Diff for /imach/src/imach.c between versions 1.21 and 1.140

version 1.21, 2002/02/21 18:42:24 version 1.140, 2011/09/02 10:37:54
Line 1 Line 1
      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.140  2011/09/02 10:37:54  brouard
   individuals from different ages are interviewed on their health status    Summary: times.h is ok with mingw32 now.
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.139  2010/06/14 07:50:17  brouard
   Health expectancies are computed from the transistions observed between    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   waves and are computed for each degree of severity of disability (number    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   of life states). More degrees you consider, more time is necessary to  
   reach the Maximum Likelihood of the parameters involved in the model.    Revision 1.138  2010/04/30 18:19:40  brouard
   The simplest model is the multinomial logistic model where pij is    *** empty log message ***
   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 1.137  2010/04/29 18:11:38  brouard
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    (Module): Checking covariates for more complex models
   is a covariate. If you want to have a more complex model than "constant and    than V1+V2. A lot of change to be done. Unstable.
   age", you should modify the program where the markup  
     *Covariates have to be included here again* invites you to do it.    Revision 1.136  2010/04/26 20:30:53  brouard
   More covariates you add, less is the speed of the convergence.    (Module): merging some libgsl code. Fixing computation
     of likelione (using inter/intrapolation if mle = 0) in order to
   The advantage that this computer programme claims, comes from that if the    get same likelihood as if mle=1.
   delay between waves is not identical for each individual, or if some    Some cleaning of code and comments added.
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    Revision 1.135  2009/10/29 15:33:14  brouard
   hPijx is the probability to be    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Revision 1.134  2009/10/29 13:18:53  brouard
   unobserved intermediate  states. This elementary transition (by month or    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   quarter trimester, semester or year) is model as a multinomial logistic.  
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.133  2009/07/06 10:21:25  brouard
   and the contribution of each individual to the likelihood is simply hPijx.    just nforces
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.132  2009/07/06 08:22:05  brouard
   of the life expectancies. It also computes the prevalence limits.    Many tings
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.131  2009/06/20 16:22:47  brouard
            Institut national d'études démographiques, Paris.    Some dimensions resccaled
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.130  2009/05/26 06:44:34  brouard
   It is copyrighted identically to a GNU software product, ie programme and    (Module): Max Covariate is now set to 20 instead of 8. A
   software can be distributed freely for non commercial use. Latest version    lot of cleaning with variables initialized to 0. Trying to make
   can be accessed at http://euroreves.ined.fr/imach .    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   **********************************************************************/  
      Revision 1.129  2007/08/31 13:49:27  lievre
 #include <math.h>    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.128  2006/06/30 13:02:05  brouard
 #include <unistd.h>    (Module): Clarifications on computing e.j
   
 #define MAXLINE 256    Revision 1.127  2006/04/28 18:11:50  brouard
 #define FILENAMELENGTH 80    (Module): Yes the sum of survivors was wrong since
 /*#define DEBUG*/    imach-114 because nhstepm was no more computed in the age
 #define windows    loop. Now we define nhstepma in the age loop.
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): In order to speed up (in case of numerous covariates) we
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    compute health expectancies (without variances) in a first step
     and then all the health expectancies with variances or standard
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    deviation (needs data from the Hessian matrices) which slows the
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    computation.
     In the future we should be able to stop the program is only health
 #define NINTERVMAX 8    expectancies and graph are needed without standard deviations.
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.126  2006/04/28 17:23:28  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): Yes the sum of survivors was wrong since
 #define MAXN 20000    imach-114 because nhstepm was no more computed in the age
 #define YEARM 12. /* Number of months per year */    loop. Now we define nhstepma in the age loop.
 #define AGESUP 130    Version 0.98h
 #define AGEBASE 40  
     Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 int erreur; /* Error number */    Forecasting file added.
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Revision 1.124  2006/03/22 17:13:53  lievre
 int npar=NPARMAX;    Parameters are printed with %lf instead of %f (more numbers after the comma).
 int nlstate=2; /* Number of live states */    The log-likelihood is printed in the log file
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.123  2006/03/20 10:52:43  brouard
 int popbased=0;    * imach.c (Module): <title> changed, corresponds to .htm file
     name. <head> headers where missing.
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    * imach.c (Module): Weights can have a decimal point as for
 int jmin, jmax; /* min, max spacing between 2 waves */    English (a comma might work with a correct LC_NUMERIC environment,
 int mle, weightopt;    otherwise the weight is truncated).
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Modification of warning when the covariates values are not 0 or
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    1.
 double jmean; /* Mean space between 2 waves */    Version 0.98g
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Revision 1.122  2006/03/20 09:45:41  brouard
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    (Module): Weights can have a decimal point as for
 FILE *ficgp, *fichtm,*ficresprob,*ficpop;    English (a comma might work with a correct LC_NUMERIC environment,
 FILE *ficreseij;    otherwise the weight is truncated).
   char filerese[FILENAMELENGTH];    Modification of warning when the covariates values are not 0 or
  FILE  *ficresvij;    1.
   char fileresv[FILENAMELENGTH];    Version 0.98g
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.121  2006/03/16 17:45:01  lievre
     * imach.c (Module): Comments concerning covariates added
 #define NR_END 1  
 #define FREE_ARG char*    * imach.c (Module): refinements in the computation of lli if
 #define FTOL 1.0e-10    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
 #define NRANSI  
 #define ITMAX 200    Revision 1.120  2006/03/16 15:10:38  lievre
     (Module): refinements in the computation of lli if
 #define TOL 2.0e-4    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10    Revision 1.119  2006/03/15 17:42:26  brouard
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.118  2006/03/14 18:20:07  brouard
 #define TINY 1.0e-20    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 static double maxarg1,maxarg2;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    (Module): Function pstamp added
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    (Module): Version 0.98d
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.117  2006/03/14 17:16:22  brouard
 #define rint(a) floor(a+0.5)    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 static double sqrarg;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    (Module): Function pstamp added
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): Version 0.98d
   
 int imx;    Revision 1.116  2006/03/06 10:29:27  brouard
 int stepm;    (Module): Variance-covariance wrong links and
 /* Stepm, step in month: minimum step interpolation*/    varian-covariance of ej. is needed (Saito).
   
 int m,nb;    Revision 1.115  2006/02/27 12:17:45  brouard
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    (Module): One freematrix added in mlikeli! 0.98c
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.114  2006/02/26 12:57:58  brouard
 double dateintmean=0;    (Module): Some improvements in processing parameter
     filename with strsep.
 double *weight;  
 int **s; /* Status */    Revision 1.113  2006/02/24 14:20:24  brouard
 double *agedc, **covar, idx;    (Module): Memory leaks checks with valgrind and:
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */    Revision 1.112  2006/01/30 09:55:26  brouard
     (Module): Back to gnuplot.exe instead of wgnuplot.exe
 /**************** split *************************/  
 static  int split( char *path, char *dirc, char *name )    Revision 1.111  2006/01/25 20:38:18  brouard
 {    (Module): Lots of cleaning and bugs added (Gompertz)
    char *s;                             /* pointer */    (Module): Comments can be added in data file. Missing date values
    int  l1, l2;                         /* length counters */    can be a simple dot '.'.
   
    l1 = strlen( path );                 /* length of path */    Revision 1.110  2006/01/25 00:51:50  brouard
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): Lots of cleaning and bugs added (Gompertz)
    s = strrchr( path, '\\' );           /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.109  2006/01/24 19:37:15  brouard
 #if     defined(__bsd__)                /* get current working directory */    (Module): Comments (lines starting with a #) are allowed in data.
       extern char       *getwd( );  
     Revision 1.108  2006/01/19 18:05:42  lievre
       if ( getwd( dirc ) == NULL ) {    Gnuplot problem appeared...
 #else    To be fixed
       extern char       *getcwd( );  
     Revision 1.107  2006/01/19 16:20:37  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Test existence of gnuplot in imach path
 #endif  
          return( GLOCK_ERROR_GETCWD );    Revision 1.106  2006/01/19 13:24:36  brouard
       }    Some cleaning and links added in html output
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Revision 1.105  2006/01/05 20:23:19  lievre
       s++;                              /* after this, the filename */    *** empty log message ***
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.104  2005/09/30 16:11:43  lievre
       strcpy( name, s );                /* save file name */    (Module): sump fixed, loop imx fixed, and simplifications.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    (Module): If the status is missing at the last wave but we know
       dirc[l1-l2] = 0;                  /* add zero */    that the person is alive, then we can code his/her status as -2
    }    (instead of missing=-1 in earlier versions) and his/her
    l1 = strlen( dirc );                 /* length of directory */    contributions to the likelihood is 1 - Prob of dying from last
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    health status (= 1-p13= p11+p12 in the easiest case of somebody in
    return( 0 );                         /* we're done */    the healthy state at last known wave). Version is 0.98
 }  
     Revision 1.103  2005/09/30 15:54:49  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 /******************************************/  
     Revision 1.102  2004/09/15 17:31:30  brouard
 void replace(char *s, char*t)    Add the possibility to read data file including tab characters.
 {  
   int i;    Revision 1.101  2004/09/15 10:38:38  brouard
   int lg=20;    Fix on curr_time
   i=0;  
   lg=strlen(t);    Revision 1.100  2004/07/12 18:29:06  brouard
   for(i=0; i<= lg; i++) {    Add version for Mac OS X. Just define UNIX in Makefile
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.99  2004/06/05 08:57:40  brouard
   }    *** empty log message ***
 }  
     Revision 1.98  2004/05/16 15:05:56  brouard
 int nbocc(char *s, char occ)    New version 0.97 . First attempt to estimate force of mortality
 {    directly from the data i.e. without the need of knowing the health
   int i,j=0;    state at each age, but using a Gompertz model: log u =a + b*age .
   int lg=20;    This is the basic analysis of mortality and should be done before any
   i=0;    other analysis, in order to test if the mortality estimated from the
   lg=strlen(s);    cross-longitudinal survey is different from the mortality estimated
   for(i=0; i<= lg; i++) {    from other sources like vital statistic data.
   if  (s[i] == occ ) j++;  
   }    The same imach parameter file can be used but the option for mle should be -3.
   return j;  
 }    Agnès, who wrote this part of the code, tried to keep most of the
     former routines in order to include the new code within the former code.
 void cutv(char *u,char *v, char*t, char occ)  
 {    The output is very simple: only an estimate of the intercept and of
   int i,lg,j,p=0;    the slope with 95% confident intervals.
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {    Current limitations:
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    A) Even if you enter covariates, i.e. with the
   }    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
     B) There is no computation of Life Expectancy nor Life Table.
   lg=strlen(t);  
   for(j=0; j<p; j++) {    Revision 1.97  2004/02/20 13:25:42  lievre
     (u[j] = t[j]);    Version 0.96d. Population forecasting command line is (temporarily)
   }    suppressed.
      u[p]='\0';  
     Revision 1.96  2003/07/15 15:38:55  brouard
    for(j=0; j<= lg; j++) {    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
     if (j>=(p+1))(v[j-p-1] = t[j]);    rewritten within the same printf. Workaround: many printfs.
   }  
 }    Revision 1.95  2003/07/08 07:54:34  brouard
     * imach.c (Repository):
 /********************** nrerror ********************/    (Repository): Using imachwizard code to output a more meaningful covariance
     matrix (cov(a12,c31) instead of numbers.
 void nrerror(char error_text[])  
 {    Revision 1.94  2003/06/27 13:00:02  brouard
   fprintf(stderr,"ERREUR ...\n");    Just cleaning
   fprintf(stderr,"%s\n",error_text);  
   exit(1);    Revision 1.93  2003/06/25 16:33:55  brouard
 }    (Module): On windows (cygwin) function asctime_r doesn't
 /*********************** vector *******************/    exist so I changed back to asctime which exists.
 double *vector(int nl, int nh)    (Module): Version 0.96b
 {  
   double *v;    Revision 1.92  2003/06/25 16:30:45  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Module): On windows (cygwin) function asctime_r doesn't
   if (!v) nrerror("allocation failure in vector");    exist so I changed back to asctime which exists.
   return v-nl+NR_END;  
 }    Revision 1.91  2003/06/25 15:30:29  brouard
     * imach.c (Repository): Duplicated warning errors corrected.
 /************************ free vector ******************/    (Repository): Elapsed time after each iteration is now output. It
 void free_vector(double*v, int nl, int nh)    helps to forecast when convergence will be reached. Elapsed time
 {    is stamped in powell.  We created a new html file for the graphs
   free((FREE_ARG)(v+nl-NR_END));    concerning matrix of covariance. It has extension -cov.htm.
 }  
     Revision 1.90  2003/06/24 12:34:15  brouard
 /************************ivector *******************************/    (Module): Some bugs corrected for windows. Also, when
 int *ivector(long nl,long nh)    mle=-1 a template is output in file "or"mypar.txt with the design
 {    of the covariance matrix to be input.
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Revision 1.89  2003/06/24 12:30:52  brouard
   if (!v) nrerror("allocation failure in ivector");    (Module): Some bugs corrected for windows. Also, when
   return v-nl+NR_END;    mle=-1 a template is output in file "or"mypar.txt with the design
 }    of the covariance matrix to be input.
   
 /******************free ivector **************************/    Revision 1.88  2003/06/23 17:54:56  brouard
 void free_ivector(int *v, long nl, long nh)    * 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.
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.87  2003/06/18 12:26:01  brouard
 }    Version 0.96
   
 /******************* imatrix *******************************/    Revision 1.86  2003/06/17 20:04:08  brouard
 int **imatrix(long nrl, long nrh, long ncl, long nch)    (Module): Change position of html and gnuplot routines and added
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    routine fileappend.
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Revision 1.85  2003/06/17 13:12:43  brouard
   int **m;    * imach.c (Repository): Check when date of death was earlier that
      current date of interview. It may happen when the death was just
   /* allocate pointers to rows */    prior to the death. In this case, dh was negative and likelihood
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    was wrong (infinity). We still send an "Error" but patch by
   if (!m) nrerror("allocation failure 1 in matrix()");    assuming that the date of death was just one stepm after the
   m += NR_END;    interview.
   m -= nrl;    (Repository): Because some people have very long ID (first column)
      we changed int to long in num[] and we added a new lvector for
      memory allocation. But we also truncated to 8 characters (left
   /* allocate rows and set pointers to them */    truncation)
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    (Repository): No more line truncation errors.
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.84  2003/06/13 21:44:43  brouard
   m[nrl] -= ncl;    * imach.c (Repository): Replace "freqsummary" at a correct
      place. It differs from routine "prevalence" which may be called
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    many times. Probs is memory consuming and must be used with
      parcimony.
   /* return pointer to array of pointers to rows */    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   return m;  
 }    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Revision 1.82  2003/06/05 15:57:20  brouard
       int **m;    Add log in  imach.c and  fullversion number is now printed.
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */  */
 {  /*
   free((FREE_ARG) (m[nrl]+ncl-NR_END));     Interpolated Markov Chain
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Short summary of the programme:
     
 /******************* matrix *******************************/    This program computes Healthy Life Expectancies from
 double **matrix(long nrl, long nrh, long ncl, long nch)    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 {    first survey ("cross") where individuals from different ages are
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    interviewed on their health status or degree of disability (in the
   double **m;    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    (if any) in individual health status.  Health expectancies are
   if (!m) nrerror("allocation failure 1 in matrix()");    computed from the time spent in each health state according to a
   m += NR_END;    model. More health states you consider, more time is necessary to reach the
   m -= nrl;    Maximum Likelihood of the parameters involved in the model.  The
     simplest model is the multinomial logistic model where pij is the
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    probability to be observed in state j at the second wave
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    conditional to be observed in state i at the first wave. Therefore
   m[nrl] += NR_END;    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   m[nrl] -= ncl;    '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
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    where the markup *Covariates have to be included here again* invites
   return m;    you to do it.  More covariates you add, slower the
 }    convergence.
   
 /*************************free matrix ************************/    The advantage of this computer programme, compared to a simple
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    multinomial logistic model, is clear when the delay between waves is not
 {    identical for each individual. Also, if a individual missed an
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    intermediate interview, the information is lost, but taken into
   free((FREE_ARG)(m+nrl-NR_END));    account using an interpolation or extrapolation.  
 }  
     hPijx is the probability to be observed in state i at age x+h
 /******************* ma3x *******************************/    conditional to the observed state i at age x. The delay 'h' can be
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    split into an exact number (nh*stepm) of unobserved intermediate
 {    states. This elementary transition (by month, quarter,
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    semester or year) is modelled as a multinomial logistic.  The hPx
   double ***m;    matrix is simply the matrix product of nh*stepm elementary matrices
     and the contribution of each individual to the likelihood is simply
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    hPijx.
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Also this programme outputs the covariance matrix of the parameters but also
   m -= nrl;    of the life expectancies. It also computes the period (stable) prevalence. 
     
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");             Institut national d'études démographiques, Paris.
   m[nrl] += NR_END;    This software have been partly granted by Euro-REVES, a concerted action
   m[nrl] -= ncl;    from the European Union.
     It is copyrighted identically to a GNU software product, ie programme and
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    software can be distributed freely for non commercial use. Latest version
     can be accessed at http://euroreves.ined.fr/imach .
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m[nrl][ncl] += NR_END;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   m[nrl][ncl] -= nll;    
   for (j=ncl+1; j<=nch; j++)    **********************************************************************/
     m[nrl][j]=m[nrl][j-1]+nlay;  /*
      main
   for (i=nrl+1; i<=nrh; i++) {    read parameterfile
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    read datafile
     for (j=ncl+1; j<=nch; j++)    concatwav
       m[i][j]=m[i][j-1]+nlay;    freqsummary
   }    if (mle >= 1)
   return m;      mlikeli
 }    print results files
     if mle==1 
 /*************************free ma3x ************************/       computes hessian
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    read end of parameter file: agemin, agemax, bage, fage, estepm
 {        begin-prev-date,...
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    open gnuplot file
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    open html file
   free((FREE_ARG)(m+nrl-NR_END));    period (stable) prevalence
 }     for age prevalim()
     h Pij x
 /***************** f1dim *************************/    variance of p varprob
 extern int ncom;    forecasting if prevfcast==1 prevforecast call prevalence()
 extern double *pcom,*xicom;    health expectancies
 extern double (*nrfunc)(double []);    Variance-covariance of DFLE
      prevalence()
 double f1dim(double x)     movingaverage()
 {    varevsij() 
   int j;    if popbased==1 varevsij(,popbased)
   double f;    total life expectancies
   double *xt;    Variance of period (stable) prevalence
     end
   xt=vector(1,ncom);  */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  
   return f;   
 }  #include <math.h>
   #include <stdio.h>
 /*****************brent *************************/  #include <stdlib.h>
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #include <string.h>
 {  #include <unistd.h>
   int iter;  
   double a,b,d,etemp;  #include <limits.h>
   double fu,fv,fw,fx;  #include <sys/types.h>
   double ftemp;  #include <sys/stat.h>
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #include <errno.h>
   double e=0.0;  extern int errno;
    
   a=(ax < cx ? ax : cx);  #include <sys/time.h>
   b=(ax > cx ? ax : cx);  /*
   x=w=v=bx;  #include <time.h>
   fw=fv=fx=(*f)(x);  #include "timeval.h"
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);  #ifdef GSL
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  #include <gsl/gsl_errno.h>
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  #include <gsl/gsl_multimin.h>
     printf(".");fflush(stdout);  #endif
 #ifdef DEBUG  
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  /* #include <libintl.h> */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  /* #define _(String) gettext (String) */
 #endif  
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  #define MAXLINE 256
       *xmin=x;  
       return fx;  #define GNUPLOTPROGRAM "gnuplot"
     }  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
     ftemp=fu;  #define FILENAMELENGTH 132
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
       q=(x-v)*(fx-fw);  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
       if (q > 0.0) p = -p;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
       q=fabs(q);  
       etemp=e;  #define NINTERVMAX 8
       e=d;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define NCOVMAX 20 /* Maximum number of covariates */
       else {  #define MAXN 20000
         d=p/q;  #define YEARM 12. /* Number of months per year */
         u=x+d;  #define AGESUP 130
         if (u-a < tol2 || b-u < tol2)  #define AGEBASE 40
           d=SIGN(tol1,xm-x);  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
       }  #ifdef UNIX
     } else {  #define DIRSEPARATOR '/'
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define CHARSEPARATOR "/"
     }  #define ODIRSEPARATOR '\\'
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  #else
     fu=(*f)(u);  #define DIRSEPARATOR '\\'
     if (fu <= fx) {  #define CHARSEPARATOR "\\"
       if (u >= x) a=x; else b=x;  #define ODIRSEPARATOR '/'
       SHFT(v,w,x,u)  #endif
         SHFT(fv,fw,fx,fu)  
         } else {  /* $Id$ */
           if (u < x) a=u; else b=u;  /* $State$ */
           if (fu <= fw || w == x) {  
             v=w;  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
             w=u;  char fullversion[]="$Revision$ $Date$"; 
             fv=fw;  char strstart[80];
             fw=fu;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
           } else if (fu <= fv || v == x || v == w) {  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
             v=u;  int nvar=0, nforce=0; /* Number of variables, number of forces */
             fv=fu;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
           }  int npar=NPARMAX;
         }  int nlstate=2; /* Number of live states */
   }  int ndeath=1; /* Number of dead states */
   nrerror("Too many iterations in brent");  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   *xmin=x;  int popbased=0;
   return fx;  
 }  int *wav; /* Number of waves for this individuual 0 is possible */
   int maxwav=0; /* Maxim number of waves */
 /****************** mnbrak ***********************/  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
   int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
             double (*func)(double))                     to the likelihood and the sum of weights (done by funcone)*/
 {  int mle=1, weightopt=0;
   double ulim,u,r,q, dum;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   double fu;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
    int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   *fa=(*func)(*ax);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   *fb=(*func)(*bx);  double jmean=1; /* Mean space between 2 waves */
   if (*fb > *fa) {  double **oldm, **newm, **savm; /* Working pointers to matrices */
     SHFT(dum,*ax,*bx,dum)  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       SHFT(dum,*fb,*fa,dum)  /*FILE *fic ; */ /* Used in readdata only */
       }  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   *cx=(*bx)+GOLD*(*bx-*ax);  FILE *ficlog, *ficrespow;
   *fc=(*func)(*cx);  int globpr=0; /* Global variable for printing or not */
   while (*fb > *fc) {  double fretone; /* Only one call to likelihood */
     r=(*bx-*ax)*(*fb-*fc);  long ipmx=0; /* Number of contributions */
     q=(*bx-*cx)*(*fb-*fa);  double sw; /* Sum of weights */
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  char filerespow[FILENAMELENGTH];
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     ulim=(*bx)+GLIMIT*(*cx-*bx);  FILE *ficresilk;
     if ((*bx-u)*(u-*cx) > 0.0) {  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       fu=(*func)(u);  FILE *ficresprobmorprev;
     } else if ((*cx-u)*(u-ulim) > 0.0) {  FILE *fichtm, *fichtmcov; /* Html File */
       fu=(*func)(u);  FILE *ficreseij;
       if (fu < *fc) {  char filerese[FILENAMELENGTH];
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  FILE *ficresstdeij;
           SHFT(*fb,*fc,fu,(*func)(u))  char fileresstde[FILENAMELENGTH];
           }  FILE *ficrescveij;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  char filerescve[FILENAMELENGTH];
       u=ulim;  FILE  *ficresvij;
       fu=(*func)(u);  char fileresv[FILENAMELENGTH];
     } else {  FILE  *ficresvpl;
       u=(*cx)+GOLD*(*cx-*bx);  char fileresvpl[FILENAMELENGTH];
       fu=(*func)(u);  char title[MAXLINE];
     }  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     SHFT(*ax,*bx,*cx,u)  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       SHFT(*fa,*fb,*fc,fu)  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
       }  char command[FILENAMELENGTH];
 }  int  outcmd=0;
   
 /*************** linmin ************************/  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   
 int ncom;  char filelog[FILENAMELENGTH]; /* Log file */
 double *pcom,*xicom;  char filerest[FILENAMELENGTH];
 double (*nrfunc)(double []);  char fileregp[FILENAMELENGTH];
    char popfile[FILENAMELENGTH];
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   double f1dim(double x);  struct timezone tzp;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  extern int gettimeofday();
               double *fc, double (*func)(double));  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   int j;  long time_value;
   double xx,xmin,bx,ax;  extern long time();
   double fx,fb,fa;  char strcurr[80], strfor[80];
    
   ncom=n;  char *endptr;
   pcom=vector(1,n);  long lval;
   xicom=vector(1,n);  double dval;
   nrfunc=func;  
   for (j=1;j<=n;j++) {  #define NR_END 1
     pcom[j]=p[j];  #define FREE_ARG char*
     xicom[j]=xi[j];  #define FTOL 1.0e-10
   }  
   ax=0.0;  #define NRANSI 
   xx=1.0;  #define ITMAX 200 
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  #define TOL 2.0e-4 
 #ifdef DEBUG  
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  #define CGOLD 0.3819660 
 #endif  #define ZEPS 1.0e-10 
   for (j=1;j<=n;j++) {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     xi[j] *= xmin;  
     p[j] += xi[j];  #define GOLD 1.618034 
   }  #define GLIMIT 100.0 
   free_vector(xicom,1,n);  #define TINY 1.0e-20 
   free_vector(pcom,1,n);  
 }  static double maxarg1,maxarg2;
   #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 /*************** powell ************************/  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    
             double (*func)(double []))  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 {  #define rint(a) floor(a+0.5)
   void linmin(double p[], double xi[], int n, double *fret,  
               double (*func)(double []));  static double sqrarg;
   int i,ibig,j;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   double del,t,*pt,*ptt,*xit;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   double fp,fptt;  int agegomp= AGEGOMP;
   double *xits;  
   pt=vector(1,n);  int imx; 
   ptt=vector(1,n);  int stepm=1;
   xit=vector(1,n);  /* Stepm, step in month: minimum step interpolation*/
   xits=vector(1,n);  
   *fret=(*func)(p);  int estepm;
   for (j=1;j<=n;j++) pt[j]=p[j];  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   for (*iter=1;;++(*iter)) {  
     fp=(*fret);  int m,nb;
     ibig=0;  long *num;
     del=0.0;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     for (i=1;i<=n;i++)  double **pmmij, ***probs;
       printf(" %d %.12f",i, p[i]);  double *ageexmed,*agecens;
     printf("\n");  double dateintmean=0;
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  double *weight;
       fptt=(*fret);  int **s; /* Status */
 #ifdef DEBUG  double *agedc, **covar, idx;
       printf("fret=%lf \n",*fret);  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 #endif  double *lsurv, *lpop, *tpop;
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
       if (fabs(fptt-(*fret)) > del) {  double ftolhess; /* Tolerance for computing hessian */
         del=fabs(fptt-(*fret));  
         ibig=i;  /**************** split *************************/
       }  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 #ifdef DEBUG  {
       printf("%d %.12e",i,(*fret));    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       for (j=1;j<=n;j++) {       the name of the file (name), its extension only (ext) and its first part of the name (finame)
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    */ 
         printf(" x(%d)=%.12e",j,xit[j]);    char  *ss;                            /* pointer */
       }    int   l1, l2;                         /* length counters */
       for(j=1;j<=n;j++)  
         printf(" p=%.12e",p[j]);    l1 = strlen(path );                   /* length of path */
       printf("\n");    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 #endif    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     }    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      strcpy( name, path );               /* we got the fullname name because no directory */
 #ifdef DEBUG      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
       int k[2],l;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       k[0]=1;      /* get current working directory */
       k[1]=-1;      /*    extern  char* getcwd ( char *buf , int len);*/
       printf("Max: %.12e",(*func)(p));      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       for (j=1;j<=n;j++)        return( GLOCK_ERROR_GETCWD );
         printf(" %.12e",p[j]);      }
       printf("\n");      /* got dirc from getcwd*/
       for(l=0;l<=1;l++) {      printf(" DIRC = %s \n",dirc);
         for (j=1;j<=n;j++) {    } else {                              /* strip direcotry from path */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      ss++;                               /* after this, the filename */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);      l2 = strlen( ss );                  /* length of filename */
         }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));      strcpy( name, ss );         /* save file name */
       }      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 #endif      dirc[l1-l2] = 0;                    /* add zero */
       printf(" DIRC2 = %s \n",dirc);
     }
       free_vector(xit,1,n);    /* We add a separator at the end of dirc if not exists */
       free_vector(xits,1,n);    l1 = strlen( dirc );                  /* length of directory */
       free_vector(ptt,1,n);    if( dirc[l1-1] != DIRSEPARATOR ){
       free_vector(pt,1,n);      dirc[l1] =  DIRSEPARATOR;
       return;      dirc[l1+1] = 0; 
     }      printf(" DIRC3 = %s \n",dirc);
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    }
     for (j=1;j<=n;j++) {    ss = strrchr( name, '.' );            /* find last / */
       ptt[j]=2.0*p[j]-pt[j];    if (ss >0){
       xit[j]=p[j]-pt[j];      ss++;
       pt[j]=p[j];      strcpy(ext,ss);                     /* save extension */
     }      l1= strlen( name);
     fptt=(*func)(ptt);      l2= strlen(ss)+1;
     if (fptt < fp) {      strncpy( finame, name, l1-l2);
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);      finame[l1-l2]= 0;
       if (t < 0.0) {    }
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {    return( 0 );                          /* we're done */
           xi[j][ibig]=xi[j][n];  }
           xi[j][n]=xit[j];  
         }  
 #ifdef DEBUG  /******************************************/
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  
         for(j=1;j<=n;j++)  void replace_back_to_slash(char *s, char*t)
           printf(" %.12e",xit[j]);  {
         printf("\n");    int i;
 #endif    int lg=0;
       }    i=0;
     }    lg=strlen(t);
   }    for(i=0; i<= lg; i++) {
 }      (s[i] = t[i]);
       if (t[i]== '\\') s[i]='/';
 /**** Prevalence limit ****************/    }
   }
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  
 {  char *trimbb(char *out, char *in)
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
      matrix by transitions matrix until convergence is reached */    char *s;
     s=out;
   int i, ii,j,k;    while (*in != '\0'){
   double min, max, maxmin, maxmax,sumnew=0.;      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
   double **matprod2();        in++;
   double **out, cov[NCOVMAX], **pmij();      }
   double **newm;      *out++ = *in++;
   double agefin, delaymax=50 ; /* Max number of years to converge */    }
     *out='\0';
   for (ii=1;ii<=nlstate+ndeath;ii++)    return s;
     for (j=1;j<=nlstate+ndeath;j++){  }
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  char *cutv(char *blocc, char *alocc, char *in, char occ)
   {
    cov[1]=1.;    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
         and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */       gives blocc="abcdef2ghi" and alocc="j".
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){       If occ is not found blocc is null and alocc is equal to in. Returns alocc
     newm=savm;    */
     /* Covariates have to be included here again */    char *s, *t;
      cov[2]=agefin;    t=in;s=in;
      while (*in != '\0'){
       for (k=1; k<=cptcovn;k++) {      while( *in == occ){
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];        *blocc++ = *in++;
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/        s=in;
       }      }
       for (k=1; k<=cptcovage;k++)      *blocc++ = *in++;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    }
       for (k=1; k<=cptcovprod;k++)    if (s == t) /* occ not found */
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      *(blocc-(in-s))='\0';
     else
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/      *(blocc-(in-s)-1)='\0';
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    in=s;
     while ( *in != '\0'){
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);      *alocc++ = *in++;
     }
     savm=oldm;  
     oldm=newm;    *alocc='\0';
     maxmax=0.;    return s;
     for(j=1;j<=nlstate;j++){  }
       min=1.;  
       max=0.;  int nbocc(char *s, char occ)
       for(i=1; i<=nlstate; i++) {  {
         sumnew=0;    int i,j=0;
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    int lg=20;
         prlim[i][j]= newm[i][j]/(1-sumnew);    i=0;
         max=FMAX(max,prlim[i][j]);    lg=strlen(s);
         min=FMIN(min,prlim[i][j]);    for(i=0; i<= lg; i++) {
       }    if  (s[i] == occ ) j++;
       maxmin=max-min;    }
       maxmax=FMAX(maxmax,maxmin);    return j;
     }  }
     if(maxmax < ftolpl){  
       return prlim;  /* void cutv(char *u,char *v, char*t, char occ) */
     }  /* { */
   }  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
 }  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
   /*      gives u="abcdef2ghi" and v="j" *\/ */
 /*************** transition probabilities ***************/  /*   int i,lg,j,p=0; */
   /*   i=0; */
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  /*   lg=strlen(t); */
 {  /*   for(j=0; j<=lg-1; j++) { */
   double s1, s2;  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   /*double t34;*/  /*   } */
   int i,j,j1, nc, ii, jj;  
   /*   for(j=0; j<p; j++) { */
     for(i=1; i<= nlstate; i++){  /*     (u[j] = t[j]); */
     for(j=1; j<i;j++){  /*   } */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  /*      u[p]='\0'; */
         /*s2 += param[i][j][nc]*cov[nc];*/  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  /*    for(j=0; j<= lg; j++) { */
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
       }  /*   } */
       ps[i][j]=s2;  /* } */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  
     }  /********************** nrerror ********************/
     for(j=i+1; j<=nlstate+ndeath;j++){  
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  void nrerror(char error_text[])
         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);*/    fprintf(stderr,"ERREUR ...\n");
       }    fprintf(stderr,"%s\n",error_text);
       ps[i][j]=(s2);    exit(EXIT_FAILURE);
     }  }
   }  /*********************** vector *******************/
     /*ps[3][2]=1;*/  double *vector(int nl, int nh)
   {
   for(i=1; i<= nlstate; i++){    double *v;
      s1=0;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     for(j=1; j<i; j++)    if (!v) nrerror("allocation failure in vector");
       s1+=exp(ps[i][j]);    return v-nl+NR_END;
     for(j=i+1; j<=nlstate+ndeath; j++)  }
       s1+=exp(ps[i][j]);  
     ps[i][i]=1./(s1+1.);  /************************ free vector ******************/
     for(j=1; j<i; j++)  void free_vector(double*v, int nl, int nh)
       ps[i][j]= exp(ps[i][j])*ps[i][i];  {
     for(j=i+1; j<=nlstate+ndeath; j++)    free((FREE_ARG)(v+nl-NR_END));
       ps[i][j]= exp(ps[i][j])*ps[i][i];  }
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  
   } /* end i */  /************************ivector *******************************/
   int *ivector(long nl,long nh)
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  {
     for(jj=1; jj<= nlstate+ndeath; jj++){    int *v;
       ps[ii][jj]=0;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       ps[ii][ii]=1;    if (!v) nrerror("allocation failure in ivector");
     }    return v-nl+NR_END;
   }  }
   
   /******************free ivector **************************/
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  void free_ivector(int *v, long nl, long nh)
     for(jj=1; jj<= nlstate+ndeath; jj++){  {
      printf("%lf ",ps[ii][jj]);    free((FREE_ARG)(v+nl-NR_END));
    }  }
     printf("\n ");  
     }  /************************lvector *******************************/
     printf("\n ");printf("%lf ",cov[2]);*/  long *lvector(long nl,long nh)
 /*  {
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    long *v;
   goto end;*/    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     return ps;    if (!v) nrerror("allocation failure in ivector");
 }    return v-nl+NR_END;
   }
 /**************** Product of 2 matrices ******************/  
   /******************free lvector **************************/
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  void free_lvector(long *v, long nl, long nh)
 {  {
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    free((FREE_ARG)(v+nl-NR_END));
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  }
   /* in, b, out are matrice of pointers which should have been initialized  
      before: only the contents of out is modified. The function returns  /******************* imatrix *******************************/
      a pointer to pointers identical to out */  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   long i, j, k;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   for(i=nrl; i<= nrh; i++)  { 
     for(k=ncolol; k<=ncoloh; k++)    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    int **m; 
         out[i][k] +=in[i][j]*b[j][k];    
     /* allocate pointers to rows */ 
   return out;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
 }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
     m -= nrl; 
 /************* Higher Matrix Product ***************/    
     
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    /* allocate rows and set pointers to them */ 
 {    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
      duration (i.e. until    m[nrl] += NR_END; 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    m[nrl] -= ncl; 
      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(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
      Model is determined by parameters x and covariates have to be    
      included manually here.    /* return pointer to array of pointers to rows */ 
     return m; 
      */  } 
   
   int i, j, d, h, k;  /****************** free_imatrix *************************/
   double **out, cov[NCOVMAX];  void free_imatrix(m,nrl,nrh,ncl,nch)
   double **newm;        int **m;
         long nch,ncl,nrh,nrl; 
   /* Hstepm could be zero and should return the unit matrix */       /* free an int matrix allocated by imatrix() */ 
   for (i=1;i<=nlstate+ndeath;i++)  { 
     for (j=1;j<=nlstate+ndeath;j++){    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       oldm[i][j]=(i==j ? 1.0 : 0.0);    free((FREE_ARG) (m+nrl-NR_END)); 
       po[i][j][0]=(i==j ? 1.0 : 0.0);  } 
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /******************* matrix *******************************/
   for(h=1; h <=nhstepm; h++){  double **matrix(long nrl, long nrh, long ncl, long nch)
     for(d=1; d <=hstepm; d++){  {
       newm=savm;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       /* Covariates have to be included here again */    double **m;
       cov[1]=1.;  
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if (!m) nrerror("allocation failure 1 in matrix()");
       for (k=1; k<=cptcovage;k++)    m += NR_END;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m -= nrl;
       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]]];    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    m[nrl] -= ncl;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    return m;
       savm=oldm;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       oldm=newm;     */
     }  }
     for(i=1; i<=nlstate+ndeath; i++)  
       for(j=1;j<=nlstate+ndeath;j++) {  /*************************free matrix ************************/
         po[i][j][h]=newm[i][j];  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  {
          */    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       }    free((FREE_ARG)(m+nrl-NR_END));
   } /* end h */  }
   return po;  
 }  /******************* ma3x *******************************/
   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   {
 /*************** log-likelihood *************/    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
 double func( double *x)    double ***m;
 {  
   int i, ii, j, k, mi, d, kk;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    if (!m) nrerror("allocation failure 1 in matrix()");
   double **out;    m += NR_END;
   double sw; /* Sum of weights */    m -= nrl;
   double lli; /* Individual log likelihood */  
   long ipmx;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   /*extern weight */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   /* We are differentiating ll according to initial status */    m[nrl] += NR_END;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    m[nrl] -= ncl;
   /*for(i=1;i<imx;i++)  
     printf(" %d\n",s[4][i]);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   */  
   cov[1]=1.;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   for(k=1; k<=nlstate; k++) ll[k]=0.;    m[nrl][ncl] += NR_END;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    m[nrl][ncl] -= nll;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    for (j=ncl+1; j<=nch; j++) 
     for(mi=1; mi<= wav[i]-1; mi++){      m[nrl][j]=m[nrl][j-1]+nlay;
       for (ii=1;ii<=nlstate+ndeath;ii++)    
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    for (i=nrl+1; i<=nrh; i++) {
       for(d=0; d<dh[mi][i]; d++){      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
         newm=savm;      for (j=ncl+1; j<=nch; j++) 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;        m[i][j]=m[i][j-1]+nlay;
         for (kk=1; kk<=cptcovage;kk++) {    }
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    return m; 
         }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
                     &(m[i][j][k]) <=> *((*(m+i) + j)+k)
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    */
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  }
         savm=oldm;  
         oldm=newm;  /*************************free ma3x ************************/
          void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
          {
       } /* end mult */    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
          free((FREE_ARG)(m[nrl]+ncl-NR_END));
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    free((FREE_ARG)(m+nrl-NR_END));
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  }
       ipmx +=1;  
       sw += weight[i];  /*************** function subdirf ***********/
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  char *subdirf(char fileres[])
     } /* end of wave */  {
   } /* end of individual */    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    strcat(tmpout,"/"); /* Add to the right */
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    strcat(tmpout,fileres);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    return tmpout;
   return -l;  }
 }  
   /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
 /*********** Maximum Likelihood Estimation ***************/  {
     
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    /* Caution optionfilefiname is hidden */
 {    strcpy(tmpout,optionfilefiname);
   int i,j, iter;    strcat(tmpout,"/");
   double **xi,*delti;    strcat(tmpout,preop);
   double fret;    strcat(tmpout,fileres);
   xi=matrix(1,npar,1,npar);    return tmpout;
   for (i=1;i<=npar;i++)  }
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);  /*************** function subdirf3 ***********/
   printf("Powell\n");  char *subdirf3(char fileres[], char *preop, char *preop2)
   powell(p,xi,npar,ftol,&iter,&fret,func);  {
     
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    /* Caution optionfilefiname is hidden */
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
 }    strcat(tmpout,preop);
     strcat(tmpout,preop2);
 /**** Computes Hessian and covariance matrix ***/    strcat(tmpout,fileres);
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    return tmpout;
 {  }
   double  **a,**y,*x,pd;  
   double **hess;  /***************** f1dim *************************/
   int i, j,jk;  extern int ncom; 
   int *indx;  extern double *pcom,*xicom;
   extern double (*nrfunc)(double []); 
   double hessii(double p[], double delta, int theta, double delti[]);   
   double hessij(double p[], double delti[], int i, int j);  double f1dim(double x) 
   void lubksb(double **a, int npar, int *indx, double b[]) ;  { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;    int j; 
     double f;
   hess=matrix(1,npar,1,npar);    double *xt; 
    
   printf("\nCalculation of the hessian matrix. Wait...\n");    xt=vector(1,ncom); 
   for (i=1;i<=npar;i++){    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     printf("%d",i);fflush(stdout);    f=(*nrfunc)(xt); 
     hess[i][i]=hessii(p,ftolhess,i,delti);    free_vector(xt,1,ncom); 
     /*printf(" %f ",p[i]);*/    return f; 
     /*printf(" %lf ",hess[i][i]);*/  } 
   }  
    /*****************brent *************************/
   for (i=1;i<=npar;i++) {  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     for (j=1;j<=npar;j++)  {  { 
       if (j>i) {    int iter; 
         printf(".%d%d",i,j);fflush(stdout);    double a,b,d,etemp;
         hess[i][j]=hessij(p,delti,i,j);    double fu,fv,fw,fx;
         hess[j][i]=hess[i][j];        double ftemp;
         /*printf(" %lf ",hess[i][j]);*/    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       }    double e=0.0; 
     }   
   }    a=(ax < cx ? ax : cx); 
   printf("\n");    b=(ax > cx ? ax : cx); 
     x=w=v=bx; 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    fw=fv=fx=(*f)(x); 
      for (iter=1;iter<=ITMAX;iter++) { 
   a=matrix(1,npar,1,npar);      xm=0.5*(a+b); 
   y=matrix(1,npar,1,npar);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   x=vector(1,npar);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   indx=ivector(1,npar);      printf(".");fflush(stdout);
   for (i=1;i<=npar;i++)      fprintf(ficlog,".");fflush(ficlog);
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  #ifdef DEBUG
   ludcmp(a,npar,indx,&pd);      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   for (j=1;j<=npar;j++) {      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     for (i=1;i<=npar;i++) x[i]=0;  #endif
     x[j]=1;      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     lubksb(a,npar,indx,x);        *xmin=x; 
     for (i=1;i<=npar;i++){        return fx; 
       matcov[i][j]=x[i];      } 
     }      ftemp=fu;
   }      if (fabs(e) > tol1) { 
         r=(x-w)*(fx-fv); 
   printf("\n#Hessian matrix#\n");        q=(x-v)*(fx-fw); 
   for (i=1;i<=npar;i++) {        p=(x-v)*q-(x-w)*r; 
     for (j=1;j<=npar;j++) {        q=2.0*(q-r); 
       printf("%.3e ",hess[i][j]);        if (q > 0.0) p = -p; 
     }        q=fabs(q); 
     printf("\n");        etemp=e; 
   }        e=d; 
         if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   /* Recompute Inverse */          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   for (i=1;i<=npar;i++)        else { 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];          d=p/q; 
   ludcmp(a,npar,indx,&pd);          u=x+d; 
           if (u-a < tol2 || b-u < tol2) 
   /*  printf("\n#Hessian matrix recomputed#\n");            d=SIGN(tol1,xm-x); 
         } 
   for (j=1;j<=npar;j++) {      } else { 
     for (i=1;i<=npar;i++) x[i]=0;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     x[j]=1;      } 
     lubksb(a,npar,indx,x);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     for (i=1;i<=npar;i++){      fu=(*f)(u); 
       y[i][j]=x[i];      if (fu <= fx) { 
       printf("%.3e ",y[i][j]);        if (u >= x) a=x; else b=x; 
     }        SHFT(v,w,x,u) 
     printf("\n");          SHFT(fv,fw,fx,fu) 
   }          } else { 
   */            if (u < x) a=u; else b=u; 
             if (fu <= fw || w == x) { 
   free_matrix(a,1,npar,1,npar);              v=w; 
   free_matrix(y,1,npar,1,npar);              w=u; 
   free_vector(x,1,npar);              fv=fw; 
   free_ivector(indx,1,npar);              fw=fu; 
   free_matrix(hess,1,npar,1,npar);            } else if (fu <= fv || v == x || v == w) { 
               v=u; 
               fv=fu; 
 }            } 
           } 
 /*************** hessian matrix ****************/    } 
 double hessii( double x[], double delta, int theta, double delti[])    nrerror("Too many iterations in brent"); 
 {    *xmin=x; 
   int i;    return fx; 
   int l=1, lmax=20;  } 
   double k1,k2;  
   double p2[NPARMAX+1];  /****************** mnbrak ***********************/
   double res;  
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   double fx;              double (*func)(double)) 
   int k=0,kmax=10;  { 
   double l1;    double ulim,u,r,q, dum;
     double fu; 
   fx=func(x);   
   for (i=1;i<=npar;i++) p2[i]=x[i];    *fa=(*func)(*ax); 
   for(l=0 ; l <=lmax; l++){    *fb=(*func)(*bx); 
     l1=pow(10,l);    if (*fb > *fa) { 
     delts=delt;      SHFT(dum,*ax,*bx,dum) 
     for(k=1 ; k <kmax; k=k+1){        SHFT(dum,*fb,*fa,dum) 
       delt = delta*(l1*k);        } 
       p2[theta]=x[theta] +delt;    *cx=(*bx)+GOLD*(*bx-*ax); 
       k1=func(p2)-fx;    *fc=(*func)(*cx); 
       p2[theta]=x[theta]-delt;    while (*fb > *fc) { 
       k2=func(p2)-fx;      r=(*bx-*ax)*(*fb-*fc); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */      q=(*bx-*cx)*(*fb-*fa); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
              (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
 #ifdef DEBUG      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       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);      if ((*bx-u)*(u-*cx) > 0.0) { 
 #endif        fu=(*func)(u); 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */      } else if ((*cx-u)*(u-ulim) > 0.0) { 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        fu=(*func)(u); 
         k=kmax;        if (fu < *fc) { 
       }          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */            SHFT(*fb,*fc,fu,(*func)(u)) 
         k=kmax; l=lmax*10.;            } 
       }      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        u=ulim; 
         delts=delt;        fu=(*func)(u); 
       }      } else { 
     }        u=(*cx)+GOLD*(*cx-*bx); 
   }        fu=(*func)(u); 
   delti[theta]=delts;      } 
   return res;      SHFT(*ax,*bx,*cx,u) 
          SHFT(*fa,*fb,*fc,fu) 
 }        } 
   } 
 double hessij( double x[], double delti[], int thetai,int thetaj)  
 {  /*************** linmin ************************/
   int i;  
   int l=1, l1, lmax=20;  int ncom; 
   double k1,k2,k3,k4,res,fx;  double *pcom,*xicom;
   double p2[NPARMAX+1];  double (*nrfunc)(double []); 
   int k;   
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   fx=func(x);  { 
   for (k=1; k<=2; k++) {    double brent(double ax, double bx, double cx, 
     for (i=1;i<=npar;i++) p2[i]=x[i];                 double (*f)(double), double tol, double *xmin); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    double f1dim(double x); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     k1=func(p2)-fx;                double *fc, double (*func)(double)); 
      int j; 
     p2[thetai]=x[thetai]+delti[thetai]/k;    double xx,xmin,bx,ax; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    double fx,fb,fa;
     k2=func(p2)-fx;   
      ncom=n; 
     p2[thetai]=x[thetai]-delti[thetai]/k;    pcom=vector(1,n); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    xicom=vector(1,n); 
     k3=func(p2)-fx;    nrfunc=func; 
      for (j=1;j<=n;j++) { 
     p2[thetai]=x[thetai]-delti[thetai]/k;      pcom[j]=p[j]; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      xicom[j]=xi[j]; 
     k4=func(p2)-fx;    } 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    ax=0.0; 
 #ifdef DEBUG    xx=1.0; 
     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);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
 #endif    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   }  #ifdef DEBUG
   return res;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 }    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
 /************** Inverse of matrix **************/    for (j=1;j<=n;j++) { 
 void ludcmp(double **a, int n, int *indx, double *d)      xi[j] *= xmin; 
 {      p[j] += xi[j]; 
   int i,imax,j,k;    } 
   double big,dum,sum,temp;    free_vector(xicom,1,n); 
   double *vv;    free_vector(pcom,1,n); 
    } 
   vv=vector(1,n);  
   *d=1.0;  char *asc_diff_time(long time_sec, char ascdiff[])
   for (i=1;i<=n;i++) {  {
     big=0.0;    long sec_left, days, hours, minutes;
     for (j=1;j<=n;j++)    days = (time_sec) / (60*60*24);
       if ((temp=fabs(a[i][j])) > big) big=temp;    sec_left = (time_sec) % (60*60*24);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    hours = (sec_left) / (60*60) ;
     vv[i]=1.0/big;    sec_left = (sec_left) %(60*60);
   }    minutes = (sec_left) /60;
   for (j=1;j<=n;j++) {    sec_left = (sec_left) % (60);
     for (i=1;i<j;i++) {    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
       sum=a[i][j];    return ascdiff;
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  }
       a[i][j]=sum;  
     }  /*************** powell ************************/
     big=0.0;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     for (i=j;i<=n;i++) {              double (*func)(double [])) 
       sum=a[i][j];  { 
       for (k=1;k<j;k++)    void linmin(double p[], double xi[], int n, double *fret, 
         sum -= a[i][k]*a[k][j];                double (*func)(double [])); 
       a[i][j]=sum;    int i,ibig,j; 
       if ( (dum=vv[i]*fabs(sum)) >= big) {    double del,t,*pt,*ptt,*xit;
         big=dum;    double fp,fptt;
         imax=i;    double *xits;
       }    int niterf, itmp;
     }  
     if (j != imax) {    pt=vector(1,n); 
       for (k=1;k<=n;k++) {    ptt=vector(1,n); 
         dum=a[imax][k];    xit=vector(1,n); 
         a[imax][k]=a[j][k];    xits=vector(1,n); 
         a[j][k]=dum;    *fret=(*func)(p); 
       }    for (j=1;j<=n;j++) pt[j]=p[j]; 
       *d = -(*d);    for (*iter=1;;++(*iter)) { 
       vv[imax]=vv[j];      fp=(*fret); 
     }      ibig=0; 
     indx[j]=imax;      del=0.0; 
     if (a[j][j] == 0.0) a[j][j]=TINY;      last_time=curr_time;
     if (j != n) {      (void) gettimeofday(&curr_time,&tzp);
       dum=1.0/(a[j][j]);      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
       for (i=j+1;i<=n;i++) a[i][j] *= dum;      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);
     }  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   }     for (i=1;i<=n;i++) {
   free_vector(vv,1,n);  /* Doesn't work */        printf(" %d %.12f",i, p[i]);
 ;        fprintf(ficlog," %d %.12lf",i, p[i]);
 }        fprintf(ficrespow," %.12lf", p[i]);
       }
 void lubksb(double **a, int n, int *indx, double b[])      printf("\n");
 {      fprintf(ficlog,"\n");
   int i,ii=0,ip,j;      fprintf(ficrespow,"\n");fflush(ficrespow);
   double sum;      if(*iter <=3){
          tm = *localtime(&curr_time.tv_sec);
   for (i=1;i<=n;i++) {        strcpy(strcurr,asctime(&tm));
     ip=indx[i];  /*       asctime_r(&tm,strcurr); */
     sum=b[ip];        forecast_time=curr_time; 
     b[ip]=b[i];        itmp = strlen(strcurr);
     if (ii)        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          strcurr[itmp-1]='\0';
     else if (sum) ii=i;        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     b[i]=sum;        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){
   for (i=n;i>=1;i--) {          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     sum=b[i];          tmf = *localtime(&forecast_time.tv_sec);
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];  /*      asctime_r(&tmf,strfor); */
     b[i]=sum/a[i][i];          strcpy(strfor,asctime(&tmf));
   }          itmp = strlen(strfor);
 }          if(strfor[itmp-1]=='\n')
           strfor[itmp-1]='\0';
 /************ Frequencies ********************/          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);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2)          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);
 {  /* Some frequencies */        }
        }
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;      for (i=1;i<=n;i++) { 
   double ***freq; /* Frequencies */        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   double *pp;        fptt=(*fret); 
   double pos, k2, dateintsum=0,k2cpt=0;  #ifdef DEBUG
   FILE *ficresp;        printf("fret=%lf \n",*fret);
   char fileresp[FILENAMELENGTH];        fprintf(ficlog,"fret=%lf \n",*fret);
   #endif
   pp=vector(1,nlstate);        printf("%d",i);fflush(stdout);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        fprintf(ficlog,"%d",i);fflush(ficlog);
   strcpy(fileresp,"p");        linmin(p,xit,n,fret,func); 
   strcat(fileresp,fileres);        if (fabs(fptt-(*fret)) > del) { 
   if((ficresp=fopen(fileresp,"w"))==NULL) {          del=fabs(fptt-(*fret)); 
     printf("Problem with prevalence resultfile: %s\n", fileresp);          ibig=i; 
     exit(0);        } 
   }  #ifdef DEBUG
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        printf("%d %.12e",i,(*fret));
   j1=0;        fprintf(ficlog,"%d %.12e",i,(*fret));
         for (j=1;j<=n;j++) {
   j=cptcoveff;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          printf(" x(%d)=%.12e",j,xit[j]);
           fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   for(k1=1; k1<=j;k1++){        }
    for(i1=1; i1<=ncodemax[k1];i1++){        for(j=1;j<=n;j++) {
        j1++;          printf(" p=%.12e",p[j]);
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          fprintf(ficlog," p=%.12e",p[j]);
          scanf("%d", i);*/        }
         for (i=-1; i<=nlstate+ndeath; i++)          printf("\n");
          for (jk=-1; jk<=nlstate+ndeath; jk++)          fprintf(ficlog,"\n");
            for(m=agemin; m <= agemax+3; m++)  #endif
              freq[i][jk][m]=0;      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
         dateintsum=0;  #ifdef DEBUG
         k2cpt=0;        int k[2],l;
        for (i=1; i<=imx; i++) {        k[0]=1;
          bool=1;        k[1]=-1;
          if  (cptcovn>0) {        printf("Max: %.12e",(*func)(p));
            for (z1=1; z1<=cptcoveff; z1++)        fprintf(ficlog,"Max: %.12e",(*func)(p));
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        for (j=1;j<=n;j++) {
                bool=0;          printf(" %.12e",p[j]);
          }          fprintf(ficlog," %.12e",p[j]);
          if (bool==1) {        }
            for(m=firstpass; m<=lastpass; m++){        printf("\n");
              k2=anint[m][i]+(mint[m][i]/12.);        fprintf(ficlog,"\n");
              if ((k2>=dateprev1) && (k2<=dateprev2)) {        for(l=0;l<=1;l++) {
                if(agev[m][i]==0) agev[m][i]=agemax+1;          for (j=1;j<=n;j++) {
                if(agev[m][i]==1) agev[m][i]=agemax+2;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {          }
                  dateintsum=dateintsum+k2;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                  k2cpt++;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                }        }
   #endif
              }  
            }  
          }        free_vector(xit,1,n); 
        }        free_vector(xits,1,n); 
         if  (cptcovn>0) {        free_vector(ptt,1,n); 
          fprintf(ficresp, "\n#********** Variable ");        free_vector(pt,1,n); 
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        return; 
        fprintf(ficresp, "**********\n#");      } 
         }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
        for(i=1; i<=nlstate;i++)      for (j=1;j<=n;j++) { 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        ptt[j]=2.0*p[j]-pt[j]; 
        fprintf(ficresp, "\n");        xit[j]=p[j]-pt[j]; 
                pt[j]=p[j]; 
   for(i=(int)agemin; i <= (int)agemax+3; i++){      } 
     if(i==(int)agemax+3)      fptt=(*func)(ptt); 
       printf("Total");      if (fptt < fp) { 
     else        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       printf("Age %d", i);        if (t < 0.0) { 
     for(jk=1; jk <=nlstate ; jk++){          linmin(p,xit,n,fret,func); 
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          for (j=1;j<=n;j++) { 
         pp[jk] += freq[jk][m][i];            xi[j][ibig]=xi[j][n]; 
     }            xi[j][n]=xit[j]; 
     for(jk=1; jk <=nlstate ; jk++){          }
       for(m=-1, pos=0; m <=0 ; m++)  #ifdef DEBUG
         pos += freq[jk][m][i];          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       if(pp[jk]>=1.e-10)          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          for(j=1;j<=n;j++){
       else            printf(" %.12e",xit[j]);
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);            fprintf(ficlog," %.12e",xit[j]);
     }          }
           printf("\n");
      for(jk=1; jk <=nlstate ; jk++){          fprintf(ficlog,"\n");
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  #endif
         pp[jk] += freq[jk][m][i];        }
      }      } 
     } 
     for(jk=1,pos=0; jk <=nlstate ; jk++)  } 
       pos += pp[jk];  
     for(jk=1; jk <=nlstate ; jk++){  /**** Prevalence limit (stable or period prevalence)  ****************/
       if(pos>=1.e-5)  
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       else  {
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       if( i <= (int) agemax){       matrix by transitions matrix until convergence is reached */
         if(pos>=1.e-5){  
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    int i, ii,j,k;
           probs[i][jk][j1]= pp[jk]/pos;    double min, max, maxmin, maxmax,sumnew=0.;
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/    double **matprod2();
         }    double **out, cov[NCOVMAX+1], **pmij();
       else    double **newm;
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    double agefin, delaymax=50 ; /* Max number of years to converge */
       }  
     }    for (ii=1;ii<=nlstate+ndeath;ii++)
     for(jk=-1; jk <=nlstate+ndeath; jk++)      for (j=1;j<=nlstate+ndeath;j++){
       for(m=-1; m <=nlstate+ndeath; m++)        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      }
     if(i <= (int) agemax)  
       fprintf(ficresp,"\n");     cov[1]=1.;
     printf("\n");   
     }   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     }    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
  }      newm=savm;
   dateintmean=dateintsum/k2cpt;      /* Covariates have to be included here again */
        cov[2]=agefin;
   fclose(ficresp);      
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      for (k=1; k<=cptcovn;k++) {
   free_vector(pp,1,nlstate);        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         /*        printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
   /* End of Freq */      }
 }      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       for (k=1; k<=cptcovprod;k++)
 /************ Prevalence ********************/        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
 void prevalence(int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)      
 {  /* Some frequencies */      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   double ***freq; /* Frequencies */      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   double *pp;      
   double pos, k2;      savm=oldm;
       oldm=newm;
   pp=vector(1,nlstate);      maxmax=0.;
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(j=1;j<=nlstate;j++){
          min=1.;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        max=0.;
   j1=0;        for(i=1; i<=nlstate; i++) {
            sumnew=0;
   j=cptcoveff;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          prlim[i][j]= newm[i][j]/(1-sumnew);
            max=FMAX(max,prlim[i][j]);
  for(k1=1; k1<=j;k1++){          min=FMIN(min,prlim[i][j]);
     for(i1=1; i1<=ncodemax[k1];i1++){        }
       j1++;        maxmin=max-min;
          maxmax=FMAX(maxmax,maxmin);
       for (i=-1; i<=nlstate+ndeath; i++)        }
         for (jk=-1; jk<=nlstate+ndeath; jk++)        if(maxmax < ftolpl){
           for(m=agemin; m <= agemax+3; m++)        return prlim;
             freq[i][jk][m]=0;      }
          }
       for (i=1; i<=imx; i++) {  }
         bool=1;  
         if  (cptcovn>0) {  /*************** transition probabilities ***************/ 
           for (z1=1; z1<=cptcoveff; z1++)  
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
               bool=0;  {
         }    /* According to parameters values stored in x and the covariate's values stored in cov,
         if (bool==1) {       computes the probability to be observed in state j being in state i by appying the
           for(m=firstpass; m<=lastpass; m++){       model to the ncovmodel covariates (including constant and age).
             k2=anint[m][i]+(mint[m][i]/12.);       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
             if ((k2>=dateprev1) && (k2<=dateprev2)) {       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
               if(agev[m][i]==0) agev[m][i]=agemax+1;       ncth covariate in the global vector x is given by the formula:
               if(agev[m][i]==1) agev[m][i]=agemax+2;       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
               freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];         Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
             }       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
           }       Outputs ps[i][j] the probability to be observed in j being in j according to
         }       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
       }    */
          double s1, lnpijopii;
         for(i=(int)agemin; i <= (int)agemax+3; i++){    /*double t34;*/
           for(jk=1; jk <=nlstate ; jk++){    int i,j,j1, nc, ii, jj;
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  
               pp[jk] += freq[jk][m][i];      for(i=1; i<= nlstate; i++){
           }        for(j=1; j<i;j++){
           for(jk=1; jk <=nlstate ; jk++){          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
             for(m=-1, pos=0; m <=0 ; m++)            /*lnpijopii += param[i][j][nc]*cov[nc];*/
             pos += freq[jk][m][i];            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
         }  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
                  }
          for(jk=1; jk <=nlstate ; jk++){          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
              pp[jk] += freq[jk][m][i];        }
          }        for(j=i+1; j<=nlstate+ndeath;j++){
                    for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
             lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
          for(jk=1; jk <=nlstate ; jk++){            /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
            if( i <= (int) agemax){          }
              if(pos>=1.e-5){          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
                probs[i][jk][j1]= pp[jk]/pos;        }
              }      }
            }      
          }      for(i=1; i<= nlstate; i++){
                  s1=0;
         }        for(j=1; j<i; j++){
     }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   }          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
          }
          for(j=i+1; j<=nlstate+ndeath; j++){
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   free_vector(pp,1,nlstate);          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
          }
 }  /* End of Freq */        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
         ps[i][i]=1./(s1+1.);
 /************* Waves Concatenation ***************/        /* Computing other pijs */
         for(j=1; j<i; j++)
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          ps[i][j]= exp(ps[i][j])*ps[i][i];
 {        for(j=i+1; j<=nlstate+ndeath; j++)
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          ps[i][j]= exp(ps[i][j])*ps[i][i];
      Death is a valid wave (if date is known).        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i      } /* end 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.      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
      */        for(jj=1; jj<= nlstate+ndeath; jj++){
           ps[ii][jj]=0;
   int i, mi, m;          ps[ii][ii]=1;
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        }
      double sum=0., jmean=0.;*/      }
       
   int j, k=0,jk, ju, jl;  
   double sum=0.;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   jmin=1e+5;  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   jmax=-1;  /*         printf("ddd %lf ",ps[ii][jj]); */
   jmean=0.;  /*       } */
   for(i=1; i<=imx; i++){  /*       printf("\n "); */
     mi=0;  /*        } */
     m=firstpass;  /*        printf("\n ");printf("%lf ",cov[2]); */
     while(s[m][i] <= nlstate){         /*
       if(s[m][i]>=1)        for(i=1; i<= npar; i++) printf("%f ",x[i]);
         mw[++mi][i]=m;        goto end;*/
       if(m >=lastpass)      return ps;
         break;  }
       else  
         m++;  /**************** Product of 2 matrices ******************/
     }/* end while */  
     if (s[m][i] > nlstate){  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       mi++;     /* Death is another wave */  {
       /* if(mi==0)  never been interviewed correctly before death */    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
          /* Only death is a correct wave */       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
       mw[mi][i]=m;    /* in, b, out are matrice of pointers which should have been initialized 
     }       before: only the contents of out is modified. The function returns
        a pointer to pointers identical to out */
     wav[i]=mi;    long i, j, k;
     if(mi==0)    for(i=nrl; i<= nrh; i++)
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);      for(k=ncolol; k<=ncoloh; k++)
   }        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
   for(i=1; i<=imx; i++){  
     for(mi=1; mi<wav[i];mi++){    return out;
       if (stepm <=0)  }
         dh[mi][i]=1;  
       else{  
         if (s[mw[mi+1][i]][i] > nlstate) {  /************* Higher Matrix Product ***************/
           if (agedc[i] < 2*AGESUP) {  
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
           if(j==0) j=1;  /* Survives at least one month after exam */  {
           k=k+1;    /* Computes the transition matrix starting at age 'age' over 
           if (j >= jmax) jmax=j;       'nhstepm*hstepm*stepm' months (i.e. until
           if (j <= jmin) jmin=j;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
           sum=sum+j;       nhstepm*hstepm matrices. 
           /* if (j<10) printf("j=%d num=%d ",j,i); */       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).
         else{       Model is determined by parameters x and covariates have to be 
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));       included manually here. 
           k=k+1;  
           if (j >= jmax) jmax=j;       */
           else if (j <= jmin)jmin=j;  
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    int i, j, d, h, k;
           sum=sum+j;    double **out, cov[NCOVMAX+1];
         }    double **newm;
         jk= j/stepm;  
         jl= j -jk*stepm;    /* Hstepm could be zero and should return the unit matrix */
         ju= j -(jk+1)*stepm;    for (i=1;i<=nlstate+ndeath;i++)
         if(jl <= -ju)      for (j=1;j<=nlstate+ndeath;j++){
           dh[mi][i]=jk;        oldm[i][j]=(i==j ? 1.0 : 0.0);
         else        po[i][j][0]=(i==j ? 1.0 : 0.0);
           dh[mi][i]=jk+1;      }
         if(dh[mi][i]==0)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           dh[mi][i]=1; /* At least one step */    for(h=1; h <=nhstepm; h++){
       }      for(d=1; d <=hstepm; d++){
     }        newm=savm;
   }        /* Covariates have to be included here again */
   jmean=sum/k;        cov[1]=1.;
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
  }        for (k=1; k<=cptcovn;k++) 
 /*********** Tricode ****************************/          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
 void tricode(int *Tvar, int **nbcode, int imx)        for (k=1; k<=cptcovage;k++)
 {          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   int Ndum[20],ij=1, k, j, i;        for (k=1; k<=cptcovprod;k++)
   int cptcode=0;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   cptcoveff=0;  
    
   for (k=0; k<19; k++) Ndum[k]=0;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   for (k=1; k<=7; k++) ncodemax[k]=0;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {                     pmij(pmmij,cov,ncovmodel,x,nlstate));
     for (i=1; i<=imx; i++) {        savm=oldm;
       ij=(int)(covar[Tvar[j]][i]);        oldm=newm;
       Ndum[ij]++;      }
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/      for(i=1; i<=nlstate+ndeath; i++)
       if (ij > cptcode) cptcode=ij;        for(j=1;j<=nlstate+ndeath;j++) {
     }          po[i][j][h]=newm[i][j];
           /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
     for (i=0; i<=cptcode; i++) {        }
       if(Ndum[i]!=0) ncodemax[j]++;      /*printf("h=%d ",h);*/
     }    } /* end h */
     ij=1;  /*     printf("\n H=%d \n",h); */
     return po;
   }
     for (i=1; i<=ncodemax[j]; i++) {  
       for (k=0; k<=19; k++) {  
         if (Ndum[k] != 0) {  /*************** log-likelihood *************/
           nbcode[Tvar[j]][ij]=k;  double func( double *x)
           ij++;  {
         }    int i, ii, j, k, mi, d, kk;
         if (ij > ncodemax[j]) break;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
       }      double **out;
     }    double sw; /* Sum of weights */
   }      double lli; /* Individual log likelihood */
     int s1, s2;
  for (k=0; k<19; k++) Ndum[k]=0;    double bbh, survp;
     long ipmx;
  for (i=1; i<=ncovmodel-2; i++) {    /*extern weight */
       ij=Tvar[i];    /* We are differentiating ll according to initial status */
       Ndum[ij]++;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     }    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
  ij=1;    */
  for (i=1; i<=10; i++) {    cov[1]=1.;
    if((Ndum[i]!=0) && (i<=ncov)){  
      Tvaraff[ij]=i;    for(k=1; k<=nlstate; k++) ll[k]=0.;
      ij++;  
    }    if(mle==1){
  }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          /* Computes the values of the ncovmodel covariates of the model
     cptcoveff=ij-1;           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
 }           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
            to be observed in j being in i according to the model.
 /*********** Health Expectancies ****************/         */
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
 {           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
   /* Health expectancies */           has been calculated etc */
   int i, j, nhstepm, hstepm, h;        for(mi=1; mi<= wav[i]-1; mi++){
   double age, agelim,hf;          for (ii=1;ii<=nlstate+ndeath;ii++)
   double ***p3mat;            for (j=1;j<=nlstate+ndeath;j++){
                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficreseij,"# Health expectancies\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficreseij,"# Age");            }
   for(i=1; i<=nlstate;i++)          for(d=0; d<dh[mi][i]; d++){
     for(j=1; j<=nlstate;j++)            newm=savm;
       fprintf(ficreseij," %1d-%1d",i,j);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficreseij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
   hstepm=1*YEARM; /*  Every j years of age (in month) */            }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          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 age range expressed in number of stepm */          } /* end mult */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);        
     /* Typically if 20 years = 20*12/6=40 stepm */          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     if (stepm >= YEARM) hstepm=1;          /* But now since version 0.9 we anticipate for bias at large stepm.
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           * (in months) between two waves is not a multiple of stepm, we rounded to 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored           * the nearest (and in case of equal distance, to the lowest) interval but now
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);             * (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
            * from savm to out if bh is negative or even beyond if bh is positive. bh varies
     for(i=1; i<=nlstate;i++)           * -stepm/2 to stepm/2 .
       for(j=1; j<=nlstate;j++)           * For stepm=1 the results are the same as for previous versions of Imach.
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){           * For stepm > 1 the results are less biased than in previous versions. 
           eij[i][j][(int)age] +=p3mat[i][j][h];           */
         }          s1=s[mw[mi][i]][i];
              s2=s[mw[mi+1][i]][i];
     hf=1;          bbh=(double)bh[mi][i]/(double)stepm; 
     if (stepm >= YEARM) hf=stepm/YEARM;          /* bias bh is positive if real duration
     fprintf(ficreseij,"%.0f",age );           * is higher than the multiple of stepm and negative otherwise.
     for(i=1; i<=nlstate;i++)           */
       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]));*/
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);          if( s2 > nlstate){ 
       }            /* i.e. if s2 is a death state and if the date of death is known 
     fprintf(ficreseij,"\n");               then the contribution to the likelihood is the probability to 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);               die between last step unit time and current  step unit time, 
   }               which is also equal to probability to die before dh 
 }               minus probability to die before dh-stepm . 
                In version up to 0.92 likelihood was computed
 /************ Variance ******************/          as if date of death was unknown. Death was treated as any other
 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)          health state: the date of the interview describes the actual state
 {          and not the date of a change in health state. The former idea was
   /* Variance of health expectancies */          to consider that at each interview the state was recorded
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          (healthy, disable or death) and IMaCh was corrected; but when we
   double **newm;          introduced the exact date of death then we should have modified
   double **dnewm,**doldm;          the contribution of an exact death to the likelihood. This new
   int i, j, nhstepm, hstepm, h;          contribution is smaller and very dependent of the step unit
   int k, cptcode;          stepm. It is no more the probability to die between last interview
   double *xp;          and month of death but the probability to survive from last
   double **gp, **gm;          interview up to one month before death multiplied by the
   double ***gradg, ***trgradg;          probability to die within a month. Thanks to Chris
   double ***p3mat;          Jackson for correcting this bug.  Former versions increased
   double age,agelim;          mortality artificially. The bad side is that we add another loop
   int theta;          which slows down the processing. The difference can be up to 10%
           lower mortality.
    fprintf(ficresvij,"# Covariances of life expectancies\n");            */
   fprintf(ficresvij,"# Age");            lli=log(out[s1][s2] - savm[s1][s2]);
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)  
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          } else if  (s2==-2) {
   fprintf(ficresvij,"\n");            for (j=1,survp=0. ; j<=nlstate; j++) 
               survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   xp=vector(1,npar);            /*survp += out[s1][j]; */
   dnewm=matrix(1,nlstate,1,npar);            lli= log(survp);
   doldm=matrix(1,nlstate,1,nlstate);          }
            
   hstepm=1*YEARM; /* Every year of age */          else if  (s2==-4) { 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            for (j=3,survp=0. ; j<=nlstate; j++)  
   agelim = AGESUP;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            lli= log(survp); 
     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 */          else if  (s2==-5) { 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for (j=1,survp=0. ; j<=2; j++)  
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     gp=matrix(0,nhstepm,1,nlstate);            lli= log(survp); 
     gm=matrix(0,nhstepm,1,nlstate);          } 
           
     for(theta=1; theta <=npar; theta++){          else{
       for(i=1; i<=npar; i++){ /* Computes gradient */            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
       }          } 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          /*if(lli ==000.0)*/
           /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       if (popbased==1) {          ipmx +=1;
         for(i=1; i<=nlstate;i++)          sw += weight[i];
           prlim[i][i]=probs[(int)age][i][ij];          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        } /* end of wave */
            } /* end of individual */
       for(j=1; j<= nlstate; j++){    }  else if(mle==2){
         for(h=0; h<=nhstepm; h++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
       }            for (j=1;j<=nlstate+ndeath;j++){
                  oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(i=1; i<=npar; i++) /* Computes gradient */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for(d=0; d<=dh[mi][i]; d++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       if (popbased==1) {            for (kk=1; kk<=cptcovage;kk++) {
         for(i=1; i<=nlstate;i++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           prlim[i][i]=probs[(int)age][i][ij];            }
       }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1; j<= nlstate; j++){            savm=oldm;
         for(h=0; h<=nhstepm; h++){            oldm=newm;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          } /* end mult */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        
         }          s1=s[mw[mi][i]][i];
       }          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
       for(j=1; j<= nlstate; j++)          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(h=0; h<=nhstepm; h++){          ipmx +=1;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          sw += weight[i];
         }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     } /* End theta */        } /* end of wave */
       } /* end of individual */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    }  else if(mle==3){  /* exponential inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(h=0; h<=nhstepm; h++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1; j<=nlstate;j++)        for(mi=1; mi<= wav[i]-1; mi++){
         for(theta=1; theta <=npar; theta++)          for (ii=1;ii<=nlstate+ndeath;ii++)
           trgradg[h][j][theta]=gradg[h][theta][j];            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i=1;i<=nlstate;i++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1;j<=nlstate;j++)            }
         vareij[i][j][(int)age] =0.;          for(d=0; d<dh[mi][i]; d++){
     for(h=0;h<=nhstepm;h++){            newm=savm;
       for(k=0;k<=nhstepm;k++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);            for (kk=1; kk<=cptcovage;kk++) {
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for(i=1;i<=nlstate;i++)            }
           for(j=1;j<=nlstate;j++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             vareij[i][j][(int)age] += doldm[i][j];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       }            savm=oldm;
     }            oldm=newm;
     h=1;          } /* end mult */
     if (stepm >= YEARM) h=stepm/YEARM;        
     fprintf(ficresvij,"%.0f ",age );          s1=s[mw[mi][i]][i];
     for(i=1; i<=nlstate;i++)          s2=s[mw[mi+1][i]][i];
       for(j=1; j<=nlstate;j++){          bbh=(double)bh[mi][i]/(double)stepm; 
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);          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 */
       }          ipmx +=1;
     fprintf(ficresvij,"\n");          sw += weight[i];
     free_matrix(gp,0,nhstepm,1,nlstate);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     free_matrix(gm,0,nhstepm,1,nlstate);        } /* end of wave */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      } /* end of individual */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   } /* End age */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          for(mi=1; mi<= wav[i]-1; mi++){
   free_vector(xp,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
   free_matrix(doldm,1,nlstate,1,npar);            for (j=1;j<=nlstate+ndeath;j++){
   free_matrix(dnewm,1,nlstate,1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
 }            }
           for(d=0; d<dh[mi][i]; d++){
 /************ Variance of prevlim ******************/            newm=savm;
 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)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 {            for (kk=1; kk<=cptcovage;kk++) {
   /* Variance of prevalence limit */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            }
   double **newm;          
   double **dnewm,**doldm;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int i, j, nhstepm, hstepm;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   int k, cptcode;            savm=oldm;
   double *xp;            oldm=newm;
   double *gp, *gm;          } /* end mult */
   double **gradg, **trgradg;        
   double age,agelim;          s1=s[mw[mi][i]][i];
   int theta;          s2=s[mw[mi+1][i]][i];
              if( s2 > nlstate){ 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");            lli=log(out[s1][s2] - savm[s1][s2]);
   fprintf(ficresvpl,"# Age");          }else{
   for(i=1; i<=nlstate;i++)            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       fprintf(ficresvpl," %1d-%1d",i,i);          }
   fprintf(ficresvpl,"\n");          ipmx +=1;
           sw += weight[i];
   xp=vector(1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   dnewm=matrix(1,nlstate,1,npar);  /*      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]); */
   doldm=matrix(1,nlstate,1,nlstate);        } /* end of wave */
        } /* end of individual */
   hstepm=1*YEARM; /* Every year of age */    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   agelim = AGESUP;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        for(mi=1; mi<= wav[i]-1; mi++){
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          for (ii=1;ii<=nlstate+ndeath;ii++)
     if (stepm >= YEARM) hstepm=1;            for (j=1;j<=nlstate+ndeath;j++){
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     gradg=matrix(1,npar,1,nlstate);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     gp=vector(1,nlstate);            }
     gm=vector(1,nlstate);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
     for(theta=1; theta <=npar; theta++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(i=1; i<=npar; i++){ /* Computes gradient */            for (kk=1; kk<=cptcovage;kk++) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          
       for(i=1;i<=nlstate;i++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         gp[i] = prlim[i][i];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                savm=oldm;
       for(i=1; i<=npar; i++) /* Computes gradient */            oldm=newm;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          } /* end mult */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        
       for(i=1;i<=nlstate;i++)          s1=s[mw[mi][i]][i];
         gm[i] = prlim[i][i];          s2=s[mw[mi+1][i]][i];
           lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       for(i=1;i<=nlstate;i++)          ipmx +=1;
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          sw += weight[i];
     } /* End theta */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
     trgradg =matrix(1,nlstate,1,npar);        } /* end of wave */
       } /* end of individual */
     for(j=1; j<=nlstate;j++)    } /* End of if */
       for(theta=1; theta <=npar; theta++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         trgradg[j][theta]=gradg[theta][j];    /* 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<=nlstate;i++)    return -l;
       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);  /*************** log-likelihood *************/
     for(i=1;i<=nlstate;i++)  double funcone( double *x)
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  {
     /* Same as likeli but slower because of a lot of printf and if */
     fprintf(ficresvpl,"%.0f ",age );    int i, ii, j, k, mi, d, kk;
     for(i=1; i<=nlstate;i++)    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    double **out;
     fprintf(ficresvpl,"\n");    double lli; /* Individual log likelihood */
     free_vector(gp,1,nlstate);    double llt;
     free_vector(gm,1,nlstate);    int s1, s2;
     free_matrix(gradg,1,npar,1,nlstate);    double bbh, survp;
     free_matrix(trgradg,1,nlstate,1,npar);    /*extern weight */
   } /* End age */    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   free_vector(xp,1,npar);    /*for(i=1;i<imx;i++) 
   free_matrix(doldm,1,nlstate,1,npar);      printf(" %d\n",s[4][i]);
   free_matrix(dnewm,1,nlstate,1,nlstate);    */
     cov[1]=1.;
 }  
     for(k=1; k<=nlstate; k++) ll[k]=0.;
 /************ Variance of one-step probabilities  ******************/  
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 {      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int i, j;      for(mi=1; mi<= wav[i]-1; mi++){
   int k=0, cptcode;        for (ii=1;ii<=nlstate+ndeath;ii++)
   double **dnewm,**doldm;          for (j=1;j<=nlstate+ndeath;j++){
   double *xp;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double *gp, *gm;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **gradg, **trgradg;          }
   double age,agelim, cov[NCOVMAX];        for(d=0; d<dh[mi][i]; d++){
   int theta;          newm=savm;
   char fileresprob[FILENAMELENGTH];          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           for (kk=1; kk<=cptcovage;kk++) {
   strcpy(fileresprob,"prob");            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   strcat(fileresprob,fileres);          }
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     printf("Problem with resultfile: %s\n", fileresprob);                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   }          savm=oldm;
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);          oldm=newm;
          } /* end mult */
         
   xp=vector(1,npar);        s1=s[mw[mi][i]][i];
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        s2=s[mw[mi+1][i]][i];
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));        bbh=(double)bh[mi][i]/(double)stepm; 
          /* bias is positive if real duration
   cov[1]=1;         * is higher than the multiple of stepm and negative otherwise.
   for (age=bage; age<=fage; age ++){         */
     cov[2]=age;        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     gradg=matrix(1,npar,1,9);          lli=log(out[s1][s2] - savm[s1][s2]);
     trgradg=matrix(1,9,1,npar);        } else if  (s2==-2) {
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          for (j=1,survp=0. ; j<=nlstate; j++) 
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
              lli= log(survp);
     for(theta=1; theta <=npar; theta++){        }else if (mle==1){
       for(i=1; i<=npar; i++)          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        } else if(mle==2){
                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 */
       pmij(pmmij,cov,ncovmodel,xp,nlstate);        } else if(mle==3){  /* exponential inter-extrapolation */
              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 */
       k=0;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
       for(i=1; i<= (nlstate+ndeath); i++){          lli=log(out[s1][s2]); /* Original formula */
         for(j=1; j<=(nlstate+ndeath);j++){        } else{  /* mle=0 back to 1 */
            k=k+1;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           gp[k]=pmmij[i][j];          /*lli=log(out[s1][s2]); */ /* Original formula */
         }        } /* End of if */
       }        ipmx +=1;
         sw += weight[i];
       for(i=1; i<=npar; i++)        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
            if(globpr){
           fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
       pmij(pmmij,cov,ncovmodel,xp,nlstate);   %11.6f %11.6f %11.6f ", \
       k=0;                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
       for(i=1; i<=(nlstate+ndeath); i++){                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
         for(j=1; j<=(nlstate+ndeath);j++){          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
           k=k+1;            llt +=ll[k]*gipmx/gsw;
           gm[k]=pmmij[i][j];            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         }          }
       }          fprintf(ficresilk," %10.6f\n", -llt);
              }
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)      } /* end of wave */
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      } /* end of individual */
     }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       for(theta=1; theta <=npar; theta++)    if(globpr==0){ /* First time we count the contributions and weights */
       trgradg[j][theta]=gradg[theta][j];      gipmx=ipmx;
        gsw=sw;
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    }
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    return -l;
   }
      pmij(pmmij,cov,ncovmodel,x,nlstate);  
   
      k=0;  /*************** function likelione ***********/
      for(i=1; i<=(nlstate+ndeath); i++){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
        for(j=1; j<=(nlstate+ndeath);j++){  {
          k=k+1;    /* This routine should help understanding what is done with 
          gm[k]=pmmij[i][j];       the selection of individuals/waves and
         }       to check the exact contribution to the likelihood.
      }       Plotting could be done.
           */
      /*printf("\n%d ",(int)age);    int k;
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){  
            if(*globpri !=0){ /* Just counts and sums, no printings */
       strcpy(fileresilk,"ilk"); 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      strcat(fileresilk,fileres);
      }*/      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", fileresilk);
   fprintf(ficresprob,"\n%d ",(int)age);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      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");
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
   }      for(k=1; k<=nlstate; k++) 
         fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    }
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    *fretone=(*funcone)(p);
 }    if(*globpri !=0){
  free_vector(xp,1,npar);      fclose(ficresilk);
 fclose(ficresprob);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
  exit(0);      fflush(fichtm); 
 }    } 
     return;
 /***********************************************/  }
 /**************** Main Program *****************/  
 /***********************************************/  
   /*********** Maximum Likelihood Estimation ***************/
 /*int main(int argc, char *argv[])*/  
 int main()  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
 {  {
     int i,j, iter;
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    double **xi;
   double agedeb, agefin,hf;    double fret;
   double agemin=1.e20, agemax=-1.e20;    double fretone; /* Only one call to likelihood */
     /*  char filerespow[FILENAMELENGTH];*/
   double fret;    xi=matrix(1,npar,1,npar);
   double **xi,tmp,delta;    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++)
   double dum; /* Dummy variable */        xi[i][j]=(i==j ? 1.0 : 0.0);
   double ***p3mat;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   int *indx;    strcpy(filerespow,"pow"); 
   char line[MAXLINE], linepar[MAXLINE];    strcat(filerespow,fileres);
   char title[MAXLINE];    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];      printf("Problem with resultfile: %s\n", filerespow);
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   char filerest[FILENAMELENGTH];    }
   char fileregp[FILENAMELENGTH];    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   char popfile[FILENAMELENGTH];    for (i=1;i<=nlstate;i++)
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      for(j=1;j<=nlstate+ndeath;j++)
   int firstobs=1, lastobs=10;        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   int sdeb, sfin; /* Status at beginning and end */    fprintf(ficrespow,"\n");
   int c,  h , cpt,l;  
   int ju,jl, mi;    powell(p,xi,npar,ftol,&iter,&fret,func);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;  
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    free_matrix(xi,1,npar,1,npar);
   int mobilav=0,popforecast=0;    fclose(ficrespow);
   int hstepm, nhstepm;    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
   int *popage;/*boolprev=0 if date and zero if wave*/    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   
   double bage, fage, age, agelim, agebase;  }
   double ftolpl=FTOL;  
   double **prlim;  /**** Computes Hessian and covariance matrix ***/
   double *severity;  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   double ***param; /* Matrix of parameters */  {
   double  *p;    double  **a,**y,*x,pd;
   double **matcov; /* Matrix of covariance */    double **hess;
   double ***delti3; /* Scale */    int i, j,jk;
   double *delti; /* Scale */    int *indx;
   double ***eij, ***vareij;  
   double **varpl; /* Variances of prevalence limits by age */    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   double *epj, vepp;    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   double kk1, kk2;    void lubksb(double **a, int npar, int *indx, double b[]) ;
   double *popeffectif,*popcount;    void ludcmp(double **a, int npar, int *indx, double *d) ;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,jprojmean,mprojmean,anprojmean, calagedate;    double gompertz(double p[]);
   double yp,yp1,yp2;    hess=matrix(1,npar,1,npar);
   
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";    printf("\nCalculation of the hessian matrix. Wait...\n");
   char *alph[]={"a","a","b","c","d","e"}, str[4];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
   char z[1]="c", occ;      fprintf(ficlog,"%d",i);fflush(ficlog);
 #include <sys/time.h>     
 #include <time.h>       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];      
        /*  printf(" %f ",p[i]);
   /* long total_usecs;          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   struct timeval start_time, end_time;    }
      
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    for (i=1;i<=npar;i++) {
       for (j=1;j<=npar;j++)  {
         if (j>i) { 
   printf("\nIMACH, Version 0.7");          printf(".%d%d",i,j);fflush(stdout);
   printf("\nEnter the parameter file name: ");          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
           hess[i][j]=hessij(p,delti,i,j,func,npar);
 #ifdef windows          
   scanf("%s",pathtot);          hess[j][i]=hess[i][j];    
   getcwd(pathcd, size);          /*printf(" %lf ",hess[i][j]);*/
   /*cygwin_split_path(pathtot,path,optionfile);        }
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      }
   /* cutv(path,optionfile,pathtot,'\\');*/    }
     printf("\n");
 split(pathtot, path,optionfile);    fprintf(ficlog,"\n");
   chdir(path);  
   replace(pathc,path);    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
 #endif    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 #ifdef unix    
   scanf("%s",optionfile);    a=matrix(1,npar,1,npar);
 #endif    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
 /*-------- arguments in the command line --------*/    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
   strcpy(fileres,"r");      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   strcat(fileres, optionfile);    ludcmp(a,npar,indx,&pd);
   
   /*---------arguments file --------*/    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {      x[j]=1;
     printf("Problem with optionfile %s\n",optionfile);      lubksb(a,npar,indx,x);
     goto end;      for (i=1;i<=npar;i++){ 
   }        matcov[i][j]=x[i];
       }
   strcpy(filereso,"o");    }
   strcat(filereso,fileres);  
   if((ficparo=fopen(filereso,"w"))==NULL) {    printf("\n#Hessian matrix#\n");
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    fprintf(ficlog,"\n#Hessian matrix#\n");
   }    for (i=1;i<=npar;i++) { 
       for (j=1;j<=npar;j++) { 
   /* Reads comments: lines beginning with '#' */        printf("%.3e ",hess[i][j]);
   while((c=getc(ficpar))=='#' && c!= EOF){        fprintf(ficlog,"%.3e ",hess[i][j]);
     ungetc(c,ficpar);      }
     fgets(line, MAXLINE, ficpar);      printf("\n");
     puts(line);      fprintf(ficlog,"\n");
     fputs(line,ficparo);    }
   }  
   ungetc(c,ficpar);    /* Recompute Inverse */
     for (i=1;i<=npar;i++)
   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);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   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);    ludcmp(a,npar,indx,&pd);
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);  
 while((c=getc(ficpar))=='#' && c!= EOF){    /*  printf("\n#Hessian matrix recomputed#\n");
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    for (j=1;j<=npar;j++) {
     puts(line);      for (i=1;i<=npar;i++) x[i]=0;
     fputs(line,ficparo);      x[j]=1;
   }      lubksb(a,npar,indx,x);
   ungetc(c,ficpar);      for (i=1;i<=npar;i++){ 
          y[i][j]=x[i];
            printf("%.3e ",y[i][j]);
   covar=matrix(0,NCOVMAX,1,n);        fprintf(ficlog,"%.3e ",y[i][j]);
   cptcovn=0;      }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      printf("\n");
       fprintf(ficlog,"\n");
   ncovmodel=2+cptcovn;    }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    */
    
   /* Read guess parameters */    free_matrix(a,1,npar,1,npar);
   /* Reads comments: lines beginning with '#' */    free_matrix(y,1,npar,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_vector(x,1,npar);
     ungetc(c,ficpar);    free_ivector(indx,1,npar);
     fgets(line, MAXLINE, ficpar);    free_matrix(hess,1,npar,1,npar);
     puts(line);  
     fputs(line,ficparo);  
   }  }
   ungetc(c,ficpar);  
    /*************** hessian matrix ****************/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     for(i=1; i <=nlstate; i++)  {
     for(j=1; j <=nlstate+ndeath-1; j++){    int i;
       fscanf(ficpar,"%1d%1d",&i1,&j1);    int l=1, lmax=20;
       fprintf(ficparo,"%1d%1d",i1,j1);    double k1,k2;
       printf("%1d%1d",i,j);    double p2[MAXPARM+1]; /* identical to x */
       for(k=1; k<=ncovmodel;k++){    double res;
         fscanf(ficpar," %lf",&param[i][j][k]);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
         printf(" %lf",param[i][j][k]);    double fx;
         fprintf(ficparo," %lf",param[i][j][k]);    int k=0,kmax=10;
       }    double l1;
       fscanf(ficpar,"\n");  
       printf("\n");    fx=func(x);
       fprintf(ficparo,"\n");    for (i=1;i<=npar;i++) p2[i]=x[i];
     }    for(l=0 ; l <=lmax; l++){
        l1=pow(10,l);
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;      delts=delt;
       for(k=1 ; k <kmax; k=k+1){
   p=param[1][1];        delt = delta*(l1*k);
          p2[theta]=x[theta] +delt;
   /* Reads comments: lines beginning with '#' */        k1=func(p2)-fx;
   while((c=getc(ficpar))=='#' && c!= EOF){        p2[theta]=x[theta]-delt;
     ungetc(c,ficpar);        k2=func(p2)-fx;
     fgets(line, MAXLINE, ficpar);        /*res= (k1-2.0*fx+k2)/delt/delt; */
     puts(line);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     fputs(line,ficparo);        
   }  #ifdef DEBUGHESS
   ungetc(c,ficpar);        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);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  #endif
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   for(i=1; i <=nlstate; i++){        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     for(j=1; j <=nlstate+ndeath-1; j++){          k=kmax;
       fscanf(ficpar,"%1d%1d",&i1,&j1);        }
       printf("%1d%1d",i,j);        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       fprintf(ficparo,"%1d%1d",i1,j1);          k=kmax; l=lmax*10.;
       for(k=1; k<=ncovmodel;k++){        }
         fscanf(ficpar,"%le",&delti3[i][j][k]);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
         printf(" %le",delti3[i][j][k]);          delts=delt;
         fprintf(ficparo," %le",delti3[i][j][k]);        }
       }      }
       fscanf(ficpar,"\n");    }
       printf("\n");    delti[theta]=delts;
       fprintf(ficparo,"\n");    return res; 
     }    
   }  }
   delti=delti3[1][1];  
    double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   /* Reads comments: lines beginning with '#' */  {
   while((c=getc(ficpar))=='#' && c!= EOF){    int i;
     ungetc(c,ficpar);    int l=1, l1, lmax=20;
     fgets(line, MAXLINE, ficpar);    double k1,k2,k3,k4,res,fx;
     puts(line);    double p2[MAXPARM+1];
     fputs(line,ficparo);    int k;
   }  
   ungetc(c,ficpar);    fx=func(x);
      for (k=1; k<=2; k++) {
   matcov=matrix(1,npar,1,npar);      for (i=1;i<=npar;i++) p2[i]=x[i];
   for(i=1; i <=npar; i++){      p2[thetai]=x[thetai]+delti[thetai]/k;
     fscanf(ficpar,"%s",&str);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     printf("%s",str);      k1=func(p2)-fx;
     fprintf(ficparo,"%s",str);    
     for(j=1; j <=i; j++){      p2[thetai]=x[thetai]+delti[thetai]/k;
       fscanf(ficpar," %le",&matcov[i][j]);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       printf(" %.5le",matcov[i][j]);      k2=func(p2)-fx;
       fprintf(ficparo," %.5le",matcov[i][j]);    
     }      p2[thetai]=x[thetai]-delti[thetai]/k;
     fscanf(ficpar,"\n");      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     printf("\n");      k3=func(p2)-fx;
     fprintf(ficparo,"\n");    
   }      p2[thetai]=x[thetai]-delti[thetai]/k;
   for(i=1; i <=npar; i++)      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     for(j=i+1;j<=npar;j++)      k4=func(p2)-fx;
       matcov[i][j]=matcov[j][i];      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
      #ifdef DEBUG
   printf("\n");      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
       fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   #endif
     /*-------- data file ----------*/    }
     if((ficres =fopen(fileres,"w"))==NULL) {    return res;
       printf("Problem with resultfile: %s\n", fileres);goto end;  }
     }  
     fprintf(ficres,"#%s\n",version);  /************** Inverse of matrix **************/
      void ludcmp(double **a, int n, int *indx, double *d) 
     if((fic=fopen(datafile,"r"))==NULL)    {  { 
       printf("Problem with datafile: %s\n", datafile);goto end;    int i,imax,j,k; 
     }    double big,dum,sum,temp; 
     double *vv; 
     n= lastobs;   
     severity = vector(1,maxwav);    vv=vector(1,n); 
     outcome=imatrix(1,maxwav+1,1,n);    *d=1.0; 
     num=ivector(1,n);    for (i=1;i<=n;i++) { 
     moisnais=vector(1,n);      big=0.0; 
     annais=vector(1,n);      for (j=1;j<=n;j++) 
     moisdc=vector(1,n);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     andc=vector(1,n);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     agedc=vector(1,n);      vv[i]=1.0/big; 
     cod=ivector(1,n);    } 
     weight=vector(1,n);    for (j=1;j<=n;j++) { 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */      for (i=1;i<j;i++) { 
     mint=matrix(1,maxwav,1,n);        sum=a[i][j]; 
     anint=matrix(1,maxwav,1,n);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     s=imatrix(1,maxwav+1,1,n);        a[i][j]=sum; 
     adl=imatrix(1,maxwav+1,1,n);          } 
     tab=ivector(1,NCOVMAX);      big=0.0; 
     ncodemax=ivector(1,8);      for (i=j;i<=n;i++) { 
         sum=a[i][j]; 
     i=1;        for (k=1;k<j;k++) 
     while (fgets(line, MAXLINE, fic) != NULL)    {          sum -= a[i][k]*a[k][j]; 
       if ((i >= firstobs) && (i <=lastobs)) {        a[i][j]=sum; 
                if ( (dum=vv[i]*fabs(sum)) >= big) { 
         for (j=maxwav;j>=1;j--){          big=dum; 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          imax=i; 
           strcpy(line,stra);        } 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      } 
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      if (j != imax) { 
         }        for (k=1;k<=n;k++) { 
                  dum=a[imax][k]; 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);          a[imax][k]=a[j][k]; 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          a[j][k]=dum; 
         } 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);        *d = -(*d); 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        vv[imax]=vv[j]; 
       } 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      indx[j]=imax; 
         for (j=ncov;j>=1;j--){      if (a[j][j] == 0.0) a[j][j]=TINY; 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      if (j != n) { 
         }        dum=1.0/(a[j][j]); 
         num[i]=atol(stra);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
              } 
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    } 
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/    free_vector(vv,1,n);  /* Doesn't work */
   ;
         i=i+1;  } 
       }  
     }  void lubksb(double **a, int n, int *indx, double b[]) 
     /* printf("ii=%d", ij);  { 
        scanf("%d",i);*/    int i,ii=0,ip,j; 
   imx=i-1; /* Number of individuals */    double sum; 
    
   /* for (i=1; i<=imx; i++){    for (i=1;i<=n;i++) { 
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      ip=indx[i]; 
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;      sum=b[ip]; 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;      b[ip]=b[i]; 
     }      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     for (i=1; i<=imx; i++)      else if (sum) ii=i; 
     if (covar[1][i]==0) printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/      b[i]=sum; 
     } 
   /* Calculation of the number of parameter from char model*/    for (i=n;i>=1;i--) { 
   Tvar=ivector(1,15);      sum=b[i]; 
   Tprod=ivector(1,15);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   Tvaraff=ivector(1,15);      b[i]=sum/a[i][i]; 
   Tvard=imatrix(1,15,1,2);    } 
   Tage=ivector(1,15);        } 
      
   if (strlen(model) >1){  void pstamp(FILE *fichier)
     j=0, j1=0, k1=1, k2=1;  {
     j=nbocc(model,'+');    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
     j1=nbocc(model,'*');  }
     cptcovn=j+1;  
     cptcovprod=j1;  /************ 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 */
     strcpy(modelsav,model);    
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    int i, m, jk, k1,i1, j1, bool, z1,j;
       printf("Error. Non available option model=%s ",model);    int first;
       goto end;    double ***freq; /* Frequencies */
     }    double *pp, **prop;
        double pos,posprop, k2, dateintsum=0,k2cpt=0;
     for(i=(j+1); i>=1;i--){    char fileresp[FILENAMELENGTH];
       cutv(stra,strb,modelsav,'+');    
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    pp=vector(1,nlstate);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/    prop=matrix(1,nlstate,iagemin,iagemax+3);
       /*scanf("%d",i);*/    strcpy(fileresp,"p");
       if (strchr(strb,'*')) {    strcat(fileresp,fileres);
         cutv(strd,strc,strb,'*');    if((ficresp=fopen(fileresp,"w"))==NULL) {
         if (strcmp(strc,"age")==0) {      printf("Problem with prevalence resultfile: %s\n", fileresp);
           cptcovprod--;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
           cutv(strb,stre,strd,'V');      exit(0);
           Tvar[i]=atoi(stre);    }
           cptcovage++;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
             Tage[cptcovage]=i;    j1=0;
             /*printf("stre=%s ", stre);*/    
         }    j=cptcoveff;
         else if (strcmp(strd,"age")==0) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           cptcovprod--;  
           cutv(strb,stre,strc,'V');    first=1;
           Tvar[i]=atoi(stre);  
           cptcovage++;    for(k1=1; k1<=j;k1++){
           Tage[cptcovage]=i;      for(i1=1; i1<=ncodemax[k1];i1++){
         }        j1++;
         else {        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           cutv(strb,stre,strc,'V');          scanf("%d", i);*/
           Tvar[i]=ncov+k1;        for (i=-5; i<=nlstate+ndeath; i++)  
           cutv(strb,strc,strd,'V');          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           Tprod[k1]=i;            for(m=iagemin; m <= iagemax+3; m++)
           Tvard[k1][1]=atoi(strc);              freq[i][jk][m]=0;
           Tvard[k1][2]=atoi(stre);  
           Tvar[cptcovn+k2]=Tvard[k1][1];      for (i=1; i<=nlstate; i++)  
           Tvar[cptcovn+k2+1]=Tvard[k1][2];        for(m=iagemin; m <= iagemax+3; m++)
           for (k=1; k<=lastobs;k++)          prop[i][m]=0;
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        
           k1++;        dateintsum=0;
           k2=k2+2;        k2cpt=0;
         }        for (i=1; i<=imx; i++) {
       }          bool=1;
       else {          if  (cptcovn>0) {
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/            for (z1=1; z1<=cptcoveff; z1++) 
        /*  scanf("%d",i);*/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       cutv(strd,strc,strb,'V');                bool=0;
       Tvar[i]=atoi(strc);          }
       }          if (bool==1){
       strcpy(modelsav,stra);              for(m=firstpass; m<=lastpass; m++){
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);              k2=anint[m][i]+(mint[m][i]/12.);
         scanf("%d",i);*/              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
 }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                  if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);                if (m<lastpass) {
   printf("cptcovprod=%d ", cptcovprod);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   scanf("%d ",i);*/                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     fclose(fic);                }
                 
     /*  if(mle==1){*/                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     if (weightopt != 1) { /* Maximisation without weights*/                  dateintsum=dateintsum+k2;
       for(i=1;i<=n;i++) weight[i]=1.0;                  k2cpt++;
     }                }
     /*-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 ((mint[m][i]== 99) && (s[m][i] <= nlstate)){        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
          anint[m][i]=9999;        pstamp(ficresp);
          s[m][i]=-1;        if  (cptcovn>0) {
        }          fprintf(ficresp, "\n#********** Variable "); 
              for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for (i=1; i<=imx; i++)  {          fprintf(ficresp, "**********\n#");
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        }
       for(m=1; (m<= maxwav); m++){        for(i=1; i<=nlstate;i++) 
         if(s[m][i] >0){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
           if (s[m][i] == nlstate+1) {        fprintf(ficresp, "\n");
             if(agedc[i]>0)        
               if(moisdc[i]!=99 && andc[i]!=9999)        for(i=iagemin; i <= iagemax+3; i++){
               agev[m][i]=agedc[i];          if(i==iagemax+3){
             else {            fprintf(ficlog,"Total");
               if (andc[i]!=9999){          }else{
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            if(first==1){
               agev[m][i]=-1;              first=0;
               }              printf("See log file for details...\n");
             }            }
           }            fprintf(ficlog,"Age %d", i);
           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]);          for(jk=1; jk <=nlstate ; jk++){
             if(mint[m][i]==99 || anint[m][i]==9999)            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               agev[m][i]=1;              pp[jk] += freq[jk][m][i]; 
             else if(agev[m][i] <agemin){          }
               agemin=agev[m][i];          for(jk=1; jk <=nlstate ; jk++){
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/            for(m=-1, pos=0; m <=0 ; m++)
             }              pos += freq[jk][m][i];
             else if(agev[m][i] >agemax){            if(pp[jk]>=1.e-10){
               agemax=agev[m][i];              if(first==1){
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             }              }
             /*agev[m][i]=anint[m][i]-annais[i];*/              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             /*   agev[m][i] = age[i]+2*m;*/            }else{
           }              if(first==1)
           else { /* =9 */                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             agev[m][i]=1;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             s[m][i]=-1;            }
           }          }
         }  
         else /*= 0 Unknown */          for(jk=1; jk <=nlstate ; jk++){
           agev[m][i]=1;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
       }              pp[jk] += freq[jk][m][i];
              }       
     }          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     for (i=1; i<=imx; i++)  {            pos += pp[jk];
       for(m=1; (m<= maxwav); m++){            posprop += prop[jk][i];
         if (s[m][i] > (nlstate+ndeath)) {          }
           printf("Error: Wrong value in nlstate or ndeath\n");            for(jk=1; jk <=nlstate ; jk++){
           goto end;            if(pos>=1.e-5){
         }              if(first==1)
       }                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     }              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);              if(first==1)
                 printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     free_vector(severity,1,maxwav);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     free_imatrix(outcome,1,maxwav+1,1,n);            }
     free_vector(moisnais,1,n);            if( i <= iagemax){
     free_vector(annais,1,n);              if(pos>=1.e-5){
     /* free_matrix(mint,1,maxwav,1,n);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
        free_matrix(anint,1,maxwav,1,n);*/                /*probs[i][jk][j1]= pp[jk]/pos;*/
     free_vector(moisdc,1,n);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     free_vector(andc,1,n);              }
               else
                    fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     wav=ivector(1,imx);            }
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          }
     mw=imatrix(1,lastpass-firstpass+1,1,imx);          
              for(jk=-1; jk <=nlstate+ndeath; jk++)
     /* Concatenates waves */            for(m=-1; m <=nlstate+ndeath; m++)
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);              if(freq[jk][m][i] !=0 ) {
               if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
       Tcode=ivector(1,100);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);              }
       ncodemax[1]=1;          if(i <= iagemax)
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);            fprintf(ficresp,"\n");
                if(first==1)
    codtab=imatrix(1,100,1,10);            printf("Others in log...\n");
    h=0;          fprintf(ficlog,"\n");
    m=pow(2,cptcoveff);        }
        }
    for(k=1;k<=cptcoveff; k++){    }
      for(i=1; i <=(m/pow(2,k));i++){    dateintmean=dateintsum/k2cpt; 
        for(j=1; j <= ncodemax[k]; j++){   
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    fclose(ficresp);
            h++;    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
            if (h>m) h=1;codtab[h][k]=j;    free_vector(pp,1,nlstate);
          }    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
        }    /* End of Freq */
      }  }
    }  
      /************ Prevalence ********************/
    /* Calculates basic frequencies. Computes observed prevalence at single age  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)
        and prints on file fileres'p'. */  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
           in each health status at the date of interview (if between dateprev1 and dateprev2).
           We still use firstpass and lastpass as another selection.
     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 */    int i, m, jk, k1, i1, j1, bool, z1,j;
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double ***freq; /* Frequencies */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    double *pp, **prop;
          double pos,posprop; 
     /* For Powell, parameters are in a vector p[] starting at p[1]    double  y2; /* in fractional years */
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    int iagemin, iagemax;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */  
     iagemin= (int) agemin;
     if(mle==1){    iagemax= (int) agemax;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    /*pp=vector(1,nlstate);*/
     }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
        /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     /*--------- results files --------------*/    j1=0;
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);    
      j=cptcoveff;
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
    jk=1;    
    fprintf(ficres,"# Parameters\n");    for(k1=1; k1<=j;k1++){
    printf("# Parameters\n");      for(i1=1; i1<=ncodemax[k1];i1++){
    for(i=1,jk=1; i <=nlstate; i++){        j1++;
      for(k=1; k <=(nlstate+ndeath); k++){        
        if (k != i)        for (i=1; i<=nlstate; i++)  
          {          for(m=iagemin; m <= iagemax+3; m++)
            printf("%d%d ",i,k);            prop[i][m]=0.0;
            fprintf(ficres,"%1d%1d ",i,k);       
            for(j=1; j <=ncovmodel; j++){        for (i=1; i<=imx; i++) { /* Each individual */
              printf("%f ",p[jk]);          bool=1;
              fprintf(ficres,"%f ",p[jk]);          if  (cptcovn>0) {
              jk++;            for (z1=1; z1<=cptcoveff; z1++) 
            }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
            printf("\n");                bool=0;
            fprintf(ficres,"\n");          } 
          }          if (bool==1) { 
      }            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
    }              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
  if(mle==1){              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     /* Computing hessian and covariance matrix */                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     ftolhess=ftol; /* Usually correct */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     hesscov(matcov, p, npar, delti, ftolhess, func);                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
  }                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     fprintf(ficres,"# Scales\n");                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
     printf("# Scales\n");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
      for(i=1,jk=1; i <=nlstate; i++){                  prop[s[m][i]][iagemax+3] += weight[i]; 
       for(j=1; j <=nlstate+ndeath; j++){                } 
         if (j!=i) {              }
           fprintf(ficres,"%1d%1d",i,j);            } /* end selection of waves */
           printf("%1d%1d",i,j);          }
           for(k=1; k<=ncovmodel;k++){        }
             printf(" %.5e",delti[jk]);        for(i=iagemin; i <= iagemax+3; i++){  
             fprintf(ficres," %.5e",delti[jk]);          
             jk++;          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
           }            posprop += prop[jk][i]; 
           printf("\n");          } 
           fprintf(ficres,"\n");  
         }          for(jk=1; jk <=nlstate ; jk++){     
       }            if( i <=  iagemax){ 
      }              if(posprop>=1.e-5){ 
                    probs[i][jk][j1]= prop[jk][i]/posprop;
     k=1;              } else
     fprintf(ficres,"# Covariance\n");                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
     printf("# Covariance\n");            } 
     for(i=1;i<=npar;i++){          }/* end jk */ 
       /*  if (k>nlstate) k=1;        }/* end i */ 
       i1=(i-1)/(ncovmodel*nlstate)+1;      } /* end i1 */
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    } /* end k1 */
       printf("%s%d%d",alph[k],i1,tab[i]);*/    
       fprintf(ficres,"%3d",i);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
       printf("%3d",i);    /*free_vector(pp,1,nlstate);*/
       for(j=1; j<=i;j++){    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
         fprintf(ficres," %.5e",matcov[i][j]);  }  /* End of prevalence */
         printf(" %.5e",matcov[i][j]);  
       }  /************* Waves Concatenation ***************/
       fprintf(ficres,"\n");  
       printf("\n");  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
       k++;  {
     }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           Death is a valid wave (if date is known).
     while((c=getc(ficpar))=='#' && c!= EOF){       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       ungetc(c,ficpar);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
       fgets(line, MAXLINE, ficpar);       and mw[mi+1][i]. dh depends on stepm.
       puts(line);       */
       fputs(line,ficparo);  
     }    int i, mi, m;
     ungetc(c,ficpar);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
         double sum=0., jmean=0.;*/
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    int first;
        int j, k=0,jk, ju, jl;
     if (fage <= 2) {    double sum=0.;
       bage = agemin;    first=0;
       fage = agemax;    jmin=1e+5;
     }    jmax=-1;
     jmean=0.;
     fprintf(ficres,"# agemin agemax for life expectancy.\n");    for(i=1; i<=imx; i++){
       mi=0;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      m=firstpass;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      while(s[m][i] <= nlstate){
          if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     while((c=getc(ficpar))=='#' && c!= EOF){          mw[++mi][i]=m;
     ungetc(c,ficpar);        if(m >=lastpass)
     fgets(line, MAXLINE, ficpar);          break;
     puts(line);        else
     fputs(line,ficparo);          m++;
   }      }/* end while */
   ungetc(c,ficpar);      if (s[m][i] > nlstate){
          mi++;     /* Death is another wave */
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mob_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);        /* if(mi==0)  never been interviewed correctly before death */
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);           /* Only death is a correct wave */
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);        mw[mi][i]=m;
            }
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);      wav[i]=mi;
     fgets(line, MAXLINE, ficpar);      if(mi==0){
     puts(line);        nbwarn++;
     fputs(line,ficparo);        if(first==0){
   }          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   ungetc(c,ficpar);          first=1;
          }
         if(first==1){
    dateprev1=anprev1+mprev1/12.+jprev1/365.;          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;        }
       } /* end mi==0 */
   fscanf(ficpar,"pop_based=%d\n",&popbased);    } /* End individuals */
    fprintf(ficparo,"pop_based=%d\n",popbased);    
    fprintf(ficres,"pop_based=%d\n",popbased);      for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
   while((c=getc(ficpar))=='#' && c!= EOF){        if (stepm <=0)
     ungetc(c,ficpar);          dh[mi][i]=1;
     fgets(line, MAXLINE, ficpar);        else{
     puts(line);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     fputs(line,ficparo);            if (agedc[i] < 2*AGESUP) {
   }              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   ungetc(c,ficpar);              if(j==0) j=1;  /* Survives at least one month after exam */
   fscanf(ficpar,"popforecast=%d popfile=%s starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf\n",&popforecast,popfile,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2);              else if(j<0){
 fprintf(ficparo,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);                nberr++;
 fprintf(ficres,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);                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]);
                 j=1; /* Temporary Dangerous patch */
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2);                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]);
  /*------------ gnuplot -------------*/                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);
 chdir(pathcd);              }
   if((ficgp=fopen("graph.plt","w"))==NULL) {              k=k+1;
     printf("Problem with file graph.gp");goto end;              if (j >= jmax){
   }                jmax=j;
 #ifdef windows                ijmax=i;
   fprintf(ficgp,"cd \"%s\" \n",pathc);              }
 #endif              if (j <= jmin){
 m=pow(2,cptcoveff);                jmin=j;
                  ijmin=i;
  /* 1eme*/              }
   for (cpt=1; cpt<= nlstate ; cpt ++) {              sum=sum+j;
    for (k1=1; k1<= m ; k1 ++) {              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
               /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
 #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);          }
 #endif          else{
 #ifdef unix            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);  /*        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]); */
 #endif  
             k=k+1;
 for (i=1; i<= nlstate ; i ++) {            if (j >= jmax) {
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              jmax=j;
   else fprintf(ficgp," \%%*lf (\%%*lf)");              ijmax=i;
 }            }
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            else if (j <= jmin){
     for (i=1; i<= nlstate ; i ++) {              jmin=j;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              ijmin=i;
   else fprintf(ficgp," \%%*lf (\%%*lf)");            }
 }            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
      for (i=1; i<= nlstate ; i ++) {            if(j<0){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              nberr++;
   else fprintf(ficgp," \%%*lf (\%%*lf)");              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
 }                fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));            }
 #ifdef unix            sum=sum+j;
 fprintf(ficgp,"\nset ter gif small size 400,300");          }
 #endif          jk= j/stepm;
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          jl= j -jk*stepm;
    }          ju= j -(jk+1)*stepm;
   }          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   /*2 eme*/            if(jl==0){
               dh[mi][i]=jk;
   for (k1=1; k1<= m ; k1 ++) {              bh[mi][i]=0;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);            }else{ /* We want a negative bias in order to only have interpolation ie
                        * to avoid the price of an extra matrix product in likelihood */
     for (i=1; i<= nlstate+1 ; i ++) {              dh[mi][i]=jk+1;
       k=2*i;              bh[mi][i]=ju;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);            }
       for (j=1; j<= nlstate+1 ; j ++) {          }else{
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");            if(jl <= -ju){
   else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=jk;
 }                bh[mi][i]=jl;       /* bias is positive if real duration
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");                                   * is higher than the multiple of stepm and negative otherwise.
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);                                   */
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);            }
       for (j=1; j<= nlstate+1 ; j ++) {            else{
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              dh[mi][i]=jk+1;
         else fprintf(ficgp," \%%*lf (\%%*lf)");              bh[mi][i]=ju;
 }              }
       fprintf(ficgp,"\" t\"\" w l 0,");            if(dh[mi][i]==0){
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);              dh[mi][i]=1; /* At least one step */
       for (j=1; j<= nlstate+1 ; j ++) {              bh[mi][i]=ju; /* At least one step */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              /*  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);*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");            }
 }            } /* end if mle */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        }
       else fprintf(ficgp,"\" t\"\" w l 0,");      } /* end wave */
     }    }
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);    jmean=sum/k;
   }    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
      fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
   /*3eme*/   }
   
   for (k1=1; k1<= m ; k1 ++) {  /*********** Tricode ****************************/
     for (cpt=1; cpt<= nlstate ; cpt ++) {  void tricode(int *Tvar, int **nbcode, int imx)
       k=2+nlstate*(cpt-1);  {
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);    /* Uses cptcovn+2*cptcovprod as the number of covariates */
       for (i=1; i< nlstate ; i ++) {    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
         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);  
       }    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    int modmaxcovj=0; /* Modality max of covariates j */
     }    cptcoveff=0; 
   }   
      for (k=0; k<maxncov; k++) Ndum[k]=0;
   /* CV preval stat */    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
   for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
       k=3;      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);                                 modality of this covariate Vj*/ 
       for (i=1; i< nlstate ; i ++)        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
         fprintf(ficgp,"+$%d",k+i+1);                                        modality of the nth covariate of individual i. */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
              /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
       l=3+(nlstate+ndeath)*cpt;        if (ij > modmaxcovj) modmaxcovj=ij; 
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);        /* getting the maximum value of the modality of the covariate
       for (i=1; i< nlstate ; i ++) {           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
         l=3+(nlstate+ndeath)*cpt;           female is 1, then modmaxcovj=1.*/
         fprintf(ficgp,"+$%d",l+i+1);      }
       }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);        for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        if( Ndum[i] != 0 )
     }          ncodemax[j]++; 
   }          /* Number of modalities of the j th covariate. In fact
            ncodemax[j]=2 (dichotom. variables only) but it could be more for
   /* proba elementaires */           historical reasons */
    for(i=1,jk=1; i <=nlstate; i++){      } /* Ndum[-1] number of undefined modalities */
     for(k=1; k <=(nlstate+ndeath); k++){  
       if (k != i) {      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
         for(j=1; j <=ncovmodel; j++){      ij=1; 
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
           /*fprintf(ficgp,"%s",alph[1]);*/        for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
           jk++;            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
           fprintf(ficgp,"\n");                                       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; */
       }            ij++;
     }          }
     }          if (ij > ncodemax[j]) break; 
         }  /* end of loop on */
   for(jk=1; jk <=m; jk++) {      } /* end of loop on modality */ 
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
    i=1;    
    for(k2=1; k2<=nlstate; k2++) {    for (k=0; k< maxncov; k++) Ndum[k]=0;
      k3=i;    
      for(k=1; k<=(nlstate+ndeath); k++) {    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
        if (k != k2){     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
 ij=1;     Ndum[ij]++;
         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=1;
             ij++;   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
           }     if((Ndum[i]!=0) && (i<=ncovcol)){
           else       Tvaraff[ij]=i; /*For printing */
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);       ij++;
         }     }
           fprintf(ficgp,")/(1");   }
           ij--;
         for(k1=1; k1 <=nlstate; k1++){     cptcoveff=ij; /*Number of simple covariates*/
           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++){  /*********** Health Expectancies ****************/
           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]]]);  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
             ij++;  
           }  {
           else    /* Health expectancies, no variances */
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
           }    int nhstepma, nstepma; /* Decreasing with age */
           fprintf(ficgp,")");    double age, agelim, hf;
         }    double ***p3mat;
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    double eip;
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");  
         i=i+ncovmodel;    pstamp(ficreseij);
        }    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
      }    fprintf(ficreseij,"# Age");
    }    for(i=1; i<=nlstate;i++){
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      for(j=1; j<=nlstate;j++){
   }        fprintf(ficreseij," e%1d%1d ",i,j);
          }
   fclose(ficgp);      fprintf(ficreseij," e%1d. ",i);
   /* end gnuplot */    }
        fprintf(ficreseij,"\n");
 chdir(path);  
        
     free_ivector(wav,1,imx);    if(estepm < stepm){
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      printf ("Problem %d lower than %d\n",estepm, stepm);
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      }
     free_ivector(num,1,n);    else  hstepm=estepm;   
     free_vector(agedc,1,n);    /* We compute the life expectancy from trapezoids spaced every estepm months
     /*free_matrix(covar,1,NCOVMAX,1,n);*/     * This is mainly to measure the difference between two models: for example
     fclose(ficparo);     * if stepm=24 months pijx are given only every 2 years and by summing them
     fclose(ficres);     * we are calculating an estimate of the Life Expectancy assuming a linear 
     /*  }*/     * progression in between and thus overestimating or underestimating according
         * to the curvature of the survival function. If, for the same date, we 
    /*________fin mle=1_________*/     * estimate the model with stepm=1 month, we can keep estepm to 24 months
         * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
       * curvature will be obtained if estepm is as small as stepm. */
     /* No more information from the sample is required now */  
   /* Reads comments: lines beginning with '#' */    /* For example we decided to compute the life expectancy with the smallest unit */
   while((c=getc(ficpar))=='#' && c!= EOF){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     ungetc(c,ficpar);       nhstepm is the number of hstepm from age to agelim 
     fgets(line, MAXLINE, ficpar);       nstepm is the number of stepm from age to agelin. 
     puts(line);       Look at hpijx to understand the reason of that which relies in memory size
     fputs(line,ficparo);       and note for a fixed period like estepm months */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   ungetc(c,ficpar);       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
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);       results. So we changed our mind and took the option of the best precision.
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    */
 /*--------- index.htm --------*/    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   
   strcpy(optionfilehtm,optionfile);    agelim=AGESUP;
   strcat(optionfilehtm,".htm");    /* If stepm=6 months */
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     printf("Problem with %s \n",optionfilehtm);goto end;         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   }      
   /* nhstepm age range expressed in number of stepm */
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
 Total number of observations=%d <br>    /* if (stepm >= YEARM) hstepm=1;*/
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
 <hr  size=\"2\" color=\"#EC5E5E\">    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 <li>Outputs files<br><br>\n  
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    for (age=bage; age<=fage; age ++){ 
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      /* if (stepm >= YEARM) hstepm=1;*/
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
         - 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 stepm=6 months */
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>      /* Computed by stepm unit matrices, product of hstepma matrices, stored
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
         - Prevalences and population forecasting: <a href=\"f%s\">f%s</a> <br>      
 <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       
  fprintf(fichtm," <li>Graphs</li><p>");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       
  m=cptcoveff;      printf("%d|",(int)age);fflush(stdout);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       
  j1=0;      /* Computing expectancies */
  for(k1=1; k1<=m;k1++){      for(i=1; i<=nlstate;i++)
    for(i1=1; i1<=ncodemax[k1];i1++){        for(j=1; j<=nlstate;j++)
        j1++;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
        if (cptcovn > 0) {            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");            
          for (cpt=1; cpt<=cptcoveff;cpt++)            /* 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(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);  
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");          }
        }  
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      fprintf(ficreseij,"%3.0f",age );
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          for(i=1; i<=nlstate;i++){
        for(cpt=1; cpt<nlstate;cpt++){        eip=0;
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>        for(j=1; j<=nlstate;j++){
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);          eip +=eij[i][j][(int)age];
        }          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
     for(cpt=1; cpt<=nlstate;cpt++) {        }
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident        fprintf(ficreseij,"%9.4f", eip );
 interval) in state (%d): v%s%d%d.gif <br>      }
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        fprintf(ficreseij,"\n");
      }      
      for(cpt=1; cpt<=nlstate;cpt++) {    }
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    printf("\n");
      }    fprintf(ficlog,"\n");
      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);  
 fprintf(fichtm,"\n</body>");  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
    }  
  }  {
 fclose(fichtm);    /* Covariances of health expectancies eij and of total life expectancies according
      to initial status i, ei. .
   /*--------------- Prevalence limit --------------*/    */
      int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   strcpy(filerespl,"pl");    int nhstepma, nstepma; /* Decreasing with age */
   strcat(filerespl,fileres);    double age, agelim, hf;
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    double ***p3matp, ***p3matm, ***varhe;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    double **dnewm,**doldm;
   }    double *xp, *xm;
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    double **gp, **gm;
   fprintf(ficrespl,"#Prevalence limit\n");    double ***gradg, ***trgradg;
   fprintf(ficrespl,"#Age ");    int theta;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");    double eip, vip;
    
   prlim=matrix(1,nlstate,1,nlstate);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    xp=vector(1,npar);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    xm=vector(1,npar);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    dnewm=matrix(1,nlstate*nlstate,1,npar);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    
   k=0;    pstamp(ficresstdeij);
   agebase=agemin;    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   agelim=agemax;    fprintf(ficresstdeij,"# Age");
   ftolpl=1.e-10;    for(i=1; i<=nlstate;i++){
   i1=cptcoveff;      for(j=1; j<=nlstate;j++)
   if (cptcovn < 1){i1=1;}        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
       fprintf(ficresstdeij," e%1d. ",i);
   for(cptcov=1;cptcov<=i1;cptcov++){    }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    fprintf(ficresstdeij,"\n");
         k=k+1;  
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    pstamp(ficrescveij);
         fprintf(ficrespl,"\n#******");    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
         for(j=1;j<=cptcoveff;j++)    fprintf(ficrescveij,"# Age");
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for(i=1; i<=nlstate;i++)
         fprintf(ficrespl,"******\n");      for(j=1; j<=nlstate;j++){
                cptj= (j-1)*nlstate+i;
         for (age=agebase; age<=agelim; age++){        for(i2=1; i2<=nlstate;i2++)
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);          for(j2=1; j2<=nlstate;j2++){
           fprintf(ficrespl,"%.0f",age );            cptj2= (j2-1)*nlstate+i2;
           for(i=1; i<=nlstate;i++)            if(cptj2 <= cptj)
           fprintf(ficrespl," %.5f", prlim[i][i]);              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           fprintf(ficrespl,"\n");          }
         }      }
       }    fprintf(ficrescveij,"\n");
     }    
   fclose(ficrespl);    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
   /*------------- h Pij x at various ages ------------*/    }
      else  hstepm=estepm;   
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    /* We compute the life expectancy from trapezoids spaced every estepm months
   if((ficrespij=fopen(filerespij,"w"))==NULL) {     * This is mainly to measure the difference between two models: for example
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;     * if stepm=24 months pijx are given only every 2 years and by summing them
   }     * we are calculating an estimate of the Life Expectancy assuming a linear 
   printf("Computing pij: result on file '%s' \n", filerespij);     * progression in between and thus overestimating or underestimating according
       * to the curvature of the survival function. If, for the same date, we 
   stepsize=(int) (stepm+YEARM-1)/YEARM;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   /*if (stepm<=24) stepsize=2;*/     * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
   agelim=AGESUP;     * curvature will be obtained if estepm is as small as stepm. */
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    /* 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. 
   k=0;       nhstepm is the number of hstepm from age to agelim 
   for(cptcov=1;cptcov<=i1;cptcov++){       nstepm is the number of stepm from age to agelin. 
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       Look at hpijx to understand the reason of that which relies in memory size
       k=k+1;       and note for a fixed period like estepm months */
         fprintf(ficrespij,"\n#****** ");    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         for(j=1;j<=cptcoveff;j++)       survival function given by stepm (the optimization length). Unfortunately it
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][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 
               results. So we changed our mind and took the option of the best precision.
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* If stepm=6 months */
           oldm=oldms;savm=savms;    /* nhstepm age range expressed in number of stepm */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      agelim=AGESUP;
           fprintf(ficrespij,"# Age");    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
           for(i=1; i<=nlstate;i++)    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             for(j=1; j<=nlstate+ndeath;j++)    /* if (stepm >= YEARM) hstepm=1;*/
               fprintf(ficrespij," %1d-%1d",i,j);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
           fprintf(ficrespij,"\n");    
           for (h=0; h<=nhstepm; h++){    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             for(i=1; i<=nlstate;i++)    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
               for(j=1; j<=nlstate+ndeath;j++)    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
             fprintf(ficrespij,"\n");    gm=matrix(0,nhstepm,1,nlstate*nlstate);
           }  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for (age=bage; age<=fage; age ++){ 
           fprintf(ficrespij,"\n");      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
         }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     }      /* if (stepm >= YEARM) hstepm=1;*/
   }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/      /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
   fclose(ficrespij);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   if(stepm == 1) {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   /*---------- Forecasting ------------------*/  
   calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;      /* Computing  Variances of health expectancies */
       /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   /*printf("calage= %f", calagedate);*/         decrease memory allocation */
        for(theta=1; theta <=npar; theta++){
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
   strcpy(fileresf,"f");        }
   strcat(fileresf,fileres);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   if((ficresf=fopen(fileresf,"w"))==NULL) {        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;    
   }        for(j=1; j<= nlstate; j++){
   printf("Computing forecasting: result on file '%s' \n", fileresf);          for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
   free_matrix(mint,1,maxwav,1,n);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   free_matrix(anint,1,maxwav,1,n);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   free_matrix(agev,1,maxwav,1,imx);            }
   /* Mobile average */          }
         }
   if (cptcoveff==0) ncodemax[cptcoveff]=1;       
         for(ij=1; ij<= nlstate*nlstate; ij++)
   if (mobilav==1) {          for(h=0; h<=nhstepm-1; h++){
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)          }
       for (i=1; i<=nlstate;i++)      }/* End theta */
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)      
           mobaverage[(int)agedeb][i][cptcod]=0.;      
          for(h=0; h<=nhstepm-1; h++)
     for (agedeb=bage+4; agedeb<=fage; agedeb++){        for(j=1; j<=nlstate*nlstate;j++)
       for (i=1; i<=nlstate;i++){          for(theta=1; theta <=npar; theta++)
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            trgradg[h][j][theta]=gradg[h][theta][j];
           for (cpt=0;cpt<=4;cpt++){      
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];  
           }       for(ij=1;ij<=nlstate*nlstate;ij++)
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;        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++){
   stepsize=(int) (stepm+YEARM-1)/YEARM;        for(k=0;k<=nhstepm-1;k++){
   if (stepm<=12) stepsize=1;          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]);
   agelim=AGESUP;          for(ij=1;ij<=nlstate*nlstate;ij++)
   /*hstepm=stepsize*YEARM; *//* Every year of age */            for(ji=1;ji<=nlstate*nlstate;ji++)
   hstepm=1;              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */        }
   yp1=modf(dateintmean,&yp);      }
   anprojmean=yp;  
   yp2=modf((yp1*12),&yp);      /* Computing expectancies */
   mprojmean=yp;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   yp1=modf((yp2*30.5),&yp);      for(i=1; i<=nlstate;i++)
   jprojmean=yp;        for(j=1; j<=nlstate;j++)
   if(jprojmean==0) jprojmean=1;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   if(mprojmean==0) jprojmean=1;            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);            /* 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]);*/
   
   if (popforecast==1) {          }
     if((ficpop=fopen(popfile,"r"))==NULL)    {  
       printf("Problem with population file : %s\n",popfile);goto end;      fprintf(ficresstdeij,"%3.0f",age );
     }      for(i=1; i<=nlstate;i++){
     popage=ivector(0,AGESUP);        eip=0.;
     popeffectif=vector(0,AGESUP);        vip=0.;
     popcount=vector(0,AGESUP);        for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
     i=1;            for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)            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]) );
         i=i+1;        }
       }        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
     imx=i;      }
          fprintf(ficresstdeij,"\n");
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];  
   }      fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
   for(cptcov=1;cptcov<=i1;cptcov++){        for(j=1; j<=nlstate;j++){
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){          cptj= (j-1)*nlstate+i;
       k=k+1;          for(i2=1; i2<=nlstate;i2++)
       fprintf(ficresf,"\n#******");            for(j2=1; j2<=nlstate;j2++){
       for(j=1;j<=cptcoveff;j++) {              cptj2= (j2-1)*nlstate+i2;
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              if(cptj2 <= cptj)
       }                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
       fprintf(ficresf,"******\n");            }
       fprintf(ficresf,"# StartingAge FinalAge");        }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);      fprintf(ficrescveij,"\n");
       if (popforecast==1)  fprintf(ficresf," [Population]");     
        }
       for (cpt=0; cpt<4;cpt++) {    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         fprintf(ficresf,"\n");    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(bage-((int)calagedate %12)/12.); agedeb--){ /* If stepm=6 months */    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         nhstepm = nhstepm/hstepm;    printf("\n");
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/    fprintf(ficlog,"\n");
   
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_vector(xm,1,npar);
         oldm=oldms;savm=savms;    free_vector(xp,1,npar);
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      free_matrix(dnewm,1,nlstate*nlstate,1,npar);
            free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
         for (h=0; h<=nhstepm; h++){    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
           if (h==(int) (calagedate+YEARM*cpt)) {  }
             fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);  
           }  /************ Variance ******************/
           for(j=1; j<=nlstate+ndeath;j++) {  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[])
             kk1=0.;kk2=0;  {
             for(i=1; i<=nlstate;i++) {            /* Variance of health expectancies */
               if (mobilav==1)    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
                 kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    /* double **newm;*/
               else {    double **dnewm,**doldm;
                 kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    double **dnewmp,**doldmp;
                 /* fprintf(ficresf," p3=%.3f p=%.3f ", p3mat[i][j][h], probs[(int)(agedeb)+1][i][cptcod]);*/    int i, j, nhstepm, hstepm, h, nstepm ;
               }    int k, cptcode;
     double *xp;
               if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];    double **gp, **gm;  /* for var eij */
             }    double ***gradg, ***trgradg; /*for var eij */
              double **gradgp, **trgradgp; /* for var p point j */
             if (h==(int)(calagedate+12*cpt)){    double *gpp, *gmp; /* for var p point j */
               fprintf(ficresf," %.3f", kk1);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
                  double ***p3mat;
               if (popforecast==1) fprintf(ficresf," [%.f]", kk2);    double age,agelim, hf;
             }    double ***mobaverage;
           }    int theta;
         }    char digit[4];
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    char digitp[25];
       }  
       }    char fileresprobmorprev[FILENAMELENGTH];
     }  
   }    if(popbased==1){
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      if(mobilav!=0)
   if (popforecast==1) {        strcpy(digitp,"-populbased-mobilav-");
     free_ivector(popage,0,AGESUP);      else strcpy(digitp,"-populbased-nomobil-");
     free_vector(popeffectif,0,AGESUP);    }
     free_vector(popcount,0,AGESUP);    else 
   }      strcpy(digitp,"-stablbased-");
   free_imatrix(s,1,maxwav+1,1,n);  
   free_vector(weight,1,n);    if (mobilav!=0) {
   fclose(ficresf);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   }/* End forecasting */      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   else{        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
     erreur=108;        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     printf("Error %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d\n", erreur, stepm);      }
   }    }
   
   /*---------- Health expectancies and variances ------------*/    strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
   strcpy(filerest,"t");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   strcat(filerest,fileres);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
   if((ficrest=fopen(filerest,"w"))==NULL) {    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    strcat(fileresprobmorprev,fileres);
   }    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
   strcpy(filerese,"e");    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   strcat(filerese,fileres);   
   if((ficreseij=fopen(filerese,"w"))==NULL) {    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    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);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
  strcpy(fileresv,"v");      fprintf(ficresprobmorprev," p.%-d SE",j);
   strcat(fileresv,fileres);      for(i=1; i<=nlstate;i++)
   if((ficresvij=fopen(fileresv,"w"))==NULL) {        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    }  
   }    fprintf(ficresprobmorprev,"\n");
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    fprintf(ficgp,"\n# Routine varevsij");
     /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
   k=0;    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");
   for(cptcov=1;cptcov<=i1;cptcov++){    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  /*   } */
       k=k+1;    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fprintf(ficrest,"\n#****** ");    pstamp(ficresvij);
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    if(popbased==1)
       fprintf(ficrest,"******\n");      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
     else
       fprintf(ficreseij,"\n#****** ");      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresvij,"# Age");
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    for(i=1; i<=nlstate;i++)
       fprintf(ficreseij,"******\n");      for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
       fprintf(ficresvij,"\n#****** ");    fprintf(ficresvij,"\n");
       for(j=1;j<=cptcoveff;j++)  
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    xp=vector(1,npar);
       fprintf(ficresvij,"******\n");    dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       oldm=oldms;savm=savms;    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);    
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       oldm=oldms;savm=savms;    gpp=vector(nlstate+1,nlstate+ndeath);
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    gmp=vector(nlstate+1,nlstate+ndeath);
          trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    if(estepm < stepm){
       fprintf(ficrest,"\n");      printf ("Problem %d lower than %d\n",estepm, stepm);
            }
       hf=1;    else  hstepm=estepm;   
       if (stepm >= YEARM) hf=stepm/YEARM;    /* For example we decided to compute the life expectancy with the smallest unit */
       epj=vector(1,nlstate+1);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       for(age=bage; age <=fage ;age++){       nhstepm is the number of hstepm from age to agelim 
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);       nstepm is the number of stepm from age to agelin. 
         if (popbased==1) {       Look at function hpijx to understand why (it is linked to memory size questions) */
           for(i=1; i<=nlstate;i++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             prlim[i][i]=probs[(int)age][i][k];       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 
         fprintf(ficrest," %.0f",age);       results. So we changed our mind and took the option of the best precision.
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    */
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    agelim = AGESUP;
           }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
           epj[nlstate+1] +=epj[j];      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
         }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         for(i=1, vepp=0.;i <=nlstate;i++)      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           for(j=1;j <=nlstate;j++)      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
             vepp += vareij[i][j][(int)age];      gp=matrix(0,nhstepm,1,nlstate);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));      gm=matrix(0,nhstepm,1,nlstate);
         for(j=1;j <=nlstate;j++){  
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));  
         }      for(theta=1; theta <=npar; theta++){
         fprintf(ficrest,"\n");        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){
  fclose(ficreseij);            for(i=1; i<=nlstate;i++)
  fclose(ficresvij);              prlim[i][i]=probs[(int)age][i][ij];
   fclose(ficrest);          }else{ /* mobilav */ 
   fclose(ficpar);            for(i=1; i<=nlstate;i++)
   free_vector(epj,1,nlstate+1);              prlim[i][i]=mobaverage[(int)age][i][ij];
   /*  scanf("%d ",i); */          }
         }
   /*------- Variance limit prevalence------*/      
         for(j=1; j<= nlstate; j++){
 strcpy(fileresvpl,"vpl");          for(h=0; h<=nhstepm; h++){
   strcat(fileresvpl,fileres);            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          }
     exit(0);        }
   }        /* This for computing probability of death (h=1 means
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
  k=0;        */
  for(cptcov=1;cptcov<=i1;cptcov++){        for(j=nlstate+1;j<=nlstate+ndeath;j++){
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for(i=1,gpp[j]=0.; i<= nlstate; i++)
      k=k+1;            gpp[j] += prlim[i][i]*p3mat[i][j][1];
      fprintf(ficresvpl,"\n#****** ");        }    
      for(j=1;j<=cptcoveff;j++)        /* end probability of death */
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
      fprintf(ficresvpl,"******\n");        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
                xp[i] = x[i] - (i==theta ?delti[theta]:0);
      varpl=matrix(1,nlstate,(int) bage, (int) fage);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
      oldm=oldms;savm=savms;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);   
    }        if (popbased==1) {
  }          if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
   fclose(ficresvpl);              prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
   /*---------- End : free ----------------*/            for(i=1; i<=nlstate;i++)
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);              prlim[i][i]=mobaverage[(int)age][i][ij];
            }
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        }
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
          for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
            for(h=0; h<=nhstepm; h++){
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          }
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);        }
          /* This for computing probability of death (h=1 means
   free_matrix(matcov,1,npar,1,npar);           computed over hstepm matrices product = hstepm*stepm months) 
   free_vector(delti,1,npar);           as a weighted average of prlim.
          */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
   if(erreur >0)           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     printf("End of Imach with error %d\n",erreur);        }    
   else   printf("End of Imach\n");        /* end probability of death */
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  
          for(j=1; j<= nlstate; j++) /* vareij */
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/          for(h=0; h<=nhstepm; h++){
   /*printf("Total time was %d uSec.\n", total_usecs);*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   /*------ End -----------*/          }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
  end:          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
 #ifdef windows        }
  chdir(pathcd);  
 #endif      } /* End theta */
    
  system("..\\gp37mgw\\wgnuplot graph.plt");      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
 #ifdef windows      for(h=0; h<=nhstepm; h++) /* veij */
   while (z[0] != 'q') {        for(j=1; j<=nlstate;j++)
     chdir(pathcd);          for(theta=1; theta <=npar; theta++)
     printf("\nType e to edit output files, c to start again, and q for exiting: ");            trgradg[h][j][theta]=gradg[h][theta][j];
     scanf("%s",z);  
     if (z[0] == 'c') system("./imach");      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     else if (z[0] == 'e') {        for(theta=1; theta <=npar; theta++)
       chdir(path);          trgradgp[j][theta]=gradgp[theta][j];
       system(optionfilehtm);    
     }  
     else if (z[0] == 'q') exit(0);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   }      for(i=1;i<=nlstate;i++)
 #endif        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,"\nunset parametric;unset label; 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; unset log 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,"\nunset parametric;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.;
                     if ((lc2 <0) || (lc1 <0) ){
                       printf("Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Continuing by making them positive: WRONG RESULTS.\n", lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
                       fprintf(ficlog,"Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e\n", lc1, lc2, v1, v2, cv12);fflush(ficlog);
                       lc1=fabs(lc1);
                       lc2=fabs(lc2);
                     }
   
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   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;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     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]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+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);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* 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);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     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;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           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 '%s' at line number %ld 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);
             fprintf(ficlog,"Error reading data around '%s' at line number %ld 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);fflush(ficlog);
             return 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 for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 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 for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 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 for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 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);
         fprintf(ficlog,"Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 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);
           fprintf(ficlog,"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);fflush(ficlog);
           return 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 */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     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; /* Number of covariates V1+V2*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(k=cptcovn; k>=1;k--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 
                                       */ 
         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 V2+V1+V4+V3*age strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=2 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1]=atoi(strc); /* m 1 for V1*/
             Tvard[k1][2]=atoi(stre); /* n 4 for V4*/
             Tvar[cptcovn+k2]=Tvard[k1][1]; /* Tvar[(cptcovn=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovn+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovn=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
             k1++;
             k2=k2+2;
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[k]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*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);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     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(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\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);     
           return 1;
         }
       }
     }
   
     /*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); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  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, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*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 ***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  *strt;*/
     char strtend[80];
   
     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 plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     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++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       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 */
   
   
     n= lastobs;
     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); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8); /* hard coded ? */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,15); 
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2); /* For V3*V2 Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,15); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     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 */
   
     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++){ /* scans any effective covariate */
       for(i=1; i <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             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 codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][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); 
   /*     ximort=gsl_matrix_alloc(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]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       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);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  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");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       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);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       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;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
    endfree:
     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_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.21  
changed lines
  Added in v.1.140


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