Diff for /imach/src/imach.c between versions 1.9 and 1.126

version 1.9, 2001/05/02 18:44:18 version 1.126, 2006/04/28 17:23:28
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      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.126  2006/04/28 17:23:28  brouard
   individuals from different ages are interviewed on their health status    (Module): Yes the sum of survivors was wrong since
   or degree of  disability. At least a second wave of interviews    imach-114 because nhstepm was no more computed in the age
   ("longitudinal") should  measure each new individual health status.    loop. Now we define nhstepma in the age loop.
   Health expectancies are computed from the transistions observed between    Version 0.98h
   waves and are computed for each degree of severity of disability (number  
   of life states). More degrees you consider, more time is necessary to    Revision 1.125  2006/04/04 15:20:31  lievre
   reach the Maximum Likelihood of the parameters involved in the model.    Errors in calculation of health expectancies. Age was not initialized.
   The simplest model is the multinomial logistic model where pij is    Forecasting file added.
   the probabibility to be observed in state j at the second wave conditional  
   to be observed in state i at the first wave. Therefore the model is:    Revision 1.124  2006/03/22 17:13:53  lievre
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Parameters are printed with %lf instead of %f (more numbers after the comma).
   is a covariate. If you want to have a more complex model than "constant and    The log-likelihood is printed in the log file
   age", you should modify the program where the markup  
     *Covariates have to be included here again* invites you to do it.    Revision 1.123  2006/03/20 10:52:43  brouard
   More covariates you add, less is the speed of the convergence.    * imach.c (Module): <title> changed, corresponds to .htm file
     name. <head> headers where missing.
   The advantage that this computer programme claims, comes from that if the  
   delay between waves is not identical for each individual, or if some    * imach.c (Module): Weights can have a decimal point as for
   individual missed an interview, the information is not rounded or lost, but    English (a comma might work with a correct LC_NUMERIC environment,
   taken into account using an interpolation or extrapolation.    otherwise the weight is truncated).
   hPijx is the probability to be    Modification of warning when the covariates values are not 0 or
   observed in state i at age x+h conditional to the observed state i at age    1.
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Version 0.98g
   unobserved intermediate  states. This elementary transition (by month or  
   quarter trimester, semester or year) is model as a multinomial logistic.    Revision 1.122  2006/03/20 09:45:41  brouard
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    (Module): Weights can have a decimal point as for
   and the contribution of each individual to the likelihood is simply hPijx.    English (a comma might work with a correct LC_NUMERIC environment,
     otherwise the weight is truncated).
   Also this programme outputs the covariance matrix of the parameters but also    Modification of warning when the covariates values are not 0 or
   of the life expectancies. It also computes the prevalence limits.    1.
      Version 0.98g
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).  
            Institut national d'études démographiques, Paris.    Revision 1.121  2006/03/16 17:45:01  lievre
   This software have been partly granted by Euro-REVES, a concerted action    * imach.c (Module): Comments concerning covariates added
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    * imach.c (Module): refinements in the computation of lli if
   software can be distributed freely for non commercial use. Latest version    status=-2 in order to have more reliable computation if stepm is
   can be accessed at http://euroreves.ined.fr/imach .    not 1 month. Version 0.98f
   **********************************************************************/  
      Revision 1.120  2006/03/16 15:10:38  lievre
 #include <math.h>    (Module): refinements in the computation of lli if
 #include <stdio.h>    status=-2 in order to have more reliable computation if stepm is
 #include <stdlib.h>    not 1 month. Version 0.98f
 #include <unistd.h>  
     Revision 1.119  2006/03/15 17:42:26  brouard
 #define MAXLINE 256    (Module): Bug if status = -2, the loglikelihood was
 #define FILENAMELENGTH 80    computed as likelihood omitting the logarithm. Version O.98e
 /*#define DEBUG*/  
 #define windows    Revision 1.118  2006/03/14 18:20:07  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): varevsij Comments added explaining the second
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    (Module): Function pstamp added
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    (Module): Version 0.98d
   
 #define NINTERVMAX 8    Revision 1.117  2006/03/14 17:16:22  brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    (Module): varevsij Comments added explaining the second
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    table of variances if popbased=1 .
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define MAXN 20000    (Module): Function pstamp added
 #define YEARM 12. /* Number of months per year */    (Module): Version 0.98d
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Revision 1.115  2006/02/27 12:17:45  brouard
 int npar=NPARMAX;    (Module): One freematrix added in mlikeli! 0.98c
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.114  2006/02/26 12:57:58  brouard
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    (Module): Some improvements in processing parameter
     filename with strsep.
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.113  2006/02/24 14:20:24  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    (Module): Memory leaks checks with valgrind and:
 int mle, weightopt;    datafile was not closed, some imatrix were not freed and on matrix
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    allocation too.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.112  2006/01/30 09:55:26  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    Revision 1.111  2006/01/25 20:38:18  brouard
 FILE *ficgp, *fichtm;    (Module): Lots of cleaning and bugs added (Gompertz)
 FILE *ficreseij;    (Module): Comments can be added in data file. Missing date values
   char filerese[FILENAMELENGTH];    can be a simple dot '.'.
  FILE  *ficresvij;  
   char fileresv[FILENAMELENGTH];    Revision 1.110  2006/01/25 00:51:50  brouard
  FILE  *ficresvpl;    (Module): Lots of cleaning and bugs added (Gompertz)
   char fileresvpl[FILENAMELENGTH];  
     Revision 1.109  2006/01/24 19:37:15  brouard
 #define NR_END 1    (Module): Comments (lines starting with a #) are allowed in data.
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.108  2006/01/19 18:05:42  lievre
     Gnuplot problem appeared...
 #define NRANSI    To be fixed
 #define ITMAX 200  
     Revision 1.107  2006/01/19 16:20:37  brouard
 #define TOL 2.0e-4    Test existence of gnuplot in imach path
   
 #define CGOLD 0.3819660    Revision 1.106  2006/01/19 13:24:36  brouard
 #define ZEPS 1.0e-10    Some cleaning and links added in html output
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     Revision 1.105  2006/01/05 20:23:19  lievre
 #define GOLD 1.618034    *** empty log message ***
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 static double maxarg1,maxarg2;    (Module): If the status is missing at the last wave but we know
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    that the person is alive, then we can code his/her status as -2
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    (instead of missing=-1 in earlier versions) and his/her
      contributions to the likelihood is 1 - Prob of dying from last
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 #define rint(a) floor(a+0.5)    the healthy state at last known wave). Version is 0.98
   
 static double sqrarg;    Revision 1.103  2005/09/30 15:54:49  lievre
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    (Module): sump fixed, loop imx fixed, and simplifications.
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     Revision 1.102  2004/09/15 17:31:30  brouard
 int imx;    Add the possibility to read data file including tab characters.
 int stepm;  
 /* Stepm, step in month: minimum step interpolation*/    Revision 1.101  2004/09/15 10:38:38  brouard
     Fix on curr_time
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.100  2004/07/12 18:29:06  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Add version for Mac OS X. Just define UNIX in Makefile
 double **pmmij;  
     Revision 1.99  2004/06/05 08:57:40  brouard
 double *weight;    *** empty log message ***
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.98  2004/05/16 15:05:56  brouard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    state at each age, but using a Gompertz model: log u =a + b*age .
 double ftolhess; /* Tolerance for computing hessian */    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
 /**************** split *************************/    cross-longitudinal survey is different from the mortality estimated
 static  int split( char *path, char *dirc, char *name )    from other sources like vital statistic data.
 {  
    char *s;                             /* pointer */    The same imach parameter file can be used but the option for mle should be -3.
    int  l1, l2;                         /* length counters */  
     Agnès, who wrote this part of the code, tried to keep most of the
    l1 = strlen( path );                 /* length of path */    former routines in order to include the new code within the former code.
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  
    s = strrchr( path, '\\' );           /* find last / */    The output is very simple: only an estimate of the intercept and of
    if ( s == NULL ) {                   /* no directory, so use current */    the slope with 95% confident intervals.
 #if     defined(__bsd__)                /* get current working directory */  
       extern char       *getwd( );    Current limitations:
     A) Even if you enter covariates, i.e. with the
       if ( getwd( dirc ) == NULL ) {    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 #else    B) There is no computation of Life Expectancy nor Life Table.
       extern char       *getcwd( );  
     Revision 1.97  2004/02/20 13:25:42  lievre
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Version 0.96d. Population forecasting command line is (temporarily)
 #endif    suppressed.
          return( GLOCK_ERROR_GETCWD );  
       }    Revision 1.96  2003/07/15 15:38:55  brouard
       strcpy( name, path );             /* we've got it */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
    } else {                             /* strip direcotry from path */    rewritten within the same printf. Workaround: many printfs.
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.95  2003/07/08 07:54:34  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    * imach.c (Repository):
       strcpy( name, s );                /* save file name */    (Repository): Using imachwizard code to output a more meaningful covariance
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    matrix (cov(a12,c31) instead of numbers.
       dirc[l1-l2] = 0;                  /* add zero */  
    }    Revision 1.94  2003/06/27 13:00:02  brouard
    l1 = strlen( dirc );                 /* length of directory */    Just cleaning
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
    return( 0 );                         /* we're done */    Revision 1.93  2003/06/25 16:33:55  brouard
 }    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
     (Module): Version 0.96b
 /******************************************/  
     Revision 1.92  2003/06/25 16:30:45  brouard
 void replace(char *s, char*t)    (Module): On windows (cygwin) function asctime_r doesn't
 {    exist so I changed back to asctime which exists.
   int i;  
   int lg=20;    Revision 1.91  2003/06/25 15:30:29  brouard
   i=0;    * imach.c (Repository): Duplicated warning errors corrected.
   lg=strlen(t);    (Repository): Elapsed time after each iteration is now output. It
   for(i=0; i<= lg; i++) {    helps to forecast when convergence will be reached. Elapsed time
     (s[i] = t[i]);    is stamped in powell.  We created a new html file for the graphs
     if (t[i]== '\\') s[i]='/';    concerning matrix of covariance. It has extension -cov.htm.
   }  
 }    Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
 int nbocc(char *s, char occ)    mle=-1 a template is output in file "or"mypar.txt with the design
 {    of the covariance matrix to be input.
   int i,j=0;  
   int lg=20;    Revision 1.89  2003/06/24 12:30:52  brouard
   i=0;    (Module): Some bugs corrected for windows. Also, when
   lg=strlen(s);    mle=-1 a template is output in file "or"mypar.txt with the design
   for(i=0; i<= lg; i++) {    of the covariance matrix to be input.
   if  (s[i] == occ ) j++;  
   }    Revision 1.88  2003/06/23 17:54:56  brouard
   return j;    * 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.
 }  
     Revision 1.87  2003/06/18 12:26:01  brouard
 void cutv(char *u,char *v, char*t, char occ)    Version 0.96
 {  
   int i,lg,j,p=0;    Revision 1.86  2003/06/17 20:04:08  brouard
   i=0;    (Module): Change position of html and gnuplot routines and added
   for(j=0; j<=strlen(t)-1; j++) {    routine fileappend.
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  
   }    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
   lg=strlen(t);    current date of interview. It may happen when the death was just
   for(j=0; j<p; j++) {    prior to the death. In this case, dh was negative and likelihood
     (u[j] = t[j]);    was wrong (infinity). We still send an "Error" but patch by
   }    assuming that the date of death was just one stepm after the
      u[p]='\0';    interview.
     (Repository): Because some people have very long ID (first column)
    for(j=0; j<= lg; j++) {    we changed int to long in num[] and we added a new lvector for
     if (j>=(p+1))(v[j-p-1] = t[j]);    memory allocation. But we also truncated to 8 characters (left
   }    truncation)
 }    (Repository): No more line truncation errors.
   
 /********************** nrerror ********************/    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 void nrerror(char error_text[])    place. It differs from routine "prevalence" which may be called
 {    many times. Probs is memory consuming and must be used with
   fprintf(stderr,"ERREUR ...\n");    parcimony.
   fprintf(stderr,"%s\n",error_text);    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   exit(1);  
 }    Revision 1.83  2003/06/10 13:39:11  lievre
 /*********************** vector *******************/    *** empty log message ***
 double *vector(int nl, int nh)  
 {    Revision 1.82  2003/06/05 15:57:20  brouard
   double *v;    Add log in  imach.c and  fullversion number is now printed.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");  */
   return v-nl+NR_END;  /*
 }     Interpolated Markov Chain
   
 /************************ free vector ******************/    Short summary of the programme:
 void free_vector(double*v, int nl, int nh)    
 {    This program computes Healthy Life Expectancies from
   free((FREE_ARG)(v+nl-NR_END));    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 }    first survey ("cross") where individuals from different ages are
     interviewed on their health status or degree of disability (in the
 /************************ivector *******************************/    case of a health survey which is our main interest) -2- at least a
 int *ivector(long nl,long nh)    second wave of interviews ("longitudinal") which measure each change
 {    (if any) in individual health status.  Health expectancies are
   int *v;    computed from the time spent in each health state according to a
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    model. More health states you consider, more time is necessary to reach the
   if (!v) nrerror("allocation failure in ivector");    Maximum Likelihood of the parameters involved in the model.  The
   return v-nl+NR_END;    simplest model is the multinomial logistic model where pij is the
 }    probability to be observed in state j at the second wave
     conditional to be observed in state i at the first wave. Therefore
 /******************free ivector **************************/    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 void free_ivector(int *v, long nl, long nh)    'age' is age and 'sex' is a covariate. If you want to have a more
 {    complex model than "constant and age", you should modify the program
   free((FREE_ARG)(v+nl-NR_END));    where the markup *Covariates have to be included here again* invites
 }    you to do it.  More covariates you add, slower the
     convergence.
 /******************* imatrix *******************************/  
 int **imatrix(long nrl, long nrh, long ncl, long nch)    The advantage of this computer programme, compared to a simple
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    multinomial logistic model, is clear when the delay between waves is not
 {    identical for each individual. Also, if a individual missed an
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    intermediate interview, the information is lost, but taken into
   int **m;    account using an interpolation or extrapolation.  
    
   /* allocate pointers to rows */    hPijx is the probability to be observed in state i at age x+h
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    conditional to the observed state i at age x. The delay 'h' can be
   if (!m) nrerror("allocation failure 1 in matrix()");    split into an exact number (nh*stepm) of unobserved intermediate
   m += NR_END;    states. This elementary transition (by month, quarter,
   m -= nrl;    semester or year) is modelled as a multinomial logistic.  The hPx
      matrix is simply the matrix product of nh*stepm elementary matrices
      and the contribution of each individual to the likelihood is simply
   /* allocate rows and set pointers to them */    hPijx.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Also this programme outputs the covariance matrix of the parameters but also
   m[nrl] += NR_END;    of the life expectancies. It also computes the period (stable) prevalence. 
   m[nrl] -= ncl;    
      Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;             Institut national d'études démographiques, Paris.
      This software have been partly granted by Euro-REVES, a concerted action
   /* return pointer to array of pointers to rows */    from the European Union.
   return m;    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 .
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
       int **m;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
       long nch,ncl,nrh,nrl;    
      /* free an int matrix allocated by imatrix() */    **********************************************************************/
 {  /*
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    main
   free((FREE_ARG) (m+nrl-NR_END));    read parameterfile
 }    read datafile
     concatwav
 /******************* matrix *******************************/    freqsummary
 double **matrix(long nrl, long nrh, long ncl, long nch)    if (mle >= 1)
 {      mlikeli
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    print results files
   double **m;    if mle==1 
        computes hessian
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    read end of parameter file: agemin, agemax, bage, fage, estepm
   if (!m) nrerror("allocation failure 1 in matrix()");        begin-prev-date,...
   m += NR_END;    open gnuplot file
   m -= nrl;    open html file
     period (stable) prevalence
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));     for age prevalim()
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    h Pij x
   m[nrl] += NR_END;    variance of p varprob
   m[nrl] -= ncl;    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    Variance-covariance of DFLE
   return m;    prevalence()
 }     movingaverage()
     varevsij() 
 /*************************free matrix ************************/    if popbased==1 varevsij(,popbased)
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    total life expectancies
 {    Variance of period (stable) prevalence
   free((FREE_ARG)(m[nrl]+ncl-NR_END));   end
   free((FREE_ARG)(m+nrl-NR_END));  */
 }  
   
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)   
 {  #include <math.h>
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #include <stdio.h>
   double ***m;  #include <stdlib.h>
   #include <string.h>
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #include <unistd.h>
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  #include <limits.h>
   m -= nrl;  #include <sys/types.h>
   #include <sys/stat.h>
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #include <errno.h>
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  extern int errno;
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /* #include <sys/time.h> */
   #include <time.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include "timeval.h"
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  /* #include <libintl.h> */
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  /* #define _(String) gettext (String) */
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  #define MAXLINE 256
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  #define GNUPLOTPROGRAM "gnuplot"
    /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   for (i=nrl+1; i<=nrh; i++) {  #define FILENAMELENGTH 132
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
       m[i][j]=m[i][j-1]+nlay;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   }  
   return m;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 }  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   
 /*************************free ma3x ************************/  #define NINTERVMAX 8
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 {  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #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
 /***************** f1dim *************************/  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 extern int ncom;  #ifdef UNIX
 extern double *pcom,*xicom;  #define DIRSEPARATOR '/'
 extern double (*nrfunc)(double []);  #define CHARSEPARATOR "/"
    #define ODIRSEPARATOR '\\'
 double f1dim(double x)  #else
 {  #define DIRSEPARATOR '\\'
   int j;  #define CHARSEPARATOR "\\"
   double f;  #define ODIRSEPARATOR '/'
   double *xt;  #endif
    
   xt=vector(1,ncom);  /* $Id$ */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  /* $State$ */
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  char version[]="Imach version 0.98h, April 2006, INED-EUROREVES-Institut de longevite ";
   return f;  char fullversion[]="$Revision$ $Date$"; 
 }  char strstart[80];
   char optionfilext[10], optionfilefiname[FILENAMELENGTH];
 /*****************brent *************************/  int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  int nvar;
 {  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int iter;  int npar=NPARMAX;
   double a,b,d,etemp;  int nlstate=2; /* Number of live states */
   double fu,fv,fw,fx;  int ndeath=1; /* Number of dead states */
   double ftemp;  int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   double p,q,r,tol1,tol2,u,v,w,x,xm;  int popbased=0;
   double e=0.0;  
    int *wav; /* Number of waves for this individuual 0 is possible */
   a=(ax < cx ? ax : cx);  int maxwav; /* Maxim number of waves */
   b=(ax > cx ? ax : cx);  int jmin, jmax; /* min, max spacing between 2 waves */
   x=w=v=bx;  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
   fw=fv=fx=(*f)(x);  int gipmx, gsw; /* Global variables on the number of contributions 
   for (iter=1;iter<=ITMAX;iter++) {                     to the likelihood and the sum of weights (done by funcone)*/
     xm=0.5*(a+b);  int mle, weightopt;
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     printf(".");fflush(stdout);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
 #ifdef DEBUG             * wave mi and wave mi+1 is not an exact multiple of stepm. */
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  double jmean; /* Mean space between 2 waves */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  double **oldm, **newm, **savm; /* Working pointers to matrices */
 #endif  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
       *xmin=x;  FILE *ficlog, *ficrespow;
       return fx;  int globpr; /* Global variable for printing or not */
     }  double fretone; /* Only one call to likelihood */
     ftemp=fu;  long ipmx; /* Number of contributions */
     if (fabs(e) > tol1) {  double sw; /* Sum of weights */
       r=(x-w)*(fx-fv);  char filerespow[FILENAMELENGTH];
       q=(x-v)*(fx-fw);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       p=(x-v)*q-(x-w)*r;  FILE *ficresilk;
       q=2.0*(q-r);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       if (q > 0.0) p = -p;  FILE *ficresprobmorprev;
       q=fabs(q);  FILE *fichtm, *fichtmcov; /* Html File */
       etemp=e;  FILE *ficreseij;
       e=d;  char filerese[FILENAMELENGTH];
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  FILE *ficresstdeij;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  char fileresstde[FILENAMELENGTH];
       else {  FILE *ficrescveij;
         d=p/q;  char filerescve[FILENAMELENGTH];
         u=x+d;  FILE  *ficresvij;
         if (u-a < tol2 || b-u < tol2)  char fileresv[FILENAMELENGTH];
           d=SIGN(tol1,xm-x);  FILE  *ficresvpl;
       }  char fileresvpl[FILENAMELENGTH];
     } else {  char title[MAXLINE];
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     }  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
     fu=(*f)(u);  char command[FILENAMELENGTH];
     if (fu <= fx) {  int  outcmd=0;
       if (u >= x) a=x; else b=x;  
       SHFT(v,w,x,u)  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
         SHFT(fv,fw,fx,fu)  
         } else {  char filelog[FILENAMELENGTH]; /* Log file */
           if (u < x) a=u; else b=u;  char filerest[FILENAMELENGTH];
           if (fu <= fw || w == x) {  char fileregp[FILENAMELENGTH];
             v=w;  char popfile[FILENAMELENGTH];
             w=u;  
             fv=fw;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
             v=u;  struct timezone tzp;
             fv=fu;  extern int gettimeofday();
           }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
         }  long time_value;
   }  extern long time();
   nrerror("Too many iterations in brent");  char strcurr[80], strfor[80];
   *xmin=x;  
   return fx;  char *endptr;
 }  long lval;
   double dval;
 /****************** mnbrak ***********************/  
   #define NR_END 1
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  #define FREE_ARG char*
             double (*func)(double))  #define FTOL 1.0e-10
 {  
   double ulim,u,r,q, dum;  #define NRANSI 
   double fu;  #define ITMAX 200 
    
   *fa=(*func)(*ax);  #define TOL 2.0e-4 
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  #define CGOLD 0.3819660 
     SHFT(dum,*ax,*bx,dum)  #define ZEPS 1.0e-10 
       SHFT(dum,*fb,*fa,dum)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);  #define GOLD 1.618034 
   *fc=(*func)(*cx);  #define GLIMIT 100.0 
   while (*fb > *fc) {  #define TINY 1.0e-20 
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  static double maxarg1,maxarg2;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     ulim=(*bx)+GLIMIT*(*cx-*bx);    
     if ((*bx-u)*(u-*cx) > 0.0) {  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
       fu=(*func)(u);  #define rint(a) floor(a+0.5)
     } else if ((*cx-u)*(u-ulim) > 0.0) {  
       fu=(*func)(u);  static double sqrarg;
       if (fu < *fc) {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
           SHFT(*fb,*fc,fu,(*func)(u))  int agegomp= AGEGOMP;
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  int imx; 
       u=ulim;  int stepm=1;
       fu=(*func)(u);  /* Stepm, step in month: minimum step interpolation*/
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);  int estepm;
       fu=(*func)(u);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
     }  
     SHFT(*ax,*bx,*cx,u)  int m,nb;
       SHFT(*fa,*fb,*fc,fu)  long *num;
       }  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double **pmmij, ***probs;
 /*************** linmin ************************/  double *ageexmed,*agecens;
   double dateintmean=0;
 int ncom;  
 double *pcom,*xicom;  double *weight;
 double (*nrfunc)(double []);  int **s; /* Status */
    double *agedc, **covar, idx;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 {  double *lsurv, *lpop, *tpop;
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   double f1dim(double x);  double ftolhess; /* Tolerance for computing hessian */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  
               double *fc, double (*func)(double));  /**************** split *************************/
   int j;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   double xx,xmin,bx,ax;  {
   double fx,fb,fa;    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
         the name of the file (name), its extension only (ext) and its first part of the name (finame)
   ncom=n;    */ 
   pcom=vector(1,n);    char  *ss;                            /* pointer */
   xicom=vector(1,n);    int   l1, l2;                         /* length counters */
   nrfunc=func;  
   for (j=1;j<=n;j++) {    l1 = strlen(path );                   /* length of path */
     pcom[j]=p[j];    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     xicom[j]=xi[j];    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   }    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   ax=0.0;      strcpy( name, path );               /* we got the fullname name because no directory */
   xx=1.0;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);      /* get current working directory */
 #ifdef DEBUG      /*    extern  char* getcwd ( char *buf , int len);*/
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 #endif        return( GLOCK_ERROR_GETCWD );
   for (j=1;j<=n;j++) {      }
     xi[j] *= xmin;      /* got dirc from getcwd*/
     p[j] += xi[j];      printf(" DIRC = %s \n",dirc);
   }    } else {                              /* strip direcotry from path */
   free_vector(xicom,1,n);      ss++;                               /* after this, the filename */
   free_vector(pcom,1,n);      l2 = strlen( ss );                  /* length of filename */
 }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       strcpy( name, ss );         /* save file name */
 /*************** powell ************************/      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,      dirc[l1-l2] = 0;                    /* add zero */
             double (*func)(double []))      printf(" DIRC2 = %s \n",dirc);
 {    }
   void linmin(double p[], double xi[], int n, double *fret,    /* We add a separator at the end of dirc if not exists */
               double (*func)(double []));    l1 = strlen( dirc );                  /* length of directory */
   int i,ibig,j;    if( dirc[l1-1] != DIRSEPARATOR ){
   double del,t,*pt,*ptt,*xit;      dirc[l1] =  DIRSEPARATOR;
   double fp,fptt;      dirc[l1+1] = 0; 
   double *xits;      printf(" DIRC3 = %s \n",dirc);
   pt=vector(1,n);    }
   ptt=vector(1,n);    ss = strrchr( name, '.' );            /* find last / */
   xit=vector(1,n);    if (ss >0){
   xits=vector(1,n);      ss++;
   *fret=(*func)(p);      strcpy(ext,ss);                     /* save extension */
   for (j=1;j<=n;j++) pt[j]=p[j];      l1= strlen( name);
   for (*iter=1;;++(*iter)) {      l2= strlen(ss)+1;
     fp=(*fret);      strncpy( finame, name, l1-l2);
     ibig=0;      finame[l1-l2]= 0;
     del=0.0;    }
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)    return( 0 );                          /* we're done */
       printf(" %d %.12f",i, p[i]);  }
     printf("\n");  
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  /******************************************/
       fptt=(*fret);  
 #ifdef DEBUG  void replace_back_to_slash(char *s, char*t)
       printf("fret=%lf \n",*fret);  {
 #endif    int i;
       printf("%d",i);fflush(stdout);    int lg=0;
       linmin(p,xit,n,fret,func);    i=0;
       if (fabs(fptt-(*fret)) > del) {    lg=strlen(t);
         del=fabs(fptt-(*fret));    for(i=0; i<= lg; i++) {
         ibig=i;      (s[i] = t[i]);
       }      if (t[i]== '\\') s[i]='/';
 #ifdef DEBUG    }
       printf("%d %.12e",i,(*fret));  }
       for (j=1;j<=n;j++) {  
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  int nbocc(char *s, char occ)
         printf(" x(%d)=%.12e",j,xit[j]);  {
       }    int i,j=0;
       for(j=1;j<=n;j++)    int lg=20;
         printf(" p=%.12e",p[j]);    i=0;
       printf("\n");    lg=strlen(s);
 #endif    for(i=0; i<= lg; i++) {
     }    if  (s[i] == occ ) j++;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    }
 #ifdef DEBUG    return j;
       int k[2],l;  }
       k[0]=1;  
       k[1]=-1;  void cutv(char *u,char *v, char*t, char occ)
       printf("Max: %.12e",(*func)(p));  {
       for (j=1;j<=n;j++)    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
         printf(" %.12e",p[j]);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       printf("\n");       gives u="abcedf" and v="ghi2j" */
       for(l=0;l<=1;l++) {    int i,lg,j,p=0;
         for (j=1;j<=n;j++) {    i=0;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    for(j=0; j<=strlen(t)-1; j++) {
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
         }    }
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  
       }    lg=strlen(t);
 #endif    for(j=0; j<p; j++) {
       (u[j] = t[j]);
     }
       free_vector(xit,1,n);       u[p]='\0';
       free_vector(xits,1,n);  
       free_vector(ptt,1,n);     for(j=0; j<= lg; j++) {
       free_vector(pt,1,n);      if (j>=(p+1))(v[j-p-1] = t[j]);
       return;    }
     }  }
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  
     for (j=1;j<=n;j++) {  /********************** nrerror ********************/
       ptt[j]=2.0*p[j]-pt[j];  
       xit[j]=p[j]-pt[j];  void nrerror(char error_text[])
       pt[j]=p[j];  {
     }    fprintf(stderr,"ERREUR ...\n");
     fptt=(*func)(ptt);    fprintf(stderr,"%s\n",error_text);
     if (fptt < fp) {    exit(EXIT_FAILURE);
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  }
       if (t < 0.0) {  /*********************** vector *******************/
         linmin(p,xit,n,fret,func);  double *vector(int nl, int nh)
         for (j=1;j<=n;j++) {  {
           xi[j][ibig]=xi[j][n];    double *v;
           xi[j][n]=xit[j];    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
         }    if (!v) nrerror("allocation failure in vector");
 #ifdef DEBUG    return v-nl+NR_END;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  }
         for(j=1;j<=n;j++)  
           printf(" %.12e",xit[j]);  /************************ free vector ******************/
         printf("\n");  void free_vector(double*v, int nl, int nh)
 #endif  {
       }    free((FREE_ARG)(v+nl-NR_END));
     }  }
   }  
 }  /************************ivector *******************************/
   int *ivector(long nl,long nh)
 /**** Prevalence limit ****************/  {
     int *v;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
 {    if (!v) nrerror("allocation failure in ivector");
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    return v-nl+NR_END;
      matrix by transitions matrix until convergence is reached */  }
   
   int i, ii,j,k;  /******************free ivector **************************/
   double min, max, maxmin, maxmax,sumnew=0.;  void free_ivector(int *v, long nl, long nh)
   double **matprod2();  {
   double **out, cov[NCOVMAX], **pmij();    free((FREE_ARG)(v+nl-NR_END));
   double **newm;  }
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /************************lvector *******************************/
   for (ii=1;ii<=nlstate+ndeath;ii++)  long *lvector(long nl,long nh)
     for (j=1;j<=nlstate+ndeath;j++){  {
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    long *v;
     }    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     if (!v) nrerror("allocation failure in ivector");
    cov[1]=1.;    return v-nl+NR_END;
    }
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  /******************free lvector **************************/
     newm=savm;  void free_lvector(long *v, long nl, long nh)
     /* Covariates have to be included here again */  {
      cov[2]=agefin;    free((FREE_ARG)(v+nl-NR_END));
    }
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /******************* imatrix *******************************/
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/  int **imatrix(long nrl, long nrh, long ncl, long nch) 
       }       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       for (k=1; k<=cptcovage;k++)  { 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       for (k=1; k<=cptcovprod;k++)    int **m; 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    
     /* allocate pointers to rows */ 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    m -= nrl; 
     
     savm=oldm;    
     oldm=newm;    /* allocate rows and set pointers to them */ 
     maxmax=0.;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     for(j=1;j<=nlstate;j++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       min=1.;    m[nrl] += NR_END; 
       max=0.;    m[nrl] -= ncl; 
       for(i=1; i<=nlstate; i++) {    
         sumnew=0;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    
         prlim[i][j]= newm[i][j]/(1-sumnew);    /* return pointer to array of pointers to rows */ 
         max=FMAX(max,prlim[i][j]);    return m; 
         min=FMIN(min,prlim[i][j]);  } 
       }  
       maxmin=max-min;  /****************** free_imatrix *************************/
       maxmax=FMAX(maxmax,maxmin);  void free_imatrix(m,nrl,nrh,ncl,nch)
     }        int **m;
     if(maxmax < ftolpl){        long nch,ncl,nrh,nrl; 
       return prlim;       /* free an int matrix allocated by imatrix() */ 
     }  { 
   }    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 }    free((FREE_ARG) (m+nrl-NR_END)); 
   } 
 /*************** transition probabilities **********/  
   /******************* matrix *******************************/
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  double **matrix(long nrl, long nrh, long ncl, long nch)
 {  {
   double s1, s2;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   /*double t34;*/    double **m;
   int i,j,j1, nc, ii, jj;  
     m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     for(i=1; i<= nlstate; i++){    if (!m) nrerror("allocation failure 1 in matrix()");
     for(j=1; j<i;j++){    m += NR_END;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    m -= nrl;
         /*s2 += param[i][j][nc]*cov[nc];*/  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       }    m[nrl] += NR_END;
       ps[i][j]=s2;    m[nrl] -= ncl;
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  
     }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     for(j=i+1; j<=nlstate+ndeath;j++){    return m;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];     */
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  }
       }  
       ps[i][j]=s2;  /*************************free matrix ************************/
     }  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   }  {
   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++)  /******************* ma3x *******************************/
       s1+=exp(ps[i][j]);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     ps[i][i]=1./(s1+1.);  {
     for(j=1; j<i; j++)    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       ps[i][j]= exp(ps[i][j])*ps[i][i];    double ***m;
     for(j=i+1; j<=nlstate+ndeath; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    if (!m) nrerror("allocation failure 1 in matrix()");
   } /* end i */    m += NR_END;
     m -= nrl;
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       ps[ii][jj]=0;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       ps[ii][ii]=1;    m[nrl] += NR_END;
     }    m[nrl] -= ncl;
   }  
     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
      printf("%lf ",ps[ii][jj]);    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
    }    m[nrl][ncl] += NR_END;
     printf("\n ");    m[nrl][ncl] -= nll;
     }    for (j=ncl+1; j<=nch; j++) 
     printf("\n ");printf("%lf ",cov[2]);*/      m[nrl][j]=m[nrl][j-1]+nlay;
 /*    
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    for (i=nrl+1; i<=nrh; i++) {
   goto end;*/      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     return ps;      for (j=ncl+1; j<=nch; j++) 
 }        m[i][j]=m[i][j-1]+nlay;
     }
 /**************** Product of 2 matrices ******************/    return m; 
     /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
 {    */
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  }
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  
   /* in, b, out are matrice of pointers which should have been initialized  /*************************free ma3x ************************/
      before: only the contents of out is modified. The function returns  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
      a pointer to pointers identical to out */  {
   long i, j, k;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   for(i=nrl; i<= nrh; i++)    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     for(k=ncolol; k<=ncoloh; k++)    free((FREE_ARG)(m+nrl-NR_END));
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  }
         out[i][k] +=in[i][j]*b[j][k];  
   /*************** function subdirf ***********/
   return out;  char *subdirf(char fileres[])
 }  {
     /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
 /************* Higher Matrix Product ***************/    strcat(tmpout,"/"); /* Add to the right */
     strcat(tmpout,fileres);
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    return tmpout;
 {  }
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until  /*************** function subdirf2 ***********/
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  char *subdirf2(char fileres[], char *preop)
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  {
      (typically every 2 years instead of every month which is too big).    
      Model is determined by parameters x and covariates have to be    /* Caution optionfilefiname is hidden */
      included manually here.    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
      */    strcat(tmpout,preop);
     strcat(tmpout,fileres);
   int i, j, d, h, k;    return tmpout;
   double **out, cov[NCOVMAX];  }
   double **newm;  
   /*************** function subdirf3 ***********/
   /* Hstepm could be zero and should return the unit matrix */  char *subdirf3(char fileres[], char *preop, char *preop2)
   for (i=1;i<=nlstate+ndeath;i++)  {
     for (j=1;j<=nlstate+ndeath;j++){    
       oldm[i][j]=(i==j ? 1.0 : 0.0);    /* Caution optionfilefiname is hidden */
       po[i][j][0]=(i==j ? 1.0 : 0.0);    strcpy(tmpout,optionfilefiname);
     }    strcat(tmpout,"/");
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    strcat(tmpout,preop);
   for(h=1; h <=nhstepm; h++){    strcat(tmpout,preop2);
     for(d=1; d <=hstepm; d++){    strcat(tmpout,fileres);
       newm=savm;    return tmpout;
       /* Covariates have to be included here again */  }
       cov[1]=1.;  
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  /***************** f1dim *************************/
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  extern int ncom; 
 for (k=1; k<=cptcovage;k++)  extern double *pcom,*xicom;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  extern double (*nrfunc)(double []); 
    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]]];  double f1dim(double x) 
   { 
     int j; 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    double f;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    double *xt; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,   
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    xt=vector(1,ncom); 
       savm=oldm;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       oldm=newm;    f=(*nrfunc)(xt); 
     }    free_vector(xt,1,ncom); 
     for(i=1; i<=nlstate+ndeath; i++)    return f; 
       for(j=1;j<=nlstate+ndeath;j++) {  } 
         po[i][j][h]=newm[i][j];  
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  /*****************brent *************************/
          */  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
       }  { 
   } /* end h */    int iter; 
   return po;    double a,b,d,etemp;
 }    double fu,fv,fw,fx;
     double ftemp;
     double p,q,r,tol1,tol2,u,v,w,x,xm; 
 /*************** log-likelihood *************/    double e=0.0; 
 double func( double *x)   
 {    a=(ax < cx ? ax : cx); 
   int i, ii, j, k, mi, d, kk;    b=(ax > cx ? ax : cx); 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    x=w=v=bx; 
   double **out;    fw=fv=fx=(*f)(x); 
   double sw; /* Sum of weights */    for (iter=1;iter<=ITMAX;iter++) { 
   double lli; /* Individual log likelihood */      xm=0.5*(a+b); 
   long ipmx;      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   /*extern weight */      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   /* We are differentiating ll according to initial status */      printf(".");fflush(stdout);
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/      fprintf(ficlog,".");fflush(ficlog);
   /*for(i=1;i<imx;i++)  #ifdef DEBUG
     printf(" %d\n",s[4][i]);      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   */      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   cov[1]=1.;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   #endif
   for(k=1; k<=nlstate; k++) ll[k]=0.;      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){        *xmin=x; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];        return fx; 
     for(mi=1; mi<= wav[i]-1; mi++){      } 
       for (ii=1;ii<=nlstate+ndeath;ii++)      ftemp=fu;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      if (fabs(e) > tol1) { 
       for(d=0; d<dh[mi][i]; d++){        r=(x-w)*(fx-fv); 
         newm=savm;        q=(x-v)*(fx-fw); 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;        p=(x-v)*q-(x-w)*r; 
         for (kk=1; kk<=cptcovage;kk++) {        q=2.0*(q-r); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];        if (q > 0.0) p = -p; 
         }        q=fabs(q); 
                etemp=e; 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,        e=d; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
         savm=oldm;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         oldm=newm;        else { 
                  d=p/q; 
                  u=x+d; 
       } /* end mult */          if (u-a < tol2 || b-u < tol2) 
                  d=SIGN(tol1,xm-x); 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);        } 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      } else { 
       ipmx +=1;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       sw += weight[i];      } 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     } /* end of wave */      fu=(*f)(u); 
   } /* end of individual */      if (fu <= fx) { 
         if (u >= x) a=x; else b=x; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];        SHFT(v,w,x,u) 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */          SHFT(fv,fw,fx,fu) 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */          } else { 
   return -l;            if (u < x) a=u; else b=u; 
 }            if (fu <= fw || w == x) { 
               v=w; 
               w=u; 
 /*********** Maximum Likelihood Estimation ***************/              fv=fw; 
               fw=fu; 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))            } else if (fu <= fv || v == x || v == w) { 
 {              v=u; 
   int i,j, iter;              fv=fu; 
   double **xi,*delti;            } 
   double fret;          } 
   xi=matrix(1,npar,1,npar);    } 
   for (i=1;i<=npar;i++)    nrerror("Too many iterations in brent"); 
     for (j=1;j<=npar;j++)    *xmin=x; 
       xi[i][j]=(i==j ? 1.0 : 0.0);    return fx; 
   printf("Powell\n");  } 
   powell(p,xi,npar,ftol,&iter,&fret,func);  
   /****************** mnbrak ***********************/
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
               double (*func)(double)) 
 }  { 
     double ulim,u,r,q, dum;
 /**** Computes Hessian and covariance matrix ***/    double fu; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))   
 {    *fa=(*func)(*ax); 
   double  **a,**y,*x,pd;    *fb=(*func)(*bx); 
   double **hess;    if (*fb > *fa) { 
   int i, j,jk;      SHFT(dum,*ax,*bx,dum) 
   int *indx;        SHFT(dum,*fb,*fa,dum) 
         } 
   double hessii(double p[], double delta, int theta, double delti[]);    *cx=(*bx)+GOLD*(*bx-*ax); 
   double hessij(double p[], double delti[], int i, int j);    *fc=(*func)(*cx); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    while (*fb > *fc) { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;      r=(*bx-*ax)*(*fb-*fc); 
       q=(*bx-*cx)*(*fb-*fa); 
       u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   hess=matrix(1,npar,1,npar);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       ulim=(*bx)+GLIMIT*(*cx-*bx); 
   printf("\nCalculation of the hessian matrix. Wait...\n");      if ((*bx-u)*(u-*cx) > 0.0) { 
   for (i=1;i<=npar;i++){        fu=(*func)(u); 
     printf("%d",i);fflush(stdout);      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     hess[i][i]=hessii(p,ftolhess,i,delti);        fu=(*func)(u); 
     /*printf(" %f ",p[i]);*/        if (fu < *fc) { 
   }          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
   for (i=1;i<=npar;i++) {            } 
     for (j=1;j<=npar;j++)  {      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       if (j>i) {        u=ulim; 
         printf(".%d%d",i,j);fflush(stdout);        fu=(*func)(u); 
         hess[i][j]=hessij(p,delti,i,j);      } else { 
         hess[j][i]=hess[i][j];        u=(*cx)+GOLD*(*cx-*bx); 
       }        fu=(*func)(u); 
     }      } 
   }      SHFT(*ax,*bx,*cx,u) 
   printf("\n");        SHFT(*fa,*fb,*fc,fu) 
         } 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  } 
    
   a=matrix(1,npar,1,npar);  /*************** linmin ************************/
   y=matrix(1,npar,1,npar);  
   x=vector(1,npar);  int ncom; 
   indx=ivector(1,npar);  double *pcom,*xicom;
   for (i=1;i<=npar;i++)  double (*nrfunc)(double []); 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];   
   ludcmp(a,npar,indx,&pd);  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   { 
   for (j=1;j<=npar;j++) {    double brent(double ax, double bx, double cx, 
     for (i=1;i<=npar;i++) x[i]=0;                 double (*f)(double), double tol, double *xmin); 
     x[j]=1;    double f1dim(double x); 
     lubksb(a,npar,indx,x);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     for (i=1;i<=npar;i++){                double *fc, double (*func)(double)); 
       matcov[i][j]=x[i];    int j; 
     }    double xx,xmin,bx,ax; 
   }    double fx,fb,fa;
    
   printf("\n#Hessian matrix#\n");    ncom=n; 
   for (i=1;i<=npar;i++) {    pcom=vector(1,n); 
     for (j=1;j<=npar;j++) {    xicom=vector(1,n); 
       printf("%.3e ",hess[i][j]);    nrfunc=func; 
     }    for (j=1;j<=n;j++) { 
     printf("\n");      pcom[j]=p[j]; 
   }      xicom[j]=xi[j]; 
     } 
   /* Recompute Inverse */    ax=0.0; 
   for (i=1;i<=npar;i++)    xx=1.0; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   ludcmp(a,npar,indx,&pd);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   #ifdef DEBUG
   /*  printf("\n#Hessian matrix recomputed#\n");    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   for (j=1;j<=npar;j++) {  #endif
     for (i=1;i<=npar;i++) x[i]=0;    for (j=1;j<=n;j++) { 
     x[j]=1;      xi[j] *= xmin; 
     lubksb(a,npar,indx,x);      p[j] += xi[j]; 
     for (i=1;i<=npar;i++){    } 
       y[i][j]=x[i];    free_vector(xicom,1,n); 
       printf("%.3e ",y[i][j]);    free_vector(pcom,1,n); 
     }  } 
     printf("\n");  
   }  char *asc_diff_time(long time_sec, char ascdiff[])
   */  {
     long sec_left, days, hours, minutes;
   free_matrix(a,1,npar,1,npar);    days = (time_sec) / (60*60*24);
   free_matrix(y,1,npar,1,npar);    sec_left = (time_sec) % (60*60*24);
   free_vector(x,1,npar);    hours = (sec_left) / (60*60) ;
   free_ivector(indx,1,npar);    sec_left = (sec_left) %(60*60);
   free_matrix(hess,1,npar,1,npar);    minutes = (sec_left) /60;
     sec_left = (sec_left) % (60);
     sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
 }    return ascdiff;
   }
 /*************** hessian matrix ****************/  
 double hessii( double x[], double delta, int theta, double delti[])  /*************** powell ************************/
 {  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   int i;              double (*func)(double [])) 
   int l=1, lmax=20;  { 
   double k1,k2;    void linmin(double p[], double xi[], int n, double *fret, 
   double p2[NPARMAX+1];                double (*func)(double [])); 
   double res;    int i,ibig,j; 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    double del,t,*pt,*ptt,*xit;
   double fx;    double fp,fptt;
   int k=0,kmax=10;    double *xits;
   double l1;    int niterf, itmp;
   
   fx=func(x);    pt=vector(1,n); 
   for (i=1;i<=npar;i++) p2[i]=x[i];    ptt=vector(1,n); 
   for(l=0 ; l <=lmax; l++){    xit=vector(1,n); 
     l1=pow(10,l);    xits=vector(1,n); 
     delts=delt;    *fret=(*func)(p); 
     for(k=1 ; k <kmax; k=k+1){    for (j=1;j<=n;j++) pt[j]=p[j]; 
       delt = delta*(l1*k);    for (*iter=1;;++(*iter)) { 
       p2[theta]=x[theta] +delt;      fp=(*fret); 
       k1=func(p2)-fx;      ibig=0; 
       p2[theta]=x[theta]-delt;      del=0.0; 
       k2=func(p2)-fx;      last_time=curr_time;
       /*res= (k1-2.0*fx+k2)/delt/delt; */      (void) gettimeofday(&curr_time,&tzp);
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
            fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
 #ifdef DEBUG  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);     for (i=1;i<=n;i++) {
 #endif        printf(" %d %.12f",i, p[i]);
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        fprintf(ficlog," %d %.12lf",i, p[i]);
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        fprintf(ficrespow," %.12lf", p[i]);
         k=kmax;      }
       }      printf("\n");
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */      fprintf(ficlog,"\n");
         k=kmax; l=lmax*10.;      fprintf(ficrespow,"\n");fflush(ficrespow);
       }      if(*iter <=3){
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        tm = *localtime(&curr_time.tv_sec);
         delts=delt;        strcpy(strcurr,asctime(&tm));
       }  /*       asctime_r(&tm,strcurr); */
     }        forecast_time=curr_time; 
   }        itmp = strlen(strcurr);
   delti[theta]=delts;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   return res;          strcurr[itmp-1]='\0';
          printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 }        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         for(niterf=10;niterf<=30;niterf+=10){
 double hessij( double x[], double delti[], int thetai,int thetaj)          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
 {          tmf = *localtime(&forecast_time.tv_sec);
   int i;  /*      asctime_r(&tmf,strfor); */
   int l=1, l1, lmax=20;          strcpy(strfor,asctime(&tmf));
   double k1,k2,k3,k4,res,fx;          itmp = strlen(strfor);
   double p2[NPARMAX+1];          if(strfor[itmp-1]=='\n')
   int k;          strfor[itmp-1]='\0';
           printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   fx=func(x);          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);
   for (k=1; k<=2; k++) {        }
     for (i=1;i<=npar;i++) p2[i]=x[i];      }
     p2[thetai]=x[thetai]+delti[thetai]/k;      for (i=1;i<=n;i++) { 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     k1=func(p2)-fx;        fptt=(*fret); 
    #ifdef DEBUG
     p2[thetai]=x[thetai]+delti[thetai]/k;        printf("fret=%lf \n",*fret);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        fprintf(ficlog,"fret=%lf \n",*fret);
     k2=func(p2)-fx;  #endif
          printf("%d",i);fflush(stdout);
     p2[thetai]=x[thetai]-delti[thetai]/k;        fprintf(ficlog,"%d",i);fflush(ficlog);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        linmin(p,xit,n,fret,func); 
     k3=func(p2)-fx;        if (fabs(fptt-(*fret)) > del) { 
            del=fabs(fptt-(*fret)); 
     p2[thetai]=x[thetai]-delti[thetai]/k;          ibig=i; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        } 
     k4=func(p2)-fx;  #ifdef DEBUG
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        printf("%d %.12e",i,(*fret));
 #ifdef DEBUG        fprintf(ficlog,"%d %.12e",i,(*fret));
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);        for (j=1;j<=n;j++) {
 #endif          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   }          printf(" x(%d)=%.12e",j,xit[j]);
   return res;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
 }        }
         for(j=1;j<=n;j++) {
 /************** Inverse of matrix **************/          printf(" p=%.12e",p[j]);
 void ludcmp(double **a, int n, int *indx, double *d)          fprintf(ficlog," p=%.12e",p[j]);
 {        }
   int i,imax,j,k;        printf("\n");
   double big,dum,sum,temp;        fprintf(ficlog,"\n");
   double *vv;  #endif
        } 
   vv=vector(1,n);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   *d=1.0;  #ifdef DEBUG
   for (i=1;i<=n;i++) {        int k[2],l;
     big=0.0;        k[0]=1;
     for (j=1;j<=n;j++)        k[1]=-1;
       if ((temp=fabs(a[i][j])) > big) big=temp;        printf("Max: %.12e",(*func)(p));
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");        fprintf(ficlog,"Max: %.12e",(*func)(p));
     vv[i]=1.0/big;        for (j=1;j<=n;j++) {
   }          printf(" %.12e",p[j]);
   for (j=1;j<=n;j++) {          fprintf(ficlog," %.12e",p[j]);
     for (i=1;i<j;i++) {        }
       sum=a[i][j];        printf("\n");
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        fprintf(ficlog,"\n");
       a[i][j]=sum;        for(l=0;l<=1;l++) {
     }          for (j=1;j<=n;j++) {
     big=0.0;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     for (i=j;i<=n;i++) {            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       sum=a[i][j];            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       for (k=1;k<j;k++)          }
         sum -= a[i][k]*a[k][j];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       a[i][j]=sum;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       if ( (dum=vv[i]*fabs(sum)) >= big) {        }
         big=dum;  #endif
         imax=i;  
       }  
     }        free_vector(xit,1,n); 
     if (j != imax) {        free_vector(xits,1,n); 
       for (k=1;k<=n;k++) {        free_vector(ptt,1,n); 
         dum=a[imax][k];        free_vector(pt,1,n); 
         a[imax][k]=a[j][k];        return; 
         a[j][k]=dum;      } 
       }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       *d = -(*d);      for (j=1;j<=n;j++) { 
       vv[imax]=vv[j];        ptt[j]=2.0*p[j]-pt[j]; 
     }        xit[j]=p[j]-pt[j]; 
     indx[j]=imax;        pt[j]=p[j]; 
     if (a[j][j] == 0.0) a[j][j]=TINY;      } 
     if (j != n) {      fptt=(*func)(ptt); 
       dum=1.0/(a[j][j]);      if (fptt < fp) { 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     }        if (t < 0.0) { 
   }          linmin(p,xit,n,fret,func); 
   free_vector(vv,1,n);  /* Doesn't work */          for (j=1;j<=n;j++) { 
 ;            xi[j][ibig]=xi[j][n]; 
 }            xi[j][n]=xit[j]; 
           }
 void lubksb(double **a, int n, int *indx, double b[])  #ifdef DEBUG
 {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   int i,ii=0,ip,j;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   double sum;          for(j=1;j<=n;j++){
              printf(" %.12e",xit[j]);
   for (i=1;i<=n;i++) {            fprintf(ficlog," %.12e",xit[j]);
     ip=indx[i];          }
     sum=b[ip];          printf("\n");
     b[ip]=b[i];          fprintf(ficlog,"\n");
     if (ii)  #endif
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        }
     else if (sum) ii=i;      } 
     b[i]=sum;    } 
   }  } 
   for (i=n;i>=1;i--) {  
     sum=b[i];  /**** Prevalence limit (stable or period prevalence)  ****************/
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];  
     b[i]=sum/a[i][i];  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   }  {
 }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
        matrix by transitions matrix until convergence is reached */
 /************ Frequencies ********************/  
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)    int i, ii,j,k;
 {  /* Some frequencies */    double min, max, maxmin, maxmax,sumnew=0.;
      double **matprod2();
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    double **out, cov[NCOVMAX], **pmij();
   double ***freq; /* Frequencies */    double **newm;
   double *pp;    double agefin, delaymax=50 ; /* Max number of years to converge */
   double pos;  
   FILE *ficresp;    for (ii=1;ii<=nlstate+ndeath;ii++)
   char fileresp[FILENAMELENGTH];      for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   pp=vector(1,nlstate);      }
   
   strcpy(fileresp,"p");     cov[1]=1.;
   strcat(fileresp,fileres);   
   if((ficresp=fopen(fileresp,"w"))==NULL) {   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     printf("Problem with prevalence resultfile: %s\n", fileresp);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     exit(0);      newm=savm;
   }      /* Covariates have to be included here again */
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);       cov[2]=agefin;
   j1=0;    
         for (k=1; k<=cptcovn;k++) {
   j=cptcoveff;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
         }
   for(k1=1; k1<=j;k1++){        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
    for(i1=1; i1<=ncodemax[k1];i1++){        for (k=1; k<=cptcovprod;k++)
        j1++;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);  
          scanf("%d", i);*/        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         for (i=-1; i<=nlstate+ndeath; i++)          /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
          for (jk=-1; jk<=nlstate+ndeath; jk++)          /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
            for(m=agemin; m <= agemax+3; m++)      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
              freq[i][jk][m]=0;  
              savm=oldm;
        for (i=1; i<=imx; i++) {      oldm=newm;
          bool=1;      maxmax=0.;
          if  (cptcovn>0) {      for(j=1;j<=nlstate;j++){
            for (z1=1; z1<=cptcoveff; z1++)        min=1.;
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        max=0.;
                bool=0;        for(i=1; i<=nlstate; i++) {
          }          sumnew=0;
           if (bool==1) {          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
            for(m=firstpass; m<=lastpass-1; m++){          prlim[i][j]= newm[i][j]/(1-sumnew);
              if(agev[m][i]==0) agev[m][i]=agemax+1;          max=FMAX(max,prlim[i][j]);
              if(agev[m][i]==1) agev[m][i]=agemax+2;          min=FMIN(min,prlim[i][j]);
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        }
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        maxmin=max-min;
            }        maxmax=FMAX(maxmax,maxmin);
          }      }
        }      if(maxmax < ftolpl){
         if  (cptcovn>0) {        return prlim;
          fprintf(ficresp, "\n#********** Variable ");      }
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    }
        fprintf(ficresp, "**********\n#");  }
         }  
        for(i=1; i<=nlstate;i++)  /*************** transition probabilities ***************/ 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  
        fprintf(ficresp, "\n");  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
          {
   for(i=(int)agemin; i <= (int)agemax+3; i++){    double s1, s2;
     if(i==(int)agemax+3)    /*double t34;*/
       printf("Total");    int i,j,j1, nc, ii, jj;
     else  
       printf("Age %d", i);      for(i=1; i<= nlstate; i++){
     for(jk=1; jk <=nlstate ; jk++){        for(j=1; j<i;j++){
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
         pp[jk] += freq[jk][m][i];            /*s2 += param[i][j][nc]*cov[nc];*/
     }            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     for(jk=1; jk <=nlstate ; jk++){  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
       for(m=-1, pos=0; m <=0 ; m++)          }
         pos += freq[jk][m][i];          ps[i][j]=s2;
       if(pp[jk]>=1.e-10)  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        }
       else        for(j=i+1; j<=nlstate+ndeath;j++){
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
     }            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
     for(jk=1; jk <=nlstate ; jk++){  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)          }
         pp[jk] += freq[jk][m][i];          ps[i][j]=s2;
     }        }
     for(jk=1,pos=0; jk <=nlstate ; jk++)      }
       pos += pp[jk];      /*ps[3][2]=1;*/
     for(jk=1; jk <=nlstate ; jk++){      
       if(pos>=1.e-5)      for(i=1; i<= nlstate; i++){
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        s1=0;
       else        for(j=1; j<i; j++)
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          s1+=exp(ps[i][j]);
       if( i <= (int) agemax){        for(j=i+1; j<=nlstate+ndeath; j++)
         if(pos>=1.e-5)          s1+=exp(ps[i][j]);
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        ps[i][i]=1./(s1+1.);
       else        for(j=1; j<i; j++)
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);          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];
     for(jk=-1; jk <=nlstate+ndeath; jk++)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
       for(m=-1; m <=nlstate+ndeath; m++)      } /* end i */
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      
     if(i <= (int) agemax)      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       fprintf(ficresp,"\n");        for(jj=1; jj<= nlstate+ndeath; jj++){
     printf("\n");          ps[ii][jj]=0;
     }          ps[ii][ii]=1;
     }        }
  }      }
        
   fclose(ficresp);  
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   free_vector(pp,1,nlstate);  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   /*         printf("ddd %lf ",ps[ii][jj]); */
 }  /* End of Freq */  /*       } */
   /*       printf("\n "); */
 /************* Waves Concatenation ***************/  /*        } */
   /*        printf("\n ");printf("%lf ",cov[2]); */
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)         /*
 {        for(i=1; i<= npar; i++) printf("%f ",x[i]);
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        goto end;*/
      Death is a valid wave (if date is known).      return ps;
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i  }
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]  
      and mw[mi+1][i]. dh depends on stepm.  /**************** Product of 2 matrices ******************/
      */  
   double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   int i, mi, m;  {
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
      double sum=0., jmean=0.;*/       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     /* in, b, out are matrice of pointers which should have been initialized 
 int j, k=0,jk, ju, jl;       before: only the contents of out is modified. The function returns
      double sum=0.;       a pointer to pointers identical to out */
 jmin=1e+5;    long i, j, k;
  jmax=-1;    for(i=nrl; i<= nrh; i++)
 jmean=0.;      for(k=ncolol; k<=ncoloh; k++)
   for(i=1; i<=imx; i++){        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     mi=0;          out[i][k] +=in[i][j]*b[j][k];
     m=firstpass;  
     while(s[m][i] <= nlstate){    return out;
       if(s[m][i]>=1)  }
         mw[++mi][i]=m;  
       if(m >=lastpass)  
         break;  /************* Higher Matrix Product ***************/
       else  
         m++;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     }/* end while */  {
     if (s[m][i] > nlstate){    /* Computes the transition matrix starting at age 'age' over 
       mi++;     /* Death is another wave */       'nhstepm*hstepm*stepm' months (i.e. until
       /* if(mi==0)  never been interviewed correctly before death */       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
          /* Only death is a correct wave */       nhstepm*hstepm matrices. 
       mw[mi][i]=m;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     }       (typically every 2 years instead of every month which is too big 
        for the memory).
     wav[i]=mi;       Model is determined by parameters x and covariates have to be 
     if(mi==0)       included manually here. 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  
   }       */
   
   for(i=1; i<=imx; i++){    int i, j, d, h, k;
     for(mi=1; mi<wav[i];mi++){    double **out, cov[NCOVMAX];
       if (stepm <=0)    double **newm;
         dh[mi][i]=1;  
       else{    /* Hstepm could be zero and should return the unit matrix */
         if (s[mw[mi+1][i]][i] > nlstate) {    for (i=1;i<=nlstate+ndeath;i++)
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);      for (j=1;j<=nlstate+ndeath;j++){
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/        oldm[i][j]=(i==j ? 1.0 : 0.0);
           if(j==0) j=1;  /* Survives at least one month after exam */        po[i][j][0]=(i==j ? 1.0 : 0.0);
           k=k+1;      }
           if (j >= jmax) jmax=j;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           else if (j <= jmin)jmin=j;    for(h=1; h <=nhstepm; h++){
           sum=sum+j;      for(d=1; d <=hstepm; d++){
         }        newm=savm;
         else{        /* Covariates have to be included here again */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        cov[1]=1.;
           /*if ((j<0) || (j>28)) printf("j=%d num=%d ",j,i);*/        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
           k=k+1;        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           if (j >= jmax) jmax=j;        for (k=1; k<=cptcovage;k++)
           else if (j <= jmin)jmin=j;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           sum=sum+j;        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]]];
         jk= j/stepm;  
         jl= j -jk*stepm;  
         ju= j -(jk+1)*stepm;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
         if(jl <= -ju)        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           dh[mi][i]=jk;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         else                     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 */      }
       }      for(i=1; i<=nlstate+ndeath; i++)
     }        for(j=1;j<=nlstate+ndeath;j++) {
   }          po[i][j][h]=newm[i][j];
   jmean=sum/k;          /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);           */
 }        }
 /*********** Tricode ****************************/    } /* end h */
 void tricode(int *Tvar, int **nbcode, int imx)    return po;
 {  }
   int Ndum[20],ij=1, k, j, i;  
   int cptcode=0;  
   cptcoveff=0;  /*************** log-likelihood *************/
    double func( double *x)
   for (k=0; k<19; k++) Ndum[k]=0;  {
   for (k=1; k<=7; k++) ncodemax[k]=0;    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX], cov[NCOVMAX];
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {    double **out;
     for (i=1; i<=imx; i++) {    double sw; /* Sum of weights */
       ij=(int)(covar[Tvar[j]][i]);    double lli; /* Individual log likelihood */
       Ndum[ij]++;    int s1, s2;
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    double bbh, survp;
       if (ij > cptcode) cptcode=ij;    long ipmx;
     }    /*extern weight */
     /* We are differentiating ll according to initial status */
     for (i=0; i<=cptcode; i++) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       if(Ndum[i]!=0) ncodemax[j]++;    /*for(i=1;i<imx;i++) 
     }      printf(" %d\n",s[4][i]);
     ij=1;    */
     cov[1]=1.;
   
     for (i=1; i<=ncodemax[j]; i++) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
       for (k=0; k<=19; k++) {  
         if (Ndum[k] != 0) {    if(mle==1){
           nbcode[Tvar[j]][ij]=k;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           ij++;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
         if (ij > ncodemax[j]) break;          for (ii=1;ii<=nlstate+ndeath;ii++)
       }              for (j=1;j<=nlstate+ndeath;j++){
     }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   }                savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
  for (k=0; k<19; k++) Ndum[k]=0;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
  for (i=1; i<=ncovmodel; i++) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       ij=Tvar[i];            for (kk=1; kk<=cptcovage;kk++) {
       Ndum[ij]++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  ij=1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
  for (i=1; i<=10; i++) {            savm=oldm;
    if((Ndum[i]!=0) && (i<=ncov)){            oldm=newm;
      Tvaraff[ij]=i;          } /* end mult */
      ij++;        
    }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
  }          /* But now since version 0.9 we anticipate for bias at large stepm.
             * If stepm is larger than one month (smallest stepm) and if the exact delay 
     cptcoveff=ij-1;           * (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
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
 /*********** Health Expectancies ****************/           * (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
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
 {           * -stepm/2 to stepm/2 .
   /* Health expectancies */           * For stepm=1 the results are the same as for previous versions of Imach.
   int i, j, nhstepm, hstepm, h;           * For stepm > 1 the results are less biased than in previous versions. 
   double age, agelim,hf;           */
   double ***p3mat;          s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
   fprintf(ficreseij,"# Health expectancies\n");          bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficreseij,"# Age");          /* bias bh is positive if real duration
   for(i=1; i<=nlstate;i++)           * is higher than the multiple of stepm and negative otherwise.
     for(j=1; j<=nlstate;j++)           */
       fprintf(ficreseij," %1d-%1d",i,j);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   fprintf(ficreseij,"\n");          if( s2 > nlstate){ 
             /* i.e. if s2 is a death state and if the date of death is known 
   hstepm=1*YEARM; /*  Every j years of age (in month) */               then the contribution to the likelihood is the probability to 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */               die between last step unit time and current  step unit time, 
                which is also equal to probability to die before dh 
   agelim=AGESUP;               minus probability to die before dh-stepm . 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */               In version up to 0.92 likelihood was computed
     /* nhstepm age range expressed in number of stepm */          as if date of death was unknown. Death was treated as any other
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);          health state: the date of the interview describes the actual state
     /* Typically if 20 years = 20*12/6=40 stepm */          and not the date of a change in health state. The former idea was
     if (stepm >= YEARM) hstepm=1;          to consider that at each interview the state was recorded
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */          (healthy, disable or death) and IMaCh was corrected; but when we
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          introduced the exact date of death then we should have modified
     /* Computed by stepm unit matrices, product of hstepm matrices, stored          the contribution of an exact death to the likelihood. This new
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          contribution is smaller and very dependent of the step unit
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            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
     for(i=1; i<=nlstate;i++)          probability to die within a month. Thanks to Chris
       for(j=1; j<=nlstate;j++)          Jackson for correcting this bug.  Former versions increased
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){          mortality artificially. The bad side is that we add another loop
           eij[i][j][(int)age] +=p3mat[i][j][h];          which slows down the processing. The difference can be up to 10%
         }          lower mortality.
                */
     hf=1;            lli=log(out[s1][s2] - savm[s1][s2]);
     if (stepm >= YEARM) hf=stepm/YEARM;  
     fprintf(ficreseij,"%.0f",age );  
     for(i=1; i<=nlstate;i++)          } else if  (s2==-2) {
       for(j=1; j<=nlstate;j++){            for (j=1,survp=0. ; j<=nlstate; j++) 
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       }            /*survp += out[s1][j]; */
     fprintf(ficreseij,"\n");            lli= log(survp);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          }
   }          
 }          else if  (s2==-4) { 
             for (j=3,survp=0. ; j<=nlstate; j++)  
 /************ Variance ******************/              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
 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)            lli= log(survp); 
 {          } 
   /* Variance of health expectancies */  
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          else if  (s2==-5) { 
   double **newm;            for (j=1,survp=0. ; j<=2; j++)  
   double **dnewm,**doldm;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   int i, j, nhstepm, hstepm, h;            lli= log(survp); 
   int k, cptcode;          } 
    double *xp;          
   double **gp, **gm;          else{
   double ***gradg, ***trgradg;            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   double ***p3mat;            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
   double age,agelim;          } 
   int theta;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
           /*if(lli ==000.0)*/
    fprintf(ficresvij,"# Covariances of life expectancies\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); */
   fprintf(ficresvij,"# Age");          ipmx +=1;
   for(i=1; i<=nlstate;i++)          sw += weight[i];
     for(j=1; j<=nlstate;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        } /* end of wave */
   fprintf(ficresvij,"\n");      } /* end of individual */
     }  else if(mle==2){
   xp=vector(1,npar);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   dnewm=matrix(1,nlstate,1,npar);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   doldm=matrix(1,nlstate,1,nlstate);        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
   hstepm=1*YEARM; /* Every year of age */            for (j=1;j<=nlstate+ndeath;j++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   agelim = AGESUP;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          for(d=0; d<=dh[mi][i]; d++){
     if (stepm >= YEARM) hstepm=1;            newm=savm;
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for (kk=1; kk<=cptcovage;kk++) {
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     gp=matrix(0,nhstepm,1,nlstate);            }
     gm=matrix(0,nhstepm,1,nlstate);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(theta=1; theta <=npar; theta++){            savm=oldm;
       for(i=1; i<=npar; i++){ /* Computes gradient */            oldm=newm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          } /* end mult */
       }        
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            s1=s[mw[mi][i]][i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          s2=s[mw[mi+1][i]][i];
       for(j=1; j<= nlstate; j++){          bbh=(double)bh[mi][i]/(double)stepm; 
         for(h=0; h<=nhstepm; h++){          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, gp[h][j]=0.;i<=nlstate;i++)          ipmx +=1;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          sw += weight[i];
         }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        } /* end of wave */
          } /* end of individual */
       for(i=1; i<=npar; i++) /* Computes gradient */    }  else if(mle==3){  /* exponential inter-extrapolation */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j<= nlstate; j++){          for (ii=1;ii<=nlstate+ndeath;ii++)
         for(h=0; h<=nhstepm; h++){            for (j=1;j<=nlstate+ndeath;j++){
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];              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 */            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
     for(h=0; h<=nhstepm; h++)            oldm=newm;
       for(j=1; j<=nlstate;j++)          } /* end mult */
         for(theta=1; theta <=npar; theta++)        
           trgradg[h][j][theta]=gradg[h][theta][j];          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
     for(i=1;i<=nlstate;i++)          bbh=(double)bh[mi][i]/(double)stepm; 
       for(j=1;j<=nlstate;j++)          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 */
         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);        } /* end of wave */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      } /* end of individual */
         for(i=1;i<=nlstate;i++)    }else if (mle==4){  /* ml=4 no inter-extrapolation */
           for(j=1;j<=nlstate;j++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
             vareij[i][j][(int)age] += doldm[i][j];        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++)
     h=1;            for (j=1;j<=nlstate+ndeath;j++){
     if (stepm >= YEARM) h=stepm/YEARM;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     fprintf(ficresvij,"%.0f ",age );              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i=1; i<=nlstate;i++)            }
       for(j=1; j<=nlstate;j++){          for(d=0; d<dh[mi][i]; d++){
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);            newm=savm;
       }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     fprintf(ficresvij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
     free_matrix(gp,0,nhstepm,1,nlstate);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     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);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   } /* End age */            savm=oldm;
              oldm=newm;
   free_vector(xp,1,npar);          } /* end mult */
   free_matrix(doldm,1,nlstate,1,npar);        
   free_matrix(dnewm,1,nlstate,1,nlstate);          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
 }          if( s2 > nlstate){ 
             lli=log(out[s1][s2] - savm[s1][s2]);
 /************ Variance of prevlim ******************/          }else{
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 {          }
   /* Variance of prevalence limit */          ipmx +=1;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          sw += weight[i];
   double **newm;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **dnewm,**doldm;  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   int i, j, nhstepm, hstepm;        } /* end of wave */
   int k, cptcode;      } /* end of individual */
   double *xp;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   double *gp, *gm;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double **gradg, **trgradg;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double age,agelim;        for(mi=1; mi<= wav[i]-1; mi++){
   int theta;          for (ii=1;ii<=nlstate+ndeath;ii++)
                for (j=1;j<=nlstate+ndeath;j++){
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficresvpl,"# Age");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(i=1; i<=nlstate;i++)            }
       fprintf(ficresvpl," %1d-%1d",i,i);          for(d=0; d<dh[mi][i]; d++){
   fprintf(ficresvpl,"\n");            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   xp=vector(1,npar);            for (kk=1; kk<=cptcovage;kk++) {
   dnewm=matrix(1,nlstate,1,npar);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   doldm=matrix(1,nlstate,1,nlstate);            }
            
   hstepm=1*YEARM; /* Every year of age */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   agelim = AGESUP;            savm=oldm;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            oldm=newm;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          } /* end mult */
     if (stepm >= YEARM) hstepm=1;        
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          s1=s[mw[mi][i]][i];
     gradg=matrix(1,npar,1,nlstate);          s2=s[mw[mi+1][i]][i];
     gp=vector(1,nlstate);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     gm=vector(1,nlstate);          ipmx +=1;
           sw += weight[i];
     for(theta=1; theta <=npar; theta++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1; i<=npar; i++){ /* Computes gradient */          /*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]);*/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        } /* end of wave */
       }      } /* end of individual */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    } /* End of if */
       for(i=1;i<=nlstate;i++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         gp[i] = prlim[i][i];    /* 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 */
       for(i=1; i<=npar; i++) /* Computes gradient */    return -l;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)  /*************** log-likelihood *************/
         gm[i] = prlim[i][i];  double funcone( double *x)
   {
       for(i=1;i<=nlstate;i++)    /* Same as likeli but slower because of a lot of printf and if */
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    int i, ii, j, k, mi, d, kk;
     } /* End theta */    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     double **out;
     trgradg =matrix(1,nlstate,1,npar);    double lli; /* Individual log likelihood */
     double llt;
     for(j=1; j<=nlstate;j++)    int s1, s2;
       for(theta=1; theta <=npar; theta++)    double bbh, survp;
         trgradg[j][theta]=gradg[theta][j];    /*extern weight */
     /* We are differentiating ll according to initial status */
     for(i=1;i<=nlstate;i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       varpl[i][(int)age] =0.;    /*for(i=1;i<imx;i++) 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      printf(" %d\n",s[4][i]);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    */
     for(i=1;i<=nlstate;i++)    cov[1]=1.;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  
     for(k=1; k<=nlstate; k++) ll[k]=0.;
     fprintf(ficresvpl,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     fprintf(ficresvpl,"\n");      for(mi=1; mi<= wav[i]-1; mi++){
     free_vector(gp,1,nlstate);        for (ii=1;ii<=nlstate+ndeath;ii++)
     free_vector(gm,1,nlstate);          for (j=1;j<=nlstate+ndeath;j++){
     free_matrix(gradg,1,npar,1,nlstate);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(trgradg,1,nlstate,1,npar);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   } /* End age */          }
         for(d=0; d<dh[mi][i]; d++){
   free_vector(xp,1,npar);          newm=savm;
   free_matrix(doldm,1,nlstate,1,npar);          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   free_matrix(dnewm,1,nlstate,1,nlstate);          for (kk=1; kk<=cptcovage;kk++) {
             cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 }          }
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           savm=oldm;
 /***********************************************/          oldm=newm;
 /**************** Main Program *****************/        } /* end mult */
 /***********************************************/        
         s1=s[mw[mi][i]][i];
 /*int main(int argc, char *argv[])*/        s2=s[mw[mi+1][i]][i];
 int main()        bbh=(double)bh[mi][i]/(double)stepm; 
 {        /* bias is positive if real duration
          * is higher than the multiple of stepm and negative otherwise.
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;         */
   double agedeb, agefin,hf;        if( s2 > nlstate && (mle <5) ){  /* Jackson */
   double agemin=1.e20, agemax=-1.e20;          lli=log(out[s1][s2] - savm[s1][s2]);
         } else if  (s2==-2) {
   double fret;          for (j=1,survp=0. ; j<=nlstate; j++) 
   double **xi,tmp,delta;            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           lli= log(survp);
   double dum; /* Dummy variable */        }else if (mle==1){
   double ***p3mat;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   int *indx;        } else if(mle==2){
   char line[MAXLINE], linepar[MAXLINE];          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 */
   char title[MAXLINE];        } else if(mle==3){  /* exponential inter-extrapolation */
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];          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 */
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   char filerest[FILENAMELENGTH];          lli=log(out[s1][s2]); /* Original formula */
   char fileregp[FILENAMELENGTH];        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];          lli=log(out[s1][s2]); /* Original formula */
   int firstobs=1, lastobs=10;        } /* End of if */
   int sdeb, sfin; /* Status at beginning and end */        ipmx +=1;
   int c,  h , cpt,l;        sw += weight[i];
   int ju,jl, mi;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;  /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        if(globpr){
            fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   int hstepm, nhstepm;   %11.6f %11.6f %11.6f ", \
   double bage, fage, age, agelim, agebase;                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
   double ftolpl=FTOL;                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
   double **prlim;          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   double *severity;            llt +=ll[k]*gipmx/gsw;
   double ***param; /* Matrix of parameters */            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   double  *p;          }
   double **matcov; /* Matrix of covariance */          fprintf(ficresilk," %10.6f\n", -llt);
   double ***delti3; /* Scale */        }
   double *delti; /* Scale */      } /* end of wave */
   double ***eij, ***vareij;    } /* end of individual */
   double **varpl; /* Variances of prevalence limits by age */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   double *epj, vepp;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   char *alph[]={"a","a","b","c","d","e"}, str[4];    if(globpr==0){ /* First time we count the contributions and weights */
       gipmx=ipmx;
   char z[1]="c", occ;      gsw=sw;
 #include <sys/time.h>    }
 #include <time.h>    return -l;
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  }
   /* long total_usecs;  
   struct timeval start_time, end_time;  
    /*************** function likelione ***********/
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
     /* This routine should help understanding what is done with 
   printf("\nIMACH, Version 0.64b");       the selection of individuals/waves and
   printf("\nEnter the parameter file name: ");       to check the exact contribution to the likelihood.
        Plotting could be done.
 #ifdef windows     */
   scanf("%s",pathtot);    int k;
   getcwd(pathcd, size);  
   /*cygwin_split_path(pathtot,path,optionfile);    if(*globpri !=0){ /* Just counts and sums, no printings */
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      strcpy(fileresilk,"ilk"); 
   /* cutv(path,optionfile,pathtot,'\\');*/      strcat(fileresilk,fileres);
       if((ficresilk=fopen(fileresilk,"w"))==NULL) {
 split(pathtot, path,optionfile);        printf("Problem with resultfile: %s\n", fileresilk);
   chdir(path);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
   replace(pathc,path);      }
 #endif      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");
 #ifdef unix      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   scanf("%s",optionfile);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
 #endif      for(k=1; k<=nlstate; k++) 
         fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
 /*-------- arguments in the command line --------*/      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     }
   strcpy(fileres,"r");  
   strcat(fileres, optionfile);    *fretone=(*funcone)(p);
     if(*globpri !=0){
   /*---------arguments file --------*/      fclose(ficresilk);
       fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   if((ficpar=fopen(optionfile,"r"))==NULL)    {      fflush(fichtm); 
     printf("Problem with optionfile %s\n",optionfile);    } 
     goto end;    return;
   }  }
   
   strcpy(filereso,"o");  
   strcat(filereso,fileres);  /*********** Maximum Likelihood Estimation ***************/
   if((ficparo=fopen(filereso,"w"))==NULL) {  
     printf("Problem with Output resultfile: %s\n", filereso);goto end;  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   }  {
     int i,j, iter;
   /* Reads comments: lines beginning with '#' */    double **xi;
   while((c=getc(ficpar))=='#' && c!= EOF){    double fret;
     ungetc(c,ficpar);    double fretone; /* Only one call to likelihood */
     fgets(line, MAXLINE, ficpar);    /*  char filerespow[FILENAMELENGTH];*/
     puts(line);    xi=matrix(1,npar,1,npar);
     fputs(line,ficparo);    for (i=1;i<=npar;i++)
   }      for (j=1;j<=npar;j++)
   ungetc(c,ficpar);        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    strcpy(filerespow,"pow"); 
   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);    strcat(filerespow,fileres);
   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);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", filerespow);
   covar=matrix(0,NCOVMAX,1,n);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   cptcovn=0;    }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     for (i=1;i<=nlstate;i++)
   ncovmodel=2+cptcovn;      for(j=1;j<=nlstate+ndeath;j++)
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
      fprintf(ficrespow,"\n");
   /* Read guess parameters */  
   /* Reads comments: lines beginning with '#' */    powell(p,xi,npar,ftol,&iter,&fret,func);
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    free_matrix(xi,1,npar,1,npar);
     fgets(line, MAXLINE, ficpar);    fclose(ficrespow);
     puts(line);    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fputs(line,ficparo);    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));
   ungetc(c,ficpar);  
    }
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)  /**** Computes Hessian and covariance matrix ***/
     for(j=1; j <=nlstate+ndeath-1; j++){  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       fscanf(ficpar,"%1d%1d",&i1,&j1);  {
       fprintf(ficparo,"%1d%1d",i1,j1);    double  **a,**y,*x,pd;
       printf("%1d%1d",i,j);    double **hess;
       for(k=1; k<=ncovmodel;k++){    int i, j,jk;
         fscanf(ficpar," %lf",&param[i][j][k]);    int *indx;
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       }    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
       fscanf(ficpar,"\n");    void lubksb(double **a, int npar, int *indx, double b[]) ;
       printf("\n");    void ludcmp(double **a, int npar, int *indx, double *d) ;
       fprintf(ficparo,"\n");    double gompertz(double p[]);
     }    hess=matrix(1,npar,1,npar);
    
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    printf("\nCalculation of the hessian matrix. Wait...\n");
   p=param[1][1];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
      for (i=1;i<=npar;i++){
   /* Reads comments: lines beginning with '#' */      printf("%d",i);fflush(stdout);
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficlog,"%d",i);fflush(ficlog);
     ungetc(c,ficpar);     
     fgets(line, MAXLINE, ficpar);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     puts(line);      
     fputs(line,ficparo);      /*  printf(" %f ",p[i]);
   }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   ungetc(c,ficpar);    }
     
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    for (i=1;i<=npar;i++) {
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      for (j=1;j<=npar;j++)  {
   for(i=1; i <=nlstate; i++){        if (j>i) { 
     for(j=1; j <=nlstate+ndeath-1; j++){          printf(".%d%d",i,j);fflush(stdout);
       fscanf(ficpar,"%1d%1d",&i1,&j1);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
       printf("%1d%1d",i,j);          hess[i][j]=hessij(p,delti,i,j,func,npar);
       fprintf(ficparo,"%1d%1d",i1,j1);          
       for(k=1; k<=ncovmodel;k++){          hess[j][i]=hess[i][j];    
         fscanf(ficpar,"%le",&delti3[i][j][k]);          /*printf(" %lf ",hess[i][j]);*/
         printf(" %le",delti3[i][j][k]);        }
         fprintf(ficparo," %le",delti3[i][j][k]);      }
       }    }
       fscanf(ficpar,"\n");    printf("\n");
       printf("\n");    fprintf(ficlog,"\n");
       fprintf(ficparo,"\n");  
     }    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   }    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   delti=delti3[1][1];    
      a=matrix(1,npar,1,npar);
   /* Reads comments: lines beginning with '#' */    y=matrix(1,npar,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    x=vector(1,npar);
     ungetc(c,ficpar);    indx=ivector(1,npar);
     fgets(line, MAXLINE, ficpar);    for (i=1;i<=npar;i++)
     puts(line);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     fputs(line,ficparo);    ludcmp(a,npar,indx,&pd);
   }  
   ungetc(c,ficpar);    for (j=1;j<=npar;j++) {
        for (i=1;i<=npar;i++) x[i]=0;
   matcov=matrix(1,npar,1,npar);      x[j]=1;
   for(i=1; i <=npar; i++){      lubksb(a,npar,indx,x);
     fscanf(ficpar,"%s",&str);      for (i=1;i<=npar;i++){ 
     printf("%s",str);        matcov[i][j]=x[i];
     fprintf(ficparo,"%s",str);      }
     for(j=1; j <=i; j++){    }
       fscanf(ficpar," %le",&matcov[i][j]);  
       printf(" %.5le",matcov[i][j]);    printf("\n#Hessian matrix#\n");
       fprintf(ficparo," %.5le",matcov[i][j]);    fprintf(ficlog,"\n#Hessian matrix#\n");
     }    for (i=1;i<=npar;i++) { 
     fscanf(ficpar,"\n");      for (j=1;j<=npar;j++) { 
     printf("\n");        printf("%.3e ",hess[i][j]);
     fprintf(ficparo,"\n");        fprintf(ficlog,"%.3e ",hess[i][j]);
   }      }
   for(i=1; i <=npar; i++)      printf("\n");
     for(j=i+1;j<=npar;j++)      fprintf(ficlog,"\n");
       matcov[i][j]=matcov[j][i];    }
      
   printf("\n");    /* Recompute Inverse */
     for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     /*-------- data file ----------*/    ludcmp(a,npar,indx,&pd);
     if((ficres =fopen(fileres,"w"))==NULL) {  
       printf("Problem with resultfile: %s\n", fileres);goto end;    /*  printf("\n#Hessian matrix recomputed#\n");
     }  
     fprintf(ficres,"#%s\n",version);    for (j=1;j<=npar;j++) {
          for (i=1;i<=npar;i++) x[i]=0;
     if((fic=fopen(datafile,"r"))==NULL)    {      x[j]=1;
       printf("Problem with datafile: %s\n", datafile);goto end;      lubksb(a,npar,indx,x);
     }      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
     n= lastobs;        printf("%.3e ",y[i][j]);
     severity = vector(1,maxwav);        fprintf(ficlog,"%.3e ",y[i][j]);
     outcome=imatrix(1,maxwav+1,1,n);      }
     num=ivector(1,n);      printf("\n");
     moisnais=vector(1,n);      fprintf(ficlog,"\n");
     annais=vector(1,n);    }
     moisdc=vector(1,n);    */
     andc=vector(1,n);  
     agedc=vector(1,n);    free_matrix(a,1,npar,1,npar);
     cod=ivector(1,n);    free_matrix(y,1,npar,1,npar);
     weight=vector(1,n);    free_vector(x,1,npar);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    free_ivector(indx,1,npar);
     mint=matrix(1,maxwav,1,n);    free_matrix(hess,1,npar,1,npar);
     anint=matrix(1,maxwav,1,n);  
     s=imatrix(1,maxwav+1,1,n);  
     adl=imatrix(1,maxwav+1,1,n);      }
     tab=ivector(1,NCOVMAX);  
     ncodemax=ivector(1,8);  /*************** hessian matrix ****************/
   double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     i=1;  {
     while (fgets(line, MAXLINE, fic) != NULL)    {    int i;
       if ((i >= firstobs) && (i <=lastobs)) {    int l=1, lmax=20;
            double k1,k2;
         for (j=maxwav;j>=1;j--){    double p2[NPARMAX+1];
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    double res;
           strcpy(line,stra);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    double fx;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int k=0,kmax=10;
         }    double l1;
          
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    fx=func(x);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    for (i=1;i<=npar;i++) p2[i]=x[i];
     for(l=0 ; l <=lmax; l++){
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      l1=pow(10,l);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      delts=delt;
       for(k=1 ; k <kmax; k=k+1){
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        delt = delta*(l1*k);
         for (j=ncov;j>=1;j--){        p2[theta]=x[theta] +delt;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        k1=func(p2)-fx;
         }        p2[theta]=x[theta]-delt;
         num[i]=atol(stra);        k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
         /*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]));*/        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         
         i=i+1;  #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);
     }        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
     /*scanf("%d",i);*/        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   imx=i-1; /* Number of individuals */        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
   /* Calculation of the number of parameter from char model*/        }
   Tvar=ivector(1,15);        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   Tprod=ivector(1,15);          k=kmax; l=lmax*10.;
   Tvaraff=ivector(1,15);        }
   Tvard=imatrix(1,15,1,2);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   Tage=ivector(1,15);                delts=delt;
            }
   if (strlen(model) >1){      }
     j=0, j1=0, k1=1, k2=1;    }
     j=nbocc(model,'+');    delti[theta]=delts;
     j1=nbocc(model,'*');    return res; 
     cptcovn=j+1;    
     cptcovprod=j1;  }
      
      double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
     strcpy(modelsav,model);  {
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    int i;
       printf("Error. Non available option model=%s ",model);    int l=1, l1, lmax=20;
       goto end;    double k1,k2,k3,k4,res,fx;
     }    double p2[NPARMAX+1];
        int k;
     for(i=(j+1); i>=1;i--){  
       cutv(stra,strb,modelsav,'+');    fx=func(x);
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    for (k=1; k<=2; k++) {
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/      for (i=1;i<=npar;i++) p2[i]=x[i];
       /*scanf("%d",i);*/      p2[thetai]=x[thetai]+delti[thetai]/k;
       if (strchr(strb,'*')) {      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
         cutv(strd,strc,strb,'*');      k1=func(p2)-fx;
         if (strcmp(strc,"age")==0) {    
           cptcovprod--;      p2[thetai]=x[thetai]+delti[thetai]/k;
           cutv(strb,stre,strd,'V');      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           Tvar[i]=atoi(stre);      k2=func(p2)-fx;
           cptcovage++;    
             Tage[cptcovage]=i;      p2[thetai]=x[thetai]-delti[thetai]/k;
             /*printf("stre=%s ", stre);*/      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
         }      k3=func(p2)-fx;
         else if (strcmp(strd,"age")==0) {    
           cptcovprod--;      p2[thetai]=x[thetai]-delti[thetai]/k;
           cutv(strb,stre,strc,'V');      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           Tvar[i]=atoi(stre);      k4=func(p2)-fx;
           cptcovage++;      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
           Tage[cptcovage]=i;  #ifdef DEBUG
         }      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         else {      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);
           cutv(strb,stre,strc,'V');  #endif
           Tvar[i]=ncov+k1;    }
           cutv(strb,strc,strd,'V');    return res;
           Tprod[k1]=i;  }
           Tvard[k1][1]=atoi(strc);  
           Tvard[k1][2]=atoi(stre);  /************** Inverse of matrix **************/
           Tvar[cptcovn+k2]=Tvard[k1][1];  void ludcmp(double **a, int n, int *indx, double *d) 
           Tvar[cptcovn+k2+1]=Tvard[k1][2];  { 
           for (k=1; k<=lastobs;k++)    int i,imax,j,k; 
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    double big,dum,sum,temp; 
           k1++;    double *vv; 
           k2=k2+2;   
         }    vv=vector(1,n); 
       }    *d=1.0; 
       else {    for (i=1;i<=n;i++) { 
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/      big=0.0; 
        /*  scanf("%d",i);*/      for (j=1;j<=n;j++) 
       cutv(strd,strc,strb,'V');        if ((temp=fabs(a[i][j])) > big) big=temp; 
       Tvar[i]=atoi(strc);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       }      vv[i]=1.0/big; 
       strcpy(modelsav,stra);      } 
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    for (j=1;j<=n;j++) { 
         scanf("%d",i);*/      for (i=1;i<j;i++) { 
     }        sum=a[i][j]; 
 }        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
          a[i][j]=sum; 
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);      } 
   printf("cptcovprod=%d ", cptcovprod);      big=0.0; 
   scanf("%d ",i);*/      for (i=j;i<=n;i++) { 
     fclose(fic);        sum=a[i][j]; 
         for (k=1;k<j;k++) 
     /*  if(mle==1){*/          sum -= a[i][k]*a[k][j]; 
     if (weightopt != 1) { /* Maximisation without weights*/        a[i][j]=sum; 
       for(i=1;i<=n;i++) weight[i]=1.0;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
     }          big=dum; 
     /*-calculation of age at interview from date of interview and age at death -*/          imax=i; 
     agev=matrix(1,maxwav,1,imx);        } 
          } 
     for (i=1; i<=imx; i++)  {      if (j != imax) { 
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        for (k=1;k<=n;k++) { 
       for(m=1; (m<= maxwav); m++){          dum=a[imax][k]; 
         if(s[m][i] >0){          a[imax][k]=a[j][k]; 
           if (s[m][i] == nlstate+1) {          a[j][k]=dum; 
             if(agedc[i]>0)        } 
               if(moisdc[i]!=99 && andc[i]!=9999)        *d = -(*d); 
               agev[m][i]=agedc[i];        vv[imax]=vv[j]; 
             else {      } 
               if (andc[i]!=9999){      indx[j]=imax; 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);      if (a[j][j] == 0.0) a[j][j]=TINY; 
               agev[m][i]=-1;      if (j != n) { 
               }        dum=1.0/(a[j][j]); 
             }        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
           }      } 
           else if(s[m][i] !=9){ /* Should no more exist */    } 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    free_vector(vv,1,n);  /* Doesn't work */
             if(mint[m][i]==99 || anint[m][i]==9999)  ;
               agev[m][i]=1;  } 
             else if(agev[m][i] <agemin){  
               agemin=agev[m][i];  void lubksb(double **a, int n, int *indx, double b[]) 
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/  { 
             }    int i,ii=0,ip,j; 
             else if(agev[m][i] >agemax){    double sum; 
               agemax=agev[m][i];   
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    for (i=1;i<=n;i++) { 
             }      ip=indx[i]; 
             /*agev[m][i]=anint[m][i]-annais[i];*/      sum=b[ip]; 
             /*   agev[m][i] = age[i]+2*m;*/      b[ip]=b[i]; 
           }      if (ii) 
           else { /* =9 */        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
             agev[m][i]=1;      else if (sum) ii=i; 
             s[m][i]=-1;      b[i]=sum; 
           }    } 
         }    for (i=n;i>=1;i--) { 
         else /*= 0 Unknown */      sum=b[i]; 
           agev[m][i]=1;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       }      b[i]=sum/a[i][i]; 
        } 
     }  } 
     for (i=1; i<=imx; i++)  {  
       for(m=1; (m<= maxwav); m++){  void pstamp(FILE *fichier)
         if (s[m][i] > (nlstate+ndeath)) {  {
           printf("Error: Wrong value in nlstate or ndeath\n");      fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
           goto end;  }
         }  
       }  /************ 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[])
   {  /* Some frequencies */
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    
     int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     free_vector(severity,1,maxwav);    int first;
     free_imatrix(outcome,1,maxwav+1,1,n);    double ***freq; /* Frequencies */
     free_vector(moisnais,1,n);    double *pp, **prop;
     free_vector(annais,1,n);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     free_matrix(mint,1,maxwav,1,n);    char fileresp[FILENAMELENGTH];
     free_matrix(anint,1,maxwav,1,n);    
     free_vector(moisdc,1,n);    pp=vector(1,nlstate);
     free_vector(andc,1,n);    prop=matrix(1,nlstate,iagemin,iagemax+3);
     strcpy(fileresp,"p");
        strcat(fileresp,fileres);
     wav=ivector(1,imx);    if((ficresp=fopen(fileresp,"w"))==NULL) {
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      printf("Problem with prevalence resultfile: %s\n", fileresp);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
          exit(0);
     /* Concatenates waves */    }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
     j1=0;
     
       Tcode=ivector(1,100);    j=cptcoveff;
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       ncodemax[1]=1;  
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);    first=1;
        
    codtab=imatrix(1,100,1,10);    for(k1=1; k1<=j;k1++){
    h=0;      for(i1=1; i1<=ncodemax[k1];i1++){
    m=pow(2,cptcoveff);        j1++;
          /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
    for(k=1;k<=cptcoveff; k++){          scanf("%d", i);*/
      for(i=1; i <=(m/pow(2,k));i++){        for (i=-5; i<=nlstate+ndeath; i++)  
        for(j=1; j <= ncodemax[k]; j++){          for (jk=-5; jk<=nlstate+ndeath; jk++)  
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){            for(m=iagemin; m <= iagemax+3; m++)
            h++;              freq[i][jk][m]=0;
            if (h>m) h=1;codtab[h][k]=j;  
          }      for (i=1; i<=nlstate; i++)  
        }        for(m=iagemin; m <= iagemax+3; m++)
      }          prop[i][m]=0;
    }        
         dateintsum=0;
         k2cpt=0;
    /*for(i=1; i <=m ;i++){        for (i=1; i<=imx; i++) {
      for(k=1; k <=cptcovn; k++){          bool=1;
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);          if  (cptcovn>0) {
      }            for (z1=1; z1<=cptcoveff; z1++) 
      printf("\n");              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
    }                bool=0;
    scanf("%d",i);*/          }
              if (bool==1){
    /* Calculates basic frequencies. Computes observed prevalence at single age            for(m=firstpass; m<=lastpass; m++){
        and prints on file fileres'p'. */              k2=anint[m][i]+(mint[m][i]/12.);
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                if (m<lastpass) {
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                    }
     /* 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] */                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */                  dateintsum=dateintsum+k2;
                   k2cpt++;
     if(mle==1){                }
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);                /*}*/
     }            }
              }
     /*--------- results files --------------*/        }
     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);         
            /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
    jk=1;        pstamp(ficresp);
    fprintf(ficres,"# Parameters\n");        if  (cptcovn>0) {
    printf("# Parameters\n");          fprintf(ficresp, "\n#********** Variable "); 
    for(i=1,jk=1; i <=nlstate; i++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
      for(k=1; k <=(nlstate+ndeath); k++){          fprintf(ficresp, "**********\n#");
        if (k != i)        }
          {        for(i=1; i<=nlstate;i++) 
            printf("%d%d ",i,k);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
            fprintf(ficres,"%1d%1d ",i,k);        fprintf(ficresp, "\n");
            for(j=1; j <=ncovmodel; j++){        
              printf("%f ",p[jk]);        for(i=iagemin; i <= iagemax+3; i++){
              fprintf(ficres,"%f ",p[jk]);          if(i==iagemax+3){
              jk++;            fprintf(ficlog,"Total");
            }          }else{
            printf("\n");            if(first==1){
            fprintf(ficres,"\n");              first=0;
          }              printf("See log file for details...\n");
      }            }
    }            fprintf(ficlog,"Age %d", i);
  if(mle==1){          }
     /* Computing hessian and covariance matrix */          for(jk=1; jk <=nlstate ; jk++){
     ftolhess=ftol; /* Usually correct */            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     hesscov(matcov, p, npar, delti, ftolhess, func);              pp[jk] += freq[jk][m][i]; 
  }          }
     fprintf(ficres,"# Scales\n");          for(jk=1; jk <=nlstate ; jk++){
     printf("# Scales\n");            for(m=-1, pos=0; m <=0 ; m++)
      for(i=1,jk=1; i <=nlstate; i++){              pos += freq[jk][m][i];
       for(j=1; j <=nlstate+ndeath; j++){            if(pp[jk]>=1.e-10){
         if (j!=i) {              if(first==1){
           fprintf(ficres,"%1d%1d",i,j);              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           printf("%1d%1d",i,j);              }
           for(k=1; k<=ncovmodel;k++){              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             printf(" %.5e",delti[jk]);            }else{
             fprintf(ficres," %.5e",delti[jk]);              if(first==1)
             jk++;                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           printf("\n");            }
           fprintf(ficres,"\n");          }
         }  
       }          for(jk=1; jk <=nlstate ; jk++){
       }            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
                  pp[jk] += freq[jk][m][i];
     k=1;          }       
     fprintf(ficres,"# Covariance\n");          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     printf("# Covariance\n");            pos += pp[jk];
     for(i=1;i<=npar;i++){            posprop += prop[jk][i];
       /*  if (k>nlstate) k=1;          }
       i1=(i-1)/(ncovmodel*nlstate)+1;          for(jk=1; jk <=nlstate ; jk++){
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);            if(pos>=1.e-5){
       printf("%s%d%d",alph[k],i1,tab[i]);*/              if(first==1)
       fprintf(ficres,"%3d",i);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       printf("%3d",i);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       for(j=1; j<=i;j++){            }else{
         fprintf(ficres," %.5e",matcov[i][j]);              if(first==1)
         printf(" %.5e",matcov[i][j]);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       }              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficres,"\n");            }
       printf("\n");            if( i <= iagemax){
       k++;              if(pos>=1.e-5){
     }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                    /*probs[i][jk][j1]= pp[jk]/pos;*/
     while((c=getc(ficpar))=='#' && c!= EOF){                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
       ungetc(c,ficpar);              }
       fgets(line, MAXLINE, ficpar);              else
       puts(line);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
       fputs(line,ficparo);            }
     }          }
     ungetc(c,ficpar);          
            for(jk=-1; jk <=nlstate+ndeath; jk++)
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);            for(m=-1; m <=nlstate+ndeath; m++)
                  if(freq[jk][m][i] !=0 ) {
     if (fage <= 2) {              if(first==1)
       bage = agemin;                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
       fage = agemax;                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     }              }
           if(i <= iagemax)
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");            fprintf(ficresp,"\n");
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);          if(first==1)
             printf("Others in log...\n");
              fprintf(ficlog,"\n");
 /*------------ gnuplot -------------*/        }
 chdir(pathcd);      }
   if((ficgp=fopen("graph.plt","w"))==NULL) {    }
     printf("Problem with file graph.gp");goto end;    dateintmean=dateintsum/k2cpt; 
   }   
 #ifdef windows    fclose(ficresp);
   fprintf(ficgp,"cd \"%s\" \n",pathc);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 #endif    free_vector(pp,1,nlstate);
 m=pow(2,cptcoveff);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
      /* End of Freq */
  /* 1eme*/  }
   for (cpt=1; cpt<= nlstate ; cpt ++) {  
    for (k1=1; k1<= m ; k1 ++) {  /************ Prevalence ********************/
   void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
 #ifdef windows  {  
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
 #endif       in each health status at the date of interview (if between dateprev1 and dateprev2).
 #ifdef unix       We still use firstpass and lastpass as another selection.
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);    */
 #endif   
     int i, m, jk, k1, i1, j1, bool, z1,z2,j;
 for (i=1; i<= nlstate ; i ++) {    double ***freq; /* Frequencies */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double *pp, **prop;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double pos,posprop; 
 }    double  y2; /* in fractional years */
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    int iagemin, iagemax;
     for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    iagemin= (int) agemin;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    iagemax= (int) agemax;
 }    /*pp=vector(1,nlstate);*/
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
      for (i=1; i<= nlstate ; i ++) {    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    j1=0;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    
 }      j=cptcoveff;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    if (cptcovn<1) {j=1;ncodemax[1]=1;}
 #ifdef unix    
 fprintf(ficgp,"\nset ter gif small size 400,300");    for(k1=1; k1<=j;k1++){
 #endif      for(i1=1; i1<=ncodemax[k1];i1++){
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        j1++;
    }        
   }        for (i=1; i<=nlstate; i++)  
   /*2 eme*/          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
   for (k1=1; k1<= m ; k1 ++) {       
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);        for (i=1; i<=imx; i++) { /* Each individual */
              bool=1;
     for (i=1; i<= nlstate+1 ; i ++) {          if  (cptcovn>0) {
       k=2*i;            for (z1=1; z1<=cptcoveff; z1++) 
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       for (j=1; j<= nlstate+1 ; j ++) {                bool=0;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");          if (bool==1) { 
 }              for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
       for (j=1; j<= nlstate+1 ; j ++) {                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                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); 
         else fprintf(ficgp," \%%*lf (\%%*lf)");                if (s[m][i]>0 && s[m][i]<=nlstate) { 
 }                    /*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]]);*/
       fprintf(ficgp,"\" t\"\" w l 0,");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);                  prop[s[m][i]][iagemax+3] += weight[i]; 
       for (j=1; j<= nlstate+1 ; j ++) {                } 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            } /* end selection of waves */
 }            }
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        }
       else fprintf(ficgp,"\" t\"\" w l 0,");        for(i=iagemin; i <= iagemax+3; i++){  
     }          
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
   }            posprop += prop[jk][i]; 
            } 
   /*3eme*/  
           for(jk=1; jk <=nlstate ; jk++){     
   for (k1=1; k1<= m ; k1 ++) {            if( i <=  iagemax){ 
     for (cpt=1; cpt<= nlstate ; cpt ++) {              if(posprop>=1.e-5){ 
       k=2+nlstate*(cpt-1);                probs[i][jk][j1]= prop[jk][i]/posprop;
       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);              } 
       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);          }/* end jk */ 
       }        }/* end i */ 
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      } /* end i1 */
     }    } /* end k1 */
   }    
      /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
   /* CV preval stat */    /*free_vector(pp,1,nlstate);*/
   for (k1=1; k1<= m ; k1 ++) {    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     for (cpt=1; cpt<nlstate ; cpt ++) {  }  /* End of prevalence */
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);  /************* Waves Concatenation ***************/
       for (i=1; i< nlstate ; i ++)  
         fprintf(ficgp,"+$%d",k+i+1);  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)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);  {
          /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       l=3+(nlstate+ndeath)*cpt;       Death is a valid wave (if date is known).
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       for (i=1; i< nlstate ; i ++) {       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
         l=3+(nlstate+ndeath)*cpt;       and mw[mi+1][i]. dh depends on stepm.
         fprintf(ficgp,"+$%d",l+i+1);       */
       }  
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      int i, mi, m;
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     }       double sum=0., jmean=0.;*/
   }    int first;
     int j, k=0,jk, ju, jl;
   /* proba elementaires */    double sum=0.;
    for(i=1,jk=1; i <=nlstate; i++){    first=0;
     for(k=1; k <=(nlstate+ndeath); k++){    jmin=1e+5;
       if (k != i) {    jmax=-1;
         for(j=1; j <=ncovmodel; j++){    jmean=0.;
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    for(i=1; i<=imx; i++){
           /*fprintf(ficgp,"%s",alph[1]);*/      mi=0;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);      m=firstpass;
           jk++;      while(s[m][i] <= nlstate){
           fprintf(ficgp,"\n");        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
         }          mw[++mi][i]=m;
       }        if(m >=lastpass)
     }          break;
     }        else
           m++;
   for(jk=1; jk <=m; jk++) {      }/* end while */
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);      if (s[m][i] > nlstate){
    i=1;        mi++;     /* Death is another wave */
    for(k2=1; k2<=nlstate; k2++) {        /* if(mi==0)  never been interviewed correctly before death */
      k3=i;           /* Only death is a correct wave */
      for(k=1; k<=(nlstate+ndeath); k++) {        mw[mi][i]=m;
        if (k != k2){      }
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);  
 ij=1;      wav[i]=mi;
         for(j=3; j <=ncovmodel; j++) {      if(mi==0){
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        nbwarn++;
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        if(first==0){
             ij++;          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
           }          first=1;
           else        }
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        if(first==1){
         }          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
           fprintf(ficgp,")/(1");        }
              } /* end mi==0 */
         for(k1=1; k1 <=nlstate; k1++){      } /* End individuals */
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);  
 ij=1;    for(i=1; i<=imx; i++){
           for(j=3; j <=ncovmodel; j++){      for(mi=1; mi<wav[i];mi++){
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        if (stepm <=0)
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          dh[mi][i]=1;
             ij++;        else{
           }          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
           else            if (agedc[i] < 2*AGESUP) {
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
           }              if(j==0) j=1;  /* Survives at least one month after exam */
           fprintf(ficgp,")");              else if(j<0){
         }                nberr++;
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);                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 ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");                j=1; /* Temporary Dangerous patch */
         i=i+ncovmodel;                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);
        }                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
      }                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
    }              }
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);              k=k+1;
   }              if (j >= jmax){
                    jmax=j;
   fclose(ficgp);                ijmax=i;
                  }
 chdir(path);              if (j <= jmin){
     free_matrix(agev,1,maxwav,1,imx);                jmin=j;
     free_ivector(wav,1,imx);                ijmin=i;
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);              }
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);              sum=sum+j;
                  /*if (j<0) printf("j=%d num=%d \n",j,i);*/
     free_imatrix(s,1,maxwav+1,1,n);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
                }
              }
     free_ivector(num,1,n);          else{
     free_vector(agedc,1,n);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     free_vector(weight,1,n);  /*        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]); */
     /*free_matrix(covar,1,NCOVMAX,1,n);*/  
     fclose(ficparo);            k=k+1;
     fclose(ficres);            if (j >= jmax) {
     /*  }*/              jmax=j;
                  ijmax=i;
    /*________fin mle=1_________*/            }
                else if (j <= jmin){
               jmin=j;
                ijmin=i;
     /* No more information from the sample is required now */            }
   /* Reads comments: lines beginning with '#' */            /*        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;
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);          jl= j -jk*stepm;
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);          ju= j -(jk+1)*stepm;
 /*--------- index.htm --------*/          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
             if(jl==0){
   strcpy(optionfilehtm,optionfile);              dh[mi][i]=jk;
   strcat(optionfilehtm,".htm");              bh[mi][i]=0;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {            }else{ /* We want a negative bias in order to only have interpolation ie
     printf("Problem with %s \n",optionfilehtm);goto end;                    * at the price of an extra matrix product in likelihood */
   }              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
  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>          }else{
 Total number of observations=%d <br>            if(jl <= -ju){
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>              dh[mi][i]=jk;
 <hr  size=\"2\" color=\"#EC5E5E\">              bh[mi][i]=jl;       /* bias is positive if real duration
 <li>Outputs files<br><br>\n                                   * is higher than the multiple of stepm and negative otherwise.
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n                                   */
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>            }
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>            else{
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>              dh[mi][i]=jk+1;
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>              bh[mi][i]=ju;
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>            }
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>            if(dh[mi][i]==0){
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>              dh[mi][i]=1; /* At least one step */
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);              bh[mi][i]=ju; /* At least one step */
               /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
  fprintf(fichtm," <li>Graphs</li><p>");            }
           } /* end if mle */
  m=cptcoveff;        }
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      } /* end wave */
     }
  j1=0;    jmean=sum/k;
  for(k1=1; k1<=m;k1++){    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);
    for(i1=1; i1<=ncodemax[k1];i1++){    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);
        j1++;   }
        if (cptcovn > 0) {  
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");  /*********** Tricode ****************************/
          for (cpt=1; cpt<=cptcoveff;cpt++)  void tricode(int *Tvar, int **nbcode, int imx)
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);  {
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    
        }    int Ndum[20],ij=1, k, j, i, maxncov=19;
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>    int cptcode=0;
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);        cptcoveff=0; 
        for(cpt=1; cpt<nlstate;cpt++){   
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    for (k=0; k<maxncov; k++) Ndum[k]=0;
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    for (k=1; k<=7; k++) ncodemax[k]=0;
        }  
     for(cpt=1; cpt<=nlstate;cpt++) {    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
 interval) in state (%d): v%s%d%d.gif <br>                                 modality*/ 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);          ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
      }        Ndum[ij]++; /*store the modality */
      for(cpt=1; cpt<=nlstate;cpt++) {        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);                                         Tvar[j]. If V=sex and male is 0 and 
      }                                         female is 1, then  cptcode=1.*/
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      }
 health expectancies in states (1) and (2): e%s%d.gif<br>  
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);      for (i=0; i<=cptcode; i++) {
 fprintf(fichtm,"\n</body>");        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 */
    }      }
  }  
 fclose(fichtm);      ij=1; 
       for (i=1; i<=ncodemax[j]; i++) {
   /*--------------- Prevalence limit --------------*/        for (k=0; k<= maxncov; k++) {
            if (Ndum[k] != 0) {
   strcpy(filerespl,"pl");            nbcode[Tvar[j]][ij]=k; 
   strcat(filerespl,fileres);            /* 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((ficrespl=fopen(filerespl,"w"))==NULL) {            
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;            ij++;
   }          }
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          if (ij > ncodemax[j]) break; 
   fprintf(ficrespl,"#Prevalence limit\n");        }  
   fprintf(ficrespl,"#Age ");      } 
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    }  
   fprintf(ficrespl,"\n");  
     for (k=0; k< maxncov; k++) Ndum[k]=0;
   prlim=matrix(1,nlstate,1,nlstate);  
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   for (i=1; i<=ncovmodel-2; i++) { 
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     ij=Tvar[i];
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     Ndum[ij]++;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */   }
   k=0;  
   agebase=agemin;   ij=1;
   agelim=agemax;   for (i=1; i<= maxncov; i++) {
   ftolpl=1.e-10;     if((Ndum[i]!=0) && (i<=ncovcol)){
   i1=cptcoveff;       Tvaraff[ij]=i; /*For printing */
   if (cptcovn < 1){i1=1;}       ij++;
      }
   for(cptcov=1;cptcov<=i1;cptcov++){   }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   
         k=k+1;   cptcoveff=ij-1; /*Number of simple covariates*/
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/  }
         fprintf(ficrespl,"\n#******");  
         for(j=1;j<=cptcoveff;j++)  /*********** Health Expectancies ****************/
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
         fprintf(ficrespl,"******\n");  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 (age=agebase; age<=agelim; age++){  {
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    /* Health expectancies, no variances */
           fprintf(ficrespl,"%.0f",age );    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
           for(i=1; i<=nlstate;i++)    int nhstepma, nstepma; /* Decreasing with age */
           fprintf(ficrespl," %.5f", prlim[i][i]);    double age, agelim, hf;
           fprintf(ficrespl,"\n");    double ***p3mat;
         }    double eip;
       }  
     }    pstamp(ficreseij);
   fclose(ficrespl);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   /*------------- h Pij x at various ages ------------*/    fprintf(ficreseij,"# Age");
      for(i=1; i<=nlstate;i++){
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      for(j=1; j<=nlstate;j++){
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        fprintf(ficreseij," e%1d%1d ",i,j);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;      }
   }      fprintf(ficreseij," e%1d. ",i);
   printf("Computing pij: result on file '%s' \n", filerespij);    }
      fprintf(ficreseij,"\n");
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=24) stepsize=2;    
     if(estepm < stepm){
   agelim=AGESUP;      printf ("Problem %d lower than %d\n",estepm, stepm);
   hstepm=stepsize*YEARM; /* Every year of age */    }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    else  hstepm=estepm;   
      /* We compute the life expectancy from trapezoids spaced every estepm months
   k=0;     * This is mainly to measure the difference between two models: for example
   for(cptcov=1;cptcov<=i1;cptcov++){     * if stepm=24 months pijx are given only every 2 years and by summing them
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){     * we are calculating an estimate of the Life Expectancy assuming a linear 
       k=k+1;     * progression in between and thus overestimating or underestimating according
         fprintf(ficrespij,"\n#****** ");     * to the curvature of the survival function. If, for the same date, we 
         for(j=1;j<=cptcoveff;j++)     * estimate the model with stepm=1 month, we can keep estepm to 24 months
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     * to compare the new estimate of Life expectancy with the same linear 
         fprintf(ficrespij,"******\n");     * hypothesis. A more precise result, taking into account a more precise
             * curvature will be obtained if estepm is as small as stepm. */
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    /* For example we decided to compute the life expectancy with the smallest unit */
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       nhstepm is the number of hstepm from age to agelim 
           oldm=oldms;savm=savms;       nstepm is the number of stepm from age to agelin. 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);         Look at hpijx to understand the reason of that which relies in memory size
           fprintf(ficrespij,"# Age");       and note for a fixed period like estepm months */
           for(i=1; i<=nlstate;i++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             for(j=1; j<=nlstate+ndeath;j++)       survival function given by stepm (the optimization length). Unfortunately it
               fprintf(ficrespij," %1d-%1d",i,j);       means that if the survival funtion is printed only each two years of age and if
           fprintf(ficrespij,"\n");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           for (h=0; h<=nhstepm; h++){       results. So we changed our mind and took the option of the best precision.
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    */
             for(i=1; i<=nlstate;i++)    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
               for(j=1; j<=nlstate+ndeath;j++)  
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    agelim=AGESUP;
             fprintf(ficrespij,"\n");    /* If stepm=6 months */
           }      /* Computed by stepm unit matrices, product of hstepm matrices, stored
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
           fprintf(ficrespij,"\n");      
         }  /* nhstepm age range expressed in number of stepm */
     }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
   fclose(ficrespij);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*---------- Health expectancies and variances ------------*/  
     for (age=bage; age<=fage; age ++){ 
   strcpy(filerest,"t");      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   strcat(filerest,fileres);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   if((ficrest=fopen(filerest,"w"))==NULL) {      /* if (stepm >= YEARM) hstepm=1;*/
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   }  
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   strcpy(filerese,"e");      
   strcat(filerese,fileres);      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   if((ficreseij=fopen(filerese,"w"))==NULL) {      
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   }      
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
  strcpy(fileresv,"v");      
   strcat(fileresv,fileres);      /* Computing expectancies */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {      for(i=1; i<=nlstate;i++)
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);        for(j=1; j<=nlstate;j++)
   }          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
   k=0;            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          }
       k=k+1;  
       fprintf(ficrest,"\n#****** ");      fprintf(ficreseij,"%3.0f",age );
       for(j=1;j<=cptcoveff;j++)      for(i=1; i<=nlstate;i++){
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        eip=0;
       fprintf(ficrest,"******\n");        for(j=1; j<=nlstate;j++){
           eip +=eij[i][j][(int)age];
       fprintf(ficreseij,"\n#****** ");          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
       for(j=1;j<=cptcoveff;j++)        }
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);        fprintf(ficreseij,"%9.4f", eip );
       fprintf(ficreseij,"******\n");      }
       fprintf(ficreseij,"\n");
       fprintf(ficresvij,"\n#****** ");      
       for(j=1;j<=cptcoveff;j++)    }
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficresvij,"******\n");    printf("\n");
     fprintf(ficlog,"\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);    
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  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[] )
       oldm=oldms;savm=savms;  
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  {
          /* Covariances of health expectancies eij and of total life expectancies according
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");     to initial status i, ei. .
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    */
       fprintf(ficrest,"\n");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
            int nhstepma, nstepma; /* Decreasing with age */
       hf=1;    double age, agelim, hf;
       if (stepm >= YEARM) hf=stepm/YEARM;    double ***p3matp, ***p3matm, ***varhe;
       epj=vector(1,nlstate+1);    double **dnewm,**doldm;
       for(age=bage; age <=fage ;age++){    double *xp, *xm;
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    double **gp, **gm;
         fprintf(ficrest," %.0f",age);    double ***gradg, ***trgradg;
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    int theta;
           for(i=1, epj[j]=0.;i <=nlstate;i++) {  
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    double eip, vip;
           }  
           epj[nlstate+1] +=epj[j];    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
         }    xp=vector(1,npar);
         for(i=1, vepp=0.;i <=nlstate;i++)    xm=vector(1,npar);
           for(j=1;j <=nlstate;j++)    dnewm=matrix(1,nlstate*nlstate,1,npar);
             vepp += vareij[i][j][(int)age];    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    
         for(j=1;j <=nlstate;j++){    pstamp(ficresstdeij);
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
         }    fprintf(ficresstdeij,"# Age");
         fprintf(ficrest,"\n");    for(i=1; i<=nlstate;i++){
       }      for(j=1; j<=nlstate;j++)
     }        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   }      fprintf(ficresstdeij," e%1d. ",i);
            }
  fclose(ficreseij);    fprintf(ficresstdeij,"\n");
  fclose(ficresvij);  
   fclose(ficrest);    pstamp(ficrescveij);
   fclose(ficpar);    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   free_vector(epj,1,nlstate+1);    fprintf(ficrescveij,"# Age");
   /*  scanf("%d ",i); */    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++){
   /*------- Variance limit prevalence------*/          cptj= (j-1)*nlstate+i;
         for(i2=1; i2<=nlstate;i2++)
 strcpy(fileresvpl,"vpl");          for(j2=1; j2<=nlstate;j2++){
   strcat(fileresvpl,fileres);            cptj2= (j2-1)*nlstate+i2;
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {            if(cptj2 <= cptj)
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
     exit(0);          }
   }      }
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    fprintf(ficrescveij,"\n");
     
  k=0;    if(estepm < stepm){
  for(cptcov=1;cptcov<=i1;cptcov++){      printf ("Problem %d lower than %d\n",estepm, stepm);
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    }
      k=k+1;    else  hstepm=estepm;   
      fprintf(ficresvpl,"\n#****** ");    /* We compute the life expectancy from trapezoids spaced every estepm months
      for(j=1;j<=cptcoveff;j++)     * This is mainly to measure the difference between two models: for example
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     * if stepm=24 months pijx are given only every 2 years and by summing them
      fprintf(ficresvpl,"******\n");     * we are calculating an estimate of the Life Expectancy assuming a linear 
           * progression in between and thus overestimating or underestimating according
      varpl=matrix(1,nlstate,(int) bage, (int) fage);     * to the curvature of the survival function. If, for the same date, we 
      oldm=oldms;savm=savms;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);     * to compare the new estimate of Life expectancy with the same linear 
    }     * hypothesis. A more precise result, taking into account a more precise
  }     * curvature will be obtained if estepm is as small as stepm. */
   
   fclose(ficresvpl);    /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   /*---------- End : free ----------------*/       nhstepm is the number of hstepm from age to agelim 
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);       nstepm is the number of stepm from age to agelin. 
         Look at hpijx to understand the reason of that which relies in memory size
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);       and note for a fixed period like estepm months */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         survival function given by stepm (the optimization length). Unfortunately it
         means that if the survival funtion is printed only each two years of age and if
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);       results. So we changed our mind and took the option of the best precision.
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    */
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
    
   free_matrix(matcov,1,npar,1,npar);    /* If stepm=6 months */
   free_vector(delti,1,npar);    /* nhstepm age range expressed in number of stepm */
      agelim=AGESUP;
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   printf("End of Imach\n");    /* if (stepm >= YEARM) hstepm=1;*/
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
      
   /* 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);*/    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*printf("Total time was %d uSec.\n", total_usecs);*/    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*------ End -----------*/    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
  end:    gp=matrix(0,nhstepm,1,nlstate*nlstate);
 #ifdef windows    gm=matrix(0,nhstepm,1,nlstate*nlstate);
  chdir(pathcd);  
 #endif    for (age=bage; age<=fage; age ++){ 
  /*system("wgnuplot graph.plt");*/      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
  system("../gp37mgw/wgnuplot graph.plt");      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
 #ifdef windows      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   while (z[0] != 'q') {  
     chdir(pathcd);      /* If stepm=6 months */
     printf("\nType e to edit output files, c to start again, and q for exiting: ");      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     scanf("%s",z);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     if (z[0] == 'c') system("./imach");      
     else if (z[0] == 'e') {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       chdir(path);  
       system("index.htm");      /* Computing  Variances of health expectancies */
     }      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
     else if (z[0] == 'q') exit(0);         decrease memory allocation */
   }      for(theta=1; theta <=npar; theta++){
 #endif        for(i=1; i<=npar; i++){ 
 }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
         hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     
         for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
               gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
               gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
             }
           }
         }
        
         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];
           }
       }/* End theta */
       
       
       for(h=0; h<=nhstepm-1; h++)
         for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
       
   
        for(ij=1;ij<=nlstate*nlstate;ij++)
         for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
   
        printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        for(h=0;h<=nhstepm-1;h++){
         for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(ij=1;ij<=nlstate*nlstate;ij++)
             for(ji=1;ji<=nlstate*nlstate;ji++)
               varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
         }
       }
   
       /* Computing expectancies */
       hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
             /* 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]);*/
   
           }
   
       fprintf(ficresstdeij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
         eip=0.;
         vip=0.;
         for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
           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];
           fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         }
         fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }
       fprintf(ficresstdeij,"\n");
   
       fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
               if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
         }
       fprintf(ficrescveij,"\n");
      
     }
     free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
     fprintf(ficlog,"\n");
   
     free_vector(xm,1,npar);
     free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
   
   /************ Variance ******************/
   void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   {
     /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /* double **newm;*/
     double **dnewm,**doldm;
     double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
     int k, cptcode;
     double *xp;
     double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
     double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
     double age,agelim, hf;
     double ***mobaverage;
     int theta;
     char digit[4];
     char digitp[25];
   
     char fileresprobmorprev[FILENAMELENGTH];
   
     if(popbased==1){
       if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
     }
     else 
       strcpy(digitp,"-stablbased-");
   
     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);
       }
     }
   
     strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     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);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }  
     fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
     /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
     fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pstamp(ficresvij);
     fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     if(popbased==1)
       fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
     else
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like k years */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
       gm=matrix(0,nhstepm,1,nlstate);
   
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         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++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
     
         for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
             for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         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++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
   
         for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm 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 */
   
         for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
   
       } /* End theta */
   
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
       for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,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++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* 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 . If one or more covariate are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), eij are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences (i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2): %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char  *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %d %s for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
           exit(1);
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           exit(1);
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         exit(1);
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line,j);
         exit(1);
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         exit(1);
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           exit(1);
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       } 
       lstra=strlen(stra);
       
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
     fclose(fic);
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
     /* for (i=1; i<=imx; i++) */
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
       
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /*---------- Health expectancies and variances ------------*/
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficreseij,"\n#****** ");
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
           cvevsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav, strstart);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav, strstart);
           }
   
           pstamp(ficrest);
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n# Age ( e.. (std) ");
           for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
           fprintf(ficrest,"\n");
   
           epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             if (popbased==1) {
               if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=probs[(int)age][i][k];
               }else{ /* mobilav */ 
                 for(i=1; i<=nlstate;i++)
                   prlim[i][i]=mobaverage[(int)age][i][k];
               }
             }
           
             fprintf(ficrest," %4.0f",age);
             for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
               for(i=1, epj[j]=0.;i <=nlstate;i++) {
                 epj[j] += prlim[i][i]*eij[i][j][(int)age];
                 /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
               }
               epj[nlstate+1] +=epj[j];
             }
   
             for(i=1, vepp=0.;i <=nlstate;i++)
               for(j=1;j <=nlstate;j++)
                 vepp += vareij[i][j][(int)age];
             fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
             for(j=1;j <=nlstate;j++){
               fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
             }
             fprintf(ficrest,"\n");
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficreseij);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.9  
changed lines
  Added in v.1.126


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