  
        if (k != k2){  {
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    /* Covariances of health expectancies eij and of total life expectancies according
 ij=1;     to initial status i, ei. .
         for(j=3; j <=ncovmodel; j++) {    */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    int nhstepma, nstepma; /* Decreasing with age */
             ij++;    double age, agelim, hf;
           }    double ***p3matp, ***p3matm, ***varhe;
           else    double **dnewm,**doldm;
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    double *xp, *xm;
         }    double **gp, **gm;
           fprintf(ficgp,")/(1");    double ***gradg, ***trgradg;
            int theta;
         for(k1=1; k1 <=nlstate; k1++){    
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    double eip, vip;
 ij=1;  
           for(j=3; j <=ncovmodel; j++){    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    xp=vector(1,npar);
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    xm=vector(1,npar);
             ij++;    dnewm=matrix(1,nlstate*nlstate,1,npar);
           }    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
           else    
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    pstamp(ficresstdeij);
           }    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
           fprintf(ficgp,")");    fprintf(ficresstdeij,"# Age");
         }    for(i=1; i<=nlstate;i++){
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);      for(j=1; j<=nlstate;j++)
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
         i=i+ncovmodel;      fprintf(ficresstdeij," e%1d. ",i);
        }    }
      }    fprintf(ficresstdeij,"\n");
    }  
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    pstamp(ficrescveij);
   }    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
        fprintf(ficrescveij,"# Age");
   fclose(ficgp);    for(i=1; i<=nlstate;i++)
   /* end gnuplot */      for(j=1; j<=nlstate;j++){
            cptj= (j-1)*nlstate+i;
 chdir(path);        for(i2=1; i2<=nlstate;i2++)
              for(j2=1; j2<=nlstate;j2++){
     free_ivector(wav,1,imx);            cptj2= (j2-1)*nlstate+i2;
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);            if(cptj2 <= cptj)
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);                fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
     free_ivector(num,1,n);          }
     free_vector(agedc,1,n);      }
     /*free_matrix(covar,1,NCOVMAX,1,n);*/    fprintf(ficrescveij,"\n");
     fclose(ficparo);    
     fclose(ficres);    if(estepm < stepm){
     /*  }*/      printf ("Problem %d lower than %d\n",estepm, stepm);
        }
    /*________fin mle=1_________*/    else  hstepm=estepm;   
        /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
       * if stepm=24 months pijx are given only every 2 years and by summing them
     /* No more information from the sample is required now */     * we are calculating an estimate of the Life Expectancy assuming a linear 
   /* Reads comments: lines beginning with '#' */     * progression in between and thus overestimating or underestimating according
   while((c=getc(ficpar))=='#' && c!= EOF){     * to the curvature of the survival function. If, for the same date, we 
     ungetc(c,ficpar);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     fgets(line, MAXLINE, ficpar);     * to compare the new estimate of Life expectancy with the same linear 
     puts(line);     * hypothesis. A more precise result, taking into account a more precise
     fputs(line,ficparo);     * curvature will be obtained if estepm is as small as stepm. */
   }  
   ungetc(c,ficpar);    /* 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. 
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);       nhstepm is the number of hstepm from age to agelim 
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);       nstepm is the number of stepm from age to agelin. 
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);       Look at hpijx to understand the reason of that which relies in memory size
 /*--------- index.htm --------*/       and note for a fixed period like estepm months */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   strcpy(optionfilehtm,optionfile);       survival function given by stepm (the optimization length). Unfortunately it
   strcat(optionfilehtm,".htm");       means that if the survival funtion is printed only each two years of age and if
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     printf("Problem with %s \n",optionfilehtm);goto end;       results. So we changed our mind and took the option of the best precision.
   }    */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">  
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    /* If stepm=6 months */
 Total number of observations=%d <br>    /* nhstepm age range expressed in number of stepm */
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>    agelim=AGESUP;
 <hr  size=\"2\" color=\"#EC5E5E\">    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
 <li>Outputs files<br><br>\n    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    /* if (stepm >= YEARM) hstepm=1;*/
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>    
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    gp=matrix(0,nhstepm,1,nlstate*nlstate);
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>    gm=matrix(0,nhstepm,1,nlstate*nlstate);
         - Prevalences and population forecasting: <a href=\"f%s\">f%s</a> <br>  
 <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);    for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
  fprintf(fichtm," <li>Graphs</li><p>");      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
  m=cptcoveff;      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  
       /* If stepm=6 months */
  j1=0;      /* Computed by stepm unit matrices, product of hstepma matrices, stored
  for(k1=1; k1<=m;k1++){         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
    for(i1=1; i1<=ncodemax[k1];i1++){      
        j1++;      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
        if (cptcovn > 0) {  
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");      /* Computing  Variances of health expectancies */
          for (cpt=1; cpt<=cptcoveff;cpt++)      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);         decrease memory allocation */
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      for(theta=1; theta <=npar; theta++){
        }        for(i=1; i<=npar; i++){ 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);              xm[i] = x[i] - (i==theta ?delti[theta]:0);
        for(cpt=1; cpt<nlstate;cpt++){        }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
        }    
     for(cpt=1; cpt<=nlstate;cpt++) {        for(j=1; j<= nlstate; j++){
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident          for(i=1; i<=nlstate; i++){
 interval) in state (%d): v%s%d%d.gif <br>            for(h=0; h<=nhstepm-1; h++){
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);                gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
      }              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
      for(cpt=1; cpt<=nlstate;cpt++) {            }
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>          }
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        }
      }       
      fprintf(fichtm,"\n<br>- Total life expectancy by age and        for(ij=1; ij<= nlstate*nlstate; ij++)
 health expectancies in states (1) and (2): e%s%d.gif<br>          for(h=0; h<=nhstepm-1; h++){
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
 fprintf(fichtm,"\n</body>");          }
    }      }/* End theta */
  }      
 fclose(fichtm);      
       for(h=0; h<=nhstepm-1; h++)
   /*--------------- Prevalence limit --------------*/        for(j=1; j<=nlstate*nlstate;j++)
            for(theta=1; theta <=npar; theta++)
   strcpy(filerespl,"pl");            trgradg[h][j][theta]=gradg[h][theta][j];
   strcat(filerespl,fileres);      
   if((ficrespl=fopen(filerespl,"w"))==NULL) {  
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;       for(ij=1;ij<=nlstate*nlstate;ij++)
   }        for(ji=1;ji<=nlstate*nlstate;ji++)
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          varhe[ij][ji][(int)age] =0.;
   fprintf(ficrespl,"#Prevalence limit\n");  
   fprintf(ficrespl,"#Age ");       printf("%d|",(int)age);fflush(stdout);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   fprintf(ficrespl,"\n");       for(h=0;h<=nhstepm-1;h++){
          for(k=0;k<=nhstepm-1;k++){
   prlim=matrix(1,nlstate,1,nlstate);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(ij=1;ij<=nlstate*nlstate;ij++)
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for(ji=1;ji<=nlstate*nlstate;ji++)
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        }
   k=0;      }
   agebase=agemin;  
   agelim=agemax;      /* Computing expectancies */
   ftolpl=1.e-10;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   i1=cptcoveff;      for(i=1; i<=nlstate;i++)
   if (cptcovn < 1){i1=1;}        for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   for(cptcov=1;cptcov<=i1;cptcov++){            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            
         k=k+1;            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/  
         fprintf(ficrespl,"\n#******");          }
         for(j=1;j<=cptcoveff;j++)  
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      fprintf(ficresstdeij,"%3.0f",age );
         fprintf(ficrespl,"******\n");      for(i=1; i<=nlstate;i++){
                eip=0.;
         for (age=agebase; age<=agelim; age++){        vip=0.;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        for(j=1; j<=nlstate;j++){
           fprintf(ficrespl,"%.0f",age );          eip += eij[i][j][(int)age];
           for(i=1; i<=nlstate;i++)          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
           fprintf(ficrespl," %.5f", prlim[i][i]);            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           fprintf(ficrespl,"\n");          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         }        }
       }        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
     }      }
   fclose(ficrespl);      fprintf(ficresstdeij,"\n");
   
   /*------------- h Pij x at various ages ------------*/      fprintf(ficrescveij,"%3.0f",age );
        for(i=1; i<=nlstate;i++)
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        for(j=1; j<=nlstate;j++){
   if((ficrespij=fopen(filerespij,"w"))==NULL) {          cptj= (j-1)*nlstate+i;
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;          for(i2=1; i2<=nlstate;i2++)
   }            for(j2=1; j2<=nlstate;j2++){
   printf("Computing pij: result on file '%s' \n", filerespij);              cptj2= (j2-1)*nlstate+i2;
                if(cptj2 <= cptj)
   stepsize=(int) (stepm+YEARM-1)/YEARM;                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   /*if (stepm<=24) stepsize=2;*/            }
         }
   agelim=AGESUP;      fprintf(ficrescveij,"\n");
   hstepm=stepsize*YEARM; /* Every year of age */     
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    }
      free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   k=0;    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   for(cptcov=1;cptcov<=i1;cptcov++){    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       k=k+1;    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fprintf(ficrespij,"\n#****** ");    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for(j=1;j<=cptcoveff;j++)    printf("\n");
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficlog,"\n");
         fprintf(ficrespij,"******\n");  
            free_vector(xm,1,npar);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    free_vector(xp,1,npar);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
           oldm=oldms;savm=savms;  }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    
           fprintf(ficrespij,"# Age");  /************ Variance ******************/
           for(i=1; i<=nlstate;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[])
             for(j=1; j<=nlstate+ndeath;j++)  {
               fprintf(ficrespij," %1d-%1d",i,j);    /* Variance of health expectancies */
           fprintf(ficrespij,"\n");    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
           for (h=0; h<=nhstepm; h++){    /* double **newm;*/
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    double **dnewm,**doldm;
             for(i=1; i<=nlstate;i++)    double **dnewmp,**doldmp;
               for(j=1; j<=nlstate+ndeath;j++)    int i, j, nhstepm, hstepm, h, nstepm ;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    int k, cptcode;
             fprintf(ficrespij,"\n");    double *xp;
           }    double **gp, **gm;  /* for var eij */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double ***gradg, ***trgradg; /*for var eij */
           fprintf(ficrespij,"\n");    double **gradgp, **trgradgp; /* for var p point j */
         }    double *gpp, *gmp; /* for var p point j */
     }    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   }    double ***p3mat;
     double age,agelim, hf;
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/    double ***mobaverage;
     int theta;
   fclose(ficrespij);    char digit[4];
     char digitp[25];
   if(stepm == 1) {  
   /*---------- Forecasting ------------------*/    char fileresprobmorprev[FILENAMELENGTH];
   calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;  
     if(popbased==1){
   /*printf("calage= %f", calagedate);*/      if(mobilav!=0)
          strcpy(digitp,"-populbased-mobilav-");
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      else strcpy(digitp,"-populbased-nomobil-");
     }
     else 
   strcpy(fileresf,"f");      strcpy(digitp,"-stablbased-");
   strcat(fileresf,fileres);  
   if((ficresf=fopen(fileresf,"w"))==NULL) {    if (mobilav!=0) {
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   }      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   printf("Computing forecasting: result on file '%s' \n", fileresf);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
   free_matrix(mint,1,maxwav,1,n);      }
   free_matrix(anint,1,maxwav,1,n);    }
   free_matrix(agev,1,maxwav,1,imx);  
   /* Mobile average */    strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
   if (mobilav==1) {    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    strcat(fileresprobmorprev,fileres);
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       for (i=1; i<=nlstate;i++)      printf("Problem with resultfile: %s\n", fileresprobmorprev);
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           mobaverage[(int)agedeb][i][cptcod]=0.;    }
        printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     for (agedeb=bage+4; agedeb<=fage; agedeb++){   
       for (i=1; i<=nlstate;i++){    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    pstamp(ficresprobmorprev);
           for (cpt=0;cpt<=4;cpt++){    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);
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           }    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      fprintf(ficresprobmorprev," p.%-d SE",j);
         }      for(i=1; i<=nlstate;i++)
       }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }      }  
   }    fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
   stepsize=(int) (stepm+YEARM-1)/YEARM;    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
   if (stepm<=12) stepsize=1;    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);
   agelim=AGESUP;  /*   } */
   /*hstepm=stepsize*YEARM; *//* Every year of age */    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   hstepm=1;    pstamp(ficresvij);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
   yp1=modf(dateintmean,&yp);    if(popbased==1)
   anprojmean=yp;      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
   yp2=modf((yp1*12),&yp);    else
   mprojmean=yp;      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   yp1=modf((yp2*30.5),&yp);    fprintf(ficresvij,"# Age");
   jprojmean=yp;    for(i=1; i<=nlstate;i++)
   if(jprojmean==0) jprojmean=1;      for(j=1; j<=nlstate;j++)
   if(mprojmean==0) jprojmean=1;        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  
     xp=vector(1,npar);
   if (popforecast==1) {    dnewm=matrix(1,nlstate,1,npar);
     if((ficpop=fopen(popfile,"r"))==NULL)    {    doldm=matrix(1,nlstate,1,nlstate);
       printf("Problem with population file : %s\n",popfile);goto end;    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     }    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     popage=ivector(0,AGESUP);  
     popeffectif=vector(0,AGESUP);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     popcount=vector(0,AGESUP);    gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
     i=1;      trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)    
       {    if(estepm < stepm){
         i=i+1;      printf ("Problem %d lower than %d\n",estepm, stepm);
       }    }
     imx=i;    else  hstepm=estepm;   
        /* For example we decided to compute the life expectancy with the smallest unit */
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   }       nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
   for(cptcov=1;cptcov<=i1;cptcov++){       Look at function hpijx to understand why (it is linked to memory size questions) */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       k=k+1;       survival function given by stepm (the optimization length). Unfortunately it
       fprintf(ficresf,"\n#******");       means that if the survival funtion is printed every two years of age and if
       for(j=1;j<=cptcoveff;j++) {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       results. So we changed our mind and took the option of the best precision.
       }    */
       fprintf(ficresf,"******\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       fprintf(ficresf,"# StartingAge FinalAge");    agelim = AGESUP;
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       if (popforecast==1)  fprintf(ficresf," [Population]");      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
          nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       for (cpt=0; cpt<4;cpt++) {      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fprintf(ficresf,"\n");      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);        gp=matrix(0,nhstepm,1,nlstate);
       gm=matrix(0,nhstepm,1,nlstate);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(bage-((int)calagedate %12)/12.); agedeb--){ /* If stepm=6 months */  
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
         nhstepm = nhstepm/hstepm;      for(theta=1; theta <=npar; theta++){
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        }
         oldm=oldms;savm=savms;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
          
         for (h=0; h<=nhstepm; h++){        if (popbased==1) {
           if (h==(int) (calagedate+YEARM*cpt)) {          if(mobilav ==0){
             fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);            for(i=1; i<=nlstate;i++)
           }              prlim[i][i]=probs[(int)age][i][ij];
           for(j=1; j<=nlstate+ndeath;j++) {          }else{ /* mobilav */ 
             kk1=0.;kk2=0;            for(i=1; i<=nlstate;i++)
             for(i=1; i<=nlstate;i++) {                      prlim[i][i]=mobaverage[(int)age][i][ij];
               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];        for(j=1; j<= nlstate; j++){
                 /* fprintf(ficresf," p3=%.3f p=%.3f ", p3mat[i][j][h], probs[(int)(agedeb)+1][i][cptcod]);*/          for(h=0; h<=nhstepm; h++){
               }            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               gp[h][j] += prlim[i][i]*p3mat[i][j][h];
               if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];          }
             }        }
                  /* This for computing probability of death (h=1 means
             if (h==(int)(calagedate+12*cpt)){           computed over hstepm matrices product = hstepm*stepm months) 
               fprintf(ficresf," %.3f", kk1);           as a weighted average of prlim.
                      */
               if (popforecast==1) fprintf(ficresf," [%.f]", kk2);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
             }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
           }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }        }    
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        /* end probability of death */
       }  
       }        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
     }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   if (popforecast==1) {   
     free_ivector(popage,0,AGESUP);        if (popbased==1) {
     free_vector(popeffectif,0,AGESUP);          if(mobilav ==0){
     free_vector(popcount,0,AGESUP);            for(i=1; i<=nlstate;i++)
   }              prlim[i][i]=probs[(int)age][i][ij];
   free_imatrix(s,1,maxwav+1,1,n);          }else{ /* mobilav */ 
   free_vector(weight,1,n);            for(i=1; i<=nlstate;i++)
   fclose(ficresf);              prlim[i][i]=mobaverage[(int)age][i][ij];
   }/* End forecasting */          }
   else{        }
     erreur=108;  
     printf("Error %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d\n", erreur, stepm);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
   }          for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   /*---------- Health expectancies and variances ------------*/              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
   strcpy(filerest,"t");        }
   strcat(filerest,fileres);        /* This for computing probability of death (h=1 means
   if((ficrest=fopen(filerest,"w"))==NULL) {           computed over hstepm matrices product = hstepm*stepm months) 
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;           as a weighted average of prlim.
   }        */
   printf("Computing Total LEs with variances: file '%s' \n", filerest);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
   strcpy(filerese,"e");        }    
   strcat(filerese,fileres);        /* end probability of death */
   if((ficreseij=fopen(filerese,"w"))==NULL) {  
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);        for(j=1; j<= nlstate; j++) /* vareij */
   }          for(h=0; h<=nhstepm; h++){
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
  strcpy(fileresv,"v");  
   strcat(fileresv,fileres);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);        }
   }  
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);      } /* End theta */
   
   k=0;      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      for(h=0; h<=nhstepm; h++) /* veij */
       k=k+1;        for(j=1; j<=nlstate;j++)
       fprintf(ficrest,"\n#****** ");          for(theta=1; theta <=npar; theta++)
       for(j=1;j<=cptcoveff;j++)            trgradg[h][j][theta]=gradg[h][theta][j];
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficrest,"******\n");      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
       fprintf(ficreseij,"\n#****** ");          trgradgp[j][theta]=gradgp[theta][j];
       for(j=1;j<=cptcoveff;j++)    
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficreseij,"******\n");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
       fprintf(ficresvij,"\n#****** ");        for(j=1;j<=nlstate;j++)
       for(j=1;j<=cptcoveff;j++)          vareij[i][j][(int)age] =0.;
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficresvij,"******\n");      for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
       oldm=oldms;savm=savms;          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);            for(i=1;i<=nlstate;i++)
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            for(j=1;j<=nlstate;j++)
       oldm=oldms;savm=savms;              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);        }
            }
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);      /* pptj */
       fprintf(ficrest,"\n");      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
              matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       hf=1;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
       if (stepm >= YEARM) hf=stepm/YEARM;        for(i=nlstate+1;i<=nlstate+ndeath;i++)
       epj=vector(1,nlstate+1);          varppt[j][i]=doldmp[j][i];
       for(age=bage; age <=fage ;age++){      /* end ppptj */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      /*  x centered again */
         if (popbased==1) {      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
           for(i=1; i<=nlstate;i++)      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
             prlim[i][i]=probs[(int)age][i][k];   
         }      if (popbased==1) {
                if(mobilav ==0){
         fprintf(ficrest," %.0f",age);          for(i=1; i<=nlstate;i++)
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){            prlim[i][i]=probs[(int)age][i][ij];
           for(i=1, epj[j]=0.;i <=nlstate;i++) {        }else{ /* mobilav */ 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];          for(i=1; i<=nlstate;i++)
           }            prlim[i][i]=mobaverage[(int)age][i][ij];
           epj[nlstate+1] +=epj[j];        }
         }      }
         for(i=1, vepp=0.;i <=nlstate;i++)               
           for(j=1;j <=nlstate;j++)      /* This for computing probability of death (h=1 means
             vepp += vareij[i][j][(int)age];         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));         as a weighted average of prlim.
         for(j=1;j <=nlstate;j++){      */
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         }        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
         fprintf(ficrest,"\n");          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }      }    
     }      /* end probability of death */
   }  
              fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
              for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
  fclose(ficreseij);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
  fclose(ficresvij);        }
   fclose(ficrest);      } 
   fclose(ficpar);      fprintf(ficresprobmorprev,"\n");
   free_vector(epj,1,nlstate+1);  
   /*  scanf("%d ",i); */      fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
   /*------- Variance limit prevalence------*/          for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
 strcpy(fileresvpl,"vpl");        }
   strcat(fileresvpl,fileres);      fprintf(ficresvij,"\n");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {      free_matrix(gp,0,nhstepm,1,nlstate);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);      free_matrix(gm,0,nhstepm,1,nlstate);
     exit(0);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   }      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
  k=0;    free_vector(gpp,nlstate+1,nlstate+ndeath);
  for(cptcov=1;cptcov<=i1;cptcov++){    free_vector(gmp,nlstate+1,nlstate+ndeath);
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
      k=k+1;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
      fprintf(ficresvpl,"\n#****** ");    fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
      for(j=1;j<=cptcoveff;j++)    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
      fprintf(ficresvpl,"******\n");  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
        /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
      varpl=matrix(1,nlstate,(int) bage, (int) fage);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
      oldm=oldms;savm=savms;    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
    }    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
  }    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   fclose(ficresvpl);    /*  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);
   */
   /*---------- End : free ----------------*/  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
    
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    free_vector(xp,1,npar);
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    free_matrix(doldm,1,nlstate,1,nlstate);
      free_matrix(dnewm,1,nlstate,1,npar);
      free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);    fclose(ficresprobmorprev);
      fflush(ficgp);
   free_matrix(matcov,1,npar,1,npar);    fflush(fichtm); 
   free_vector(delti,1,npar);  }  /* end varevsij */
    
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   if(erreur >0)  {
     printf("End of Imach with error %d\n",erreur);    /* Variance of prevalence limit */
   else   printf("End of Imach\n");    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */    double **newm;
      double **dnewm,**doldm;
   /* 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);*/    int i, j, nhstepm, hstepm;
   /*printf("Total time was %d uSec.\n", total_usecs);*/    int k, cptcode;
   /*------ End -----------*/    double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
  end:    double age,agelim;
 #ifdef windows    int theta;
  chdir(pathcd);    
 #endif    pstamp(ficresvpl);
      fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
  system("..\\gp37mgw\\wgnuplot graph.plt");    fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
 #ifdef windows        fprintf(ficresvpl," %1d-%1d",i,i);
   while (z[0] != 'q') {    fprintf(ficresvpl,"\n");
     chdir(pathcd);  
     printf("\nType e to edit output files, c to start again, and q for exiting: ");    xp=vector(1,npar);
     scanf("%s",z);    dnewm=matrix(1,nlstate,1,npar);
     if (z[0] == 'c') system("./imach");    doldm=matrix(1,nlstate,1,nlstate);
     else if (z[0] == 'e') {    
       chdir(path);    hstepm=1*YEARM; /* Every year of age */
       system(optionfilehtm);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     }    agelim = AGESUP;
     else if (z[0] == 'q') exit(0);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   }      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
 #endif      if (stepm >= YEARM) hstepm=1;
 }      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     pstamp(ficresprobcov);
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     pstamp(ficresprobcor);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcor,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
    xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     fprintf(fichtm,"\n");
   
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
   standard deviations wide on each axis. <br>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_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, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates 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",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   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), e<sup>ij</sup> 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 (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,"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). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %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;
     int vpopbased=0;
   
     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);
           goto end;
         }
         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("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",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); */
         /*      } */
       }
     
   
       /* 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);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       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);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- 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(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);
   
       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(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;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(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;
           cvevsij(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);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# 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 (vpopbased==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(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);
     }
   }
   
   
   

Removed from v.1.21  
changed lines
  Added in v.1.129


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