Diff for /imach/src/imach.c between versions 1.14 and 1.120

version 1.14, 2002/02/20 17:05:44 version 1.120, 2006/03/16 15:10:38
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 1.120  2006/03/16 15:10:38  lievre
   individuals from different ages are interviewed on their health status    (Module): refinements in the computation of lli if
   or degree of  disability. At least a second wave of interviews    status=-2 in order to have more reliable computation if stepm is
   ("longitudinal") should  measure each new individual health status.    not 1 month. Version 0.98f
   Health expectancies are computed from the transistions observed between  
   waves and are computed for each degree of severity of disability (number    Revision 1.119  2006/03/15 17:42:26  brouard
   of life states). More degrees you consider, more time is necessary to    (Module): Bug if status = -2, the loglikelihood was
   reach the Maximum Likelihood of the parameters involved in the model.    computed as likelihood omitting the logarithm. Version O.98e
   The simplest model is the multinomial logistic model where pij is  
   the probabibility to be observed in state j at the second wave conditional    Revision 1.118  2006/03/14 18:20:07  brouard
   to be observed in state i at the first wave. Therefore the model is:    (Module): varevsij Comments added explaining the second
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    table of variances if popbased=1 .
   is a covariate. If you want to have a more complex model than "constant and    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   age", you should modify the program where the markup    (Module): Function pstamp added
     *Covariates have to be included here again* invites you to do it.    (Module): Version 0.98d
   More covariates you add, less is the speed of the convergence.  
     Revision 1.117  2006/03/14 17:16:22  brouard
   The advantage that this computer programme claims, comes from that if the    (Module): varevsij Comments added explaining the second
   delay between waves is not identical for each individual, or if some    table of variances if popbased=1 .
   individual missed an interview, the information is not rounded or lost, but    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   taken into account using an interpolation or extrapolation.    (Module): Function pstamp added
   hPijx is the probability to be    (Module): Version 0.98d
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Revision 1.116  2006/03/06 10:29:27  brouard
   unobserved intermediate  states. This elementary transition (by month or    (Module): Variance-covariance wrong links and
   quarter trimester, semester or year) is model as a multinomial logistic.    varian-covariance of ej. is needed (Saito).
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply hPijx.    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Revision 1.114  2006/02/26 12:57:58  brouard
      (Module): Some improvements in processing parameter
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    filename with strsep.
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.113  2006/02/24 14:20:24  brouard
   from the European Union.    (Module): Memory leaks checks with valgrind and:
   It is copyrighted identically to a GNU software product, ie programme and    datafile was not closed, some imatrix were not freed and on matrix
   software can be distributed freely for non commercial use. Latest version    allocation too.
   can be accessed at http://euroreves.ined.fr/imach .  
   **********************************************************************/    Revision 1.112  2006/01/30 09:55:26  brouard
      (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #include <math.h>  
 #include <stdio.h>    Revision 1.111  2006/01/25 20:38:18  brouard
 #include <stdlib.h>    (Module): Lots of cleaning and bugs added (Gompertz)
 #include <unistd.h>    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
 #define MAXLINE 256  
 #define FILENAMELENGTH 80    Revision 1.110  2006/01/25 00:51:50  brouard
 /*#define DEBUG*/    (Module): Lots of cleaning and bugs added (Gompertz)
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.109  2006/01/24 19:37:15  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    (Module): Comments (lines starting with a #) are allowed in data.
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.108  2006/01/19 18:05:42  lievre
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Gnuplot problem appeared...
     To be fixed
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.107  2006/01/19 16:20:37  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Test existence of gnuplot in imach path
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.106  2006/01/19 13:24:36  brouard
 #define YEARM 12. /* Number of months per year */    Some cleaning and links added in html output
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.105  2006/01/05 20:23:19  lievre
     *** empty log message ***
   
 int nvar;    Revision 1.104  2005/09/30 16:11:43  lievre
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    (Module): sump fixed, loop imx fixed, and simplifications.
 int npar=NPARMAX;    (Module): If the status is missing at the last wave but we know
 int nlstate=2; /* Number of live states */    that the person is alive, then we can code his/her status as -2
 int ndeath=1; /* Number of dead states */    (instead of missing=-1 in earlier versions) and his/her
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    contributions to the likelihood is 1 - Prob of dying from last
 int popbased=0, fprev,lprev;    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.103  2005/09/30 15:54:49  lievre
 int jmin, jmax; /* min, max spacing between 2 waves */    (Module): sump fixed, loop imx fixed, and simplifications.
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.102  2004/09/15 17:31:30  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Add the possibility to read data file including tab characters.
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.101  2004/09/15 10:38:38  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Fix on curr_time
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;  
 FILE *ficgp, *fichtm,*ficresprob;    Revision 1.100  2004/07/12 18:29:06  brouard
 FILE *ficreseij;    Add version for Mac OS X. Just define UNIX in Makefile
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.99  2004/06/05 08:57:40  brouard
   char fileresv[FILENAMELENGTH];    *** empty log message ***
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.98  2004/05/16 15:05:56  brouard
     New version 0.97 . First attempt to estimate force of mortality
 #define NR_END 1    directly from the data i.e. without the need of knowing the health
 #define FREE_ARG char*    state at each age, but using a Gompertz model: log u =a + b*age .
 #define FTOL 1.0e-10    This is the basic analysis of mortality and should be done before any
     other analysis, in order to test if the mortality estimated from the
 #define NRANSI    cross-longitudinal survey is different from the mortality estimated
 #define ITMAX 200    from other sources like vital statistic data.
   
 #define TOL 2.0e-4    The same imach parameter file can be used but the option for mle should be -3.
   
 #define CGOLD 0.3819660    Agnès, who wrote this part of the code, tried to keep most of the
 #define ZEPS 1.0e-10    former routines in order to include the new code within the former code.
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     The output is very simple: only an estimate of the intercept and of
 #define GOLD 1.618034    the slope with 95% confident intervals.
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Current limitations:
     A) Even if you enter covariates, i.e. with the
 static double maxarg1,maxarg2;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    B) There is no computation of Life Expectancy nor Life Table.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.97  2004/02/20 13:25:42  lievre
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Version 0.96d. Population forecasting command line is (temporarily)
 #define rint(a) floor(a+0.5)    suppressed.
   
 static double sqrarg;    Revision 1.96  2003/07/15 15:38:55  brouard
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    rewritten within the same printf. Workaround: many printfs.
   
 int imx;    Revision 1.95  2003/07/08 07:54:34  brouard
 int stepm;    * imach.c (Repository):
 /* Stepm, step in month: minimum step interpolation*/    (Repository): Using imachwizard code to output a more meaningful covariance
     matrix (cov(a12,c31) instead of numbers.
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.94  2003/06/27 13:00:02  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Just cleaning
 double **pmmij, ***probs, ***mobaverage;  
     Revision 1.93  2003/06/25 16:33:55  brouard
 double *weight;    (Module): On windows (cygwin) function asctime_r doesn't
 int **s; /* Status */    exist so I changed back to asctime which exists.
 double *agedc, **covar, idx;    (Module): Version 0.96b
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.92  2003/06/25 16:30:45  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    (Module): On windows (cygwin) function asctime_r doesn't
 double ftolhess; /* Tolerance for computing hessian */    exist so I changed back to asctime which exists.
   
 /**************** split *************************/    Revision 1.91  2003/06/25 15:30:29  brouard
 static  int split( char *path, char *dirc, char *name )    * imach.c (Repository): Duplicated warning errors corrected.
 {    (Repository): Elapsed time after each iteration is now output. It
    char *s;                             /* pointer */    helps to forecast when convergence will be reached. Elapsed time
    int  l1, l2;                         /* length counters */    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.90  2003/06/24 12:34:15  brouard
    s = strrchr( path, '\\' );           /* find last / */    (Module): Some bugs corrected for windows. Also, when
    if ( s == NULL ) {                   /* no directory, so use current */    mle=-1 a template is output in file "or"mypar.txt with the design
 #if     defined(__bsd__)                /* get current working directory */    of the covariance matrix to be input.
       extern char       *getwd( );  
     Revision 1.89  2003/06/24 12:30:52  brouard
       if ( getwd( dirc ) == NULL ) {    (Module): Some bugs corrected for windows. Also, when
 #else    mle=-1 a template is output in file "or"mypar.txt with the design
       extern char       *getcwd( );    of the covariance matrix to be input.
   
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Revision 1.88  2003/06/23 17:54:56  brouard
 #endif    * 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.
          return( GLOCK_ERROR_GETCWD );  
       }    Revision 1.87  2003/06/18 12:26:01  brouard
       strcpy( name, path );             /* we've got it */    Version 0.96
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */    Revision 1.86  2003/06/17 20:04:08  brouard
       l2 = strlen( s );                 /* length of filename */    (Module): Change position of html and gnuplot routines and added
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    routine fileappend.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.85  2003/06/17 13:12:43  brouard
       dirc[l1-l2] = 0;                  /* add zero */    * imach.c (Repository): Check when date of death was earlier that
    }    current date of interview. It may happen when the death was just
    l1 = strlen( dirc );                 /* length of directory */    prior to the death. In this case, dh was negative and likelihood
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    was wrong (infinity). We still send an "Error" but patch by
    return( 0 );                         /* we're done */    assuming that the date of death was just one stepm after the
 }    interview.
     (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
 /******************************************/    memory allocation. But we also truncated to 8 characters (left
     truncation)
 void replace(char *s, char*t)    (Repository): No more line truncation errors.
 {  
   int i;    Revision 1.84  2003/06/13 21:44:43  brouard
   int lg=20;    * imach.c (Repository): Replace "freqsummary" at a correct
   i=0;    place. It differs from routine "prevalence" which may be called
   lg=strlen(t);    many times. Probs is memory consuming and must be used with
   for(i=0; i<= lg; i++) {    parcimony.
     (s[i] = t[i]);    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.83  2003/06/10 13:39:11  lievre
 }    *** empty log message ***
   
 int nbocc(char *s, char occ)    Revision 1.82  2003/06/05 15:57:20  brouard
 {    Add log in  imach.c and  fullversion number is now printed.
   int i,j=0;  
   int lg=20;  */
   i=0;  /*
   lg=strlen(s);     Interpolated Markov Chain
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Short summary of the programme:
   }    
   return j;    This program computes Healthy Life Expectancies from
 }    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     first survey ("cross") where individuals from different ages are
 void cutv(char *u,char *v, char*t, char occ)    interviewed on their health status or degree of disability (in the
 {    case of a health survey which is our main interest) -2- at least a
   int i,lg,j,p=0;    second wave of interviews ("longitudinal") which measure each change
   i=0;    (if any) in individual health status.  Health expectancies are
   for(j=0; j<=strlen(t)-1; j++) {    computed from the time spent in each health state according to a
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    model. More health states you consider, more time is necessary to reach the
   }    Maximum Likelihood of the parameters involved in the model.  The
     simplest model is the multinomial logistic model where pij is the
   lg=strlen(t);    probability to be observed in state j at the second wave
   for(j=0; j<p; j++) {    conditional to be observed in state i at the first wave. Therefore
     (u[j] = t[j]);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   }    'age' is age and 'sex' is a covariate. If you want to have a more
      u[p]='\0';    complex model than "constant and age", you should modify the program
     where the markup *Covariates have to be included here again* invites
    for(j=0; j<= lg; j++) {    you to do it.  More covariates you add, slower the
     if (j>=(p+1))(v[j-p-1] = t[j]);    convergence.
   }  
 }    The advantage of this computer programme, compared to a simple
     multinomial logistic model, is clear when the delay between waves is not
 /********************** nrerror ********************/    identical for each individual. Also, if a individual missed an
     intermediate interview, the information is lost, but taken into
 void nrerror(char error_text[])    account using an interpolation or extrapolation.  
 {  
   fprintf(stderr,"ERREUR ...\n");    hPijx is the probability to be observed in state i at age x+h
   fprintf(stderr,"%s\n",error_text);    conditional to the observed state i at age x. The delay 'h' can be
   exit(1);    split into an exact number (nh*stepm) of unobserved intermediate
 }    states. This elementary transition (by month, quarter,
 /*********************** vector *******************/    semester or year) is modelled as a multinomial logistic.  The hPx
 double *vector(int nl, int nh)    matrix is simply the matrix product of nh*stepm elementary matrices
 {    and the contribution of each individual to the likelihood is simply
   double *v;    hPijx.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Also this programme outputs the covariance matrix of the parameters but also
   return v-nl+NR_END;    of the life expectancies. It also computes the period (stable) prevalence. 
 }    
     Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 /************************ free vector ******************/             Institut national d'études démographiques, Paris.
 void free_vector(double*v, int nl, int nh)    This software have been partly granted by Euro-REVES, a concerted action
 {    from the European Union.
   free((FREE_ARG)(v+nl-NR_END));    It is copyrighted identically to a GNU software product, ie programme and
 }    software can be distributed freely for non commercial use. Latest version
     can be accessed at http://euroreves.ined.fr/imach .
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 {    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   int *v;    
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    **********************************************************************/
   if (!v) nrerror("allocation failure in ivector");  /*
   return v-nl+NR_END;    main
 }    read parameterfile
     read datafile
 /******************free ivector **************************/    concatwav
 void free_ivector(int *v, long nl, long nh)    freqsummary
 {    if (mle >= 1)
   free((FREE_ARG)(v+nl-NR_END));      mlikeli
 }    print results files
     if mle==1 
 /******************* imatrix *******************************/       computes hessian
 int **imatrix(long nrl, long nrh, long ncl, long nch)    read end of parameter file: agemin, agemax, bage, fage, estepm
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */        begin-prev-date,...
 {    open gnuplot file
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    open html file
   int **m;    period (stable) prevalence
       for age prevalim()
   /* allocate pointers to rows */    h Pij x
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    variance of p varprob
   if (!m) nrerror("allocation failure 1 in matrix()");    forecasting if prevfcast==1 prevforecast call prevalence()
   m += NR_END;    health expectancies
   m -= nrl;    Variance-covariance of DFLE
      prevalence()
       movingaverage()
   /* allocate rows and set pointers to them */    varevsij() 
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    if popbased==1 varevsij(,popbased)
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    total life expectancies
   m[nrl] += NR_END;    Variance of period (stable) prevalence
   m[nrl] -= ncl;   end
    */
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
    
   /* return pointer to array of pointers to rows */  
   return m;   
 }  #include <math.h>
   #include <stdio.h>
 /****************** free_imatrix *************************/  #include <stdlib.h>
 void free_imatrix(m,nrl,nrh,ncl,nch)  #include <string.h>
       int **m;  #include <unistd.h>
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */  #include <limits.h>
 {  #include <sys/types.h>
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  #include <sys/stat.h>
   free((FREE_ARG) (m+nrl-NR_END));  #include <errno.h>
 }  extern int errno;
   
 /******************* matrix *******************************/  /* #include <sys/time.h> */
 double **matrix(long nrl, long nrh, long ncl, long nch)  #include <time.h>
 {  #include "timeval.h"
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  
   double **m;  /* #include <libintl.h> */
   /* #define _(String) gettext (String) */
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  #define MAXLINE 256
   m += NR_END;  
   m -= nrl;  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define FILENAMELENGTH 132
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   m[nrl] -= ncl;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   return m;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 }  
   #define NINTERVMAX 8
 /*************************free matrix ************************/  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 {  #define NCOVMAX 8 /* Maximum number of covariates */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define MAXN 20000
   free((FREE_ARG)(m+nrl-NR_END));  #define YEARM 12. /* Number of months per year */
 }  #define AGESUP 130
   #define AGEBASE 40
 /******************* ma3x *******************************/  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #ifdef UNIX
 {  #define DIRSEPARATOR '/'
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define CHARSEPARATOR "/"
   double ***m;  #define ODIRSEPARATOR '\\'
   #else
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define DIRSEPARATOR '\\'
   if (!m) nrerror("allocation failure 1 in matrix()");  #define CHARSEPARATOR "\\"
   m += NR_END;  #define ODIRSEPARATOR '/'
   m -= nrl;  #endif
   
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  /* $Id$ */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /* $State$ */
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  char version[]="Imach version 0.98f, March 2006, INED-EUROREVES-Institut de longevite ";
   char fullversion[]="$Revision$ $Date$"; 
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  char strstart[80];
   char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  int nvar;
   m[nrl][ncl] += NR_END;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   m[nrl][ncl] -= nll;  int npar=NPARMAX;
   for (j=ncl+1; j<=nch; j++)  int nlstate=2; /* Number of live states */
     m[nrl][j]=m[nrl][j-1]+nlay;  int ndeath=1; /* Number of dead states */
    int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   for (i=nrl+1; i<=nrh; i++) {  int popbased=0;
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  int *wav; /* Number of waves for this individuual 0 is possible */
       m[i][j]=m[i][j-1]+nlay;  int maxwav; /* Maxim number of waves */
   }  int jmin, jmax; /* min, max spacing between 2 waves */
   return m;  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
 }  int gipmx, gsw; /* Global variables on the number of contributions 
                      to the likelihood and the sum of weights (done by funcone)*/
 /*************************free ma3x ************************/  int mle, weightopt;
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 {  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   free((FREE_ARG)(m[nrl]+ncl-NR_END));             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   free((FREE_ARG)(m+nrl-NR_END));  double jmean; /* Mean space between 2 waves */
 }  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 /***************** f1dim *************************/  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 extern int ncom;  FILE *ficlog, *ficrespow;
 extern double *pcom,*xicom;  int globpr; /* Global variable for printing or not */
 extern double (*nrfunc)(double []);  double fretone; /* Only one call to likelihood */
    long ipmx; /* Number of contributions */
 double f1dim(double x)  double sw; /* Sum of weights */
 {  char filerespow[FILENAMELENGTH];
   int j;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   double f;  FILE *ficresilk;
   double *xt;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
    FILE *ficresprobmorprev;
   xt=vector(1,ncom);  FILE *fichtm, *fichtmcov; /* Html File */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  FILE *ficreseij;
   f=(*nrfunc)(xt);  char filerese[FILENAMELENGTH];
   free_vector(xt,1,ncom);  FILE *ficresstdeij;
   return f;  char fileresstde[FILENAMELENGTH];
 }  FILE *ficrescveij;
   char filerescve[FILENAMELENGTH];
 /*****************brent *************************/  FILE  *ficresvij;
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  char fileresv[FILENAMELENGTH];
 {  FILE  *ficresvpl;
   int iter;  char fileresvpl[FILENAMELENGTH];
   double a,b,d,etemp;  char title[MAXLINE];
   double fu,fv,fw,fx;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   double ftemp;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   double p,q,r,tol1,tol2,u,v,w,x,xm;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   double e=0.0;  char command[FILENAMELENGTH];
    int  outcmd=0;
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);  char filelog[FILENAMELENGTH]; /* Log file */
   for (iter=1;iter<=ITMAX;iter++) {  char filerest[FILENAMELENGTH];
     xm=0.5*(a+b);  char fileregp[FILENAMELENGTH];
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  char popfile[FILENAMELENGTH];
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  
     printf(".");fflush(stdout);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
 #ifdef DEBUG  
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  struct timezone tzp;
 #endif  extern int gettimeofday();
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  struct tm tmg, tm, tmf, *gmtime(), *localtime();
       *xmin=x;  long time_value;
       return fx;  extern long time();
     }  char strcurr[80], strfor[80];
     ftemp=fu;  
     if (fabs(e) > tol1) {  char *endptr;
       r=(x-w)*(fx-fv);  long lval;
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;  #define NR_END 1
       q=2.0*(q-r);  #define FREE_ARG char*
       if (q > 0.0) p = -p;  #define FTOL 1.0e-10
       q=fabs(q);  
       etemp=e;  #define NRANSI 
       e=d;  #define ITMAX 200 
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define TOL 2.0e-4 
       else {  
         d=p/q;  #define CGOLD 0.3819660 
         u=x+d;  #define ZEPS 1.0e-10 
         if (u-a < tol2 || b-u < tol2)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
           d=SIGN(tol1,xm-x);  
       }  #define GOLD 1.618034 
     } else {  #define GLIMIT 100.0 
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define TINY 1.0e-20 
     }  
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  static double maxarg1,maxarg2;
     fu=(*f)(u);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
     if (fu <= fx) {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
       if (u >= x) a=x; else b=x;    
       SHFT(v,w,x,u)  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
         SHFT(fv,fw,fx,fu)  #define rint(a) floor(a+0.5)
         } else {  
           if (u < x) a=u; else b=u;  static double sqrarg;
           if (fu <= fw || w == x) {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
             v=w;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
             w=u;  int agegomp= AGEGOMP;
             fv=fw;  
             fw=fu;  int imx; 
           } else if (fu <= fv || v == x || v == w) {  int stepm=1;
             v=u;  /* Stepm, step in month: minimum step interpolation*/
             fv=fu;  
           }  int estepm;
         }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   }  
   nrerror("Too many iterations in brent");  int m,nb;
   *xmin=x;  long *num;
   return fx;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double **pmmij, ***probs;
 /****************** mnbrak ***********************/  double *ageexmed,*agecens;
   double dateintmean=0;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  double *weight;
 {  int **s; /* Status */
   double ulim,u,r,q, dum;  double *agedc, **covar, idx;
   double fu;  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
    double *lsurv, *lpop, *tpop;
   *fa=(*func)(*ax);  
   *fb=(*func)(*bx);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   if (*fb > *fa) {  double ftolhess; /* Tolerance for computing hessian */
     SHFT(dum,*ax,*bx,dum)  
       SHFT(dum,*fb,*fa,dum)  /**************** split *************************/
       }  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   *cx=(*bx)+GOLD*(*bx-*ax);  {
   *fc=(*func)(*cx);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   while (*fb > *fc) {       the name of the file (name), its extension only (ext) and its first part of the name (finame)
     r=(*bx-*ax)*(*fb-*fc);    */ 
     q=(*bx-*cx)*(*fb-*fa);    char  *ss;                            /* pointer */
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    int   l1, l2;                         /* length counters */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);    l1 = strlen(path );                   /* length of path */
     if ((*bx-u)*(u-*cx) > 0.0) {    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       fu=(*func)(u);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     } else if ((*cx-u)*(u-ulim) > 0.0) {    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       fu=(*func)(u);      strcpy( name, path );               /* we got the fullname name because no directory */
       if (fu < *fc) {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
           SHFT(*fb,*fc,fu,(*func)(u))      /* get current working directory */
           }      /*    extern  char* getcwd ( char *buf , int len);*/
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       u=ulim;        return( GLOCK_ERROR_GETCWD );
       fu=(*func)(u);      }
     } else {      /* got dirc from getcwd*/
       u=(*cx)+GOLD*(*cx-*bx);      printf(" DIRC = %s \n",dirc);
       fu=(*func)(u);    } else {                              /* strip direcotry from path */
     }      ss++;                               /* after this, the filename */
     SHFT(*ax,*bx,*cx,u)      l2 = strlen( ss );                  /* length of filename */
       SHFT(*fa,*fb,*fc,fu)      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       }      strcpy( name, ss );         /* save file name */
 }      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       dirc[l1-l2] = 0;                    /* add zero */
 /*************** linmin ************************/      printf(" DIRC2 = %s \n",dirc);
     }
 int ncom;    /* We add a separator at the end of dirc if not exists */
 double *pcom,*xicom;    l1 = strlen( dirc );                  /* length of directory */
 double (*nrfunc)(double []);    if( dirc[l1-1] != DIRSEPARATOR ){
        dirc[l1] =  DIRSEPARATOR;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))      dirc[l1+1] = 0; 
 {      printf(" DIRC3 = %s \n",dirc);
   double brent(double ax, double bx, double cx,    }
                double (*f)(double), double tol, double *xmin);    ss = strrchr( name, '.' );            /* find last / */
   double f1dim(double x);    if (ss >0){
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,      ss++;
               double *fc, double (*func)(double));      strcpy(ext,ss);                     /* save extension */
   int j;      l1= strlen( name);
   double xx,xmin,bx,ax;      l2= strlen(ss)+1;
   double fx,fb,fa;      strncpy( finame, name, l1-l2);
        finame[l1-l2]= 0;
   ncom=n;    }
   pcom=vector(1,n);  
   xicom=vector(1,n);    return( 0 );                          /* we're done */
   nrfunc=func;  }
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  
     xicom[j]=xi[j];  /******************************************/
   }  
   ax=0.0;  void replace_back_to_slash(char *s, char*t)
   xx=1.0;  {
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    int i;
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    int lg=0;
 #ifdef DEBUG    i=0;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    lg=strlen(t);
 #endif    for(i=0; i<= lg; i++) {
   for (j=1;j<=n;j++) {      (s[i] = t[i]);
     xi[j] *= xmin;      if (t[i]== '\\') s[i]='/';
     p[j] += xi[j];    }
   }  }
   free_vector(xicom,1,n);  
   free_vector(pcom,1,n);  int nbocc(char *s, char occ)
 }  {
     int i,j=0;
 /*************** powell ************************/    int lg=20;
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    i=0;
             double (*func)(double []))    lg=strlen(s);
 {    for(i=0; i<= lg; i++) {
   void linmin(double p[], double xi[], int n, double *fret,    if  (s[i] == occ ) j++;
               double (*func)(double []));    }
   int i,ibig,j;    return j;
   double del,t,*pt,*ptt,*xit;  }
   double fp,fptt;  
   double *xits;  void cutv(char *u,char *v, char*t, char occ)
   pt=vector(1,n);  {
   ptt=vector(1,n);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
   xit=vector(1,n);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
   xits=vector(1,n);       gives u="abcedf" and v="ghi2j" */
   *fret=(*func)(p);    int i,lg,j,p=0;
   for (j=1;j<=n;j++) pt[j]=p[j];    i=0;
   for (*iter=1;;++(*iter)) {    for(j=0; j<=strlen(t)-1; j++) {
     fp=(*fret);      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     ibig=0;    }
     del=0.0;  
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    lg=strlen(t);
     for (i=1;i<=n;i++)    for(j=0; j<p; j++) {
       printf(" %d %.12f",i, p[i]);      (u[j] = t[j]);
     printf("\n");    }
     for (i=1;i<=n;i++) {       u[p]='\0';
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);     for(j=0; j<= lg; j++) {
 #ifdef DEBUG      if (j>=(p+1))(v[j-p-1] = t[j]);
       printf("fret=%lf \n",*fret);    }
 #endif  }
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);  /********************** nrerror ********************/
       if (fabs(fptt-(*fret)) > del) {  
         del=fabs(fptt-(*fret));  void nrerror(char error_text[])
         ibig=i;  {
       }    fprintf(stderr,"ERREUR ...\n");
 #ifdef DEBUG    fprintf(stderr,"%s\n",error_text);
       printf("%d %.12e",i,(*fret));    exit(EXIT_FAILURE);
       for (j=1;j<=n;j++) {  }
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  /*********************** vector *******************/
         printf(" x(%d)=%.12e",j,xit[j]);  double *vector(int nl, int nh)
       }  {
       for(j=1;j<=n;j++)    double *v;
         printf(" p=%.12e",p[j]);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       printf("\n");    if (!v) nrerror("allocation failure in vector");
 #endif    return v-nl+NR_END;
     }  }
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG  /************************ free vector ******************/
       int k[2],l;  void free_vector(double*v, int nl, int nh)
       k[0]=1;  {
       k[1]=-1;    free((FREE_ARG)(v+nl-NR_END));
       printf("Max: %.12e",(*func)(p));  }
       for (j=1;j<=n;j++)  
         printf(" %.12e",p[j]);  /************************ivector *******************************/
       printf("\n");  int *ivector(long nl,long nh)
       for(l=0;l<=1;l++) {  {
         for (j=1;j<=n;j++) {    int *v;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    if (!v) nrerror("allocation failure in ivector");
         }    return v-nl+NR_END;
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  }
       }  
 #endif  /******************free ivector **************************/
   void free_ivector(int *v, long nl, long nh)
   {
       free_vector(xit,1,n);    free((FREE_ARG)(v+nl-NR_END));
       free_vector(xits,1,n);  }
       free_vector(ptt,1,n);  
       free_vector(pt,1,n);  /************************lvector *******************************/
       return;  long *lvector(long nl,long nh)
     }  {
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    long *v;
     for (j=1;j<=n;j++) {    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       ptt[j]=2.0*p[j]-pt[j];    if (!v) nrerror("allocation failure in ivector");
       xit[j]=p[j]-pt[j];    return v-nl+NR_END;
       pt[j]=p[j];  }
     }  
     fptt=(*func)(ptt);  /******************free lvector **************************/
     if (fptt < fp) {  void free_lvector(long *v, long nl, long nh)
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  {
       if (t < 0.0) {    free((FREE_ARG)(v+nl-NR_END));
         linmin(p,xit,n,fret,func);  }
         for (j=1;j<=n;j++) {  
           xi[j][ibig]=xi[j][n];  /******************* imatrix *******************************/
           xi[j][n]=xit[j];  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         }       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
 #ifdef DEBUG  { 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         for(j=1;j<=n;j++)    int **m; 
           printf(" %.12e",xit[j]);    
         printf("\n");    /* allocate pointers to rows */ 
 #endif    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     }    m += NR_END; 
   }    m -= nrl; 
 }    
     
 /**** Prevalence limit ****************/    /* allocate rows and set pointers to them */ 
     m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 {    m[nrl] += NR_END; 
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    m[nrl] -= ncl; 
      matrix by transitions matrix until convergence is reached */    
     for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   int i, ii,j,k;    
   double min, max, maxmin, maxmax,sumnew=0.;    /* return pointer to array of pointers to rows */ 
   double **matprod2();    return m; 
   double **out, cov[NCOVMAX], **pmij();  } 
   double **newm;  
   double agefin, delaymax=50 ; /* Max number of years to converge */  /****************** free_imatrix *************************/
   void free_imatrix(m,nrl,nrh,ncl,nch)
   for (ii=1;ii<=nlstate+ndeath;ii++)        int **m;
     for (j=1;j<=nlstate+ndeath;j++){        long nch,ncl,nrh,nrl; 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);       /* free an int matrix allocated by imatrix() */ 
     }  { 
     free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
    cov[1]=1.;    free((FREE_ARG) (m+nrl-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){  /******************* matrix *******************************/
     newm=savm;  double **matrix(long nrl, long nrh, long ncl, long nch)
     /* Covariates have to be included here again */  {
      cov[2]=agefin;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
      double **m;
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    if (!m) nrerror("allocation failure 1 in matrix()");
       }    m += NR_END;
       for (k=1; k<=cptcovage;k++)    m -= nrl;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  
       for (k=1; k<=cptcovprod;k++)    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    m[nrl] -= ncl;
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  
     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    return m;
     /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
     savm=oldm;     */
     oldm=newm;  }
     maxmax=0.;  
     for(j=1;j<=nlstate;j++){  /*************************free matrix ************************/
       min=1.;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       max=0.;  {
       for(i=1; i<=nlstate; i++) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         sumnew=0;    free((FREE_ARG)(m+nrl-NR_END));
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  }
         prlim[i][j]= newm[i][j]/(1-sumnew);  
         max=FMAX(max,prlim[i][j]);  /******************* ma3x *******************************/
         min=FMIN(min,prlim[i][j]);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       }  {
       maxmin=max-min;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       maxmax=FMAX(maxmax,maxmin);    double ***m;
     }  
     if(maxmax < ftolpl){    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       return prlim;    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
   }    m -= nrl;
 }  
     m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 /*************** transition probabilities ***************/    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    m[nrl] -= ncl;
 {  
   double s1, s2;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   /*double t34;*/  
   int i,j,j1, nc, ii, jj;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     for(i=1; i<= nlstate; i++){    m[nrl][ncl] += NR_END;
     for(j=1; j<i;j++){    m[nrl][ncl] -= nll;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    for (j=ncl+1; j<=nch; j++) 
         /*s2 += param[i][j][nc]*cov[nc];*/      m[nrl][j]=m[nrl][j-1]+nlay;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    for (i=nrl+1; i<=nrh; i++) {
       }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       ps[i][j]=s2;      for (j=ncl+1; j<=nch; j++) 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/        m[i][j]=m[i][j-1]+nlay;
     }    }
     for(j=i+1; j<=nlstate+ndeath;j++){    return m; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    */
       }  }
       ps[i][j]=(s2);  
     }  /*************************free ma3x ************************/
   }  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     /*ps[3][2]=1;*/  {
     free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   for(i=1; i<= nlstate; i++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
      s1=0;    free((FREE_ARG)(m+nrl-NR_END));
     for(j=1; j<i; j++)  }
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)  /*************** function subdirf ***********/
       s1+=exp(ps[i][j]);  char *subdirf(char fileres[])
     ps[i][i]=1./(s1+1.);  {
     for(j=1; j<i; j++)    /* Caution optionfilefiname is hidden */
       ps[i][j]= exp(ps[i][j])*ps[i][i];    strcpy(tmpout,optionfilefiname);
     for(j=i+1; j<=nlstate+ndeath; j++)    strcat(tmpout,"/"); /* Add to the right */
       ps[i][j]= exp(ps[i][j])*ps[i][i];    strcat(tmpout,fileres);
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    return tmpout;
   } /* end i */  }
   
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  /*************** function subdirf2 ***********/
     for(jj=1; jj<= nlstate+ndeath; jj++){  char *subdirf2(char fileres[], char *preop)
       ps[ii][jj]=0;  {
       ps[ii][ii]=1;    
     }    /* Caution optionfilefiname is hidden */
   }    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
     strcat(tmpout,preop);
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    strcat(tmpout,fileres);
     for(jj=1; jj<= nlstate+ndeath; jj++){    return tmpout;
      printf("%lf ",ps[ii][jj]);  }
    }  
     printf("\n ");  /*************** function subdirf3 ***********/
     }  char *subdirf3(char fileres[], char *preop, char *preop2)
     printf("\n ");printf("%lf ",cov[2]);*/  {
 /*    
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    /* Caution optionfilefiname is hidden */
   goto end;*/    strcpy(tmpout,optionfilefiname);
     return ps;    strcat(tmpout,"/");
 }    strcat(tmpout,preop);
     strcat(tmpout,preop2);
 /**************** Product of 2 matrices ******************/    strcat(tmpout,fileres);
     return tmpout;
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  }
 {  
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  /***************** f1dim *************************/
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  extern int ncom; 
   /* in, b, out are matrice of pointers which should have been initialized  extern double *pcom,*xicom;
      before: only the contents of out is modified. The function returns  extern double (*nrfunc)(double []); 
      a pointer to pointers identical to out */   
   long i, j, k;  double f1dim(double x) 
   for(i=nrl; i<= nrh; i++)  { 
     for(k=ncolol; k<=ncoloh; k++)    int j; 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    double f;
         out[i][k] +=in[i][j]*b[j][k];    double *xt; 
    
   return out;    xt=vector(1,ncom); 
 }    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
     free_vector(xt,1,ncom); 
 /************* Higher Matrix Product ***************/    return f; 
   } 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  
 {  /*****************brent *************************/
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
      duration (i.e. until  { 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    int iter; 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    double a,b,d,etemp;
      (typically every 2 years instead of every month which is too big).    double fu,fv,fw,fx;
      Model is determined by parameters x and covariates have to be    double ftemp;
      included manually here.    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     double e=0.0; 
      */   
     a=(ax < cx ? ax : cx); 
   int i, j, d, h, k;    b=(ax > cx ? ax : cx); 
   double **out, cov[NCOVMAX];    x=w=v=bx; 
   double **newm;    fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
   /* Hstepm could be zero and should return the unit matrix */      xm=0.5*(a+b); 
   for (i=1;i<=nlstate+ndeath;i++)      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
     for (j=1;j<=nlstate+ndeath;j++){      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       oldm[i][j]=(i==j ? 1.0 : 0.0);      printf(".");fflush(stdout);
       po[i][j][0]=(i==j ? 1.0 : 0.0);      fprintf(ficlog,".");fflush(ficlog);
     }  #ifdef DEBUG
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */      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(h=1; h <=nhstepm; h++){      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
     for(d=1; d <=hstepm; d++){      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
       newm=savm;  #endif
       /* Covariates have to be included here again */      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
       cov[1]=1.;        *xmin=x; 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        return fx; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      } 
       for (k=1; k<=cptcovage;k++)      ftemp=fu;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      if (fabs(e) > tol1) { 
       for (k=1; k<=cptcovprod;k++)        r=(x-w)*(fx-fv); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        q=(x-v)*(fx-fw); 
         p=(x-v)*q-(x-w)*r; 
         q=2.0*(q-r); 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/        if (q > 0.0) p = -p; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/        q=fabs(q); 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,        etemp=e; 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        e=d; 
       savm=oldm;        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
       oldm=newm;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     }        else { 
     for(i=1; i<=nlstate+ndeath; i++)          d=p/q; 
       for(j=1;j<=nlstate+ndeath;j++) {          u=x+d; 
         po[i][j][h]=newm[i][j];          if (u-a < tol2 || b-u < tol2) 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);            d=SIGN(tol1,xm-x); 
          */        } 
       }      } else { 
   } /* end h */        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   return po;      } 
 }      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*f)(u); 
       if (fu <= fx) { 
 /*************** log-likelihood *************/        if (u >= x) a=x; else b=x; 
 double func( double *x)        SHFT(v,w,x,u) 
 {          SHFT(fv,fw,fx,fu) 
   int i, ii, j, k, mi, d, kk;          } else { 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];            if (u < x) a=u; else b=u; 
   double **out;            if (fu <= fw || w == x) { 
   double sw; /* Sum of weights */              v=w; 
   double lli; /* Individual log likelihood */              w=u; 
   long ipmx;              fv=fw; 
   /*extern weight */              fw=fu; 
   /* We are differentiating ll according to initial status */            } else if (fu <= fv || v == x || v == w) { 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/              v=u; 
   /*for(i=1;i<imx;i++)              fv=fu; 
     printf(" %d\n",s[4][i]);            } 
   */          } 
   cov[1]=1.;    } 
     nrerror("Too many iterations in brent"); 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    *xmin=x; 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    return fx; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  } 
     for(mi=1; mi<= wav[i]-1; mi++){  
       for (ii=1;ii<=nlstate+ndeath;ii++)  /****************** mnbrak ***********************/
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
       for(d=0; d<dh[mi][i]; d++){  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
         newm=savm;              double (*func)(double)) 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  { 
         for (kk=1; kk<=cptcovage;kk++) {    double ulim,u,r,q, dum;
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    double fu; 
         }   
            *fa=(*func)(*ax); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    *fb=(*func)(*bx); 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    if (*fb > *fa) { 
         savm=oldm;      SHFT(dum,*ax,*bx,dum) 
         oldm=newm;        SHFT(dum,*fb,*fa,dum) 
                } 
            *cx=(*bx)+GOLD*(*bx-*ax); 
       } /* end mult */    *fc=(*func)(*cx); 
          while (*fb > *fc) { 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      r=(*bx-*ax)*(*fb-*fc); 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      q=(*bx-*cx)*(*fb-*fa); 
       ipmx +=1;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       sw += weight[i];        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
     } /* end of wave */      if ((*bx-u)*(u-*cx) > 0.0) { 
   } /* end of individual */        fu=(*func)(u); 
       } else if ((*cx-u)*(u-ulim) > 0.0) { 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];        fu=(*func)(u); 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */        if (fu < *fc) { 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   return -l;            SHFT(*fb,*fc,fu,(*func)(u)) 
 }            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
         u=ulim; 
 /*********** Maximum Likelihood Estimation ***************/        fu=(*func)(u); 
       } else { 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        u=(*cx)+GOLD*(*cx-*bx); 
 {        fu=(*func)(u); 
   int i,j, iter;      } 
   double **xi,*delti;      SHFT(*ax,*bx,*cx,u) 
   double fret;        SHFT(*fa,*fb,*fc,fu) 
   xi=matrix(1,npar,1,npar);        } 
   for (i=1;i<=npar;i++)  } 
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);  /*************** linmin ************************/
   printf("Powell\n");  
   powell(p,xi,npar,ftol,&iter,&fret,func);  int ncom; 
   double *pcom,*xicom;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  double (*nrfunc)(double []); 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));   
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
 }  { 
     double brent(double ax, double bx, double cx, 
 /**** Computes Hessian and covariance matrix ***/                 double (*f)(double), double tol, double *xmin); 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    double f1dim(double x); 
 {    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   double  **a,**y,*x,pd;                double *fc, double (*func)(double)); 
   double **hess;    int j; 
   int i, j,jk;    double xx,xmin,bx,ax; 
   int *indx;    double fx,fb,fa;
    
   double hessii(double p[], double delta, int theta, double delti[]);    ncom=n; 
   double hessij(double p[], double delti[], int i, int j);    pcom=vector(1,n); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    xicom=vector(1,n); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;    nrfunc=func; 
     for (j=1;j<=n;j++) { 
   hess=matrix(1,npar,1,npar);      pcom[j]=p[j]; 
       xicom[j]=xi[j]; 
   printf("\nCalculation of the hessian matrix. Wait...\n");    } 
   for (i=1;i<=npar;i++){    ax=0.0; 
     printf("%d",i);fflush(stdout);    xx=1.0; 
     hess[i][i]=hessii(p,ftolhess,i,delti);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     /*printf(" %f ",p[i]);*/    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     /*printf(" %lf ",hess[i][i]);*/  #ifdef DEBUG
   }    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
      fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   for (i=1;i<=npar;i++) {  #endif
     for (j=1;j<=npar;j++)  {    for (j=1;j<=n;j++) { 
       if (j>i) {      xi[j] *= xmin; 
         printf(".%d%d",i,j);fflush(stdout);      p[j] += xi[j]; 
         hess[i][j]=hessij(p,delti,i,j);    } 
         hess[j][i]=hess[i][j];        free_vector(xicom,1,n); 
         /*printf(" %lf ",hess[i][j]);*/    free_vector(pcom,1,n); 
       }  } 
     }  
   }  char *asc_diff_time(long time_sec, char ascdiff[])
   printf("\n");  {
     long sec_left, days, hours, minutes;
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    days = (time_sec) / (60*60*24);
      sec_left = (time_sec) % (60*60*24);
   a=matrix(1,npar,1,npar);    hours = (sec_left) / (60*60) ;
   y=matrix(1,npar,1,npar);    sec_left = (sec_left) %(60*60);
   x=vector(1,npar);    minutes = (sec_left) /60;
   indx=ivector(1,npar);    sec_left = (sec_left) % (60);
   for (i=1;i<=npar;i++)    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    return ascdiff;
   ludcmp(a,npar,indx,&pd);  }
   
   for (j=1;j<=npar;j++) {  /*************** powell ************************/
     for (i=1;i<=npar;i++) x[i]=0;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     x[j]=1;              double (*func)(double [])) 
     lubksb(a,npar,indx,x);  { 
     for (i=1;i<=npar;i++){    void linmin(double p[], double xi[], int n, double *fret, 
       matcov[i][j]=x[i];                double (*func)(double [])); 
     }    int i,ibig,j; 
   }    double del,t,*pt,*ptt,*xit;
     double fp,fptt;
   printf("\n#Hessian matrix#\n");    double *xits;
   for (i=1;i<=npar;i++) {    int niterf, itmp;
     for (j=1;j<=npar;j++) {  
       printf("%.3e ",hess[i][j]);    pt=vector(1,n); 
     }    ptt=vector(1,n); 
     printf("\n");    xit=vector(1,n); 
   }    xits=vector(1,n); 
     *fret=(*func)(p); 
   /* Recompute Inverse */    for (j=1;j<=n;j++) pt[j]=p[j]; 
   for (i=1;i<=npar;i++)    for (*iter=1;;++(*iter)) { 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      fp=(*fret); 
   ludcmp(a,npar,indx,&pd);      ibig=0; 
       del=0.0; 
   /*  printf("\n#Hessian matrix recomputed#\n");      last_time=curr_time;
       (void) gettimeofday(&curr_time,&tzp);
   for (j=1;j<=npar;j++) {      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);
     for (i=1;i<=npar;i++) x[i]=0;      /*    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);
     x[j]=1;      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
     lubksb(a,npar,indx,x);      */
     for (i=1;i<=npar;i++){     for (i=1;i<=n;i++) {
       y[i][j]=x[i];        printf(" %d %.12f",i, p[i]);
       printf("%.3e ",y[i][j]);        fprintf(ficlog," %d %.12lf",i, p[i]);
     }        fprintf(ficrespow," %.12lf", p[i]);
     printf("\n");      }
   }      printf("\n");
   */      fprintf(ficlog,"\n");
       fprintf(ficrespow,"\n");fflush(ficrespow);
   free_matrix(a,1,npar,1,npar);      if(*iter <=3){
   free_matrix(y,1,npar,1,npar);        tm = *localtime(&curr_time.tv_sec);
   free_vector(x,1,npar);        strcpy(strcurr,asctime(&tm));
   free_ivector(indx,1,npar);  /*       asctime_r(&tm,strcurr); */
   free_matrix(hess,1,npar,1,npar);        forecast_time=curr_time; 
         itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
 }          strcurr[itmp-1]='\0';
         printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 /*************** hessian matrix ****************/        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 double hessii( double x[], double delta, int theta, double delti[])        for(niterf=10;niterf<=30;niterf+=10){
 {          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   int i;          tmf = *localtime(&forecast_time.tv_sec);
   int l=1, lmax=20;  /*      asctime_r(&tmf,strfor); */
   double k1,k2;          strcpy(strfor,asctime(&tmf));
   double p2[NPARMAX+1];          itmp = strlen(strfor);
   double res;          if(strfor[itmp-1]=='\n')
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;          strfor[itmp-1]='\0';
   double fx;          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);
   int k=0,kmax=10;          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   double l1;        }
       }
   fx=func(x);      for (i=1;i<=n;i++) { 
   for (i=1;i<=npar;i++) p2[i]=x[i];        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   for(l=0 ; l <=lmax; l++){        fptt=(*fret); 
     l1=pow(10,l);  #ifdef DEBUG
     delts=delt;        printf("fret=%lf \n",*fret);
     for(k=1 ; k <kmax; k=k+1){        fprintf(ficlog,"fret=%lf \n",*fret);
       delt = delta*(l1*k);  #endif
       p2[theta]=x[theta] +delt;        printf("%d",i);fflush(stdout);
       k1=func(p2)-fx;        fprintf(ficlog,"%d",i);fflush(ficlog);
       p2[theta]=x[theta]-delt;        linmin(p,xit,n,fret,func); 
       k2=func(p2)-fx;        if (fabs(fptt-(*fret)) > del) { 
       /*res= (k1-2.0*fx+k2)/delt/delt; */          del=fabs(fptt-(*fret)); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */          ibig=i; 
              } 
 #ifdef DEBUG  #ifdef DEBUG
       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);        printf("%d %.12e",i,(*fret));
 #endif        fprintf(ficlog,"%d %.12e",i,(*fret));
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        for (j=1;j<=n;j++) {
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
         k=kmax;          printf(" x(%d)=%.12e",j,xit[j]);
       }          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        }
         k=kmax; l=lmax*10.;        for(j=1;j<=n;j++) {
       }          printf(" p=%.12e",p[j]);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){          fprintf(ficlog," p=%.12e",p[j]);
         delts=delt;        }
       }        printf("\n");
     }        fprintf(ficlog,"\n");
   }  #endif
   delti[theta]=delts;      } 
   return res;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
    #ifdef DEBUG
 }        int k[2],l;
         k[0]=1;
 double hessij( double x[], double delti[], int thetai,int thetaj)        k[1]=-1;
 {        printf("Max: %.12e",(*func)(p));
   int i;        fprintf(ficlog,"Max: %.12e",(*func)(p));
   int l=1, l1, lmax=20;        for (j=1;j<=n;j++) {
   double k1,k2,k3,k4,res,fx;          printf(" %.12e",p[j]);
   double p2[NPARMAX+1];          fprintf(ficlog," %.12e",p[j]);
   int k;        }
         printf("\n");
   fx=func(x);        fprintf(ficlog,"\n");
   for (k=1; k<=2; k++) {        for(l=0;l<=1;l++) {
     for (i=1;i<=npar;i++) p2[i]=x[i];          for (j=1;j<=n;j++) {
     p2[thetai]=x[thetai]+delti[thetai]/k;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     k1=func(p2)-fx;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
            }
     p2[thetai]=x[thetai]+delti[thetai]/k;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     k2=func(p2)-fx;        }
    #endif
     p2[thetai]=x[thetai]-delti[thetai]/k;  
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k3=func(p2)-fx;        free_vector(xit,1,n); 
          free_vector(xits,1,n); 
     p2[thetai]=x[thetai]-delti[thetai]/k;        free_vector(ptt,1,n); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        free_vector(pt,1,n); 
     k4=func(p2)-fx;        return; 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      } 
 #ifdef DEBUG      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     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);      for (j=1;j<=n;j++) { 
 #endif        ptt[j]=2.0*p[j]-pt[j]; 
   }        xit[j]=p[j]-pt[j]; 
   return res;        pt[j]=p[j]; 
 }      } 
       fptt=(*func)(ptt); 
 /************** Inverse of matrix **************/      if (fptt < fp) { 
 void ludcmp(double **a, int n, int *indx, double *d)        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
 {        if (t < 0.0) { 
   int i,imax,j,k;          linmin(p,xit,n,fret,func); 
   double big,dum,sum,temp;          for (j=1;j<=n;j++) { 
   double *vv;            xi[j][ibig]=xi[j][n]; 
              xi[j][n]=xit[j]; 
   vv=vector(1,n);          }
   *d=1.0;  #ifdef DEBUG
   for (i=1;i<=n;i++) {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     big=0.0;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     for (j=1;j<=n;j++)          for(j=1;j<=n;j++){
       if ((temp=fabs(a[i][j])) > big) big=temp;            printf(" %.12e",xit[j]);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");            fprintf(ficlog," %.12e",xit[j]);
     vv[i]=1.0/big;          }
   }          printf("\n");
   for (j=1;j<=n;j++) {          fprintf(ficlog,"\n");
     for (i=1;i<j;i++) {  #endif
       sum=a[i][j];        }
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];      } 
       a[i][j]=sum;    } 
     }  } 
     big=0.0;  
     for (i=j;i<=n;i++) {  /**** Prevalence limit (stable or period prevalence)  ****************/
       sum=a[i][j];  
       for (k=1;k<j;k++)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
         sum -= a[i][k]*a[k][j];  {
       a[i][j]=sum;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       if ( (dum=vv[i]*fabs(sum)) >= big) {       matrix by transitions matrix until convergence is reached */
         big=dum;  
         imax=i;    int i, ii,j,k;
       }    double min, max, maxmin, maxmax,sumnew=0.;
     }    double **matprod2();
     if (j != imax) {    double **out, cov[NCOVMAX], **pmij();
       for (k=1;k<=n;k++) {    double **newm;
         dum=a[imax][k];    double agefin, delaymax=50 ; /* Max number of years to converge */
         a[imax][k]=a[j][k];  
         a[j][k]=dum;    for (ii=1;ii<=nlstate+ndeath;ii++)
       }      for (j=1;j<=nlstate+ndeath;j++){
       *d = -(*d);        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       vv[imax]=vv[j];      }
     }  
     indx[j]=imax;     cov[1]=1.;
     if (a[j][j] == 0.0) a[j][j]=TINY;   
     if (j != n) {   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       dum=1.0/(a[j][j]);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       for (i=j+1;i<=n;i++) a[i][j] *= dum;      newm=savm;
     }      /* Covariates have to be included here again */
   }       cov[2]=agefin;
   free_vector(vv,1,n);  /* Doesn't work */    
 ;        for (k=1; k<=cptcovn;k++) {
 }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
 void lubksb(double **a, int n, int *indx, double b[])        }
 {        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   int i,ii=0,ip,j;        for (k=1; k<=cptcovprod;k++)
   double sum;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
    
   for (i=1;i<=n;i++) {        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
     ip=indx[i];        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
     sum=b[ip];        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
     b[ip]=b[i];      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];      savm=oldm;
     else if (sum) ii=i;      oldm=newm;
     b[i]=sum;      maxmax=0.;
   }      for(j=1;j<=nlstate;j++){
   for (i=n;i>=1;i--) {        min=1.;
     sum=b[i];        max=0.;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        for(i=1; i<=nlstate; i++) {
     b[i]=sum/a[i][i];          sumnew=0;
   }          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
 }          prlim[i][j]= newm[i][j]/(1-sumnew);
           max=FMAX(max,prlim[i][j]);
 /************ Frequencies ********************/          min=FMIN(min,prlim[i][j]);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)        }
 {  /* Some frequencies */        maxmin=max-min;
          maxmax=FMAX(maxmax,maxmin);
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      }
   double ***freq; /* Frequencies */      if(maxmax < ftolpl){
   double *pp;        return prlim;
   double pos;      }
   FILE *ficresp;    }
   char fileresp[FILENAMELENGTH];  }
   
   pp=vector(1,nlstate);  /*************** transition probabilities ***************/ 
  probs= ma3x(1,130 ,1,8, 1,8);  
   strcpy(fileresp,"p");  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   strcat(fileresp,fileres);  {
   if((ficresp=fopen(fileresp,"w"))==NULL) {    double s1, s2;
     printf("Problem with prevalence resultfile: %s\n", fileresp);    /*double t34;*/
     exit(0);    int i,j,j1, nc, ii, jj;
   }  
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      for(i=1; i<= nlstate; i++){
   j1=0;        for(j=1; j<i;j++){
           for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   j=cptcoveff;            /*s2 += param[i][j][nc]*cov[nc];*/
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
   for(k1=1; k1<=j;k1++){          }
    for(i1=1; i1<=ncodemax[k1];i1++){          ps[i][j]=s2;
        j1++;  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        }
          scanf("%d", i);*/        for(j=i+1; j<=nlstate+ndeath;j++){
         for (i=-1; i<=nlstate+ndeath; i++)            for (nc=1, s2=0.;nc <=ncovmodel; nc++){
          for (jk=-1; jk<=nlstate+ndeath; jk++)              s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
            for(m=agemin; m <= agemax+3; m++)  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
              freq[i][jk][m]=0;          }
                  ps[i][j]=s2;
        for (i=1; i<=imx; i++) {        }
          bool=1;      }
          if  (cptcovn>0) {      /*ps[3][2]=1;*/
            for (z1=1; z1<=cptcoveff; z1++)      
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      for(i=1; i<= nlstate; i++){
                bool=0;        s1=0;
          }        for(j=1; j<i; j++)
           if (bool==1) {          s1+=exp(ps[i][j]);
            for(m=fprev; m<=lprev; m++){        for(j=i+1; j<=nlstate+ndeath; j++)
              if(agev[m][i]==0) agev[m][i]=agemax+1;          s1+=exp(ps[i][j]);
              if(agev[m][i]==1) agev[m][i]=agemax+2;        ps[i][i]=1./(s1+1.);
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        for(j=1; j<i; j++)
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          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];
        }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         if  (cptcovn>0) {      } /* end i */
          fprintf(ficresp, "\n#********** Variable ");      
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
        fprintf(ficresp, "**********\n#");        for(jj=1; jj<= nlstate+ndeath; jj++){
         }          ps[ii][jj]=0;
        for(i=1; i<=nlstate;i++)          ps[ii][ii]=1;
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        }
        fprintf(ficresp, "\n");      }
              
   for(i=(int)agemin; i <= (int)agemax+3; i++){  
     if(i==(int)agemax+3)  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
       printf("Total");  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
     else  /*         printf("ddd %lf ",ps[ii][jj]); */
       printf("Age %d", i);  /*       } */
     for(jk=1; jk <=nlstate ; jk++){  /*       printf("\n "); */
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  /*        } */
         pp[jk] += freq[jk][m][i];  /*        printf("\n ");printf("%lf ",cov[2]); */
     }         /*
     for(jk=1; jk <=nlstate ; jk++){        for(i=1; i<= npar; i++) printf("%f ",x[i]);
       for(m=-1, pos=0; m <=0 ; m++)        goto end;*/
         pos += freq[jk][m][i];      return ps;
       if(pp[jk]>=1.e-10)  }
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  
       else  /**************** Product of 2 matrices ******************/
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  
     }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   {
      for(jk=1; jk <=nlstate ; jk++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
         pp[jk] += freq[jk][m][i];    /* in, b, out are matrice of pointers which should have been initialized 
      }       before: only the contents of out is modified. The function returns
        a pointer to pointers identical to out */
     for(jk=1,pos=0; jk <=nlstate ; jk++)    long i, j, k;
       pos += pp[jk];    for(i=nrl; i<= nrh; i++)
     for(jk=1; jk <=nlstate ; jk++){      for(k=ncolol; k<=ncoloh; k++)
       if(pos>=1.e-5)        for(j=ncl,out[i][k]=0.; j<=nch; j++)
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          out[i][k] +=in[i][j]*b[j][k];
       else  
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    return out;
       if( i <= (int) agemax){  }
         if(pos>=1.e-5){  
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  
           probs[i][jk][j1]= pp[jk]/pos;  /************* Higher Matrix Product ***************/
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/  
         }  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
       else  {
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    /* Computes the transition matrix starting at age 'age' over 
       }       'nhstepm*hstepm*stepm' months (i.e. until
     }       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     for(jk=-1; jk <=nlstate+ndeath; jk++)       nhstepm*hstepm matrices. 
       for(m=-1; m <=nlstate+ndeath; m++)       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);       (typically every 2 years instead of every month which is too big 
     if(i <= (int) agemax)       for the memory).
       fprintf(ficresp,"\n");       Model is determined by parameters x and covariates have to be 
     printf("\n");       included manually here. 
     }  
     }       */
  }  
      int i, j, d, h, k;
   fclose(ficresp);    double **out, cov[NCOVMAX];
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    double **newm;
   free_vector(pp,1,nlstate);  
     /* Hstepm could be zero and should return the unit matrix */
 }  /* End of Freq */    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
 /************* Waves Concatenation ***************/        oldm[i][j]=(i==j ? 1.0 : 0.0);
         po[i][j][0]=(i==j ? 1.0 : 0.0);
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)      }
 {    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    for(h=1; h <=nhstepm; h++){
      Death is a valid wave (if date is known).      for(d=1; d <=hstepm; d++){
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        newm=savm;
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        /* Covariates have to be included here again */
      and mw[mi+1][i]. dh depends on stepm.        cov[1]=1.;
      */        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   int i, mi, m;        for (k=1; k<=cptcovage;k++)
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
      double sum=0., jmean=0.;*/        for (k=1; k<=cptcovprod;k++)
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   int j, k=0,jk, ju, jl;  
   double sum=0.;  
   jmin=1e+5;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   jmax=-1;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   jmean=0.;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
   for(i=1; i<=imx; i++){                     pmij(pmmij,cov,ncovmodel,x,nlstate));
     mi=0;        savm=oldm;
     m=firstpass;        oldm=newm;
     while(s[m][i] <= nlstate){      }
       if(s[m][i]>=1)      for(i=1; i<=nlstate+ndeath; i++)
         mw[++mi][i]=m;        for(j=1;j<=nlstate+ndeath;j++) {
       if(m >=lastpass)          po[i][j][h]=newm[i][j];
         break;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
       else           */
         m++;        }
     }/* end while */    } /* end h */
     if (s[m][i] > nlstate){    return po;
       mi++;     /* Death is another wave */  }
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */  
       mw[mi][i]=m;  /*************** log-likelihood *************/
     }  double func( double *x)
   {
     wav[i]=mi;    int i, ii, j, k, mi, d, kk;
     if(mi==0)    double l, ll[NLSTATEMAX], cov[NCOVMAX];
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    double **out;
   }    double sw; /* Sum of weights */
     double lli; /* Individual log likelihood */
   for(i=1; i<=imx; i++){    int s1, s2;
     for(mi=1; mi<wav[i];mi++){    double bbh, survp;
       if (stepm <=0)    long ipmx;
         dh[mi][i]=1;    /*extern weight */
       else{    /* We are differentiating ll according to initial status */
         if (s[mw[mi+1][i]][i] > nlstate) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
           if (agedc[i] < 2*AGESUP) {    /*for(i=1;i<imx;i++) 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);      printf(" %d\n",s[4][i]);
           if(j==0) j=1;  /* Survives at least one month after exam */    */
           k=k+1;    cov[1]=1.;
           if (j >= jmax) jmax=j;  
           if (j <= jmin) jmin=j;    for(k=1; k<=nlstate; k++) ll[k]=0.;
           sum=sum+j;  
           /* if (j<10) printf("j=%d num=%d ",j,i); */    if(mle==1){
           }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         else{        for(mi=1; mi<= wav[i]-1; mi++){
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          for (ii=1;ii<=nlstate+ndeath;ii++)
           k=k+1;            for (j=1;j<=nlstate+ndeath;j++){
           if (j >= jmax) jmax=j;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           else if (j <= jmin)jmin=j;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */            }
           sum=sum+j;          for(d=0; d<dh[mi][i]; d++){
         }            newm=savm;
         jk= j/stepm;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         jl= j -jk*stepm;            for (kk=1; kk<=cptcovage;kk++) {
         ju= j -(jk+1)*stepm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         if(jl <= -ju)            }
           dh[mi][i]=jk;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         else                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           dh[mi][i]=jk+1;            savm=oldm;
         if(dh[mi][i]==0)            oldm=newm;
           dh[mi][i]=1; /* At least one step */          } /* end mult */
       }        
     }          /*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.
   jmean=sum/k;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);           * (in months) between two waves is not a multiple of stepm, we rounded to 
  }           * the nearest (and in case of equal distance, to the lowest) interval but now
 /*********** Tricode ****************************/           * we keep into memory the bias bh[mi][i] and also the previous matrix product
 void tricode(int *Tvar, int **nbcode, int imx)           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
 {           * probability in order to take into account the bias as a fraction of the way
   int Ndum[20],ij=1, k, j, i;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   int cptcode=0;           * -stepm/2 to stepm/2 .
   cptcoveff=0;           * For stepm=1 the results are the same as for previous versions of Imach.
             * For stepm > 1 the results are less biased than in previous versions. 
   for (k=0; k<19; k++) Ndum[k]=0;           */
   for (k=1; k<=7; k++) ncodemax[k]=0;          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          bbh=(double)bh[mi][i]/(double)stepm; 
     for (i=1; i<=imx; i++) {          /* bias bh is positive if real duration
       ij=(int)(covar[Tvar[j]][i]);           * is higher than the multiple of stepm and negative otherwise.
       Ndum[ij]++;           */
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
       if (ij > cptcode) cptcode=ij;          if( s2 > nlstate){ 
     }            /* i.e. if s2 is a death state and if the date of death is known 
                then the contribution to the likelihood is the probability to 
     for (i=0; i<=cptcode; i++) {               die between last step unit time and current  step unit time, 
       if(Ndum[i]!=0) ncodemax[j]++;               which is also equal to probability to die before dh 
     }               minus probability to die before dh-stepm . 
     ij=1;               In version up to 0.92 likelihood was computed
           as if date of death was unknown. Death was treated as any other
           health state: the date of the interview describes the actual state
     for (i=1; i<=ncodemax[j]; i++) {          and not the date of a change in health state. The former idea was
       for (k=0; k<=19; k++) {          to consider that at each interview the state was recorded
         if (Ndum[k] != 0) {          (healthy, disable or death) and IMaCh was corrected; but when we
           nbcode[Tvar[j]][ij]=k;          introduced the exact date of death then we should have modified
           ij++;          the contribution of an exact death to the likelihood. This new
         }          contribution is smaller and very dependent of the step unit
         if (ij > ncodemax[j]) break;          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
           Jackson for correcting this bug.  Former versions increased
  for (k=0; k<19; k++) Ndum[k]=0;          mortality artificially. The bad side is that we add another loop
           which slows down the processing. The difference can be up to 10%
  for (i=1; i<=ncovmodel-2; i++) {          lower mortality.
       ij=Tvar[i];            */
       Ndum[ij]++;            lli=log(out[s1][s2] - savm[s1][s2]);
     }  
   
  ij=1;          } else if  (s2==-2) {
  for (i=1; i<=10; i++) {            for (j=1,survp=0. ; j<=nlstate; j++) 
    if((Ndum[i]!=0) && (i<=ncov)){              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
      Tvaraff[ij]=i;            /*survp += out[s1][j]; */
      ij++;            lli= log(survp);
    }          }
  }          
            else if  (s2==-4) { 
     cptcoveff=ij-1;            for (j=3,survp=0. ; j<=nlstate; j++)  
 }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             lli= log(survp); 
 /*********** Health Expectancies ****************/          } 
   
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          else if  (s2==-5) { 
 {            for (j=1,survp=0. ; j<=2; j++)  
   /* Health expectancies */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   int i, j, nhstepm, hstepm, h;            lli= log(survp); 
   double age, agelim,hf;          } 
   double ***p3mat;          
            else{
   fprintf(ficreseij,"# Health expectancies\n");            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   fprintf(ficreseij,"# Age");            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
   for(i=1; i<=nlstate;i++)          } 
     for(j=1; j<=nlstate;j++)          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       fprintf(ficreseij," %1d-%1d",i,j);          /*if(lli ==000.0)*/
   fprintf(ficreseij,"\n");          /*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;
   hstepm=1*YEARM; /*  Every j years of age (in month) */          sw += weight[i];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
   agelim=AGESUP;      } /* end of individual */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }  else if(mle==2){
     /* nhstepm age range expressed in number of stepm */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     /* Typically if 20 years = 20*12/6=40 stepm */        for(mi=1; mi<= wav[i]-1; mi++){
     if (stepm >= YEARM) hstepm=1;          for (ii=1;ii<=nlstate+ndeath;ii++)
     nhstepm = nhstepm/hstepm;/* Expressed in 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);
     /* Computed by stepm unit matrices, product of hstepm matrices, stored              savm[ii][j]=(ii==j ? 1.0 : 0.0);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            }
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            for(d=0; d<=dh[mi][i]; d++){
             newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(i=1; i<=nlstate;i++)            for (kk=1; kk<=cptcovage;kk++) {
       for(j=1; j<=nlstate;j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){            }
           eij[i][j][(int)age] +=p3mat[i][j][h];            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                savm=oldm;
     hf=1;            oldm=newm;
     if (stepm >= YEARM) hf=stepm/YEARM;          } /* end mult */
     fprintf(ficreseij,"%.0f",age );        
     for(i=1; i<=nlstate;i++)          s1=s[mw[mi][i]][i];
       for(j=1; j<=nlstate;j++){          s2=s[mw[mi+1][i]][i];
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);          bbh=(double)bh[mi][i]/(double)stepm; 
       }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
     fprintf(ficreseij,"\n");          ipmx +=1;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          sw += weight[i];
   }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 }        } /* end of wave */
       } /* end of individual */
 /************ Variance ******************/    }  else if(mle==3){  /* exponential inter-extrapolation */
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   /* Variance of health expectancies */        for(mi=1; mi<= wav[i]-1; mi++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          for (ii=1;ii<=nlstate+ndeath;ii++)
   double **newm;            for (j=1;j<=nlstate+ndeath;j++){
   double **dnewm,**doldm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j, nhstepm, hstepm, h;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int k, cptcode;            }
   double *xp;          for(d=0; d<dh[mi][i]; d++){
   double **gp, **gm;            newm=savm;
   double ***gradg, ***trgradg;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double ***p3mat;            for (kk=1; kk<=cptcovage;kk++) {
   double age,agelim;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int theta;            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
    fprintf(ficresvij,"# Covariances of life expectancies\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   fprintf(ficresvij,"# Age");            savm=oldm;
   for(i=1; i<=nlstate;i++)            oldm=newm;
     for(j=1; j<=nlstate;j++)          } /* end mult */
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        
   fprintf(ficresvij,"\n");          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   xp=vector(1,npar);          bbh=(double)bh[mi][i]/(double)stepm; 
   dnewm=matrix(1,nlstate,1,npar);          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 */
   doldm=matrix(1,nlstate,1,nlstate);          ipmx +=1;
            sw += weight[i];
   hstepm=1*YEARM; /* Every year of age */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        } /* end of wave */
   agelim = AGESUP;      } /* end of individual */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     if (stepm >= YEARM) hstepm=1;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        for(mi=1; mi<= wav[i]-1; mi++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);            for (j=1;j<=nlstate+ndeath;j++){
     gp=matrix(0,nhstepm,1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     gm=matrix(0,nhstepm,1,nlstate);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
     for(theta=1; theta <=npar; theta++){          for(d=0; d<dh[mi][i]; d++){
       for(i=1; i<=npar; i++){ /* Computes gradient */            newm=savm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            }
           
       if (popbased==1) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           prlim[i][i]=probs[(int)age][i][ij];            savm=oldm;
       }            oldm=newm;
                } /* end mult */
       for(j=1; j<= nlstate; j++){        
         for(h=0; h<=nhstepm; h++){          s1=s[mw[mi][i]][i];
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          s2=s[mw[mi+1][i]][i];
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          if( s2 > nlstate){ 
         }            lli=log(out[s1][s2] - savm[s1][s2]);
       }          }else{
                lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       for(i=1; i<=npar; i++) /* Computes gradient */          }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          ipmx +=1;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            sw += weight[i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          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]); */
       if (popbased==1) {        } /* end of wave */
         for(i=1; i<=nlstate;i++)      } /* end of individual */
           prlim[i][i]=probs[(int)age][i][ij];    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
       }      for (i=1,ipmx=0, sw=0.; i<=imx; 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++){
         for(h=0; h<=nhstepm; h++){          for (ii=1;ii<=nlstate+ndeath;ii++)
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)            for (j=1;j<=nlstate+ndeath;j++){
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
           for(d=0; d<dh[mi][i]; d++){
       for(j=1; j<= nlstate; j++)            newm=savm;
         for(h=0; h<=nhstepm; h++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];            for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     } /* End theta */            }
           
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(h=0; h<=nhstepm; h++)            savm=oldm;
       for(j=1; j<=nlstate;j++)            oldm=newm;
         for(theta=1; theta <=npar; theta++)          } /* end mult */
           trgradg[h][j][theta]=gradg[h][theta][j];        
           s1=s[mw[mi][i]][i];
     for(i=1;i<=nlstate;i++)          s2=s[mw[mi+1][i]][i];
       for(j=1;j<=nlstate;j++)          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         vareij[i][j][(int)age] =0.;          ipmx +=1;
     for(h=0;h<=nhstepm;h++){          sw += weight[i];
       for(k=0;k<=nhstepm;k++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);          /*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]);*/
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        } /* end of wave */
         for(i=1;i<=nlstate;i++)      } /* end of individual */
           for(j=1;j<=nlstate;j++)    } /* End of if */
             vareij[i][j][(int)age] += doldm[i][j];    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       }    /* 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 */
     h=1;    return -l;
     if (stepm >= YEARM) h=stepm/YEARM;  }
     fprintf(ficresvij,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)  /*************** log-likelihood *************/
       for(j=1; j<=nlstate;j++){  double funcone( double *x)
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);  {
       }    /* Same as likeli but slower because of a lot of printf and if */
     fprintf(ficresvij,"\n");    int i, ii, j, k, mi, d, kk;
     free_matrix(gp,0,nhstepm,1,nlstate);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     free_matrix(gm,0,nhstepm,1,nlstate);    double **out;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    double lli; /* Individual log likelihood */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    double llt;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int s1, s2;
   } /* End age */    double bbh, survp;
      /*extern weight */
   free_vector(xp,1,npar);    /* We are differentiating ll according to initial status */
   free_matrix(doldm,1,nlstate,1,npar);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   free_matrix(dnewm,1,nlstate,1,nlstate);    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
 }    */
     cov[1]=1.;
 /************ 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)    for(k=1; k<=nlstate; k++) ll[k]=0.;
 {  
   /* Variance of prevalence limit */    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double **newm;      for(mi=1; mi<= wav[i]-1; mi++){
   double **dnewm,**doldm;        for (ii=1;ii<=nlstate+ndeath;ii++)
   int i, j, nhstepm, hstepm;          for (j=1;j<=nlstate+ndeath;j++){
   int k, cptcode;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double *xp;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double *gp, *gm;          }
   double **gradg, **trgradg;        for(d=0; d<dh[mi][i]; d++){
   double age,agelim;          newm=savm;
   int theta;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   fprintf(ficresvpl,"# Age");          }
   for(i=1; i<=nlstate;i++)          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       fprintf(ficresvpl," %1d-%1d",i,i);                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   fprintf(ficresvpl,"\n");          savm=oldm;
           oldm=newm;
   xp=vector(1,npar);        } /* end mult */
   dnewm=matrix(1,nlstate,1,npar);        
   doldm=matrix(1,nlstate,1,nlstate);        s1=s[mw[mi][i]][i];
          s2=s[mw[mi+1][i]][i];
   hstepm=1*YEARM; /* Every year of age */        bbh=(double)bh[mi][i]/(double)stepm; 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        /* bias is positive if real duration
   agelim = AGESUP;         * is higher than the multiple of stepm and negative otherwise.
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */         */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     if (stepm >= YEARM) hstepm=1;          lli=log(out[s1][s2] - savm[s1][s2]);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        } else if  (s2==-2) {
     gradg=matrix(1,npar,1,nlstate);          for (j=1,survp=0. ; j<=nlstate; j++) 
     gp=vector(1,nlstate);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     gm=vector(1,nlstate);          lli= log(survp);
         }else if (mle==1){
     for(theta=1; theta <=npar; theta++){          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for(i=1; i<=npar; i++){ /* Computes gradient */        } else if(mle==2){
         xp[i] = x[i] + (i==theta ?delti[theta]: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 */
       }        } else if(mle==3){  /* exponential inter-extrapolation */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          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 */
       for(i=1;i<=nlstate;i++)        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         gp[i] = prlim[i][i];          lli=log(out[s1][s2]); /* Original formula */
            } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
       for(i=1; i<=npar; i++) /* Computes gradient */          lli=log(out[s1][s2]); /* Original formula */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        } /* End of if */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        ipmx +=1;
       for(i=1;i<=nlstate;i++)        sw += weight[i];
         gm[i] = prlim[i][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]); */
       for(i=1;i<=nlstate;i++)        if(globpr){
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     } /* End theta */   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     trgradg =matrix(1,nlstate,1,npar);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     for(j=1; j<=nlstate;j++)            llt +=ll[k]*gipmx/gsw;
       for(theta=1; theta <=npar; theta++)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         trgradg[j][theta]=gradg[theta][j];          }
           fprintf(ficresilk," %10.6f\n", -llt);
     for(i=1;i<=nlstate;i++)        }
       varpl[i][(int)age] =0.;      } /* end of wave */
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    } /* end of individual */
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     for(i=1;i<=nlstate;i++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     if(globpr==0){ /* First time we count the contributions and weights */
     fprintf(ficresvpl,"%.0f ",age );      gipmx=ipmx;
     for(i=1; i<=nlstate;i++)      gsw=sw;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    }
     fprintf(ficresvpl,"\n");    return -l;
     free_vector(gp,1,nlstate);  }
     free_vector(gm,1,nlstate);  
     free_matrix(gradg,1,npar,1,nlstate);  
     free_matrix(trgradg,1,nlstate,1,npar);  /*************** function likelione ***********/
   } /* End age */  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
   free_vector(xp,1,npar);    /* This routine should help understanding what is done with 
   free_matrix(doldm,1,nlstate,1,npar);       the selection of individuals/waves and
   free_matrix(dnewm,1,nlstate,1,nlstate);       to check the exact contribution to the likelihood.
        Plotting could be done.
 }     */
     int k;
 /************ Variance of one-step probabilities  ******************/  
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)    if(*globpri !=0){ /* Just counts and sums, no printings */
 {      strcpy(fileresilk,"ilk"); 
   int i, j;      strcat(fileresilk,fileres);
   int k=0, cptcode;      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   double **dnewm,**doldm;        printf("Problem with resultfile: %s\n", fileresilk);
   double *xp;        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
   double *gp, *gm;      }
   double **gradg, **trgradg;      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");
   double age,agelim, cov[NCOVMAX];      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   int theta;      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
   char fileresprob[FILENAMELENGTH];      for(k=1; k<=nlstate; k++) 
         fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   strcpy(fileresprob,"prob");      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   strcat(fileresprob,fileres);    }
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  
     printf("Problem with resultfile: %s\n", fileresprob);    *fretone=(*funcone)(p);
   }    if(*globpri !=0){
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);      fclose(ficresilk);
        fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       fflush(fichtm); 
   xp=vector(1,npar);    } 
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    return;
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));  }
    
   cov[1]=1;  
   for (age=bage; age<=fage; age ++){  /*********** Maximum Likelihood Estimation ***************/
     cov[2]=age;  
     gradg=matrix(1,npar,1,9);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     trgradg=matrix(1,9,1,npar);  {
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    int i,j, iter;
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    double **xi;
        double fret;
     for(theta=1; theta <=npar; theta++){    double fretone; /* Only one call to likelihood */
       for(i=1; i<=npar; i++)    /*  char filerespow[FILENAMELENGTH];*/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    xi=matrix(1,npar,1,npar);
          for (i=1;i<=npar;i++)
       pmij(pmmij,cov,ncovmodel,xp,nlstate);      for (j=1;j<=npar;j++)
            xi[i][j]=(i==j ? 1.0 : 0.0);
       k=0;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
       for(i=1; i<= (nlstate+ndeath); i++){    strcpy(filerespow,"pow"); 
         for(j=1; j<=(nlstate+ndeath);j++){    strcat(filerespow,fileres);
            k=k+1;    if((ficrespow=fopen(filerespow,"w"))==NULL) {
           gp[k]=pmmij[i][j];      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<=npar; i++)    for (i=1;i<=nlstate;i++)
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      for(j=1;j<=nlstate+ndeath;j++)
            if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     fprintf(ficrespow,"\n");
       pmij(pmmij,cov,ncovmodel,xp,nlstate);  
       k=0;    powell(p,xi,npar,ftol,&iter,&fret,func);
       for(i=1; i<=(nlstate+ndeath); i++){  
         for(j=1; j<=(nlstate+ndeath);j++){    free_matrix(xi,1,npar,1,npar);
           k=k+1;    fclose(ficrespow);
           gm[k]=pmmij[i][j];    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         }    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       }    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
        
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)  }
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];    
     }  /**** Computes Hessian and covariance matrix ***/
   void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)  {
       for(theta=1; theta <=npar; theta++)    double  **a,**y,*x,pd;
       trgradg[j][theta]=gradg[theta][j];    double **hess;
      int i, j,jk;
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    int *indx;
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);  
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
      pmij(pmmij,cov,ncovmodel,x,nlstate);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     void lubksb(double **a, int npar, int *indx, double b[]) ;
      k=0;    void ludcmp(double **a, int npar, int *indx, double *d) ;
      for(i=1; i<=(nlstate+ndeath); i++){    double gompertz(double p[]);
        for(j=1; j<=(nlstate+ndeath);j++){    hess=matrix(1,npar,1,npar);
          k=k+1;  
          gm[k]=pmmij[i][j];    printf("\nCalculation of the hessian matrix. Wait...\n");
         }    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
      }    for (i=1;i<=npar;i++){
            printf("%d",i);fflush(stdout);
      /*printf("\n%d ",(int)age);      fprintf(ficlog,"%d",i);fflush(ficlog);
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){     
               hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
       
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      /*  printf(" %f ",p[i]);
      }*/          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
   fprintf(ficresprob,"\n%d ",(int)age);    
     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]);        if (j>i) { 
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);          printf(".%d%d",i,j);fflush(stdout);
   }          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
           hess[i][j]=hessij(p,delti,i,j,func,npar);
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));          hess[j][i]=hess[i][j];    
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          /*printf(" %lf ",hess[i][j]);*/
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        }
 }      }
  free_vector(xp,1,npar);    }
 fclose(ficresprob);    printf("\n");
  exit(0);    fprintf(ficlog,"\n");
 }  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
 /***********************************************/    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 /**************** Main Program *****************/    
 /***********************************************/    a=matrix(1,npar,1,npar);
     y=matrix(1,npar,1,npar);
 /*int main(int argc, char *argv[])*/    x=vector(1,npar);
 int main()    indx=ivector(1,npar);
 {    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    ludcmp(a,npar,indx,&pd);
   double agedeb, agefin,hf;  
   double agemin=1.e20, agemax=-1.e20;    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   double fret;      x[j]=1;
   double **xi,tmp,delta;      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
   double dum; /* Dummy variable */        matcov[i][j]=x[i];
   double ***p3mat;      }
   int *indx;    }
   char line[MAXLINE], linepar[MAXLINE];  
   char title[MAXLINE];    printf("\n#Hessian matrix#\n");
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    fprintf(ficlog,"\n#Hessian matrix#\n");
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];    for (i=1;i<=npar;i++) { 
   char filerest[FILENAMELENGTH];      for (j=1;j<=npar;j++) { 
   char fileregp[FILENAMELENGTH];        printf("%.3e ",hess[i][j]);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        fprintf(ficlog,"%.3e ",hess[i][j]);
   int firstobs=1, lastobs=10;      }
   int sdeb, sfin; /* Status at beginning and end */      printf("\n");
   int c,  h , cpt,l;      fprintf(ficlog,"\n");
   int ju,jl, mi;    }
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;  
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    /* Recompute Inverse */
   int mobilav=0, fprevfore=1, lprevfore=1;    for (i=1;i<=npar;i++)
   int hstepm, nhstepm;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     ludcmp(a,npar,indx,&pd);
   double bage, fage, age, agelim, agebase;  
   double ftolpl=FTOL;    /*  printf("\n#Hessian matrix recomputed#\n");
   double **prlim;  
   double *severity;    for (j=1;j<=npar;j++) {
   double ***param; /* Matrix of parameters */      for (i=1;i<=npar;i++) x[i]=0;
   double  *p;      x[j]=1;
   double **matcov; /* Matrix of covariance */      lubksb(a,npar,indx,x);
   double ***delti3; /* Scale */      for (i=1;i<=npar;i++){ 
   double *delti; /* Scale */        y[i][j]=x[i];
   double ***eij, ***vareij;        printf("%.3e ",y[i][j]);
   double **varpl; /* Variances of prevalence limits by age */        fprintf(ficlog,"%.3e ",y[i][j]);
   double *epj, vepp;      }
   double kk1;      printf("\n");
       fprintf(ficlog,"\n");
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";    }
   char *alph[]={"a","a","b","c","d","e"}, str[4];    */
   
     free_matrix(a,1,npar,1,npar);
   char z[1]="c", occ;    free_matrix(y,1,npar,1,npar);
 #include <sys/time.h>    free_vector(x,1,npar);
 #include <time.h>    free_ivector(indx,1,npar);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    free_matrix(hess,1,npar,1,npar);
   /* long total_usecs;  
   struct timeval start_time, end_time;  
    }
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   /*************** hessian matrix ****************/
   double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   printf("\nIMACH, Version 0.64b");  {
   printf("\nEnter the parameter file name: ");    int i;
     int l=1, lmax=20;
 #ifdef windows    double k1,k2;
   scanf("%s",pathtot);    double p2[NPARMAX+1];
   getcwd(pathcd, size);    double res;
   /*cygwin_split_path(pathtot,path,optionfile);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    double fx;
   /* cutv(path,optionfile,pathtot,'\\');*/    int k=0,kmax=10;
     double l1;
 split(pathtot, path,optionfile);  
   chdir(path);    fx=func(x);
   replace(pathc,path);    for (i=1;i<=npar;i++) p2[i]=x[i];
 #endif    for(l=0 ; l <=lmax; l++){
 #ifdef unix      l1=pow(10,l);
   scanf("%s",optionfile);      delts=delt;
 #endif      for(k=1 ; k <kmax; k=k+1){
         delt = delta*(l1*k);
 /*-------- arguments in the command line --------*/        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;
   strcpy(fileres,"r");        p2[theta]=x[theta]-delt;
   strcat(fileres, optionfile);        k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
   /*---------arguments file --------*/        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  #ifdef DEBUG
     printf("Problem with optionfile %s\n",optionfile);        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);
     goto end;        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
         /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   strcpy(filereso,"o");        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   strcat(filereso,fileres);          k=kmax;
   if((ficparo=fopen(filereso,"w"))==NULL) {        }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   }          k=kmax; l=lmax*10.;
         }
   /* Reads comments: lines beginning with '#' */        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   while((c=getc(ficpar))=='#' && c!= EOF){          delts=delt;
     ungetc(c,ficpar);        }
     fgets(line, MAXLINE, ficpar);      }
     puts(line);    }
     fputs(line,ficparo);    delti[theta]=delts;
   }    return res; 
   ungetc(c,ficpar);    
   }
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);  
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   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);  {
 while((c=getc(ficpar))=='#' && c!= EOF){    int i;
     ungetc(c,ficpar);    int l=1, l1, lmax=20;
     fgets(line, MAXLINE, ficpar);    double k1,k2,k3,k4,res,fx;
     puts(line);    double p2[NPARMAX+1];
     fputs(line,ficparo);    int k;
   }  
   ungetc(c,ficpar);    fx=func(x);
      for (k=1; k<=2; k++) {
   fscanf(ficpar,"fprevalence=%d lprevalence=%d pop_based=%d\n",&fprev,&lprev,&popbased);      for (i=1;i<=npar;i++) p2[i]=x[i];
  while((c=getc(ficpar))=='#' && c!= EOF){      p2[thetai]=x[thetai]+delti[thetai]/k;
     ungetc(c,ficpar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     fgets(line, MAXLINE, ficpar);      k1=func(p2)-fx;
     puts(line);    
     fputs(line,ficparo);      p2[thetai]=x[thetai]+delti[thetai]/k;
   }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   ungetc(c,ficpar);      k2=func(p2)-fx;
      
   fscanf(ficpar,"fprevalence=%d lprevalence=%d mob_average=%d\n",&fprevfore,&lprevfore,&mobilav);      p2[thetai]=x[thetai]-delti[thetai]/k;
        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   covar=matrix(0,NCOVMAX,1,n);      k3=func(p2)-fx;
   cptcovn=0;    
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   ncovmodel=2+cptcovn;      k4=func(p2)-fx;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
    #ifdef DEBUG
   /* Read guess parameters */      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);
   /* Reads comments: lines beginning with '#' */      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);
   while((c=getc(ficpar))=='#' && c!= EOF){  #endif
     ungetc(c,ficpar);    }
     fgets(line, MAXLINE, ficpar);    return res;
     puts(line);  }
     fputs(line,ficparo);  
   }  /************** Inverse of matrix **************/
   ungetc(c,ficpar);  void ludcmp(double **a, int n, int *indx, double *d) 
    { 
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    int i,imax,j,k; 
     for(i=1; i <=nlstate; i++)    double big,dum,sum,temp; 
     for(j=1; j <=nlstate+ndeath-1; j++){    double *vv; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);   
       fprintf(ficparo,"%1d%1d",i1,j1);    vv=vector(1,n); 
       printf("%1d%1d",i,j);    *d=1.0; 
       for(k=1; k<=ncovmodel;k++){    for (i=1;i<=n;i++) { 
         fscanf(ficpar," %lf",&param[i][j][k]);      big=0.0; 
         printf(" %lf",param[i][j][k]);      for (j=1;j<=n;j++) 
         fprintf(ficparo," %lf",param[i][j][k]);        if ((temp=fabs(a[i][j])) > big) big=temp; 
       }      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       fscanf(ficpar,"\n");      vv[i]=1.0/big; 
       printf("\n");    } 
       fprintf(ficparo,"\n");    for (j=1;j<=n;j++) { 
     }      for (i=1;i<j;i++) { 
          sum=a[i][j]; 
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
   p=param[1][1];      } 
        big=0.0; 
   /* Reads comments: lines beginning with '#' */      for (i=j;i<=n;i++) { 
   while((c=getc(ficpar))=='#' && c!= EOF){        sum=a[i][j]; 
     ungetc(c,ficpar);        for (k=1;k<j;k++) 
     fgets(line, MAXLINE, ficpar);          sum -= a[i][k]*a[k][j]; 
     puts(line);        a[i][j]=sum; 
     fputs(line,ficparo);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   }          big=dum; 
   ungetc(c,ficpar);          imax=i; 
         } 
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      } 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      if (j != imax) { 
   for(i=1; i <=nlstate; i++){        for (k=1;k<=n;k++) { 
     for(j=1; j <=nlstate+ndeath-1; j++){          dum=a[imax][k]; 
       fscanf(ficpar,"%1d%1d",&i1,&j1);          a[imax][k]=a[j][k]; 
       printf("%1d%1d",i,j);          a[j][k]=dum; 
       fprintf(ficparo,"%1d%1d",i1,j1);        } 
       for(k=1; k<=ncovmodel;k++){        *d = -(*d); 
         fscanf(ficpar,"%le",&delti3[i][j][k]);        vv[imax]=vv[j]; 
         printf(" %le",delti3[i][j][k]);      } 
         fprintf(ficparo," %le",delti3[i][j][k]);      indx[j]=imax; 
       }      if (a[j][j] == 0.0) a[j][j]=TINY; 
       fscanf(ficpar,"\n");      if (j != n) { 
       printf("\n");        dum=1.0/(a[j][j]); 
       fprintf(ficparo,"\n");        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
     }      } 
   }    } 
   delti=delti3[1][1];    free_vector(vv,1,n);  /* Doesn't work */
    ;
   /* Reads comments: lines beginning with '#' */  } 
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);  void lubksb(double **a, int n, int *indx, double b[]) 
     fgets(line, MAXLINE, ficpar);  { 
     puts(line);    int i,ii=0,ip,j; 
     fputs(line,ficparo);    double sum; 
   }   
   ungetc(c,ficpar);    for (i=1;i<=n;i++) { 
        ip=indx[i]; 
   matcov=matrix(1,npar,1,npar);      sum=b[ip]; 
   for(i=1; i <=npar; i++){      b[ip]=b[i]; 
     fscanf(ficpar,"%s",&str);      if (ii) 
     printf("%s",str);        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     fprintf(ficparo,"%s",str);      else if (sum) ii=i; 
     for(j=1; j <=i; j++){      b[i]=sum; 
       fscanf(ficpar," %le",&matcov[i][j]);    } 
       printf(" %.5le",matcov[i][j]);    for (i=n;i>=1;i--) { 
       fprintf(ficparo," %.5le",matcov[i][j]);      sum=b[i]; 
     }      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
     fscanf(ficpar,"\n");      b[i]=sum/a[i][i]; 
     printf("\n");    } 
     fprintf(ficparo,"\n");  } 
   }  
   for(i=1; i <=npar; i++)  void pstamp(FILE *fichier)
     for(j=i+1;j<=npar;j++)  {
       matcov[i][j]=matcov[j][i];    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
      }
   printf("\n");  
   /************ Frequencies ********************/
   void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
     /*-------- data file ----------*/  {  /* Some frequencies */
     if((ficres =fopen(fileres,"w"))==NULL) {    
       printf("Problem with resultfile: %s\n", fileres);goto end;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     }    int first;
     fprintf(ficres,"#%s\n",version);    double ***freq; /* Frequencies */
        double *pp, **prop;
     if((fic=fopen(datafile,"r"))==NULL)    {    double pos,posprop, k2, dateintsum=0,k2cpt=0;
       printf("Problem with datafile: %s\n", datafile);goto end;    char fileresp[FILENAMELENGTH];
     }    
     pp=vector(1,nlstate);
     n= lastobs;    prop=matrix(1,nlstate,iagemin,iagemax+3);
     severity = vector(1,maxwav);    strcpy(fileresp,"p");
     outcome=imatrix(1,maxwav+1,1,n);    strcat(fileresp,fileres);
     num=ivector(1,n);    if((ficresp=fopen(fileresp,"w"))==NULL) {
     moisnais=vector(1,n);      printf("Problem with prevalence resultfile: %s\n", fileresp);
     annais=vector(1,n);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     moisdc=vector(1,n);      exit(0);
     andc=vector(1,n);    }
     agedc=vector(1,n);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
     cod=ivector(1,n);    j1=0;
     weight=vector(1,n);    
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    j=cptcoveff;
     mint=matrix(1,maxwav,1,n);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     anint=matrix(1,maxwav,1,n);  
     s=imatrix(1,maxwav+1,1,n);    first=1;
     adl=imatrix(1,maxwav+1,1,n);      
     tab=ivector(1,NCOVMAX);    for(k1=1; k1<=j;k1++){
     ncodemax=ivector(1,8);      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
     i=1;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
     while (fgets(line, MAXLINE, fic) != NULL)    {          scanf("%d", i);*/
       if ((i >= firstobs) && (i <=lastobs)) {        for (i=-5; i<=nlstate+ndeath; i++)  
                  for (jk=-5; jk<=nlstate+ndeath; jk++)  
         for (j=maxwav;j>=1;j--){            for(m=iagemin; m <= iagemax+3; m++)
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);              freq[i][jk][m]=0;
           strcpy(line,stra);  
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      for (i=1; i<=nlstate; i++)  
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        for(m=iagemin; m <= iagemax+3; m++)
         }          prop[i][m]=0;
                
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        dateintsum=0;
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        k2cpt=0;
         for (i=1; i<=imx; i++) {
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);          bool=1;
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
         for (j=ncov;j>=1;j--){                bool=0;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);          }
         }          if (bool==1){
         num[i]=atol(stra);            for(m=firstpass; m<=lastpass; m++){
                      k2=anint[m][i]+(mint[m][i]/12.);
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
           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;}*/                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
         i=i+1;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
       }                if (m<lastpass) {
     }                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     /* printf("ii=%d", ij);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
        scanf("%d",i);*/                }
   imx=i-1; /* Number of individuals */                
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
   /* for (i=1; i<=imx; i++){                  dateintsum=dateintsum+k2;
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;                  k2cpt++;
     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++) 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]));*/          }
         }
   /* Calculation of the number of parameter from char model*/         
   Tvar=ivector(1,15);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
   Tprod=ivector(1,15);        pstamp(ficresp);
   Tvaraff=ivector(1,15);        if  (cptcovn>0) {
   Tvard=imatrix(1,15,1,2);          fprintf(ficresp, "\n#********** Variable "); 
   Tage=ivector(1,15);                for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
              fprintf(ficresp, "**********\n#");
   if (strlen(model) >1){        }
     j=0, j1=0, k1=1, k2=1;        for(i=1; i<=nlstate;i++) 
     j=nbocc(model,'+');          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
     j1=nbocc(model,'*');        fprintf(ficresp, "\n");
     cptcovn=j+1;        
     cptcovprod=j1;        for(i=iagemin; i <= iagemax+3; i++){
              if(i==iagemax+3){
                fprintf(ficlog,"Total");
     strcpy(modelsav,model);          }else{
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){            if(first==1){
       printf("Error. Non available option model=%s ",model);              first=0;
       goto end;              printf("See log file for details...\n");
     }            }
                fprintf(ficlog,"Age %d", i);
     for(i=(j+1); i>=1;i--){          }
       cutv(stra,strb,modelsav,'+');          for(jk=1; jk <=nlstate ; jk++){
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/              pp[jk] += freq[jk][m][i]; 
       /*scanf("%d",i);*/          }
       if (strchr(strb,'*')) {          for(jk=1; jk <=nlstate ; jk++){
         cutv(strd,strc,strb,'*');            for(m=-1, pos=0; m <=0 ; m++)
         if (strcmp(strc,"age")==0) {              pos += freq[jk][m][i];
           cptcovprod--;            if(pp[jk]>=1.e-10){
           cutv(strb,stre,strd,'V');              if(first==1){
           Tvar[i]=atoi(stre);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           cptcovage++;              }
             Tage[cptcovage]=i;              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             /*printf("stre=%s ", stre);*/            }else{
         }              if(first==1)
         else if (strcmp(strd,"age")==0) {                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           cptcovprod--;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           cutv(strb,stre,strc,'V');            }
           Tvar[i]=atoi(stre);          }
           cptcovage++;  
           Tage[cptcovage]=i;          for(jk=1; jk <=nlstate ; jk++){
         }            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
         else {              pp[jk] += freq[jk][m][i];
           cutv(strb,stre,strc,'V');          }       
           Tvar[i]=ncov+k1;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
           cutv(strb,strc,strd,'V');            pos += pp[jk];
           Tprod[k1]=i;            posprop += prop[jk][i];
           Tvard[k1][1]=atoi(strc);          }
           Tvard[k1][2]=atoi(stre);          for(jk=1; jk <=nlstate ; jk++){
           Tvar[cptcovn+k2]=Tvard[k1][1];            if(pos>=1.e-5){
           Tvar[cptcovn+k2+1]=Tvard[k1][2];              if(first==1)
           for (k=1; k<=lastobs;k++)                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           k1++;            }else{
           k2=k2+2;              if(first==1)
         }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       }              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       else {            }
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/            if( i <= iagemax){
        /*  scanf("%d",i);*/              if(pos>=1.e-5){
       cutv(strd,strc,strb,'V');                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
       Tvar[i]=atoi(strc);                /*probs[i][jk][j1]= pp[jk]/pos;*/
       }                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
       strcpy(modelsav,stra);                }
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);              else
         scanf("%d",i);*/                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     }            }
 }          }
            
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);          for(jk=-1; jk <=nlstate+ndeath; jk++)
   printf("cptcovprod=%d ", cptcovprod);            for(m=-1; m <=nlstate+ndeath; m++)
   scanf("%d ",i);*/              if(freq[jk][m][i] !=0 ) {
     fclose(fic);              if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     /*  if(mle==1){*/                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     if (weightopt != 1) { /* Maximisation without weights*/              }
       for(i=1;i<=n;i++) weight[i]=1.0;          if(i <= iagemax)
     }            fprintf(ficresp,"\n");
     /*-calculation of age at interview from date of interview and age at death -*/          if(first==1)
     agev=matrix(1,maxwav,1,imx);            printf("Others in log...\n");
           fprintf(ficlog,"\n");
    for (i=1; i<=imx; i++)        }
      for(m=2; (m<= maxwav); m++)      }
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    }
          anint[m][i]=9999;    dateintmean=dateintsum/k2cpt; 
          s[m][i]=-1;   
        }    fclose(ficresp);
        free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     for (i=1; i<=imx; i++)  {    free_vector(pp,1,nlstate);
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
       for(m=1; (m<= maxwav); m++){    /* End of Freq */
         if(s[m][i] >0){  }
           if (s[m][i] == nlstate+1) {  
             if(agedc[i]>0)  /************ Prevalence ********************/
               if(moisdc[i]!=99 && andc[i]!=9999)  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)
               agev[m][i]=agedc[i];  {  
             else {    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
               if (andc[i]!=9999){       in each health status at the date of interview (if between dateprev1 and dateprev2).
               printf("Warning negative age at death: %d line:%d\n",num[i],i);       We still use firstpass and lastpass as another selection.
               agev[m][i]=-1;    */
               }   
             }    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
           }    double ***freq; /* Frequencies */
           else if(s[m][i] !=9){ /* Should no more exist */    double *pp, **prop;
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    double pos,posprop; 
             if(mint[m][i]==99 || anint[m][i]==9999)    double  y2; /* in fractional years */
               agev[m][i]=1;    int iagemin, iagemax;
             else if(agev[m][i] <agemin){  
               agemin=agev[m][i];    iagemin= (int) agemin;
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/    iagemax= (int) agemax;
             }    /*pp=vector(1,nlstate);*/
             else if(agev[m][i] >agemax){    prop=matrix(1,nlstate,iagemin,iagemax+3); 
               agemax=agev[m][i];    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    j1=0;
             }    
             /*agev[m][i]=anint[m][i]-annais[i];*/    j=cptcoveff;
             /*   agev[m][i] = age[i]+2*m;*/    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           }    
           else { /* =9 */    for(k1=1; k1<=j;k1++){
             agev[m][i]=1;      for(i1=1; i1<=ncodemax[k1];i1++){
             s[m][i]=-1;        j1++;
           }        
         }        for (i=1; i<=nlstate; i++)  
         else /*= 0 Unknown */          for(m=iagemin; m <= iagemax+3; m++)
           agev[m][i]=1;            prop[i][m]=0.0;
       }       
            for (i=1; i<=imx; i++) { /* Each individual */
     }          bool=1;
     for (i=1; i<=imx; i++)  {          if  (cptcovn>0) {
       for(m=1; (m<= maxwav); m++){            for (z1=1; z1<=cptcoveff; z1++) 
         if (s[m][i] > (nlstate+ndeath)) {              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
           printf("Error: Wrong value in nlstate or ndeath\n");                  bool=0;
           goto end;          } 
         }          if (bool==1) { 
       }            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     }              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
               if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
     free_vector(severity,1,maxwav);                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); 
     free_imatrix(outcome,1,maxwav+1,1,n);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     free_vector(moisnais,1,n);                  /*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]]);*/
     free_vector(annais,1,n);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     free_matrix(mint,1,maxwav,1,n);                  prop[s[m][i]][iagemax+3] += weight[i]; 
     free_matrix(anint,1,maxwav,1,n);                } 
     free_vector(moisdc,1,n);              }
     free_vector(andc,1,n);            } /* end selection of waves */
           }
            }
     wav=ivector(1,imx);        for(i=iagemin; i <= iagemax+3; i++){  
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          
     mw=imatrix(1,lastpass-firstpass+1,1,imx);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
                posprop += prop[jk][i]; 
     /* Concatenates waves */          } 
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  
           for(jk=1; jk <=nlstate ; jk++){     
             if( i <=  iagemax){ 
       Tcode=ivector(1,100);              if(posprop>=1.e-5){ 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);                probs[i][jk][j1]= prop[jk][i]/posprop;
       ncodemax[1]=1;              } 
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);            } 
                }/* end jk */ 
    codtab=imatrix(1,100,1,10);        }/* end i */ 
    h=0;      } /* end i1 */
    m=pow(2,cptcoveff);    } /* end k1 */
      
    for(k=1;k<=cptcoveff; k++){    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
      for(i=1; i <=(m/pow(2,k));i++){    /*free_vector(pp,1,nlstate);*/
        for(j=1; j <= ncodemax[k]; j++){    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  }  /* End of prevalence */
            h++;  
            if (h>m) h=1;codtab[h][k]=j;  /************* Waves Concatenation ***************/
          }  
        }  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
      }  {
    }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        Death is a valid wave (if date is known).
        mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
    /*for(i=1; i <=m ;i++){       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
      for(k=1; k <=cptcovn; k++){       and mw[mi+1][i]. dh depends on stepm.
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);       */
      }  
      printf("\n");    int i, mi, m;
    }    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
    scanf("%d",i);*/       double sum=0., jmean=0.;*/
        int first;
    /* Calculates basic frequencies. Computes observed prevalence at single age    int j, k=0,jk, ju, jl;
        and prints on file fileres'p'. */    double sum=0.;
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);    first=0;
     jmin=1e+5;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    jmax=-1;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    jmean=0.;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    for(i=1; i<=imx; i++){
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      mi=0;
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      m=firstpass;
            while(s[m][i] <= nlstate){
     /* For Powell, parameters are in a vector p[] starting at p[1]        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */          mw[++mi][i]=m;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */        if(m >=lastpass)
           break;
     if(mle==1){        else
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);          m++;
     }      }/* end while */
          if (s[m][i] > nlstate){
     /*--------- results files --------------*/        mi++;     /* Death is another wave */
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);        /* if(mi==0)  never been interviewed correctly before death */
               /* Only death is a correct wave */
    jk=1;        mw[mi][i]=m;
    fprintf(ficres,"# Parameters\n");      }
    printf("# Parameters\n");  
    for(i=1,jk=1; i <=nlstate; i++){      wav[i]=mi;
      for(k=1; k <=(nlstate+ndeath); k++){      if(mi==0){
        if (k != i)        nbwarn++;
          {        if(first==0){
            printf("%d%d ",i,k);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
            fprintf(ficres,"%1d%1d ",i,k);          first=1;
            for(j=1; j <=ncovmodel; j++){        }
              printf("%f ",p[jk]);        if(first==1){
              fprintf(ficres,"%f ",p[jk]);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
              jk++;        }
            }      } /* end mi==0 */
            printf("\n");    } /* End individuals */
            fprintf(ficres,"\n");  
          }    for(i=1; i<=imx; i++){
      }      for(mi=1; mi<wav[i];mi++){
    }        if (stepm <=0)
  if(mle==1){          dh[mi][i]=1;
     /* Computing hessian and covariance matrix */        else{
     ftolhess=ftol; /* Usually correct */          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     hesscov(matcov, p, npar, delti, ftolhess, func);            if (agedc[i] < 2*AGESUP) {
  }              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     fprintf(ficres,"# Scales\n");              if(j==0) j=1;  /* Survives at least one month after exam */
     printf("# Scales\n");              else if(j<0){
      for(i=1,jk=1; i <=nlstate; i++){                nberr++;
       for(j=1; j <=nlstate+ndeath; j++){                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]);
         if (j!=i) {                j=1; /* Temporary Dangerous patch */
           fprintf(ficres,"%1d%1d",i,j);                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("%1d%1d",i,j);                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(k=1; k<=ncovmodel;k++){                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);
             printf(" %.5e",delti[jk]);              }
             fprintf(ficres," %.5e",delti[jk]);              k=k+1;
             jk++;              if (j >= jmax){
           }                jmax=j;
           printf("\n");                ijmax=i;
           fprintf(ficres,"\n");              }
         }              if (j <= jmin){
       }                jmin=j;
       }                ijmin=i;
                  }
     k=1;              sum=sum+j;
     fprintf(ficres,"# Covariance\n");              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
     printf("# Covariance\n");              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     for(i=1;i<=npar;i++){            }
       /*  if (k>nlstate) k=1;          }
       i1=(i-1)/(ncovmodel*nlstate)+1;          else{
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       printf("%s%d%d",alph[k],i1,tab[i]);*/  /*        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]); */
       fprintf(ficres,"%3d",i);  
       printf("%3d",i);            k=k+1;
       for(j=1; j<=i;j++){            if (j >= jmax) {
         fprintf(ficres," %.5e",matcov[i][j]);              jmax=j;
         printf(" %.5e",matcov[i][j]);              ijmax=i;
       }            }
       fprintf(ficres,"\n");            else if (j <= jmin){
       printf("\n");              jmin=j;
       k++;              ijmin=i;
     }            }
                /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     while((c=getc(ficpar))=='#' && c!= EOF){            /*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]);*/
       ungetc(c,ficpar);            if(j<0){
       fgets(line, MAXLINE, ficpar);              nberr++;
       puts(line);              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]);
       fputs(line,ficparo);              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]);
     }            }
     ungetc(c,ficpar);            sum=sum+j;
            }
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);          jk= j/stepm;
              jl= j -jk*stepm;
     if (fage <= 2) {          ju= j -(jk+1)*stepm;
       bage = agemin;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       fage = agemax;            if(jl==0){
     }              dh[mi][i]=jk;
               bh[mi][i]=0;
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");            }else{ /* We want a negative bias in order to only have interpolation ie
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);                    * at the price of an extra matrix product in likelihood */
               dh[mi][i]=jk+1;
                  bh[mi][i]=ju;
 /*------------ gnuplot -------------*/            }
 chdir(pathcd);          }else{
   if((ficgp=fopen("graph.plt","w"))==NULL) {            if(jl <= -ju){
     printf("Problem with file graph.gp");goto end;              dh[mi][i]=jk;
   }              bh[mi][i]=jl;       /* bias is positive if real duration
 #ifdef windows                                   * is higher than the multiple of stepm and negative otherwise.
   fprintf(ficgp,"cd \"%s\" \n",pathc);                                   */
 #endif            }
 m=pow(2,cptcoveff);            else{
                dh[mi][i]=jk+1;
  /* 1eme*/              bh[mi][i]=ju;
   for (cpt=1; cpt<= nlstate ; cpt ++) {            }
    for (k1=1; k1<= m ; k1 ++) {            if(dh[mi][i]==0){
               dh[mi][i]=1; /* At least one step */
 #ifdef windows              bh[mi][i]=ju; /* At least one step */
     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);              /*  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);*/
 #endif            }
 #ifdef unix          } /* end if mle */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);        }
 #endif      } /* end wave */
     }
 for (i=1; i<= nlstate ; i ++) {    jmean=sum/k;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    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);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
 }   }
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);  
     for (i=1; i<= nlstate ; i ++) {  /*********** Tricode ****************************/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  void tricode(int *Tvar, int **nbcode, int imx)
   else fprintf(ficgp," \%%*lf (\%%*lf)");  {
 }    
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    int Ndum[20],ij=1, k, j, i, maxncov=19;
      for (i=1; i<= nlstate ; i ++) {    int cptcode=0;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    cptcoveff=0; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");   
 }      for (k=0; k<maxncov; k++) Ndum[k]=0;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    for (k=1; k<=7; k++) ncodemax[k]=0;
 #ifdef unix  
 fprintf(ficgp,"\nset ter gif small size 400,300");    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
 #endif      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);                                 modality*/ 
    }        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
   }        Ndum[ij]++; /*store the modality */
   /*2 eme*/        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
   for (k1=1; k1<= m ; k1 ++) {                                         Tvar[j]. If V=sex and male is 0 and 
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);                                         female is 1, then  cptcode=1.*/
          }
     for (i=1; i<= nlstate+1 ; i ++) {  
       k=2*i;      for (i=0; i<=cptcode; i++) {
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
       for (j=1; j<= nlstate+1 ; j ++) {      }
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");      ij=1; 
 }        for (i=1; i<=ncodemax[j]; i++) {
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");        for (k=0; k<= maxncov; k++) {
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);          if (Ndum[k] != 0) {
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);            nbcode[Tvar[j]][ij]=k; 
       for (j=1; j<= nlstate+1 ; j ++) {            /* 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; */
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");            
         else fprintf(ficgp," \%%*lf (\%%*lf)");            ij++;
 }            }
       fprintf(ficgp,"\" t\"\" w l 0,");          if (ij > ncodemax[j]) break; 
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);        }  
       for (j=1; j<= nlstate+1 ; j ++) {      } 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    }  
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }     for (k=0; k< maxncov; k++) Ndum[k]=0;
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  
       else fprintf(ficgp,"\" t\"\" w l 0,");   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.*/
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);     ij=Tvar[i];
   }     Ndum[ij]++;
     }
   /*3eme*/  
    ij=1;
   for (k1=1; k1<= m ; k1 ++) {   for (i=1; i<= maxncov; i++) {
     for (cpt=1; cpt<= nlstate ; cpt ++) {     if((Ndum[i]!=0) && (i<=ncovcol)){
       k=2+nlstate*(cpt-1);       Tvaraff[ij]=i; /*For printing */
       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);       ij++;
       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);   }
       }   
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);   cptcoveff=ij-1; /*Number of simple covariates*/
     }  }
   }  
    /*********** Health Expectancies ****************/
   /* CV preval stat */  
   for (k1=1; k1<= m ; k1 ++) {  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
     for (cpt=1; cpt<nlstate ; cpt ++) {  
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);    /* Health expectancies, no variances */
       for (i=1; i< nlstate ; i ++)    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
         fprintf(ficgp,"+$%d",k+i+1);    double age, agelim, hf;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    double ***p3mat;
          double eip;
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    pstamp(ficreseij);
       for (i=1; i< nlstate ; i ++) {    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
         l=3+(nlstate+ndeath)*cpt;    fprintf(ficreseij,"# Age");
         fprintf(ficgp,"+$%d",l+i+1);    for(i=1; i<=nlstate;i++){
       }      for(j=1; j<=nlstate;j++){
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);          fprintf(ficreseij," e%1d%1d ",i,j);
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      }
     }      fprintf(ficreseij," e%1d. ",i);
   }      }
     fprintf(ficreseij,"\n");
   /* proba elementaires */  
    for(i=1,jk=1; i <=nlstate; i++){    
     for(k=1; k <=(nlstate+ndeath); k++){    if(estepm < stepm){
       if (k != i) {      printf ("Problem %d lower than %d\n",estepm, stepm);
         for(j=1; j <=ncovmodel; j++){    }
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    else  hstepm=estepm;   
           /*fprintf(ficgp,"%s",alph[1]);*/    /* We compute the life expectancy from trapezoids spaced every estepm months
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);     * This is mainly to measure the difference between two models: for example
           jk++;     * if stepm=24 months pijx are given only every 2 years and by summing them
           fprintf(ficgp,"\n");     * we are calculating an estimate of the Life Expectancy assuming a linear 
         }     * progression in between and thus overestimating or underestimating according
       }     * to the curvature of the survival function. If, for the same date, we 
     }     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     }     * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
   for(jk=1; jk <=m; jk++) {     * curvature will be obtained if estepm is as small as stepm. */
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);  
    i=1;    /* For example we decided to compute the life expectancy with the smallest unit */
    for(k2=1; k2<=nlstate; k2++) {    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
      k3=i;       nhstepm is the number of hstepm from age to agelim 
      for(k=1; k<=(nlstate+ndeath); k++) {       nstepm is the number of stepm from age to agelin. 
        if (k != k2){       Look at hpijx to understand the reason of that which relies in memory size
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);       and note for a fixed period like estepm months */
 ij=1;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         for(j=3; j <=ncovmodel; j++) {       survival function given by stepm (the optimization length). Unfortunately it
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {       means that if the survival funtion is printed only each two years of age and if
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
             ij++;       results. So we changed our mind and took the option of the best precision.
           }    */
           else    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  
         }    agelim=AGESUP;
           fprintf(ficgp,")/(1");    /* nhstepm age range expressed in number of stepm */
            nstepm=(int) rint((agelim-age)*YEARM/stepm); 
         for(k1=1; k1 <=nlstate; k1++){      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    /* if (stepm >= YEARM) hstepm=1;*/
 ij=1;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
           for(j=3; j <=ncovmodel; j++){    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           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]]]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
             ij++;      /* Computed by stepm unit matrices, product of hstepm matrices, stored
           }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
           else      
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
           }      
           fprintf(ficgp,")");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         }      
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);      printf("%d|",(int)age);fflush(stdout);
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         i=i+ncovmodel;      
        }      /* Computing expectancies */
      }      for(i=1; i<=nlstate;i++)
    }        for(j=1; j<=nlstate;j++)
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   }            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
                
   fclose(ficgp);            /* 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]);*/
      
 chdir(path);          }
     free_matrix(agev,1,maxwav,1,imx);  
     free_ivector(wav,1,imx);      fprintf(ficreseij,"%3.0f",age );
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      for(i=1; i<=nlstate;i++){
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);        eip=0;
            for(j=1; j<=nlstate;j++){
     free_imatrix(s,1,maxwav+1,1,n);          eip +=eij[i][j][(int)age];
              fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
            }
     free_ivector(num,1,n);        fprintf(ficreseij,"%9.4f", eip );
     free_vector(agedc,1,n);      }
     free_vector(weight,1,n);      fprintf(ficreseij,"\n");
     /*free_matrix(covar,1,NCOVMAX,1,n);*/      
     fclose(ficparo);    }
     fclose(ficres);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     /*  }*/    printf("\n");
        fprintf(ficlog,"\n");
    /*________fin mle=1_________*/    
      }
   
    void cvevsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
     /* No more information from the sample is required now */  
   /* Reads comments: lines beginning with '#' */  {
   while((c=getc(ficpar))=='#' && c!= EOF){    /* Covariances of health expectancies eij and of total life expectancies according
     ungetc(c,ficpar);     to initial status i, ei. .
     fgets(line, MAXLINE, ficpar);    */
     puts(line);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
     fputs(line,ficparo);    double age, agelim, hf;
   }    double ***p3matp, ***p3matm, ***varhe;
   ungetc(c,ficpar);    double **dnewm,**doldm;
      double *xp, *xm;
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    double **gp, **gm;
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    double ***gradg, ***trgradg;
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    int theta;
 /*--------- index.htm --------*/  
     double eip, vip;
   strcpy(optionfilehtm,optionfile);  
   strcat(optionfilehtm,".htm");    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    xp=vector(1,npar);
     printf("Problem with %s \n",optionfilehtm);goto end;    xm=vector(1,npar);
   }    dnewm=matrix(1,nlstate*nlstate,1,npar);
     doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.64b </font> <hr size=\"2\" color=\"#EC5E5E\">    
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    pstamp(ficresstdeij);
 Total number of observations=%d <br>    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>    fprintf(ficresstdeij,"# Age");
 <hr  size=\"2\" color=\"#EC5E5E\">    for(i=1; i<=nlstate;i++){
 <li>Outputs files<br><br>\n      for(j=1; j<=nlstate;j++)
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>      fprintf(ficresstdeij," e%1d. ",i);
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>    }
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>    fprintf(ficresstdeij,"\n");
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    pstamp(ficrescveij);
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    fprintf(ficrescveij,"# Age");
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>    for(i=1; i<=nlstate;i++)
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>      for(j=1; j<=nlstate;j++){
 <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);        cptj= (j-1)*nlstate+i;
         for(i2=1; i2<=nlstate;i2++)
  fprintf(fichtm," <li>Graphs</li><p>");          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
  m=cptcoveff;            if(cptj2 <= cptj)
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
  j1=0;      }
  for(k1=1; k1<=m;k1++){    fprintf(ficrescveij,"\n");
    for(i1=1; i1<=ncodemax[k1];i1++){    
        j1++;    if(estepm < stepm){
        if (cptcovn > 0) {      printf ("Problem %d lower than %d\n",estepm, stepm);
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    }
          for (cpt=1; cpt<=cptcoveff;cpt++)    else  hstepm=estepm;   
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);    /* We compute the life expectancy from trapezoids spaced every estepm months
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");     * 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
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>     * we are calculating an estimate of the Life Expectancy assuming a linear 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);         * progression in between and thus overestimating or underestimating according
        for(cpt=1; cpt<nlstate;cpt++){     * to the curvature of the survival function. If, for the same date, we 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>     * estimate the model with stepm=1 month, we can keep estepm to 24 months
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);     * to compare the new estimate of Life expectancy with the same linear 
        }     * hypothesis. A more precise result, taking into account a more precise
     for(cpt=1; cpt<=nlstate;cpt++) {     * curvature will be obtained if estepm is as small as stepm. */
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  
 interval) in state (%d): v%s%d%d.gif <br>    /* For example we decided to compute the life expectancy with the smallest unit */
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
      }       nhstepm is the number of hstepm from age to agelim 
      for(cpt=1; cpt<=nlstate;cpt++) {       nstepm is the number of stepm from age to agelin. 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>       Look at hpijx to understand the reason of that which relies in memory size
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);       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(fichtm,"\n<br>- Total life expectancy by age and       survival function given by stepm (the optimization length). Unfortunately it
 health expectancies in states (1) and (2): e%s%d.gif<br>       means that if the survival funtion is printed only each two years of age and if
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
 fprintf(fichtm,"\n</body>");       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 */ 
 fclose(fichtm);  
     /* If stepm=6 months */
   /*--------------- Prevalence limit --------------*/    /* nhstepm age range expressed in number of stepm */
      agelim=AGESUP;
   strcpy(filerespl,"pl");    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
   strcat(filerespl,fileres);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    /* if (stepm >= YEARM) hstepm=1;*/
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }    
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficrespl,"#Prevalence limit\n");    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficrespl,"#Age ");    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   fprintf(ficrespl,"\n");    gp=matrix(0,nhstepm,1,nlstate*nlstate);
      gm=matrix(0,nhstepm,1,nlstate*nlstate);
   prlim=matrix(1,nlstate,1,nlstate);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    for (age=bage; age<=fage; age ++){ 
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* Computed by stepm unit matrices, product of hstepm matrices, stored
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */   
   k=0;      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   agebase=agemin;  
   agelim=agemax;      /* Computing  Variances of health expectancies */
   ftolpl=1.e-10;      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   i1=cptcoveff;         decrease memory allocation */
   if (cptcovn < 1){i1=1;}      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
   for(cptcov=1;cptcov<=i1;cptcov++){          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          xm[i] = x[i] - (i==theta ?delti[theta]:0);
         k=k+1;        }
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         fprintf(ficrespl,"\n#******");        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
         for(j=1;j<=cptcoveff;j++)    
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(j=1; j<= nlstate; j++){
         fprintf(ficrespl,"******\n");          for(i=1; i<=nlstate; i++){
                    for(h=0; h<=nhstepm-1; h++){
         for (age=agebase; age<=agelim; age++){              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
           fprintf(ficrespl,"%.0f",age );            }
           for(i=1; i<=nlstate;i++)          }
           fprintf(ficrespl," %.5f", prlim[i][i]);        }
           fprintf(ficrespl,"\n");       
         }        for(ij=1; ij<= nlstate*nlstate; ij++)
       }          for(h=0; h<=nhstepm-1; h++){
     }            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   fclose(ficrespl);          }
       }/* End theta */
   /*------------- h Pij x at various ages ------------*/      
        
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      for(h=0; h<=nhstepm-1; h++)
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        for(j=1; j<=nlstate*nlstate;j++)
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;          for(theta=1; theta <=npar; theta++)
   }            trgradg[h][j][theta]=gradg[h][theta][j];
   printf("Computing pij: result on file '%s' \n", filerespij);      
    
   stepsize=(int) (stepm+YEARM-1)/YEARM;       for(ij=1;ij<=nlstate*nlstate;ij++)
   /*if (stepm<=24) stepsize=2;*/        for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
   agelim=AGESUP;  
   hstepm=stepsize*YEARM; /* Every year of age */       printf("%d|",(int)age);fflush(stdout);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         for(h=0;h<=nhstepm-1;h++){
   k=0;        for(k=0;k<=nhstepm-1;k++){
   for(cptcov=1;cptcov<=i1;cptcov++){          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       k=k+1;          for(ij=1;ij<=nlstate*nlstate;ij++)
         fprintf(ficrespij,"\n#****** ");            for(ji=1;ji<=nlstate*nlstate;ji++)
         for(j=1;j<=cptcoveff;j++)              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        }
         fprintf(ficrespij,"******\n");      }
              /* Computing expectancies */
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for(i=1; i<=nlstate;i++)
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        for(j=1; j<=nlstate;j++)
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
           oldm=oldms;savm=savms;            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              
           fprintf(ficrespij,"# Age");            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)          }
               fprintf(ficrespij," %1d-%1d",i,j);  
           fprintf(ficrespij,"\n");      fprintf(ficresstdeij,"%3.0f",age );
           for (h=0; h<=nhstepm; h++){      for(i=1; i<=nlstate;i++){
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        eip=0.;
             for(i=1; i<=nlstate;i++)        vip=0.;
               for(j=1; j<=nlstate+ndeath;j++)        for(j=1; j<=nlstate;j++){
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          eip += eij[i][j][(int)age];
             fprintf(ficrespij,"\n");          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
           }            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
           fprintf(ficrespij,"\n");        }
         }        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
     }      }
   }      fprintf(ficresstdeij,"\n");
   
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/      fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
   fclose(ficrespij);        for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
   /*---------- Forecasting ------------------*/          for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
   strcpy(fileresf,"f");              cptj2= (j2-1)*nlstate+i2;
   strcat(fileresf,fileres);              if(cptj2 <= cptj)
   if((ficresf=fopen(fileresf,"w"))==NULL) {                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;            }
   }        }
   printf("Computing forecasting: result on file '%s' \n", fileresf);      fprintf(ficrescveij,"\n");
      
   /* Mobile average */    }
     free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   /* for (agedeb=bage; agedeb<=fage; agedeb++)    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     for (i=1; i<=nlstate;i++)    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++)    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       printf("%f %d i=%d j1=%d\n", probs[(int)agedeb][i][cptcod],(int) agedeb,i,cptcod);*/    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    printf("\n");
     fprintf(ficlog,"\n");
   if (mobilav==1) {  
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    free_vector(xm,1,npar);
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)    free_vector(xp,1,npar);
       for (i=1; i<=nlstate;i++)    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
           mobaverage[(int)agedeb][i][cptcod]=0.;    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
      }
     for (agedeb=bage+4; agedeb<=fage; agedeb++){  
       for (i=1; i<=nlstate;i++){  /************ Variance ******************/
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  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 (cpt=0;cpt<=4;cpt++){  {
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    /* Variance of health expectancies */
           }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;    /* double **newm;*/
         }    double **dnewm,**doldm;
       }    double **dnewmp,**doldmp;
     }      int i, j, nhstepm, hstepm, h, nstepm ;
   }    int k, cptcode;
     double *xp;
   stepsize=(int) (stepm+YEARM-1)/YEARM;    double **gp, **gm;  /* for var eij */
   if (stepm<=24) stepsize=2;    double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
   agelim=AGESUP;    double *gpp, *gmp; /* for var p point j */
   hstepm=stepsize*YEARM; /* Every year of age */    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    double ***p3mat;
   hstepm=12;    double age,agelim, hf;
    k=0;    double ***mobaverage;
   for(cptcov=1;cptcov<=i1;cptcov++){    int theta;
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    char digit[4];
       k=k+1;    char digitp[25];
       fprintf(ficresf,"\n#****** ");  
       for(j=1;j<=cptcoveff;j++) {    char fileresprobmorprev[FILENAMELENGTH];
         fprintf(ficresf,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       }    if(popbased==1){
            if(mobilav!=0)
       fprintf(ficresf,"******\n");        strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
       fprintf(ficresf,"# StartingAge FinalAge Horizon(in years)");    }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    else 
       strcpy(digitp,"-stablbased-");
       for (agedeb=fage; agedeb>=bage; agedeb--){  
         fprintf(ficresf,"\n%d %.f %.f 0 ",k,agedeb, agedeb);    if (mobilav!=0) {
        if (mobilav==1) {      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         for(j=1; j<=nlstate;j++)      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficresf,"%.5f ",mobaverage[(int)agedeb][j][cptcod]);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
         else {      }
           for(j=1; j<=nlstate;j++)    }
           fprintf(ficresf,"%.5f ",probs[(int)agedeb][j][cptcod]);  
         }    strcpy(fileresprobmorprev,"prmorprev"); 
            sprintf(digit,"%-d",ij);
       for(j=1; j<=ndeath;j++) fprintf(ficresf,"0.");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
       }    strcat(fileresprobmorprev,digit); /* Tvar to be done */
       for (cpt=1; cpt<=NCOVMAX;cpt++)      strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
       for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    strcat(fileresprobmorprev,fileres);
            if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      printf("Problem with resultfile: %s\n", fileresprobmorprev);
         nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
         /*printf("stepm=%d hstepm=%d nhstepm=%d \n",stepm,hstepm,nhstepm);*/    }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);   
         oldm=oldms;savm=savms;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      pstamp(ficresprobmorprev);
                    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);
         for (h=0; h<=nhstepm; h++){    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
            for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           if (h*hstepm/YEARM*stepm==cpt)      fprintf(ficresprobmorprev," p.%-d SE",j);
  fprintf(ficresf,"\n%d %.f %.f %.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm, h*hstepm/YEARM*stepm);      for(i=1; i<=nlstate;i++)
                  fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           for(j=1; j<=nlstate+ndeath;j++) {    }  
             kk1=0.;    fprintf(ficresprobmorprev,"\n");
             for(i=1; i<=nlstate;i++) {            fprintf(ficgp,"\n# Routine varevsij");
               if (mobilav==1)    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
               kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb][i][cptcod];    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");
               else kk1=kk1+p3mat[i][j][h]*probs[(int)agedeb][i][cptcod];    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
             }      /*   } */
             if (h*hstepm/YEARM*stepm==cpt) fprintf(ficresf," %.5f ", kk1);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           }    pstamp(ficresvij);
         }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if(popbased==1)
       }      fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
     }    else
   }      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    fprintf(ficresvij,"# Age");
   fclose(ficresf);    for(i=1; i<=nlstate;i++)
   /*---------- Health expectancies and variances ------------*/      for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
   strcpy(filerest,"t");    fprintf(ficresvij,"\n");
   strcat(filerest,fileres);  
   if((ficrest=fopen(filerest,"w"))==NULL) {    xp=vector(1,npar);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    dnewm=matrix(1,nlstate,1,npar);
   }    doldm=matrix(1,nlstate,1,nlstate);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
   strcpy(filerese,"e");    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   strcat(filerese,fileres);    gpp=vector(nlstate+1,nlstate+ndeath);
   if((ficreseij=fopen(filerese,"w"))==NULL) {    gmp=vector(nlstate+1,nlstate+ndeath);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   }    
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
  strcpy(fileresv,"v");    }
   strcat(fileresv,fileres);    else  hstepm=estepm;   
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    /* For example we decided to compute the life expectancy with the smallest unit */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    /* 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 
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   k=0;       and note for a fixed period like k years */
   for(cptcov=1;cptcov<=i1;cptcov++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       survival function given by stepm (the optimization length). Unfortunately it
       k=k+1;       means that if the survival funtion is printed every two years of age and if
       fprintf(ficrest,"\n#****** ");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       for(j=1;j<=cptcoveff;j++)       results. So we changed our mind and took the option of the best precision.
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    */
       fprintf(ficrest,"******\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
       fprintf(ficreseij,"\n#****** ");    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       for(j=1;j<=cptcoveff;j++)      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       fprintf(ficreseij,"******\n");      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       fprintf(ficresvij,"\n#****** ");      gp=matrix(0,nhstepm,1,nlstate);
       for(j=1;j<=cptcoveff;j++)      gm=matrix(0,nhstepm,1,nlstate);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficresvij,"******\n");  
       for(theta=1; theta <=npar; theta++){
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
       oldm=oldms;savm=savms;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);          }
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       oldm=oldms;savm=savms;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  
              if (popbased==1) {
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          if(mobilav ==0){
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);            for(i=1; i<=nlstate;i++)
       fprintf(ficrest,"\n");              prlim[i][i]=probs[(int)age][i][ij];
                  }else{ /* mobilav */ 
       hf=1;            for(i=1; i<=nlstate;i++)
       if (stepm >= YEARM) hf=stepm/YEARM;              prlim[i][i]=mobaverage[(int)age][i][ij];
       epj=vector(1,nlstate+1);          }
       for(age=bage; age <=fage ;age++){        }
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    
         if (popbased==1) {        for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate;i++)          for(h=0; h<=nhstepm; h++){
             prlim[i][i]=probs[(int)age][i][k];            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
         }              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
                  }
         fprintf(ficrest," %.0f",age);        }
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){        /* This for computing probability of death (h=1 means
           for(i=1, epj[j]=0.;i <=nlstate;i++) {           computed over hstepm matrices product = hstepm*stepm months) 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];           as a weighted average of prlim.
           }        */
           epj[nlstate+1] +=epj[j];        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
         for(i=1, vepp=0.;i <=nlstate;i++)            gpp[j] += prlim[i][i]*p3mat[i][j][1];
           for(j=1;j <=nlstate;j++)        }    
             vepp += vareij[i][j][(int)age];        /* end probability of death */
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));  
         for(j=1;j <=nlstate;j++){        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         fprintf(ficrest,"\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       }   
     }        if (popbased==1) {
   }          if(mobilav ==0){
                    for(i=1; i<=nlstate;i++)
                      prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
  fclose(ficreseij);              prlim[i][i]=mobaverage[(int)age][i][ij];
  fclose(ficresvij);          }
   fclose(ficrest);        }
   fclose(ficpar);  
   free_vector(epj,1,nlstate+1);        for(j=1; j<= nlstate; j++){
   /*  scanf("%d ",i); */          for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   /*------- Variance limit prevalence------*/                gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
 strcpy(fileresvpl,"vpl");        }
   strcat(fileresvpl,fileres);        /* This for computing probability of death (h=1 means
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {           computed over hstepm matrices product = hstepm*stepm months) 
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);           as a weighted average of prlim.
     exit(0);        */
   }        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
  k=0;        }    
  for(cptcov=1;cptcov<=i1;cptcov++){        /* end probability of death */
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
      k=k+1;        for(j=1; j<= nlstate; j++) /* vareij */
      fprintf(ficresvpl,"\n#****** ");          for(h=0; h<=nhstepm; h++){
      for(j=1;j<=cptcoveff;j++)            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          }
      fprintf(ficresvpl,"******\n");  
              for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
      varpl=matrix(1,nlstate,(int) bage, (int) fage);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
      oldm=oldms;savm=savms;        }
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  
    }      } /* End theta */
  }  
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   fclose(ficresvpl);  
       for(h=0; h<=nhstepm; h++) /* veij */
   /*---------- End : free ----------------*/        for(j=1; j<=nlstate;j++)
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);          for(theta=1; theta <=npar; theta++)
              trgradg[h][j][theta]=gradg[h][theta][j];
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
          for(theta=1; theta <=npar; theta++)
            trgradgp[j][theta]=gradgp[theta][j];
   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);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);      for(i=1;i<=nlstate;i++)
          for(j=1;j<=nlstate;j++)
   free_matrix(matcov,1,npar,1,npar);          vareij[i][j][(int)age] =0.;
   free_vector(delti,1,npar);  
        for(h=0;h<=nhstepm;h++){
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
   printf("End of Imach\n");          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          for(i=1;i<=nlstate;i++)
              for(j=1;j<=nlstate;j++)
   /* 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);*/              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
   /*printf("Total time was %d uSec.\n", total_usecs);*/        }
   /*------ End -----------*/      }
     
       /* pptj */
  end:      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
 #ifdef windows      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
  chdir(pathcd);      for(j=nlstate+1;j<=nlstate+ndeath;j++)
 #endif        for(i=nlstate+1;i<=nlstate+ndeath;i++)
            varppt[j][i]=doldmp[j][i];
  system("..\\gp37mgw\\wgnuplot graph.plt");      /* end ppptj */
       /*  x centered again */
 #ifdef windows      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
   while (z[0] != 'q') {      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     chdir(pathcd);   
     printf("\nType e to edit output files, c to start again, and q for exiting: ");      if (popbased==1) {
     scanf("%s",z);        if(mobilav ==0){
     if (z[0] == 'c') system("./imach");          for(i=1; i<=nlstate;i++)
     else if (z[0] == 'e') {            prlim[i][i]=probs[(int)age][i][ij];
       chdir(path);        }else{ /* mobilav */ 
       system(optionfilehtm);          for(i=1; i<=nlstate;i++)
     }            prlim[i][i]=mobaverage[(int)age][i][ij];
     else if (z[0] == 'q') exit(0);        }
   }      }
 #endif               
 }      /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     
     pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     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, (b) health expectancies by health status at initial age:  ei., eij (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), eij are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences (i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char  *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem 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;
       lval=strtol(strb,&endptr,10); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%d' at line number %ld %s for individual %d\nShould be a weight.  Exiting.\n",lval, i,line,linei);
         exit(1);
       }
       weight[i]=(double)(lval); 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a value of the %d covar (meaning 0 for the reference or 1. IMaCh does not build design variables, do it your self).  Exiting.\n",lval,linei, i,line,j);
           exit(1);
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       } 
       lstra=strlen(stra);
       
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
     fclose(fic);
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
     /* for (i=1; i<=imx; i++) */
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<body>\n<title>IMaCh Cov %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<body>\n<title>IMaCh %s</title>\n <font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             fileres,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
       
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%f ",p[jk]);
               fprintf(ficlog,"%f ",p[jk]);
               fprintf(ficres,"%f ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /*---------- Health expectancies and variances ------------*/
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficreseij,"\n#****** ");
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
           cvevsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav, strstart);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav, strstart);
           }
   
           pstamp(ficrest);
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n# Age ( e.. (std) ");
           for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
           fprintf(ficrest,"\n");
   
           epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             if (popbased==1) {
               if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=probs[(int)age][i][k];
               }else{ /* mobilav */ 
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=mobaverage[(int)age][i][k];
               }
             }
           
             fprintf(ficrest," %4.0f",age);
             for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
               for(i=1, epj[j]=0.;i <=nlstate;i++) {
                 epj[j] += prlim[i][i]*eij[i][j][(int)age];
                 /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
               }
               epj[nlstate+1] +=epj[j];
             }
   
             for(i=1, vepp=0.;i <=nlstate;i++)
               for(j=1;j <=nlstate;j++)
                 vepp += vareij[i][j][(int)age];
             fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
             for(j=1;j <=nlstate;j++){
               fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
             }
             fprintf(ficrest,"\n");
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficreseij);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>",strstart, strtend);
     fclose(fichtm);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

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  Added in v.1.120


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