Diff for /imach/src/imach.c between versions 1.48 and 1.143

version 1.48, 2002/06/10 13:12:49 version 1.143, 2014/01/26 09:45:38
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.143  2014/01/26 09:45:38  brouard
      Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   first survey ("cross") where individuals from different ages are    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.142  2014/01/26 03:57:36  brouard
   second wave of interviews ("longitudinal") which measure each change    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
   (if any) in individual health status.  Health expectancies are  
   computed from the time spent in each health state according to a    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.141  2014/01/26 02:42:01  brouard
   simplest model is the multinomial logistic model where pij is the    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.140  2011/09/02 10:37:54  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Summary: times.h is ok with mingw32 now.
   '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    Revision 1.139  2010/06/14 07:50:17  brouard
   where the markup *Covariates have to be included here again* invites    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   you to do it.  More covariates you add, slower the    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   convergence.  
     Revision 1.138  2010/04/30 18:19:40  brouard
   The advantage of this computer programme, compared to a simple    *** empty log message ***
   multinomial logistic model, is clear when the delay between waves is not  
   identical for each individual. Also, if a individual missed an    Revision 1.137  2010/04/29 18:11:38  brouard
   intermediate interview, the information is lost, but taken into    (Module): Checking covariates for more complex models
   account using an interpolation or extrapolation.      than V1+V2. A lot of change to be done. Unstable.
   
   hPijx is the probability to be observed in state i at age x+h    Revision 1.136  2010/04/26 20:30:53  brouard
   conditional to the observed state i at age x. The delay 'h' can be    (Module): merging some libgsl code. Fixing computation
   split into an exact number (nh*stepm) of unobserved intermediate    of likelione (using inter/intrapolation if mle = 0) in order to
   states. This elementary transition (by month or quarter trimester,    get same likelihood as if mle=1.
   semester or year) is model as a multinomial logistic.  The hPx    Some cleaning of code and comments added.
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.135  2009/10/29 15:33:14  brouard
   hPijx.    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.134  2009/10/29 13:18:53  brouard
   of the life expectancies. It also computes the prevalence limits.    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.133  2009/07/06 10:21:25  brouard
            Institut national d'études démographiques, Paris.    just nforces
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.132  2009/07/06 08:22:05  brouard
   It is copyrighted identically to a GNU software product, ie programme and    Many tings
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.131  2009/06/20 16:22:47  brouard
   **********************************************************************/    Some dimensions resccaled
    
 #include <math.h>    Revision 1.130  2009/05/26 06:44:34  brouard
 #include <stdio.h>    (Module): Max Covariate is now set to 20 instead of 8. A
 #include <stdlib.h>    lot of cleaning with variables initialized to 0. Trying to make
 #include <unistd.h>    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   
 #define MAXLINE 256    Revision 1.129  2007/08/31 13:49:27  lievre
 #define GNUPLOTPROGRAM "gnuplot"    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/  
 #define FILENAMELENGTH 80    Revision 1.128  2006/06/30 13:02:05  brouard
 /*#define DEBUG*/    (Module): Clarifications on computing e.j
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.127  2006/04/28 18:11:50  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    loop. Now we define nhstepma in the age loop.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    (Module): In order to speed up (in case of numerous covariates) we
     compute health expectancies (without variances) in a first step
 #define NINTERVMAX 8    and then all the health expectancies with variances or standard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    deviation (needs data from the Hessian matrices) which slows the
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    computation.
 #define NCOVMAX 8 /* Maximum number of covariates */    In the future we should be able to stop the program is only health
 #define MAXN 20000    expectancies and graph are needed without standard deviations.
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.126  2006/04/28 17:23:28  brouard
 #define AGEBASE 40    (Module): Yes the sum of survivors was wrong since
 #ifdef windows    imach-114 because nhstepm was no more computed in the age
 #define DIRSEPARATOR '\\'    loop. Now we define nhstepma in the age loop.
 #else    Version 0.98h
 #define DIRSEPARATOR '/'  
 #endif    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    Forecasting file added.
 int erreur; /* Error number */  
 int nvar;    Revision 1.124  2006/03/22 17:13:53  lievre
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Parameters are printed with %lf instead of %f (more numbers after the comma).
 int npar=NPARMAX;    The log-likelihood is printed in the log file
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.123  2006/03/20 10:52:43  brouard
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    * imach.c (Module): <title> changed, corresponds to .htm file
 int popbased=0;    name. <head> headers where missing.
   
 int *wav; /* Number of waves for this individuual 0 is possible */    * imach.c (Module): Weights can have a decimal point as for
 int maxwav; /* Maxim number of waves */    English (a comma might work with a correct LC_NUMERIC environment,
 int jmin, jmax; /* min, max spacing between 2 waves */    otherwise the weight is truncated).
 int mle, weightopt;    Modification of warning when the covariates values are not 0 or
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    1.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Version 0.98g
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.122  2006/03/20 09:45:41  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    (Module): Weights can have a decimal point as for
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    English (a comma might work with a correct LC_NUMERIC environment,
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    otherwise the weight is truncated).
 FILE *fichtm; /* Html File */    Modification of warning when the covariates values are not 0 or
 FILE *ficreseij;    1.
 char filerese[FILENAMELENGTH];    Version 0.98g
 FILE  *ficresvij;  
 char fileresv[FILENAMELENGTH];    Revision 1.121  2006/03/16 17:45:01  lievre
 FILE  *ficresvpl;    * imach.c (Module): Comments concerning covariates added
 char fileresvpl[FILENAMELENGTH];  
 char title[MAXLINE];    * imach.c (Module): refinements in the computation of lli if
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    status=-2 in order to have more reliable computation if stepm is
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    not 1 month. Version 0.98f
   
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    Revision 1.120  2006/03/16 15:10:38  lievre
     (Module): refinements in the computation of lli if
 char filerest[FILENAMELENGTH];    status=-2 in order to have more reliable computation if stepm is
 char fileregp[FILENAMELENGTH];    not 1 month. Version 0.98f
 char popfile[FILENAMELENGTH];  
     Revision 1.119  2006/03/15 17:42:26  brouard
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.118  2006/03/14 18:20:07  brouard
 #define FTOL 1.0e-10    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 #define NRANSI    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define ITMAX 200    (Module): Function pstamp added
     (Module): Version 0.98d
 #define TOL 2.0e-4  
     Revision 1.117  2006/03/14 17:16:22  brouard
 #define CGOLD 0.3819660    (Module): varevsij Comments added explaining the second
 #define ZEPS 1.0e-10    table of variances if popbased=1 .
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 #define GOLD 1.618034    (Module): Version 0.98d
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
 static double maxarg1,maxarg2;    varian-covariance of ej. is needed (Saito).
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.115  2006/02/27 12:17:45  brouard
      (Module): One freematrix added in mlikeli! 0.98c
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 static double sqrarg;    filename with strsep.
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.113  2006/02/24 14:20:24  brouard
     (Module): Memory leaks checks with valgrind and:
 int imx;    datafile was not closed, some imatrix were not freed and on matrix
 int stepm;    allocation too.
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.112  2006/01/30 09:55:26  brouard
 int estepm;    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
     Revision 1.111  2006/01/25 20:38:18  brouard
 int m,nb;    (Module): Lots of cleaning and bugs added (Gompertz)
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    (Module): Comments can be added in data file. Missing date values
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    can be a simple dot '.'.
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 double *weight;  
 int **s; /* Status */    Revision 1.109  2006/01/24 19:37:15  brouard
 double *agedc, **covar, idx;    (Module): Comments (lines starting with a #) are allowed in data.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.108  2006/01/19 18:05:42  lievre
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Gnuplot problem appeared...
 double ftolhess; /* Tolerance for computing hessian */    To be fixed
   
 /**************** split *************************/    Revision 1.107  2006/01/19 16:20:37  brouard
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    Test existence of gnuplot in imach path
 {  
    char *s;                             /* pointer */    Revision 1.106  2006/01/19 13:24:36  brouard
    int  l1, l2;                         /* length counters */    Some cleaning and links added in html output
   
    l1 = strlen( path );                 /* length of path */    Revision 1.105  2006/01/05 20:23:19  lievre
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    *** empty log message ***
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.104  2005/09/30 16:11:43  lievre
 #if     defined(__bsd__)                /* get current working directory */    (Module): sump fixed, loop imx fixed, and simplifications.
       extern char       *getwd( );    (Module): If the status is missing at the last wave but we know
     that the person is alive, then we can code his/her status as -2
       if ( getwd( dirc ) == NULL ) {    (instead of missing=-1 in earlier versions) and his/her
 #else    contributions to the likelihood is 1 - Prob of dying from last
       extern char       *getcwd( );    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    Revision 1.103  2005/09/30 15:54:49  lievre
          return( GLOCK_ERROR_GETCWD );    (Module): sump fixed, loop imx fixed, and simplifications.
       }  
       strcpy( name, path );             /* we've got it */    Revision 1.102  2004/09/15 17:31:30  brouard
    } else {                             /* strip direcotry from path */    Add the possibility to read data file including tab characters.
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.101  2004/09/15 10:38:38  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Fix on curr_time
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.100  2004/07/12 18:29:06  brouard
       dirc[l1-l2] = 0;                  /* add zero */    Add version for Mac OS X. Just define UNIX in Makefile
    }  
    l1 = strlen( dirc );                 /* length of directory */    Revision 1.99  2004/06/05 08:57:40  brouard
 #ifdef windows    *** empty log message ***
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Revision 1.98  2004/05/16 15:05:56  brouard
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    New version 0.97 . First attempt to estimate force of mortality
 #endif    directly from the data i.e. without the need of knowing the health
    s = strrchr( name, '.' );            /* find last / */    state at each age, but using a Gompertz model: log u =a + b*age .
    s++;    This is the basic analysis of mortality and should be done before any
    strcpy(ext,s);                       /* save extension */    other analysis, in order to test if the mortality estimated from the
    l1= strlen( name);    cross-longitudinal survey is different from the mortality estimated
    l2= strlen( s)+1;    from other sources like vital statistic data.
    strncpy( finame, name, l1-l2);  
    finame[l1-l2]= 0;    The same imach parameter file can be used but the option for mle should be -3.
    return( 0 );                         /* we're done */  
 }    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.
   
 /******************************************/    The output is very simple: only an estimate of the intercept and of
     the slope with 95% confident intervals.
 void replace(char *s, char*t)  
 {    Current limitations:
   int i;    A) Even if you enter covariates, i.e. with the
   int lg=20;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   i=0;    B) There is no computation of Life Expectancy nor Life Table.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.97  2004/02/20 13:25:42  lievre
     (s[i] = t[i]);    Version 0.96d. Population forecasting command line is (temporarily)
     if (t[i]== '\\') s[i]='/';    suppressed.
   }  
 }    Revision 1.96  2003/07/15 15:38:55  brouard
     * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 int nbocc(char *s, char occ)    rewritten within the same printf. Workaround: many printfs.
 {  
   int i,j=0;    Revision 1.95  2003/07/08 07:54:34  brouard
   int lg=20;    * imach.c (Repository):
   i=0;    (Repository): Using imachwizard code to output a more meaningful covariance
   lg=strlen(s);    matrix (cov(a12,c31) instead of numbers.
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Revision 1.94  2003/06/27 13:00:02  brouard
   }    Just cleaning
   return j;  
 }    Revision 1.93  2003/06/25 16:33:55  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 void cutv(char *u,char *v, char*t, char occ)    exist so I changed back to asctime which exists.
 {    (Module): Version 0.96b
   int i,lg,j,p=0;  
   i=0;    Revision 1.92  2003/06/25 16:30:45  brouard
   for(j=0; j<=strlen(t)-1; j++) {    (Module): On windows (cygwin) function asctime_r doesn't
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    exist so I changed back to asctime which exists.
   }  
     Revision 1.91  2003/06/25 15:30:29  brouard
   lg=strlen(t);    * imach.c (Repository): Duplicated warning errors corrected.
   for(j=0; j<p; j++) {    (Repository): Elapsed time after each iteration is now output. It
     (u[j] = t[j]);    helps to forecast when convergence will be reached. Elapsed time
   }    is stamped in powell.  We created a new html file for the graphs
      u[p]='\0';    concerning matrix of covariance. It has extension -cov.htm.
   
    for(j=0; j<= lg; j++) {    Revision 1.90  2003/06/24 12:34:15  brouard
     if (j>=(p+1))(v[j-p-1] = t[j]);    (Module): Some bugs corrected for windows. Also, when
   }    mle=-1 a template is output in file "or"mypar.txt with the design
 }    of the covariance matrix to be input.
   
 /********************** nrerror ********************/    Revision 1.89  2003/06/24 12:30:52  brouard
     (Module): Some bugs corrected for windows. Also, when
 void nrerror(char error_text[])    mle=-1 a template is output in file "or"mypar.txt with the design
 {    of the covariance matrix to be input.
   fprintf(stderr,"ERREUR ...\n");  
   fprintf(stderr,"%s\n",error_text);    Revision 1.88  2003/06/23 17:54:56  brouard
   exit(1);    * 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.
 }  
 /*********************** vector *******************/    Revision 1.87  2003/06/18 12:26:01  brouard
 double *vector(int nl, int nh)    Version 0.96
 {  
   double *v;    Revision 1.86  2003/06/17 20:04:08  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Module): Change position of html and gnuplot routines and added
   if (!v) nrerror("allocation failure in vector");    routine fileappend.
   return v-nl+NR_END;  
 }    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
 /************************ free vector ******************/    current date of interview. It may happen when the death was just
 void free_vector(double*v, int nl, int nh)    prior to the death. In this case, dh was negative and likelihood
 {    was wrong (infinity). We still send an "Error" but patch by
   free((FREE_ARG)(v+nl-NR_END));    assuming that the date of death was just one stepm after the
 }    interview.
     (Repository): Because some people have very long ID (first column)
 /************************ivector *******************************/    we changed int to long in num[] and we added a new lvector for
 int *ivector(long nl,long nh)    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   int *v;    (Repository): No more line truncation errors.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Revision 1.84  2003/06/13 21:44:43  brouard
   return v-nl+NR_END;    * imach.c (Repository): Replace "freqsummary" at a correct
 }    place. It differs from routine "prevalence" which may be called
     many times. Probs is memory consuming and must be used with
 /******************free ivector **************************/    parcimony.
 void free_ivector(int *v, long nl, long nh)    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.83  2003/06/10 13:39:11  lievre
 }    *** empty log message ***
   
 /******************* imatrix *******************************/    Revision 1.82  2003/06/05 15:57:20  brouard
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Add log in  imach.c and  fullversion number is now printed.
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {  */
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  /*
   int **m;     Interpolated Markov Chain
    
   /* allocate pointers to rows */    Short summary of the programme:
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    
   if (!m) nrerror("allocation failure 1 in matrix()");    This program computes Healthy Life Expectancies from
   m += NR_END;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   m -= nrl;    first survey ("cross") where individuals from different ages are
      interviewed on their health status or degree of disability (in the
      case of a health survey which is our main interest) -2- at least a
   /* allocate rows and set pointers to them */    second wave of interviews ("longitudinal") which measure each change
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    (if any) in individual health status.  Health expectancies are
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    computed from the time spent in each health state according to a
   m[nrl] += NR_END;    model. More health states you consider, more time is necessary to reach the
   m[nrl] -= ncl;    Maximum Likelihood of the parameters involved in the model.  The
      simplest model is the multinomial logistic model where pij is the
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    probability to be observed in state j at the second wave
      conditional to be observed in state i at the first wave. Therefore
   /* return pointer to array of pointers to rows */    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   return m;    '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
     where the markup *Covariates have to be included here again* invites
 /****************** free_imatrix *************************/    you to do it.  More covariates you add, slower the
 void free_imatrix(m,nrl,nrh,ncl,nch)    convergence.
       int **m;  
       long nch,ncl,nrh,nrl;    The advantage of this computer programme, compared to a simple
      /* free an int matrix allocated by imatrix() */    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
 /******************* matrix *******************************/    conditional to the observed state i at age x. The delay 'h' can be
 double **matrix(long nrl, long nrh, long ncl, long nch)    split into an exact number (nh*stepm) of unobserved intermediate
 {    states. This elementary transition (by month, quarter,
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+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
   return m;    can be accessed at http://euroreves.ined.fr/imach .
 }  
     Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 /*************************free matrix ************************/    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    
 {    **********************************************************************/
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  /*
   free((FREE_ARG)(m+nrl-NR_END));    main
 }    read parameterfile
     read datafile
 /******************* ma3x *******************************/    concatwav
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    freqsummary
 {    if (mle >= 1)
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;      mlikeli
   double ***m;    print results files
     if mle==1 
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));       computes hessian
   if (!m) nrerror("allocation failure 1 in matrix()");    read end of parameter file: agemin, agemax, bage, fage, estepm
   m += NR_END;        begin-prev-date,...
   m -= nrl;    open gnuplot file
     open html file
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    period (stable) prevalence
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");     for age prevalim()
   m[nrl] += NR_END;    h Pij x
   m[nrl] -= ncl;    variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    health expectancies
     Variance-covariance of DFLE
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    prevalence()
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");     movingaverage()
   m[nrl][ncl] += NR_END;    varevsij() 
   m[nrl][ncl] -= nll;    if popbased==1 varevsij(,popbased)
   for (j=ncl+1; j<=nch; j++)    total life expectancies
     m[nrl][j]=m[nrl][j-1]+nlay;    Variance of period (stable) prevalence
     end
   for (i=nrl+1; i<=nrh; i++) {  */
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;  
   }   
   return m;  #include <math.h>
 }  #include <stdio.h>
   #include <stdlib.h>
 /*************************free ma3x ************************/  #include <string.h>
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #include <unistd.h>
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #include <limits.h>
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #include <sys/types.h>
   free((FREE_ARG)(m+nrl-NR_END));  #include <sys/stat.h>
 }  #include <errno.h>
   extern int errno;
 /***************** f1dim *************************/  
 extern int ncom;  #ifdef LINUX
 extern double *pcom,*xicom;  #include <time.h>
 extern double (*nrfunc)(double []);  #include "timeval.h"
    #else
 double f1dim(double x)  #include <sys/time.h>
 {  #endif
   int j;  
   double f;  #ifdef GSL
   double *xt;  #include <gsl/gsl_errno.h>
    #include <gsl/gsl_multimin.h>
   xt=vector(1,ncom);  #endif
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);  /* #include <libintl.h> */
   free_vector(xt,1,ncom);  /* #define _(String) gettext (String) */
   return f;  
 }  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   
 /*****************brent *************************/  #define GNUPLOTPROGRAM "gnuplot"
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 {  #define FILENAMELENGTH 132
   int iter;  
   double a,b,d,etemp;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   double fu,fv,fw,fx;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   double ftemp;  
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
   double e=0.0;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
    
   a=(ax < cx ? ax : cx);  #define NINTERVMAX 8
   b=(ax > cx ? ax : cx);  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   x=w=v=bx;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   fw=fv=fx=(*f)(x);  #define NCOVMAX 20 /* Maximum number of covariates */
   for (iter=1;iter<=ITMAX;iter++) {  #define MAXN 20000
     xm=0.5*(a+b);  #define YEARM 12. /* Number of months per year */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  #define AGESUP 130
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  #define AGEBASE 40
     printf(".");fflush(stdout);  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 #ifdef DEBUG  #ifdef UNIX
     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);  #define DIRSEPARATOR '/'
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  #define CHARSEPARATOR "/"
 #endif  #define ODIRSEPARATOR '\\'
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  #else
       *xmin=x;  #define DIRSEPARATOR '\\'
       return fx;  #define CHARSEPARATOR "\\"
     }  #define ODIRSEPARATOR '/'
     ftemp=fu;  #endif
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  /* $Id$ */
       q=(x-v)*(fx-fw);  /* $State$ */
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  char version[]="Imach version 0.98nR2, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
       if (q > 0.0) p = -p;  char fullversion[]="$Revision$ $Date$"; 
       q=fabs(q);  char strstart[80];
       etemp=e;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       e=d;  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  int nvar=0, nforce=0; /* Number of variables, number of forces */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
       else {  int npar=NPARMAX;
         d=p/q;  int nlstate=2; /* Number of live states */
         u=x+d;  int ndeath=1; /* Number of dead states */
         if (u-a < tol2 || b-u < tol2)  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
           d=SIGN(tol1,xm-x);  int popbased=0;
       }  
     } else {  int *wav; /* Number of waves for this individuual 0 is possible */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  int maxwav=0; /* Maxim number of waves */
     }  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
     fu=(*f)(u);  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
     if (fu <= fx) {                     to the likelihood and the sum of weights (done by funcone)*/
       if (u >= x) a=x; else b=x;  int mle=1, weightopt=0;
       SHFT(v,w,x,u)  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
         SHFT(fv,fw,fx,fu)  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
         } else {  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
           if (u < x) a=u; else b=u;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
           if (fu <= fw || w == x) {  double jmean=1; /* Mean space between 2 waves */
             v=w;  double **oldm, **newm, **savm; /* Working pointers to matrices */
             w=u;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
             fv=fw;  /*FILE *fic ; */ /* Used in readdata only */
             fw=fu;  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
           } else if (fu <= fv || v == x || v == w) {  FILE *ficlog, *ficrespow;
             v=u;  int globpr=0; /* Global variable for printing or not */
             fv=fu;  double fretone; /* Only one call to likelihood */
           }  long ipmx=0; /* Number of contributions */
         }  double sw; /* Sum of weights */
   }  char filerespow[FILENAMELENGTH];
   nrerror("Too many iterations in brent");  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   *xmin=x;  FILE *ficresilk;
   return fx;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 }  FILE *ficresprobmorprev;
   FILE *fichtm, *fichtmcov; /* Html File */
 /****************** mnbrak ***********************/  FILE *ficreseij;
   char filerese[FILENAMELENGTH];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  FILE *ficresstdeij;
             double (*func)(double))  char fileresstde[FILENAMELENGTH];
 {  FILE *ficrescveij;
   double ulim,u,r,q, dum;  char filerescve[FILENAMELENGTH];
   double fu;  FILE  *ficresvij;
    char fileresv[FILENAMELENGTH];
   *fa=(*func)(*ax);  FILE  *ficresvpl;
   *fb=(*func)(*bx);  char fileresvpl[FILENAMELENGTH];
   if (*fb > *fa) {  char title[MAXLINE];
     SHFT(dum,*ax,*bx,dum)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       SHFT(dum,*fb,*fa,dum)  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       }  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   *cx=(*bx)+GOLD*(*bx-*ax);  char command[FILENAMELENGTH];
   *fc=(*func)(*cx);  int  outcmd=0;
   while (*fb > *fc) {  
     r=(*bx-*ax)*(*fb-*fc);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     q=(*bx-*cx)*(*fb-*fa);  
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  char filelog[FILENAMELENGTH]; /* Log file */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  char filerest[FILENAMELENGTH];
     ulim=(*bx)+GLIMIT*(*cx-*bx);  char fileregp[FILENAMELENGTH];
     if ((*bx-u)*(u-*cx) > 0.0) {  char popfile[FILENAMELENGTH];
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       fu=(*func)(u);  
       if (fu < *fc) {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  struct timezone tzp;
           SHFT(*fb,*fc,fu,(*func)(u))  extern int gettimeofday();
           }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  long time_value;
       u=ulim;  extern long time();
       fu=(*func)(u);  char strcurr[80], strfor[80];
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);  char *endptr;
       fu=(*func)(u);  long lval;
     }  double dval;
     SHFT(*ax,*bx,*cx,u)  
       SHFT(*fa,*fb,*fc,fu)  #define NR_END 1
       }  #define FREE_ARG char*
 }  #define FTOL 1.0e-10
   
 /*************** linmin ************************/  #define NRANSI 
   #define ITMAX 200 
 int ncom;  
 double *pcom,*xicom;  #define TOL 2.0e-4 
 double (*nrfunc)(double []);  
    #define CGOLD 0.3819660 
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #define ZEPS 1.0e-10 
 {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  #define GOLD 1.618034 
   double f1dim(double x);  #define GLIMIT 100.0 
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define TINY 1.0e-20 
               double *fc, double (*func)(double));  
   int j;  static double maxarg1,maxarg2;
   double xx,xmin,bx,ax;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   double fx,fb,fa;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
      
   ncom=n;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   pcom=vector(1,n);  #define rint(a) floor(a+0.5)
   xicom=vector(1,n);  
   nrfunc=func;  static double sqrarg;
   for (j=1;j<=n;j++) {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
     pcom[j]=p[j];  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
     xicom[j]=xi[j];  int agegomp= AGEGOMP;
   }  
   ax=0.0;  int imx; 
   xx=1.0;  int stepm=1;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  /* Stepm, step in month: minimum step interpolation*/
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  int estepm;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 #endif  
   for (j=1;j<=n;j++) {  int m,nb;
     xi[j] *= xmin;  long *num;
     p[j] += xi[j];  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   free_vector(xicom,1,n);  double **pmmij, ***probs;
   free_vector(pcom,1,n);  double *ageexmed,*agecens;
 }  double dateintmean=0;
   
 /*************** powell ************************/  double *weight;
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  int **s; /* Status */
             double (*func)(double []))  double *agedc;
 {  double  **covar; /**< covar[i,j], value of jth covariate for individual i,
   void linmin(double p[], double xi[], int n, double *fret,                    * covar=matrix(0,NCOVMAX,1,n); 
               double (*func)(double []));                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
   int i,ibig,j;  double  idx; 
   double del,t,*pt,*ptt,*xit;  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
   double fp,fptt;  int **codtab; /**< codtab=imatrix(1,100,1,10); */
   double *xits;  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
   pt=vector(1,n);  double *lsurv, *lpop, *tpop;
   ptt=vector(1,n);  
   xit=vector(1,n);  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
   xits=vector(1,n);  double ftolhess; /**< Tolerance for computing hessian */
   *fret=(*func)(p);  
   for (j=1;j<=n;j++) pt[j]=p[j];  /**************** split *************************/
   for (*iter=1;;++(*iter)) {  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     fp=(*fret);  {
     ibig=0;    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
     del=0.0;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    */ 
     for (i=1;i<=n;i++)    char  *ss;                            /* pointer */
       printf(" %d %.12f",i, p[i]);    int   l1, l2;                         /* length counters */
     printf("\n");  
     for (i=1;i<=n;i++) {    l1 = strlen(path );                   /* length of path */
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       fptt=(*fret);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 #ifdef DEBUG    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       printf("fret=%lf \n",*fret);      strcpy( name, path );               /* we got the fullname name because no directory */
 #endif      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
       printf("%d",i);fflush(stdout);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       linmin(p,xit,n,fret,func);      /* get current working directory */
       if (fabs(fptt-(*fret)) > del) {      /*    extern  char* getcwd ( char *buf , int len);*/
         del=fabs(fptt-(*fret));      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
         ibig=i;        return( GLOCK_ERROR_GETCWD );
       }      }
 #ifdef DEBUG      /* got dirc from getcwd*/
       printf("%d %.12e",i,(*fret));      printf(" DIRC = %s \n",dirc);
       for (j=1;j<=n;j++) {    } else {                              /* strip direcotry from path */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      ss++;                               /* after this, the filename */
         printf(" x(%d)=%.12e",j,xit[j]);      l2 = strlen( ss );                  /* length of filename */
       }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       for(j=1;j<=n;j++)      strcpy( name, ss );         /* save file name */
         printf(" p=%.12e",p[j]);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       printf("\n");      dirc[l1-l2] = 0;                    /* add zero */
 #endif      printf(" DIRC2 = %s \n",dirc);
     }    }
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    /* We add a separator at the end of dirc if not exists */
 #ifdef DEBUG    l1 = strlen( dirc );                  /* length of directory */
       int k[2],l;    if( dirc[l1-1] != DIRSEPARATOR ){
       k[0]=1;      dirc[l1] =  DIRSEPARATOR;
       k[1]=-1;      dirc[l1+1] = 0; 
       printf("Max: %.12e",(*func)(p));      printf(" DIRC3 = %s \n",dirc);
       for (j=1;j<=n;j++)    }
         printf(" %.12e",p[j]);    ss = strrchr( name, '.' );            /* find last / */
       printf("\n");    if (ss >0){
       for(l=0;l<=1;l++) {      ss++;
         for (j=1;j<=n;j++) {      strcpy(ext,ss);                     /* save extension */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      l1= strlen( name);
           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)+1;
         }      strncpy( finame, name, l1-l2);
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));      finame[l1-l2]= 0;
       }    }
 #endif  
     return( 0 );                          /* we're done */
   }
       free_vector(xit,1,n);  
       free_vector(xits,1,n);  
       free_vector(ptt,1,n);  /******************************************/
       free_vector(pt,1,n);  
       return;  void replace_back_to_slash(char *s, char*t)
     }  {
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    int i;
     for (j=1;j<=n;j++) {    int lg=0;
       ptt[j]=2.0*p[j]-pt[j];    i=0;
       xit[j]=p[j]-pt[j];    lg=strlen(t);
       pt[j]=p[j];    for(i=0; i<= lg; i++) {
     }      (s[i] = t[i]);
     fptt=(*func)(ptt);      if (t[i]== '\\') s[i]='/';
     if (fptt < fp) {    }
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  }
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);  char *trimbb(char *out, char *in)
         for (j=1;j<=n;j++) {  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
           xi[j][ibig]=xi[j][n];    char *s;
           xi[j][n]=xit[j];    s=out;
         }    while (*in != '\0'){
 #ifdef DEBUG      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);        in++;
         for(j=1;j<=n;j++)      }
           printf(" %.12e",xit[j]);      *out++ = *in++;
         printf("\n");    }
 #endif    *out='\0';
       }    return s;
     }  }
   }  
 }  char *cutv(char *blocc, char *alocc, char *in, char occ)
   {
 /**** Prevalence limit ****************/    /* 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')
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)       gives blocc="abcdef2ghi" and alocc="j".
 {       If occ is not found blocc is null and alocc is equal to in. Returns alocc
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    */
      matrix by transitions matrix until convergence is reached */    char *s, *t;
     t=in;s=in;
   int i, ii,j,k;    while (*in != '\0'){
   double min, max, maxmin, maxmax,sumnew=0.;      while( *in == occ){
   double **matprod2();        *blocc++ = *in++;
   double **out, cov[NCOVMAX], **pmij();        s=in;
   double **newm;      }
   double agefin, delaymax=50 ; /* Max number of years to converge */      *blocc++ = *in++;
     }
   for (ii=1;ii<=nlstate+ndeath;ii++)    if (s == t) /* occ not found */
     for (j=1;j<=nlstate+ndeath;j++){      *(blocc-(in-s))='\0';
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    else
     }      *(blocc-(in-s)-1)='\0';
     in=s;
    cov[1]=1.;    while ( *in != '\0'){
        *alocc++ = *in++;
  /* 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;    *alocc='\0';
     /* Covariates have to be included here again */    return s;
      cov[2]=agefin;  }
    
       for (k=1; k<=cptcovn;k++) {  int nbocc(char *s, char occ)
         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]]);*/    int i,j=0;
       }    int lg=20;
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    i=0;
       for (k=1; k<=cptcovprod;k++)    lg=strlen(s);
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for(i=0; i<= lg; i++) {
     if  (s[i] == occ ) j++;
       /*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]);*/    return j;
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  }
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  
   /* void cutv(char *u,char *v, char*t, char occ) */
     savm=oldm;  /* { */
     oldm=newm;  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
     maxmax=0.;  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
     for(j=1;j<=nlstate;j++){  /*      gives u="abcdef2ghi" and v="j" *\/ */
       min=1.;  /*   int i,lg,j,p=0; */
       max=0.;  /*   i=0; */
       for(i=1; i<=nlstate; i++) {  /*   lg=strlen(t); */
         sumnew=0;  /*   for(j=0; j<=lg-1; j++) { */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
         prlim[i][j]= newm[i][j]/(1-sumnew);  /*   } */
         max=FMAX(max,prlim[i][j]);  
         min=FMIN(min,prlim[i][j]);  /*   for(j=0; j<p; j++) { */
       }  /*     (u[j] = t[j]); */
       maxmin=max-min;  /*   } */
       maxmax=FMAX(maxmax,maxmin);  /*      u[p]='\0'; */
     }  
     if(maxmax < ftolpl){  /*    for(j=0; j<= lg; j++) { */
       return prlim;  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
     }  /*   } */
   }  /* } */
 }  
   /********************** nrerror ********************/
 /*************** transition probabilities ***************/  
   void nrerror(char error_text[])
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  {
 {    fprintf(stderr,"ERREUR ...\n");
   double s1, s2;    fprintf(stderr,"%s\n",error_text);
   /*double t34;*/    exit(EXIT_FAILURE);
   int i,j,j1, nc, ii, jj;  }
   /*********************** vector *******************/
     for(i=1; i<= nlstate; i++){  double *vector(int nl, int nh)
     for(j=1; j<i;j++){  {
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    double *v;
         /*s2 += param[i][j][nc]*cov[nc];*/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    if (!v) nrerror("allocation failure in vector");
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    return v-nl+NR_END;
       }  }
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  /************************ free vector ******************/
     }  void free_vector(double*v, int nl, int nh)
     for(j=i+1; j<=nlstate+ndeath;j++){  {
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    free((FREE_ARG)(v+nl-NR_END));
         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);*/  
       }  /************************ivector *******************************/
       ps[i][j]=s2;  int *ivector(long nl,long nh)
     }  {
   }    int *v;
     /*ps[3][2]=1;*/    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
   for(i=1; i<= nlstate; i++){    return v-nl+NR_END;
      s1=0;  }
     for(j=1; j<i; j++)  
       s1+=exp(ps[i][j]);  /******************free ivector **************************/
     for(j=i+1; j<=nlstate+ndeath; j++)  void free_ivector(int *v, long nl, long nh)
       s1+=exp(ps[i][j]);  {
     ps[i][i]=1./(s1+1.);    free((FREE_ARG)(v+nl-NR_END));
     for(j=1; j<i; j++)  }
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     for(j=i+1; j<=nlstate+ndeath; j++)  /************************lvector *******************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  long *lvector(long nl,long nh)
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  {
   } /* end i */    long *v;
     v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    if (!v) nrerror("allocation failure in ivector");
     for(jj=1; jj<= nlstate+ndeath; jj++){    return v-nl+NR_END;
       ps[ii][jj]=0;  }
       ps[ii][ii]=1;  
     }  /******************free lvector **************************/
   }  void free_lvector(long *v, long nl, long nh)
   {
     free((FREE_ARG)(v+nl-NR_END));
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /******************* imatrix *******************************/
    }  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     printf("\n ");       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     }  { 
     printf("\n ");printf("%lf ",cov[2]);*/    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
 /*    int **m; 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    
   goto end;*/    /* allocate pointers to rows */ 
     return ps;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
 }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
 /**************** Product of 2 matrices ******************/    m -= nrl; 
     
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    
 {    /* allocate rows and set pointers to them */ 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   /* in, b, out are matrice of pointers which should have been initialized    m[nrl] += NR_END; 
      before: only the contents of out is modified. The function returns    m[nrl] -= ncl; 
      a pointer to pointers identical to out */    
   long i, j, k;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   for(i=nrl; i<= nrh; i++)    
     for(k=ncolol; k<=ncoloh; k++)    /* return pointer to array of pointers to rows */ 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    return m; 
         out[i][k] +=in[i][j]*b[j][k];  } 
   
   return out;  /****************** free_imatrix *************************/
 }  void free_imatrix(m,nrl,nrh,ncl,nch)
         int **m;
         long nch,ncl,nrh,nrl; 
 /************* Higher Matrix Product ***************/       /* free an int matrix allocated by imatrix() */ 
   { 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 {    free((FREE_ARG) (m+nrl-NR_END)); 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  } 
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  /******************* matrix *******************************/
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  double **matrix(long nrl, long nrh, long ncl, long nch)
      (typically every 2 years instead of every month which is too big).  {
      Model is determined by parameters x and covariates have to be    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
      included manually here.    double **m;
   
      */    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
   int i, j, d, h, k;    m += NR_END;
   double **out, cov[NCOVMAX];    m -= nrl;
   double **newm;  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   /* Hstepm could be zero and should return the unit matrix */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   for (i=1;i<=nlstate+ndeath;i++)    m[nrl] += NR_END;
     for (j=1;j<=nlstate+ndeath;j++){    m[nrl] -= ncl;
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     }    return m;
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
   for(h=1; h <=nhstepm; h++){     */
     for(d=1; d <=hstepm; d++){  }
       newm=savm;  
       /* Covariates have to be included here again */  /*************************free matrix ************************/
       cov[1]=1.;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  {
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       for (k=1; k<=cptcovage;k++)    free((FREE_ARG)(m+nrl-NR_END));
         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]]];  /******************* ma3x *******************************/
   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   {
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    double ***m;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       savm=oldm;    if (!m) nrerror("allocation failure 1 in matrix()");
       oldm=newm;    m += NR_END;
     }    m -= nrl;
     for(i=1; i<=nlstate+ndeath; i++)  
       for(j=1;j<=nlstate+ndeath;j++) {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         po[i][j][h]=newm[i][j];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    m[nrl] += NR_END;
          */    m[nrl] -= ncl;
       }  
   } /* end h */    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   return po;  
 }    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     m[nrl][ncl] += NR_END;
 /*************** log-likelihood *************/    m[nrl][ncl] -= nll;
 double func( double *x)    for (j=ncl+1; j<=nch; j++) 
 {      m[nrl][j]=m[nrl][j-1]+nlay;
   int i, ii, j, k, mi, d, kk;    
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    for (i=nrl+1; i<=nrh; i++) {
   double **out;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   double sw; /* Sum of weights */      for (j=ncl+1; j<=nch; j++) 
   double lli; /* Individual log likelihood */        m[i][j]=m[i][j-1]+nlay;
   long ipmx;    }
   /*extern weight */    return m; 
   /* We are differentiating ll according to initial status */    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   /*for(i=1;i<imx;i++)    */
     printf(" %d\n",s[4][i]);  }
   */  
   cov[1]=1.;  /*************************free ma3x ************************/
   void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   for(k=1; k<=nlstate; k++) ll[k]=0.;  {
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     for(mi=1; mi<= wav[i]-1; mi++){    free((FREE_ARG)(m+nrl-NR_END));
       for (ii=1;ii<=nlstate+ndeath;ii++)  }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
       for(d=0; d<dh[mi][i]; d++){  /*************** function subdirf ***********/
         newm=savm;  char *subdirf(char fileres[])
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  {
         for (kk=1; kk<=cptcovage;kk++) {    /* Caution optionfilefiname is hidden */
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    strcpy(tmpout,optionfilefiname);
         }    strcat(tmpout,"/"); /* Add to the right */
            strcat(tmpout,fileres);
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    return tmpout;
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  }
         savm=oldm;  
         oldm=newm;  /*************** function subdirf2 ***********/
          char *subdirf2(char fileres[], char *preop)
          {
       } /* end mult */    
          /* Caution optionfilefiname is hidden */
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    strcpy(tmpout,optionfilefiname);
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    strcat(tmpout,"/");
       ipmx +=1;    strcat(tmpout,preop);
       sw += weight[i];    strcat(tmpout,fileres);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    return tmpout;
     } /* end of wave */  }
   } /* end of individual */  
   /*************** function subdirf3 ***********/
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  char *subdirf3(char fileres[], char *preop, char *preop2)
   /* 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 */    
   return -l;    /* Caution optionfilefiname is hidden */
 }    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
     strcat(tmpout,preop);
 /*********** Maximum Likelihood Estimation ***************/    strcat(tmpout,preop2);
     strcat(tmpout,fileres);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    return tmpout;
 {  }
   int i,j, iter;  
   double **xi,*delti;  /***************** f1dim *************************/
   double fret;  extern int ncom; 
   xi=matrix(1,npar,1,npar);  extern double *pcom,*xicom;
   for (i=1;i<=npar;i++)  extern double (*nrfunc)(double []); 
     for (j=1;j<=npar;j++)   
       xi[i][j]=(i==j ? 1.0 : 0.0);  double f1dim(double x) 
   printf("Powell\n");  { 
   powell(p,xi,npar,ftol,&iter,&fret,func);    int j; 
     double f;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    double *xt; 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));   
     xt=vector(1,ncom); 
 }    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
 /**** Computes Hessian and covariance matrix ***/    free_vector(xt,1,ncom); 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    return f; 
 {  } 
   double  **a,**y,*x,pd;  
   double **hess;  /*****************brent *************************/
   int i, j,jk;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   int *indx;  { 
     int iter; 
   double hessii(double p[], double delta, int theta, double delti[]);    double a,b,d,etemp;
   double hessij(double p[], double delti[], int i, int j);    double fu,fv,fw,fx;
   void lubksb(double **a, int npar, int *indx, double b[]) ;    double ftemp;
   void ludcmp(double **a, int npar, int *indx, double *d) ;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     double e=0.0; 
   hess=matrix(1,npar,1,npar);   
     a=(ax < cx ? ax : cx); 
   printf("\nCalculation of the hessian matrix. Wait...\n");    b=(ax > cx ? ax : cx); 
   for (i=1;i<=npar;i++){    x=w=v=bx; 
     printf("%d",i);fflush(stdout);    fw=fv=fx=(*f)(x); 
     hess[i][i]=hessii(p,ftolhess,i,delti);    for (iter=1;iter<=ITMAX;iter++) { 
     /*printf(" %f ",p[i]);*/      xm=0.5*(a+b); 
     /*printf(" %lf ",hess[i][i]);*/      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   }      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
        printf(".");fflush(stdout);
   for (i=1;i<=npar;i++) {      fprintf(ficlog,".");fflush(ficlog);
     for (j=1;j<=npar;j++)  {  #ifdef DEBUG
       if (j>i) {      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
         printf(".%d%d",i,j);fflush(stdout);      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);
         hess[i][j]=hessij(p,delti,i,j);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
         hess[j][i]=hess[i][j];      #endif
         /*printf(" %lf ",hess[i][j]);*/      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
       }        *xmin=x; 
     }        return fx; 
   }      } 
   printf("\n");      ftemp=fu;
       if (fabs(e) > tol1) { 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        r=(x-w)*(fx-fv); 
          q=(x-v)*(fx-fw); 
   a=matrix(1,npar,1,npar);        p=(x-v)*q-(x-w)*r; 
   y=matrix(1,npar,1,npar);        q=2.0*(q-r); 
   x=vector(1,npar);        if (q > 0.0) p = -p; 
   indx=ivector(1,npar);        q=fabs(q); 
   for (i=1;i<=npar;i++)        etemp=e; 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];        e=d; 
   ludcmp(a,npar,indx,&pd);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
           d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   for (j=1;j<=npar;j++) {        else { 
     for (i=1;i<=npar;i++) x[i]=0;          d=p/q; 
     x[j]=1;          u=x+d; 
     lubksb(a,npar,indx,x);          if (u-a < tol2 || b-u < tol2) 
     for (i=1;i<=npar;i++){            d=SIGN(tol1,xm-x); 
       matcov[i][j]=x[i];        } 
     }      } else { 
   }        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
   printf("\n#Hessian matrix#\n");      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   for (i=1;i<=npar;i++) {      fu=(*f)(u); 
     for (j=1;j<=npar;j++) {      if (fu <= fx) { 
       printf("%.3e ",hess[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; 
   /* Recompute Inverse */            if (fu <= fw || w == x) { 
   for (i=1;i<=npar;i++)              v=w; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];              w=u; 
   ludcmp(a,npar,indx,&pd);              fv=fw; 
               fw=fu; 
   /*  printf("\n#Hessian matrix recomputed#\n");            } else if (fu <= fv || v == x || v == w) { 
               v=u; 
   for (j=1;j<=npar;j++) {              fv=fu; 
     for (i=1;i<=npar;i++) x[i]=0;            } 
     x[j]=1;          } 
     lubksb(a,npar,indx,x);    } 
     for (i=1;i<=npar;i++){    nrerror("Too many iterations in brent"); 
       y[i][j]=x[i];    *xmin=x; 
       printf("%.3e ",y[i][j]);    return fx; 
     }  } 
     printf("\n");  
   }  /****************** mnbrak ***********************/
   */  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   free_matrix(a,1,npar,1,npar);              double (*func)(double)) 
   free_matrix(y,1,npar,1,npar);  { 
   free_vector(x,1,npar);    double ulim,u,r,q, dum;
   free_ivector(indx,1,npar);    double fu; 
   free_matrix(hess,1,npar,1,npar);   
     *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
 }    if (*fb > *fa) { 
       SHFT(dum,*ax,*bx,dum) 
 /*************** hessian matrix ****************/        SHFT(dum,*fb,*fa,dum) 
 double hessii( double x[], double delta, int theta, double delti[])        } 
 {    *cx=(*bx)+GOLD*(*bx-*ax); 
   int i;    *fc=(*func)(*cx); 
   int l=1, lmax=20;    while (*fb > *fc) { 
   double k1,k2;      r=(*bx-*ax)*(*fb-*fc); 
   double p2[NPARMAX+1];      q=(*bx-*cx)*(*fb-*fa); 
   double res;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   double fx;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
   int k=0,kmax=10;      if ((*bx-u)*(u-*cx) > 0.0) { 
   double l1;        fu=(*func)(u); 
       } else if ((*cx-u)*(u-ulim) > 0.0) { 
   fx=func(x);        fu=(*func)(u); 
   for (i=1;i<=npar;i++) p2[i]=x[i];        if (fu < *fc) { 
   for(l=0 ; l <=lmax; l++){          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
     l1=pow(10,l);            SHFT(*fb,*fc,fu,(*func)(u)) 
     delts=delt;            } 
     for(k=1 ; k <kmax; k=k+1){      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       delt = delta*(l1*k);        u=ulim; 
       p2[theta]=x[theta] +delt;        fu=(*func)(u); 
       k1=func(p2)-fx;      } else { 
       p2[theta]=x[theta]-delt;        u=(*cx)+GOLD*(*cx-*bx); 
       k2=func(p2)-fx;        fu=(*func)(u); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */      } 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      SHFT(*ax,*bx,*cx,u) 
              SHFT(*fa,*fb,*fc,fu) 
 #ifdef DEBUG        } 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);  } 
 #endif  
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  /*************** linmin ************************/
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  
         k=kmax;  int ncom; 
       }  double *pcom,*xicom;
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  double (*nrfunc)(double []); 
         k=kmax; l=lmax*10.;   
       }  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  { 
         delts=delt;    double brent(double ax, double bx, double cx, 
       }                 double (*f)(double), double tol, double *xmin); 
     }    double f1dim(double x); 
   }    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   delti[theta]=delts;                double *fc, double (*func)(double)); 
   return res;    int j; 
      double xx,xmin,bx,ax; 
 }    double fx,fb,fa;
    
 double hessij( double x[], double delti[], int thetai,int thetaj)    ncom=n; 
 {    pcom=vector(1,n); 
   int i;    xicom=vector(1,n); 
   int l=1, l1, lmax=20;    nrfunc=func; 
   double k1,k2,k3,k4,res,fx;    for (j=1;j<=n;j++) { 
   double p2[NPARMAX+1];      pcom[j]=p[j]; 
   int k;      xicom[j]=xi[j]; 
     } 
   fx=func(x);    ax=0.0; 
   for (k=1; k<=2; k++) {    xx=1.0; 
     for (i=1;i<=npar;i++) p2[i]=x[i];    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  #ifdef DEBUG
     k1=func(p2)-fx;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
      fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     p2[thetai]=x[thetai]+delti[thetai]/k;  #endif
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    for (j=1;j<=n;j++) { 
     k2=func(p2)-fx;      xi[j] *= xmin; 
        p[j] += xi[j]; 
     p2[thetai]=x[thetai]-delti[thetai]/k;    } 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    free_vector(xicom,1,n); 
     k3=func(p2)-fx;    free_vector(pcom,1,n); 
    } 
     p2[thetai]=x[thetai]-delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  char *asc_diff_time(long time_sec, char ascdiff[])
     k4=func(p2)-fx;  {
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    long sec_left, days, hours, minutes;
 #ifdef DEBUG    days = (time_sec) / (60*60*24);
     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);    sec_left = (time_sec) % (60*60*24);
 #endif    hours = (sec_left) / (60*60) ;
   }    sec_left = (sec_left) %(60*60);
   return res;    minutes = (sec_left) /60;
 }    sec_left = (sec_left) % (60);
     sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
 /************** Inverse of matrix **************/    return ascdiff;
 void ludcmp(double **a, int n, int *indx, double *d)  }
 {  
   int i,imax,j,k;  /*************** powell ************************/
   double big,dum,sum,temp;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   double *vv;              double (*func)(double [])) 
    { 
   vv=vector(1,n);    void linmin(double p[], double xi[], int n, double *fret, 
   *d=1.0;                double (*func)(double [])); 
   for (i=1;i<=n;i++) {    int i,ibig,j; 
     big=0.0;    double del,t,*pt,*ptt,*xit;
     for (j=1;j<=n;j++)    double fp,fptt;
       if ((temp=fabs(a[i][j])) > big) big=temp;    double *xits;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    int niterf, itmp;
     vv[i]=1.0/big;  
   }    pt=vector(1,n); 
   for (j=1;j<=n;j++) {    ptt=vector(1,n); 
     for (i=1;i<j;i++) {    xit=vector(1,n); 
       sum=a[i][j];    xits=vector(1,n); 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    *fret=(*func)(p); 
       a[i][j]=sum;    for (j=1;j<=n;j++) pt[j]=p[j]; 
     }    for (*iter=1;;++(*iter)) { 
     big=0.0;      fp=(*fret); 
     for (i=j;i<=n;i++) {      ibig=0; 
       sum=a[i][j];      del=0.0; 
       for (k=1;k<j;k++)      last_time=curr_time;
         sum -= a[i][k]*a[k][j];      (void) gettimeofday(&curr_time,&tzp);
       a[i][j]=sum;      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);
       if ( (dum=vv[i]*fabs(sum)) >= big) {      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);
         big=dum;  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
         imax=i;     for (i=1;i<=n;i++) {
       }        printf(" %d %.12f",i, p[i]);
     }        fprintf(ficlog," %d %.12lf",i, p[i]);
     if (j != imax) {        fprintf(ficrespow," %.12lf", p[i]);
       for (k=1;k<=n;k++) {      }
         dum=a[imax][k];      printf("\n");
         a[imax][k]=a[j][k];      fprintf(ficlog,"\n");
         a[j][k]=dum;      fprintf(ficrespow,"\n");fflush(ficrespow);
       }      if(*iter <=3){
       *d = -(*d);        tm = *localtime(&curr_time.tv_sec);
       vv[imax]=vv[j];        strcpy(strcurr,asctime(&tm));
     }  /*       asctime_r(&tm,strcurr); */
     indx[j]=imax;        forecast_time=curr_time; 
     if (a[j][j] == 0.0) a[j][j]=TINY;        itmp = strlen(strcurr);
     if (j != n) {        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       dum=1.0/(a[j][j]);          strcurr[itmp-1]='\0';
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     }        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   }        for(niterf=10;niterf<=30;niterf+=10){
   free_vector(vv,1,n);  /* Doesn't work */          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
 ;          tmf = *localtime(&forecast_time.tv_sec);
 }  /*      asctime_r(&tmf,strfor); */
           strcpy(strfor,asctime(&tmf));
 void lubksb(double **a, int n, int *indx, double b[])          itmp = strlen(strfor);
 {          if(strfor[itmp-1]=='\n')
   int i,ii=0,ip,j;          strfor[itmp-1]='\0';
   double sum;          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);
            fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   for (i=1;i<=n;i++) {        }
     ip=indx[i];      }
     sum=b[ip];      for (i=1;i<=n;i++) { 
     b[ip]=b[i];        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
     if (ii)        fptt=(*fret); 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  #ifdef DEBUG
     else if (sum) ii=i;        printf("fret=%lf \n",*fret);
     b[i]=sum;        fprintf(ficlog,"fret=%lf \n",*fret);
   }  #endif
   for (i=n;i>=1;i--) {        printf("%d",i);fflush(stdout);
     sum=b[i];        fprintf(ficlog,"%d",i);fflush(ficlog);
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        linmin(p,xit,n,fret,func); 
     b[i]=sum/a[i][i];        if (fabs(fptt-(*fret)) > del) { 
   }          del=fabs(fptt-(*fret)); 
 }          ibig=i; 
         } 
 /************ Frequencies ********************/  #ifdef DEBUG
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)        printf("%d %.12e",i,(*fret));
 {  /* Some frequencies */        fprintf(ficlog,"%d %.12e",i,(*fret));
          for (j=1;j<=n;j++) {
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   double ***freq; /* Frequencies */          printf(" x(%d)=%.12e",j,xit[j]);
   double *pp;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   double pos, k2, dateintsum=0,k2cpt=0;        }
   FILE *ficresp;        for(j=1;j<=n;j++) {
   char fileresp[FILENAMELENGTH];          printf(" p=%.12e",p[j]);
            fprintf(ficlog," p=%.12e",p[j]);
   pp=vector(1,nlstate);        }
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        printf("\n");
   strcpy(fileresp,"p");        fprintf(ficlog,"\n");
   strcat(fileresp,fileres);  #endif
   if((ficresp=fopen(fileresp,"w"))==NULL) {      } 
     printf("Problem with prevalence resultfile: %s\n", fileresp);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     exit(0);  #ifdef DEBUG
   }        int k[2],l;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        k[0]=1;
   j1=0;        k[1]=-1;
          printf("Max: %.12e",(*func)(p));
   j=cptcoveff;        fprintf(ficlog,"Max: %.12e",(*func)(p));
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for (j=1;j<=n;j++) {
            printf(" %.12e",p[j]);
   for(k1=1; k1<=j;k1++){          fprintf(ficlog," %.12e",p[j]);
     for(i1=1; i1<=ncodemax[k1];i1++){        }
       j1++;        printf("\n");
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        fprintf(ficlog,"\n");
         scanf("%d", i);*/        for(l=0;l<=1;l++) {
       for (i=-1; i<=nlstate+ndeath; i++)            for (j=1;j<=n;j++) {
         for (jk=-1; jk<=nlstate+ndeath; jk++)              ptt[j]=p[j]+(p[j]-pt[j])*k[l];
           for(m=agemin; m <= agemax+3; m++)            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             freq[i][jk][m]=0;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                }
       dateintsum=0;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       k2cpt=0;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       for (i=1; i<=imx; i++) {        }
         bool=1;  #endif
         if  (cptcovn>0) {  
           for (z1=1; z1<=cptcoveff; z1++)  
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        free_vector(xit,1,n); 
               bool=0;        free_vector(xits,1,n); 
         }        free_vector(ptt,1,n); 
         if (bool==1) {        free_vector(pt,1,n); 
           for(m=firstpass; m<=lastpass; m++){        return; 
             k2=anint[m][i]+(mint[m][i]/12.);      } 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
               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]=2.0*p[j]-pt[j]; 
               if (m<lastpass) {        xit[j]=p[j]-pt[j]; 
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        pt[j]=p[j]; 
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      } 
               }      fptt=(*func)(ptt); 
                    if (fptt < fp) { 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
                 dateintsum=dateintsum+k2;        if (t < 0.0) { 
                 k2cpt++;          linmin(p,xit,n,fret,func); 
               }          for (j=1;j<=n;j++) { 
             }            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);
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           for(j=1;j<=n;j++){
       if  (cptcovn>0) {            printf(" %.12e",xit[j]);
         fprintf(ficresp, "\n#********** Variable ");            fprintf(ficlog," %.12e",xit[j]);
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          }
         fprintf(ficresp, "**********\n#");          printf("\n");
       }          fprintf(ficlog,"\n");
       for(i=1; i<=nlstate;i++)  #endif
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        }
       fprintf(ficresp, "\n");      } 
          } 
       for(i=(int)agemin; i <= (int)agemax+3; i++){  } 
         if(i==(int)agemax+3)  
           printf("Total");  /**** Prevalence limit (stable or period prevalence)  ****************/
         else  
           printf("Age %d", i);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
         for(jk=1; jk <=nlstate ; jk++){  {
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
             pp[jk] += freq[jk][m][i];       matrix by transitions matrix until convergence is reached */
         }  
         for(jk=1; jk <=nlstate ; jk++){    int i, ii,j,k;
           for(m=-1, pos=0; m <=0 ; m++)    double min, max, maxmin, maxmax,sumnew=0.;
             pos += freq[jk][m][i];    double **matprod2();
           if(pp[jk]>=1.e-10)    double **out, cov[NCOVMAX+1], **pmij();
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);    double **newm;
           else    double agefin, delaymax=50 ; /* Max number of years to converge */
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  
         }    for (ii=1;ii<=nlstate+ndeath;ii++)
       for (j=1;j<=nlstate+ndeath;j++){
         for(jk=1; jk <=nlstate ; jk++){        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      }
             pp[jk] += freq[jk][m][i];  
         }     cov[1]=1.;
    
         for(jk=1,pos=0; jk <=nlstate ; jk++)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           pos += pp[jk];    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
         for(jk=1; jk <=nlstate ; jk++){      newm=savm;
           if(pos>=1.e-5)      /* Covariates have to be included here again */
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);      cov[2]=agefin;
           else      
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);      for (k=1; k<=cptcovn;k++) {
           if( i <= (int) agemax){        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
             if(pos>=1.e-5){        /*        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]]);*/
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      }
               probs[i][jk][j1]= pp[jk]/pos;      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/      for (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]]];
             else      
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      /*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]);*/
         }      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
              out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
         for(jk=-1; jk <=nlstate+ndeath; jk++)      
           for(m=-1; m <=nlstate+ndeath; m++)      savm=oldm;
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      oldm=newm;
         if(i <= (int) agemax)      maxmax=0.;
           fprintf(ficresp,"\n");      for(j=1;j<=nlstate;j++){
         printf("\n");        min=1.;
       }        max=0.;
     }        for(i=1; i<=nlstate; i++) {
   }          sumnew=0;
   dateintmean=dateintsum/k2cpt;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
            prlim[i][j]= newm[i][j]/(1-sumnew);
   fclose(ficresp);          max=FMAX(max,prlim[i][j]);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          min=FMIN(min,prlim[i][j]);
   free_vector(pp,1,nlstate);        }
          maxmin=max-min;
   /* End of Freq */        maxmax=FMAX(maxmax,maxmin);
 }      }
       if(maxmax < ftolpl){
 /************ Prevalence ********************/        return prlim;
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)      }
 {  /* Some frequencies */    }
    }
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  
   double ***freq; /* Frequencies */  /*************** transition probabilities ***************/ 
   double *pp;  
   double pos, k2;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   {
   pp=vector(1,nlstate);    /* According to parameters values stored in x and the covariate's values stored in cov,
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);       computes the probability to be observed in state j being in state i by appying the
         model to the ncovmodel covariates (including constant and age).
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
   j1=0;       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
         ncth covariate in the global vector x is given by the formula:
   j=cptcoveff;       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   if (cptcovn<1) {j=1;ncodemax[1]=1;}       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
         Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
   for(k1=1; k1<=j;k1++){       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
     for(i1=1; i1<=ncodemax[k1];i1++){       Outputs ps[i][j] the probability to be observed in j being in j according to
       j1++;       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
          */
       for (i=-1; i<=nlstate+ndeath; i++)      double s1, lnpijopii;
         for (jk=-1; jk<=nlstate+ndeath; jk++)      /*double t34;*/
           for(m=agemin; m <= agemax+3; m++)    int i,j,j1, nc, ii, jj;
             freq[i][jk][m]=0;  
            for(i=1; i<= nlstate; i++){
       for (i=1; i<=imx; i++) {        for(j=1; j<i;j++){
         bool=1;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
         if  (cptcovn>0) {            /*lnpijopii += param[i][j][nc]*cov[nc];*/
           for (z1=1; z1<=cptcoveff; z1++)            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
               bool=0;          }
         }          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         if (bool==1) {  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
           for(m=firstpass; m<=lastpass; m++){        }
             k2=anint[m][i]+(mint[m][i]/12.);        for(j=i+1; j<=nlstate+ndeath;j++){
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
               if(agev[m][i]==0) agev[m][i]=agemax+1;            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
               if(agev[m][i]==1) agev[m][i]=agemax+2;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
               if (m<lastpass) {  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
                 if (calagedate>0)          }
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
                 else        }
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      }
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];      
               }      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(i=(int)agemin; i <= (int)agemax+3; i++){        }
         for(jk=1; jk <=nlstate ; jk++){        for(j=i+1; j<=nlstate+ndeath; j++){
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
             pp[jk] += freq[jk][m][i];          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }        }
         for(jk=1; jk <=nlstate ; jk++){        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
           for(m=-1, pos=0; m <=0 ; m++)        ps[i][i]=1./(s1+1.);
             pos += freq[jk][m][i];        /* Computing other pijs */
         }        for(j=1; j<i; j++)
                  ps[i][j]= exp(ps[i][j])*ps[i][i];
         for(jk=1; jk <=nlstate ; jk++){        for(j=i+1; j<=nlstate+ndeath; j++)
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          ps[i][j]= exp(ps[i][j])*ps[i][i];
             pp[jk] += freq[jk][m][i];        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         }      } /* end i */
              
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
                for(jj=1; jj<= nlstate+ndeath; jj++){
         for(jk=1; jk <=nlstate ; jk++){              ps[ii][jj]=0;
           if( i <= (int) agemax){          ps[ii][ii]=1;
             if(pos>=1.e-5){        }
               probs[i][jk][j1]= pp[jk]/pos;      }
             }      
           }  
         }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
          /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       }  /*         printf("ddd %lf ",ps[ii][jj]); */
     }  /*       } */
   }  /*       printf("\n "); */
   /*        } */
    /*        printf("\n ");printf("%lf ",cov[2]); */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);         /*
   free_vector(pp,1,nlstate);        for(i=1; i<= npar; i++) printf("%f ",x[i]);
          goto end;*/
 }  /* End of Freq */      return ps;
   }
 /************* Waves Concatenation ***************/  
   /**************** Product of 2 matrices ******************/
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)  
 {  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.  {
      Death is a valid wave (if date is known).    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    /* in, b, out are matrice of pointers which should have been initialized 
      and mw[mi+1][i]. dh depends on stepm.       before: only the contents of out is modified. The function returns
      */       a pointer to pointers identical to out */
     long i, j, k;
   int i, mi, m;    for(i=nrl; i<= nrh; i++)
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;      for(k=ncolol; k<=ncoloh; k++)
      double sum=0., jmean=0.;*/        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
   int j, k=0,jk, ju, jl;  
   double sum=0.;    return out;
   jmin=1e+5;  }
   jmax=-1;  
   jmean=0.;  
   for(i=1; i<=imx; i++){  /************* Higher Matrix Product ***************/
     mi=0;  
     m=firstpass;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     while(s[m][i] <= nlstate){  {
       if(s[m][i]>=1)    /* Computes the transition matrix starting at age 'age' over 
         mw[++mi][i]=m;       'nhstepm*hstepm*stepm' months (i.e. until
       if(m >=lastpass)       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
         break;       nhstepm*hstepm matrices. 
       else       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         m++;       (typically every 2 years instead of every month which is too big 
     }/* end while */       for the memory).
     if (s[m][i] > nlstate){       Model is determined by parameters x and covariates have to be 
       mi++;     /* Death is another wave */       included manually here. 
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */       */
       mw[mi][i]=m;  
     }    int i, j, d, h, k;
     double **out, cov[NCOVMAX+1];
     wav[i]=mi;    double **newm;
     if(mi==0)  
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    /* Hstepm could be zero and should return the unit matrix */
   }    for (i=1;i<=nlstate+ndeath;i++)
       for (j=1;j<=nlstate+ndeath;j++){
   for(i=1; i<=imx; i++){        oldm[i][j]=(i==j ? 1.0 : 0.0);
     for(mi=1; mi<wav[i];mi++){        po[i][j][0]=(i==j ? 1.0 : 0.0);
       if (stepm <=0)      }
         dh[mi][i]=1;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       else{    for(h=1; h <=nhstepm; h++){
         if (s[mw[mi+1][i]][i] > nlstate) {      for(d=1; d <=hstepm; d++){
           if (agedc[i] < 2*AGESUP) {        newm=savm;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);        /* Covariates have to be included here again */
           if(j==0) j=1;  /* Survives at least one month after exam */        cov[1]=1.;
           k=k+1;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
           if (j >= jmax) jmax=j;        for (k=1; k<=cptcovn;k++) 
           if (j <= jmin) jmin=j;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           sum=sum+j;        for (k=1; k<=cptcovage;k++)
           /*if (j<0) printf("j=%d num=%d \n",j,i); */          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]]];
         else{  
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  
           k=k+1;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
           if (j >= jmax) jmax=j;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           else if (j <= jmin)jmin=j;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */                     pmij(pmmij,cov,ncovmodel,x,nlstate));
           sum=sum+j;        savm=oldm;
         }        oldm=newm;
         jk= j/stepm;      }
         jl= j -jk*stepm;      for(i=1; i<=nlstate+ndeath; i++)
         ju= j -(jk+1)*stepm;        for(j=1;j<=nlstate+ndeath;j++) {
         if(jl <= -ju)          po[i][j][h]=newm[i][j];
           dh[mi][i]=jk;          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
         else        }
           dh[mi][i]=jk+1;      /*printf("h=%d ",h);*/
         if(dh[mi][i]==0)    } /* end h */
           dh[mi][i]=1; /* At least one step */  /*     printf("\n H=%d \n",h); */
       }    return po;
     }  }
   }  
   jmean=sum/k;  
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);  /*************** log-likelihood *************/
  }  double func( double *x)
 /*********** Tricode ****************************/  {
 void tricode(int *Tvar, int **nbcode, int imx)    int i, ii, j, k, mi, d, kk;
 {    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   int Ndum[20],ij=1, k, j, i;    double **out;
   int cptcode=0;    double sw; /* Sum of weights */
   cptcoveff=0;    double lli; /* Individual log likelihood */
      int s1, s2;
   for (k=0; k<19; k++) Ndum[k]=0;    double bbh, survp;
   for (k=1; k<=7; k++) ncodemax[k]=0;    long ipmx;
     /*extern weight */
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {    /* We are differentiating ll according to initial status */
     for (i=1; i<=imx; i++) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       ij=(int)(covar[Tvar[j]][i]);    /*for(i=1;i<imx;i++) 
       Ndum[ij]++;      printf(" %d\n",s[4][i]);
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    */
       if (ij > cptcode) cptcode=ij;    cov[1]=1.;
     }  
     for(k=1; k<=nlstate; k++) ll[k]=0.;
     for (i=0; i<=cptcode; i++) {  
       if(Ndum[i]!=0) ncodemax[j]++;    if(mle==1){
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     ij=1;        /* Computes the values of the ncovmodel covariates of the model
            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
     for (i=1; i<=ncodemax[j]; i++) {           to be observed in j being in i according to the model.
       for (k=0; k<=19; k++) {         */
         if (Ndum[k] != 0) {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           nbcode[Tvar[j]][ij]=k;        /* 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] 
           ij++;           has been calculated etc */
         }        for(mi=1; mi<= wav[i]-1; mi++){
         if (ij > ncodemax[j]) break;          for (ii=1;ii<=nlstate+ndeath;ii++)
       }              for (j=1;j<=nlstate+ndeath;j++){
     }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   }                savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
  for (k=0; k<19; k++) Ndum[k]=0;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
  for (i=1; i<=ncovmodel-2; i++) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       ij=Tvar[i];            for (kk=1; kk<=cptcovage;kk++) {
       Ndum[ij]++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
     }            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  ij=1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
  for (i=1; i<=10; i++) {            savm=oldm;
    if((Ndum[i]!=0) && (i<=ncovcol)){            oldm=newm;
      Tvaraff[ij]=i;          } /* end mult */
      ij++;        
    }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
  }          /* But now since version 0.9 we anticipate for bias at large stepm.
             * If stepm is larger than one month (smallest stepm) and if the exact delay 
     cptcoveff=ij-1;           * (in months) between two waves is not a multiple of stepm, we rounded to 
 }           * the nearest (and in case of equal distance, to the lowest) interval but now
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
 /*********** Health Expectancies ****************/           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
            * probability in order to take into account the bias as a fraction of the way
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
            * -stepm/2 to stepm/2 .
 {           * For stepm=1 the results are the same as for previous versions of Imach.
   /* Health expectancies */           * For stepm > 1 the results are less biased than in previous versions. 
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;           */
   double age, agelim, hf;          s1=s[mw[mi][i]][i];
   double ***p3mat,***varhe;          s2=s[mw[mi+1][i]][i];
   double **dnewm,**doldm;          bbh=(double)bh[mi][i]/(double)stepm; 
   double *xp;          /* bias bh is positive if real duration
   double **gp, **gm;           * is higher than the multiple of stepm and negative otherwise.
   double ***gradg, ***trgradg;           */
   int theta;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           if( s2 > nlstate){ 
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);            /* i.e. if s2 is a death state and if the date of death is known 
   xp=vector(1,npar);               then the contribution to the likelihood is the probability to 
   dnewm=matrix(1,nlstate*2,1,npar);               die between last step unit time and current  step unit time, 
   doldm=matrix(1,nlstate*2,1,nlstate*2);               which is also equal to probability to die before dh 
                 minus probability to die before dh-stepm . 
   fprintf(ficreseij,"# Health expectancies\n");               In version up to 0.92 likelihood was computed
   fprintf(ficreseij,"# Age");          as if date of death was unknown. Death was treated as any other
   for(i=1; i<=nlstate;i++)          health state: the date of the interview describes the actual state
     for(j=1; j<=nlstate;j++)          and not the date of a change in health state. The former idea was
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          to consider that at each interview the state was recorded
   fprintf(ficreseij,"\n");          (healthy, disable or death) and IMaCh was corrected; but when we
           introduced the exact date of death then we should have modified
   if(estepm < stepm){          the contribution of an exact death to the likelihood. This new
     printf ("Problem %d lower than %d\n",estepm, stepm);          contribution is smaller and very dependent of the step unit
   }          stepm. It is no more the probability to die between last interview
   else  hstepm=estepm;            and month of death but the probability to survive from last
   /* We compute the life expectancy from trapezoids spaced every estepm months          interview up to one month before death multiplied by the
    * This is mainly to measure the difference between two models: for example          probability to die within a month. Thanks to Chris
    * if stepm=24 months pijx are given only every 2 years and by summing them          Jackson for correcting this bug.  Former versions increased
    * we are calculating an estimate of the Life Expectancy assuming a linear          mortality artificially. The bad side is that we add another loop
    * progression inbetween and thus overestimating or underestimating according          which slows down the processing. The difference can be up to 10%
    * to the curvature of the survival function. If, for the same date, we          lower mortality.
    * 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            lli=log(out[s1][s2] - savm[s1][s2]);
    * hypothesis. A more precise result, taking into account a more precise  
    * curvature will be obtained if estepm is as small as stepm. */  
           } else if  (s2==-2) {
   /* For example we decided to compute the life expectancy with the smallest unit */            for (j=1,survp=0. ; j<=nlstate; j++) 
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
      nhstepm is the number of hstepm from age to agelim            /*survp += out[s1][j]; */
      nstepm is the number of stepm from age to agelin.            lli= log(survp);
      Look at hpijx to understand the reason of that which relies in memory size          }
      and note for a fixed period like estepm months */          
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          else if  (s2==-4) { 
      survival function given by stepm (the optimization length). Unfortunately it            for (j=3,survp=0. ; j<=nlstate; j++)  
      means that if the survival funtion is printed only each two years of age and if              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
      you sum them up and add 1 year (area under the trapezoids) you won't get the same            lli= log(survp); 
      results. So we changed our mind and took the option of the best precision.          } 
   */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          else if  (s2==-5) { 
             for (j=1,survp=0. ; j<=2; 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 age range expressed in number of stepm */          } 
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */          else{
     /* if (stepm >= YEARM) hstepm=1;*/            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            /*  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 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          } 
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     gp=matrix(0,nhstepm,1,nlstate*2);          /*if(lli ==000.0)*/
     gm=matrix(0,nhstepm,1,nlstate*2);          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
           ipmx +=1;
     /* Computed by stepm unit matrices, product of hstepm matrices, stored          sw += weight[i];
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);          } /* end of wave */
        } /* end of individual */
     }  else if(mle==2){
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     /* Computing Variances of health expectancies */        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
      for(theta=1; theta <=npar; theta++){            for (j=1;j<=nlstate+ndeath;j++){
       for(i=1; i<=npar; i++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for(d=0; d<=dh[mi][i]; d++){
              newm=savm;
       cptj=0;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(j=1; j<= nlstate; j++){            for (kk=1; kk<=cptcovage;kk++) {
         for(i=1; i<=nlstate; i++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           cptj=cptj+1;            }
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           }            savm=oldm;
         }            oldm=newm;
       }          } /* end mult */
              
                s1=s[mw[mi][i]][i];
       for(i=1; i<=npar; i++)          s2=s[mw[mi+1][i]][i];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          bbh=(double)bh[mi][i]/(double)stepm; 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
                ipmx +=1;
       cptj=0;          sw += weight[i];
       for(j=1; j<= nlstate; j++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(i=1;i<=nlstate;i++){        } /* end of wave */
           cptj=cptj+1;      } /* end of individual */
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){    }  else if(mle==3){  /* exponential inter-extrapolation */
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
       }          for (ii=1;ii<=nlstate+ndeath;ii++)
       for(j=1; j<= nlstate*2; j++)            for (j=1;j<=nlstate+ndeath;j++){
         for(h=0; h<=nhstepm-1; h++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            }
      }          for(d=0; d<dh[mi][i]; d++){
                newm=savm;
 /* End theta */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
      for(h=0; h<=nhstepm-1; h++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       for(j=1; j<=nlstate*2;j++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(theta=1; theta <=npar; theta++)            savm=oldm;
           trgradg[h][j][theta]=gradg[h][theta][j];            oldm=newm;
                } /* end mult */
         
      for(i=1;i<=nlstate*2;i++)          s1=s[mw[mi][i]][i];
       for(j=1;j<=nlstate*2;j++)          s2=s[mw[mi+1][i]][i];
         varhe[i][j][(int)age] =0.;          bbh=(double)bh[mi][i]/(double)stepm; 
           lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
      printf("%d|",(int)age);fflush(stdout);          ipmx +=1;
      for(h=0;h<=nhstepm-1;h++){          sw += weight[i];
       for(k=0;k<=nhstepm-1;k++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);        } /* end of wave */
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      } /* end of individual */
         for(i=1;i<=nlstate*2;i++)    }else if (mle==4){  /* ml=4 no inter-extrapolation */
           for(j=1;j<=nlstate*2;j++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
     /* Computing expectancies */            for (j=1;j<=nlstate+ndeath;j++){
     for(i=1; i<=nlstate;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate;j++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){            }
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          for(d=0; d<dh[mi][i]; d++){
                      newm=savm;
 /* 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]);*/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
     fprintf(ficreseij,"%3.0f",age );          
     cptj=0;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1; j<=nlstate;j++){            savm=oldm;
         cptj++;            oldm=newm;
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          } /* end mult */
       }        
     fprintf(ficreseij,"\n");          s1=s[mw[mi][i]][i];
              s2=s[mw[mi+1][i]][i];
     free_matrix(gm,0,nhstepm,1,nlstate*2);          if( s2 > nlstate){ 
     free_matrix(gp,0,nhstepm,1,nlstate*2);            lli=log(out[s1][s2] - savm[s1][s2]);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);          }else{
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          }
   }          ipmx +=1;
   printf("\n");          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   free_vector(xp,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]); */
   free_matrix(dnewm,1,nlstate*2,1,npar);        } /* end of wave */
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);      } /* end of individual */
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
 }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 /************ Variance ******************/        for(mi=1; mi<= wav[i]-1; mi++){
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)          for (ii=1;ii<=nlstate+ndeath;ii++)
 {            for (j=1;j<=nlstate+ndeath;j++){
   /* Variance of health expectancies */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **newm;            }
   double **dnewm,**doldm;          for(d=0; d<dh[mi][i]; d++){
   int i, j, nhstepm, hstepm, h, nstepm ;            newm=savm;
   int k, cptcode;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double *xp;            for (kk=1; kk<=cptcovage;kk++) {
   double **gp, **gm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double ***gradg, ***trgradg;            }
   double ***p3mat;          
   double age,agelim, hf;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int theta;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");            oldm=newm;
   fprintf(ficresvij,"# Age");          } /* end mult */
   for(i=1; i<=nlstate;i++)        
     for(j=1; j<=nlstate;j++)          s1=s[mw[mi][i]][i];
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          s2=s[mw[mi+1][i]][i];
   fprintf(ficresvij,"\n");          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
           ipmx +=1;
   xp=vector(1,npar);          sw += weight[i];
   dnewm=matrix(1,nlstate,1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   doldm=matrix(1,nlstate,1,nlstate);          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
          } /* end of wave */
   if(estepm < stepm){      } /* end of individual */
     printf ("Problem %d lower than %d\n",estepm, stepm);    } /* End of if */
   }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   else  hstepm=estepm;      /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   /* For example we decided to compute the life expectancy with the smallest unit */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.    return -l;
      nhstepm is the number of hstepm from age to agelim  }
      nstepm is the number of stepm from age to agelin.  
      Look at hpijx to understand the reason of that which relies in memory size  /*************** log-likelihood *************/
      and note for a fixed period like k years */  double funcone( double *x)
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the  {
      survival function given by stepm (the optimization length). Unfortunately it    /* Same as likeli but slower because of a lot of printf and if */
      means that if the survival funtion is printed only each two years of age and if    int i, ii, j, k, mi, d, kk;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
      results. So we changed our mind and took the option of the best precision.    double **out;
   */    double lli; /* Individual log likelihood */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    double llt;
   agelim = AGESUP;    int s1, s2;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    double bbh, survp;
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    /*extern weight */
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */    /* We are differentiating ll according to initial status */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    /*for(i=1;i<imx;i++) 
     gp=matrix(0,nhstepm,1,nlstate);      printf(" %d\n",s[4][i]);
     gm=matrix(0,nhstepm,1,nlstate);    */
     cov[1]=1.;
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */    for(k=1; k<=nlstate; k++) ll[k]=0.;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for(mi=1; mi<= wav[i]-1; mi++){
         for (ii=1;ii<=nlstate+ndeath;ii++)
       if (popbased==1) {          for (j=1;j<=nlstate+ndeath;j++){
         for(i=1; i<=nlstate;i++)            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           prlim[i][i]=probs[(int)age][i][ij];            savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }          }
          for(d=0; d<dh[mi][i]; d++){
       for(j=1; j<= nlstate; j++){          newm=savm;
         for(h=0; h<=nhstepm; h++){          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          for (kk=1; kk<=cptcovage;kk++) {
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         }          }
       }          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(i=1; i<=npar; i++) /* Computes gradient */          savm=oldm;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          oldm=newm;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          } /* end mult */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        
          s1=s[mw[mi][i]][i];
       if (popbased==1) {        s2=s[mw[mi+1][i]][i];
         for(i=1; i<=nlstate;i++)        bbh=(double)bh[mi][i]/(double)stepm; 
           prlim[i][i]=probs[(int)age][i][ij];        /* bias is positive if real duration
       }         * is higher than the multiple of stepm and negative otherwise.
          */
       for(j=1; j<= nlstate; j++){        if( s2 > nlstate && (mle <5) ){  /* Jackson */
         for(h=0; h<=nhstepm; h++){          lli=log(out[s1][s2] - savm[s1][s2]);
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        } else if  (s2==-2) {
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          for (j=1,survp=0. ; j<=nlstate; j++) 
         }            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       }          lli= log(survp);
         }else if (mle==1){
       for(j=1; j<= nlstate; j++)          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         for(h=0; h<=nhstepm; h++){        } else if(mle==2){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         }        } else if(mle==3){  /* exponential inter-extrapolation */
     } /* End theta */          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 */
         } else if (mle==4){  /* mle=4 no inter-extrapolation */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          lli=log(out[s1][s2]); /* Original formula */
         } else{  /* mle=0 back to 1 */
     for(h=0; h<=nhstepm; h++)          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for(j=1; j<=nlstate;j++)          /*lli=log(out[s1][s2]); */ /* Original formula */
         for(theta=1; theta <=npar; theta++)        } /* End of if */
           trgradg[h][j][theta]=gradg[h][theta][j];        ipmx +=1;
         sw += weight[i];
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for(i=1;i<=nlstate;i++)        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
       for(j=1;j<=nlstate;j++)        if(globpr){
         vareij[i][j][(int)age] =0.;          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
    %11.6f %11.6f %11.6f ", \
     for(h=0;h<=nhstepm;h++){                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
       for(k=0;k<=nhstepm;k++){                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);            llt +=ll[k]*gipmx/gsw;
         for(i=1;i<=nlstate;i++)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           for(j=1;j<=nlstate;j++)          }
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;          fprintf(ficresilk," %10.6f\n", -llt);
       }        }
     }      } /* end of wave */
     } /* end of individual */
     fprintf(ficresvij,"%.0f ",age );    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     for(i=1; i<=nlstate;i++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       for(j=1; j<=nlstate;j++){    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    if(globpr==0){ /* First time we count the contributions and weights */
       }      gipmx=ipmx;
     fprintf(ficresvij,"\n");      gsw=sw;
     free_matrix(gp,0,nhstepm,1,nlstate);    }
     free_matrix(gm,0,nhstepm,1,nlstate);    return -l;
     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 */  /*************** function likelione ***********/
    void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   free_vector(xp,1,npar);  {
   free_matrix(doldm,1,nlstate,1,npar);    /* This routine should help understanding what is done with 
   free_matrix(dnewm,1,nlstate,1,nlstate);       the selection of individuals/waves and
        to check the exact contribution to the likelihood.
 }       Plotting could be done.
      */
 /************ Variance of prevlim ******************/    int k;
 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)  
 {    if(*globpri !=0){ /* Just counts and sums, no printings */
   /* Variance of prevalence limit */      strcpy(fileresilk,"ilk"); 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      strcat(fileresilk,fileres);
   double **newm;      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   double **dnewm,**doldm;        printf("Problem with resultfile: %s\n", fileresilk);
   int i, j, nhstepm, hstepm;        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
   int k, cptcode;      }
   double *xp;      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
   double *gp, *gm;      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   double **gradg, **trgradg;      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
   double age,agelim;      for(k=1; k<=nlstate; k++) 
   int theta;        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
          fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");    }
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)    *fretone=(*funcone)(p);
       fprintf(ficresvpl," %1d-%1d",i,i);    if(*globpri !=0){
   fprintf(ficresvpl,"\n");      fclose(ficresilk);
       fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   xp=vector(1,npar);      fflush(fichtm); 
   dnewm=matrix(1,nlstate,1,npar);    } 
   doldm=matrix(1,nlstate,1,nlstate);    return;
    }
   hstepm=1*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;  /*********** Maximum Likelihood Estimation ***************/
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     if (stepm >= YEARM) hstepm=1;  {
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    int i,j, iter;
     gradg=matrix(1,npar,1,nlstate);    double **xi;
     gp=vector(1,nlstate);    double fret;
     gm=vector(1,nlstate);    double fretone; /* Only one call to likelihood */
     /*  char filerespow[FILENAMELENGTH];*/
     for(theta=1; theta <=npar; theta++){    xi=matrix(1,npar,1,npar);
       for(i=1; i<=npar; i++){ /* Computes gradient */    for (i=1;i<=npar;i++)
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for (j=1;j<=npar;j++)
       }        xi[i][j]=(i==j ? 1.0 : 0.0);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
       for(i=1;i<=nlstate;i++)    strcpy(filerespow,"pow"); 
         gp[i] = prlim[i][i];    strcat(filerespow,fileres);
        if((ficrespow=fopen(filerespow,"w"))==NULL) {
       for(i=1; i<=npar; i++) /* Computes gradient */      printf("Problem with resultfile: %s\n", filerespow);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    }
       for(i=1;i<=nlstate;i++)    fprintf(ficrespow,"# Powell\n# iter -2*LL");
         gm[i] = prlim[i][i];    for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate+ndeath;j++)
       for(i=1;i<=nlstate;i++)        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    fprintf(ficrespow,"\n");
     } /* End theta */  
     powell(p,xi,npar,ftol,&iter,&fret,func);
     trgradg =matrix(1,nlstate,1,npar);  
     free_matrix(xi,1,npar,1,npar);
     for(j=1; j<=nlstate;j++)    fclose(ficrespow);
       for(theta=1; theta <=npar; theta++)    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         trgradg[j][theta]=gradg[theta][j];    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     for(i=1;i<=nlstate;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);  /**** Computes Hessian and covariance matrix ***/
     for(i=1;i<=nlstate;i++)  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  {
     double  **a,**y,*x,pd;
     fprintf(ficresvpl,"%.0f ",age );    double **hess;
     for(i=1; i<=nlstate;i++)    int i, j,jk;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    int *indx;
     fprintf(ficresvpl,"\n");  
     free_vector(gp,1,nlstate);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     free_vector(gm,1,nlstate);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     free_matrix(gradg,1,npar,1,nlstate);    void lubksb(double **a, int npar, int *indx, double b[]) ;
     free_matrix(trgradg,1,nlstate,1,npar);    void ludcmp(double **a, int npar, int *indx, double *d) ;
   } /* End age */    double gompertz(double p[]);
     hess=matrix(1,npar,1,npar);
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    printf("\nCalculation of the hessian matrix. Wait...\n");
   free_matrix(dnewm,1,nlstate,1,nlstate);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     for (i=1;i<=npar;i++){
 }      printf("%d",i);fflush(stdout);
       fprintf(ficlog,"%d",i);fflush(ficlog);
 /************ 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)       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
 {      
   int i, j,  i1, k1, l1;      /*  printf(" %f ",p[i]);
   int k2, l2, j1,  z1;          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   int k=0,l, cptcode;    }
   int first=1;    
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;    for (i=1;i<=npar;i++) {
   double **dnewm,**doldm;      for (j=1;j<=npar;j++)  {
   double *xp;        if (j>i) { 
   double *gp, *gm;          printf(".%d%d",i,j);fflush(stdout);
   double **gradg, **trgradg;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double **mu;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double age,agelim, cov[NCOVMAX];          
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */          hess[j][i]=hess[i][j];    
   int theta;          /*printf(" %lf ",hess[i][j]);*/
   char fileresprob[FILENAMELENGTH];        }
   char fileresprobcov[FILENAMELENGTH];      }
   char fileresprobcor[FILENAMELENGTH];    }
     printf("\n");
   double ***varpij;    fprintf(ficlog,"\n");
   
   strcpy(fileresprob,"prob");    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   strcat(fileresprob,fileres);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    
     printf("Problem with resultfile: %s\n", fileresprob);    a=matrix(1,npar,1,npar);
   }    y=matrix(1,npar,1,npar);
   strcpy(fileresprobcov,"probcov");    x=vector(1,npar);
   strcat(fileresprobcov,fileres);    indx=ivector(1,npar);
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    for (i=1;i<=npar;i++)
     printf("Problem with resultfile: %s\n", fileresprobcov);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   }    ludcmp(a,npar,indx,&pd);
   strcpy(fileresprobcor,"probcor");  
   strcat(fileresprobcor,fileres);    for (j=1;j<=npar;j++) {
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {      for (i=1;i<=npar;i++) x[i]=0;
     printf("Problem with resultfile: %s\n", fileresprobcor);      x[j]=1;
   }      lubksb(a,npar,indx,x);
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);      for (i=1;i<=npar;i++){ 
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);        matcov[i][j]=x[i];
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      }
      }
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");  
   fprintf(ficresprob,"# Age");    printf("\n#Hessian matrix#\n");
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");    fprintf(ficlog,"\n#Hessian matrix#\n");
   fprintf(ficresprobcov,"# Age");    for (i=1;i<=npar;i++) { 
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");      for (j=1;j<=npar;j++) { 
   fprintf(ficresprobcov,"# Age");        printf("%.3e ",hess[i][j]);
         fprintf(ficlog,"%.3e ",hess[i][j]);
       }
   for(i=1; i<=nlstate;i++)      printf("\n");
     for(j=1; j<=(nlstate+ndeath);j++){      fprintf(ficlog,"\n");
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    }
       fprintf(ficresprobcov," p%1d-%1d ",i,j);  
       fprintf(ficresprobcor," p%1d-%1d ",i,j);    /* Recompute Inverse */
     }      for (i=1;i<=npar;i++)
   fprintf(ficresprob,"\n");      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   fprintf(ficresprobcov,"\n");    ludcmp(a,npar,indx,&pd);
   fprintf(ficresprobcor,"\n");  
   xp=vector(1,npar);    /*  printf("\n#Hessian matrix recomputed#\n");
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);  
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));    for (j=1;j<=npar;j++) {
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);      for (i=1;i<=npar;i++) x[i]=0;
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);      x[j]=1;
   first=1;      lubksb(a,npar,indx,x);
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      for (i=1;i<=npar;i++){ 
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);        y[i][j]=x[i];
     exit(0);        printf("%.3e ",y[i][j]);
   }        fprintf(ficlog,"%.3e ",y[i][j]);
   else{      }
     fprintf(ficgp,"\n# Routine varprob");      printf("\n");
   }      fprintf(ficlog,"\n");
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    }
     printf("Problem with html file: %s\n", optionfilehtm);    */
     exit(0);  
   }    free_matrix(a,1,npar,1,npar);
   else{    free_matrix(y,1,npar,1,npar);
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");    free_vector(x,1,npar);
     fprintf(fichtm,"\n<br> We have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");    free_ivector(indx,1,npar);
     fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix 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> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");    free_matrix(hess,1,npar,1,npar);
   
   }  
   cov[1]=1;  }
   j=cptcoveff;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  /*************** hessian matrix ****************/
   j1=0;  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   for(k1=1; k1<=1;k1++){  {
     for(i1=1; i1<=ncodemax[k1];i1++){    int i;
     j1++;    int l=1, lmax=20;
     double k1,k2;
     if  (cptcovn>0) {    double p2[MAXPARM+1]; /* identical to x */
       fprintf(ficresprob, "\n#********** Variable ");    double res;
       fprintf(ficresprobcov, "\n#********** Variable ");    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       fprintf(ficgp, "\n#********** Variable ");    double fx;
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");    int k=0,kmax=10;
       fprintf(ficresprobcor, "\n#********** Variable ");    double l1;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  
       fprintf(ficresprob, "**********\n#");    fx=func(x);
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    for (i=1;i<=npar;i++) p2[i]=x[i];
       fprintf(ficresprobcov, "**********\n#");    for(l=0 ; l <=lmax; l++){
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      l1=pow(10,l);
       fprintf(ficgp, "**********\n#");      delts=delt;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      for(k=1 ; k <kmax; k=k+1){
       fprintf(ficgp, "**********\n#");        delt = delta*(l1*k);
       for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        p2[theta]=x[theta] +delt;
       fprintf(fichtm, "**********\n#");        k1=func(p2)-fx;
     }        p2[theta]=x[theta]-delt;
            k2=func(p2)-fx;
       for (age=bage; age<=fage; age ++){        /*res= (k1-2.0*fx+k2)/delt/delt; */
         cov[2]=age;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         for (k=1; k<=cptcovn;k++) {        
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];  #ifdef DEBUGHESS
         }        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];        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);
         for (k=1; k<=cptcovprod;k++)  #endif
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
                if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));          k=kmax;
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);        }
         gp=vector(1,(nlstate)*(nlstate+ndeath));        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
         gm=vector(1,(nlstate)*(nlstate+ndeath));          k=kmax; l=lmax*10.;
            }
         for(theta=1; theta <=npar; theta++){        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
           for(i=1; i<=npar; i++)          delts=delt;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);        }
                }
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    }
              delti[theta]=delts;
           k=0;    return res; 
           for(i=1; i<= (nlstate); i++){    
             for(j=1; j<=(nlstate+ndeath);j++){  }
               k=k+1;  
               gp[k]=pmmij[i][j];  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
             }  {
           }    int i;
              int l=1, l1, lmax=20;
           for(i=1; i<=npar; i++)    double k1,k2,k3,k4,res,fx;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);    double p2[MAXPARM+1];
        int k;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);  
           k=0;    fx=func(x);
           for(i=1; i<=(nlstate); i++){    for (k=1; k<=2; k++) {
             for(j=1; j<=(nlstate+ndeath);j++){      for (i=1;i<=npar;i++) p2[i]=x[i];
               k=k+1;      p2[thetai]=x[thetai]+delti[thetai]/k;
               gm[k]=pmmij[i][j];      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
             }      k1=func(p2)-fx;
           }    
            p2[thetai]=x[thetai]+delti[thetai]/k;
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        k2=func(p2)-fx;
         }    
       p2[thetai]=x[thetai]-delti[thetai]/k;
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           for(theta=1; theta <=npar; theta++)      k3=func(p2)-fx;
             trgradg[j][theta]=gradg[theta][j];    
              p2[thetai]=x[thetai]-delti[thetai]/k;
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);      k4=func(p2)-fx;
              res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
         pmij(pmmij,cov,ncovmodel,x,nlstate);  #ifdef DEBUG
              printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         k=0;      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);
         for(i=1; i<=(nlstate); i++){  #endif
           for(j=1; j<=(nlstate+ndeath);j++){    }
             k=k+1;    return res;
             mu[k][(int) age]=pmmij[i][j];  }
           }  
         }  /************** Inverse of matrix **************/
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)  void ludcmp(double **a, int n, int *indx, double *d) 
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)  { 
             varpij[i][j][(int)age] = doldm[i][j];    int i,imax,j,k; 
     double big,dum,sum,temp; 
         /*printf("\n%d ",(int)age);    double *vv; 
      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]));    vv=vector(1,n); 
      }*/    *d=1.0; 
     for (i=1;i<=n;i++) { 
         fprintf(ficresprob,"\n%d ",(int)age);      big=0.0; 
         fprintf(ficresprobcov,"\n%d ",(int)age);      for (j=1;j<=n;j++) 
         fprintf(ficresprobcor,"\n%d ",(int)age);        if ((temp=fabs(a[i][j])) > big) big=temp; 
       if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)      vv[i]=1.0/big; 
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));    } 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){    for (j=1;j<=n;j++) { 
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);      for (i=1;i<j;i++) { 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);        sum=a[i][j]; 
         }        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         i=0;        a[i][j]=sum; 
         for (k=1; k<=(nlstate);k++){      } 
           for (l=1; l<=(nlstate+ndeath);l++){      big=0.0; 
             i=i++;      for (i=j;i<=n;i++) { 
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);        sum=a[i][j]; 
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);        for (k=1;k<j;k++) 
             for (j=1; j<=i;j++){          sum -= a[i][k]*a[k][j]; 
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);        a[i][j]=sum; 
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));        if ( (dum=vv[i]*fabs(sum)) >= big) { 
             }          big=dum; 
           }          imax=i; 
         }/* end of loop for state */        } 
       } /* end of loop for age */      } 
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/      if (j != imax) { 
       for (k1=1; k1<=(nlstate);k1++){        for (k=1;k<=n;k++) { 
         for (l1=1; l1<=(nlstate+ndeath);l1++){          dum=a[imax][k]; 
           if(l1==k1) continue;          a[imax][k]=a[j][k]; 
           i=(k1-1)*(nlstate+ndeath)+l1;          a[j][k]=dum; 
           for (k2=1; k2<=(nlstate);k2++){        } 
             for (l2=1; l2<=(nlstate+ndeath);l2++){        *d = -(*d); 
               if(l2==k2) continue;        vv[imax]=vv[j]; 
               j=(k2-1)*(nlstate+ndeath)+l2;      } 
               if(j<=i) continue;      indx[j]=imax; 
               for (age=bage; age<=fage; age ++){      if (a[j][j] == 0.0) a[j][j]=TINY; 
                 if ((int)age %5==0){      if (j != n) { 
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;        dum=1.0/(a[j][j]); 
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;      } 
                   mu1=mu[i][(int) age]/stepm*YEARM ;    } 
                   mu2=mu[j][(int) age]/stepm*YEARM;    free_vector(vv,1,n);  /* Doesn't work */
                   /* Computing eigen value of matrix of covariance */  ;
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  } 
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);  void lubksb(double **a, int n, int *indx, double b[]) 
                   /* Eigen vectors */  { 
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));    int i,ii=0,ip,j; 
                   v21=sqrt(1.-v11*v11);    double sum; 
                   v12=-v21;   
                   v22=v11;    for (i=1;i<=n;i++) { 
                   /*printf(fignu*/      ip=indx[i]; 
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */      sum=b[ip]; 
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */      b[ip]=b[i]; 
                   if(first==1){      if (ii) 
                     first=0;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
                     fprintf(ficgp,"\nset parametric;set nolabel");      else if (sum) ii=i; 
                     fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1);      b[i]=sum; 
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");    } 
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%1d%1d-%1d%1d.png\">varpijgr%s%1d%1d-%1d%1d.png</A>, ",k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1);    for (i=n;i>=1;i--) { 
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);      sum=b[i]; 
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);      b[i]=sum/a[i][i]; 
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    } 
                     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)) t \"%d\"",\  } 
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \  
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);  void pstamp(FILE *fichier)
                   }else{  {
                     first=0;    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);  }
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);  
                     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)) t \"%d\"",\  /************ Frequencies ********************/
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \  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[])
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);  {  /* Some frequencies */
                   }/* if first */    
                 } /* age mod 5 */    int i, m, jk, k1,i1, j1, bool, z1,j;
               } /* end loop age */    int first;
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);    double ***freq; /* Frequencies */
               first=1;    double *pp, **prop;
             } /*l12 */    double pos,posprop, k2, dateintsum=0,k2cpt=0;
           } /* k12 */    char fileresp[FILENAMELENGTH];
         } /*l1 */    
       }/* k1 */    pp=vector(1,nlstate);
     } /* loop covariates */    prop=matrix(1,nlstate,iagemin,iagemax+3);
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);    strcpy(fileresp,"p");
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    strcat(fileresp,fileres);
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    if((ficresp=fopen(fileresp,"w"))==NULL) {
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);      printf("Problem with prevalence resultfile: %s\n", fileresp);
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      exit(0);
   }    }
   free_vector(xp,1,npar);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
   fclose(ficresprob);    j1=0;
   fclose(ficresprobcov);    
   fclose(ficresprobcor);    j=cptcoveff;
   fclose(ficgp);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   fclose(fichtm);  
 }    first=1;
   
     for(k1=1; k1<=j;k1++){   /* Loop on covariates */
 /******************* Printing html file ***********/      for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        j1++;
                   int lastpass, int stepm, int weightopt, char model[],\        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\          scanf("%d", i);*/
                   int popforecast, int estepm ,\        for (i=-5; i<=nlstate+ndeath; i++)  
                   double jprev1, double mprev1,double anprev1, \          for (jk=-5; jk<=nlstate+ndeath; jk++)  
                   double jprev2, double mprev2,double anprev2){            for(m=iagemin; m <= iagemax+3; m++)
   int jj1, k1, i1, cpt;              freq[i][jk][m]=0;
   /*char optionfilehtm[FILENAMELENGTH];*/        
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {        for (i=1; i<=nlstate; i++)  
     printf("Problem with %s \n",optionfilehtm), exit(0);          for(m=iagemin; m <= iagemax+3; m++)
   }            prop[i][m]=0;
         
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n        dateintsum=0;
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n        k2cpt=0;
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n        for (i=1; i<=imx; i++) {
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n          bool=1;
  - Life expectancies by age and initial health status (estepm=%2d months):          if  (cptcovn>0) {
    <a href=\"e%s\">e%s</a> <br>\n</li>", \            for (z1=1; z1<=cptcoveff; z1++) 
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n          }
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          if (bool==1){
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n            for(m=firstpass; m<=lastpass; m++){
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n              k2=anint[m][i]+(mint[m][i]/12.);
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n                if(agev[m][i]==0) agev[m][i]=iagemax+1;
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n                if(agev[m][i]==1) agev[m][i]=iagemax+2;
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                 if (m<lastpass) {
  if(popforecast==1) fprintf(fichtm,"\n                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n                }
         <br>",fileres,fileres,fileres,fileres);                
  else                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
    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);                  dateintsum=dateintsum+k2;
 fprintf(fichtm," <li>Graphs</li><p>");                  k2cpt++;
                 }
  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++){        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
      jj1++;        pstamp(ficresp);
      if (cptcovn > 0) {        if  (cptcovn>0) {
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");          fprintf(ficresp, "\n#********** Variable "); 
        for (cpt=1; cpt<=cptcoveff;cpt++)          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);          fprintf(ficresp, "**********\n#");
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");          fprintf(ficlog, "\n#********** Variable "); 
      }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
      /* Pij */          fprintf(ficlog, "**********\n#");
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>        }
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);            for(i=1; i<=nlstate;i++) 
      /* Quasi-incidences */          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
      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: pe%s%d2.png<br>        fprintf(ficresp, "\n");
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        
        /* Stable prevalence in each health state */        for(i=iagemin; i <= iagemax+3; i++){
        for(cpt=1; cpt<nlstate;cpt++){          if(i==iagemax+3){
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>            fprintf(ficlog,"Total");
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          }else{
        }            if(first==1){
     for(cpt=1; cpt<=nlstate;cpt++) {              first=0;
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              printf("See log file for details...\n");
 interval) in state (%d): v%s%d%d.png <br>            }
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              fprintf(ficlog,"Age %d", i);
      }          }
      for(cpt=1; cpt<=nlstate;cpt++) {          for(jk=1; jk <=nlstate ; jk++){
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              pp[jk] += freq[jk][m][i]; 
      }          }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          for(jk=1; jk <=nlstate ; jk++){
 health expectancies in states (1) and (2): e%s%d.png<br>            for(m=-1, pos=0; m <=0 ; m++)
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              pos += freq[jk][m][i];
    }            if(pp[jk]>=1.e-10){
  }              if(first==1){
 fclose(fichtm);                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 }              }
               fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 /******************* Gnuplot file **************/            }else{
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){              if(first==1)
                 printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   int ng;            }
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {          }
     printf("Problem with file %s",optionfilegnuplot);  
   }          for(jk=1; jk <=nlstate ; jk++){
             for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
 #ifdef windows              pp[jk] += freq[jk][m][i];
     fprintf(ficgp,"cd \"%s\" \n",pathc);          }       
 #endif          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
 m=pow(2,cptcoveff);            pos += pp[jk];
              posprop += prop[jk][i];
  /* 1eme*/          }
   for (cpt=1; cpt<= nlstate ; cpt ++) {          for(jk=1; jk <=nlstate ; jk++){
    for (k1=1; k1<= m ; k1 ++) {            if(pos>=1.e-5){
               if(first==1)
 #ifdef windows                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);            }else{
 #endif              if(first==1)
 #ifdef unix                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);            }
 #endif            if( i <= iagemax){
               if(pos>=1.e-5){
 for (i=1; i<= nlstate ; i ++) {                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");                /*probs[i][jk][j1]= pp[jk]/pos;*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
 }              }
     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
     for (i=1; i<= nlstate ; i ++) {                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          }
 }          
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);          for(jk=-1; jk <=nlstate+ndeath; jk++)
      for (i=1; i<= nlstate ; i ++) {            for(m=-1; m <=nlstate+ndeath; m++)
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              if(freq[jk][m][i] !=0 ) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");              if(first==1)
 }                  printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 #ifdef unix              }
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");          if(i <= iagemax)
 #endif            fprintf(ficresp,"\n");
    }          if(first==1)
   }            printf("Others in log...\n");
   /*2 eme*/          fprintf(ficlog,"\n");
         }
   for (k1=1; k1<= m ; k1 ++) {      }
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);    }
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    dateintmean=dateintsum/k2cpt; 
       
     for (i=1; i<= nlstate+1 ; i ++) {    fclose(ficresp);
       k=2*i;    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    free_vector(pp,1,nlstate);
       for (j=1; j<= nlstate+1 ; j ++) {    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    /* End of Freq */
   else fprintf(ficgp," \%%*lf (\%%*lf)");  }
 }    
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  /************ Prevalence ********************/
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);  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)
     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 ++) {    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       in each health status at the date of interview (if between dateprev1 and dateprev2).
         else fprintf(ficgp," \%%*lf (\%%*lf)");       We still use firstpass and lastpass as another selection.
 }      */
       fprintf(ficgp,"\" t\"\" w l 0,");   
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    int i, m, jk, k1, i1, j1, bool, z1,j;
       for (j=1; j<= nlstate+1 ; j ++) {    double ***freq; /* Frequencies */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    double *pp, **prop;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double pos,posprop; 
 }      double  y2; /* in fractional years */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    int iagemin, iagemax;
       else fprintf(ficgp,"\" t\"\" w l 0,");  
     }    iagemin= (int) agemin;
   }    iagemax= (int) agemax;
      /*pp=vector(1,nlstate);*/
   /*3eme*/    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   for (k1=1; k1<= m ; k1 ++) {    j1=0;
     for (cpt=1; cpt<= nlstate ; cpt ++) {    
       k=2+nlstate*(2*cpt-2);    j=cptcoveff;
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);    
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    for(k1=1; k1<=j;k1++){
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");      for(i1=1; i1<=ncodemax[k1];i1++){
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);        j1++;
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);        
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");        for (i=1; i<=nlstate; i++)  
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
 */       
       for (i=1; i< nlstate ; i ++) {        for (i=1; i<=imx; i++) { /* Each individual */
         fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);          bool=1;
           if  (cptcovn>0) {
       }            for (z1=1; z1<=cptcoveff; z1++) 
     }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   }                bool=0;
            } 
   /* CV preval stat */          if (bool==1) { 
     for (k1=1; k1<= m ; k1 ++) {            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     for (cpt=1; cpt<nlstate ; cpt ++) {              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       k=3;              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                 if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
       for (i=1; i< nlstate ; i ++)                if (s[m][i]>0 && s[m][i]<=nlstate) { 
         fprintf(ficgp,"+$%d",k+i+1);                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
                        prop[s[m][i]][iagemax+3] += weight[i]; 
       l=3+(nlstate+ndeath)*cpt;                } 
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);              }
       for (i=1; i< nlstate ; i ++) {            } /* end selection of waves */
         l=3+(nlstate+ndeath)*cpt;          }
         fprintf(ficgp,"+$%d",l+i+1);        }
       }        for(i=iagemin; i <= iagemax+3; i++){  
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);            
     }          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
   }              posprop += prop[jk][i]; 
            } 
   /* proba elementaires */  
    for(i=1,jk=1; i <=nlstate; i++){          for(jk=1; jk <=nlstate ; jk++){     
     for(k=1; k <=(nlstate+ndeath); k++){            if( i <=  iagemax){ 
       if (k != i) {              if(posprop>=1.e-5){ 
         for(j=1; j <=ncovmodel; j++){                probs[i][jk][j1]= prop[jk][i]/posprop;
                      } else
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
           jk++;            } 
           fprintf(ficgp,"\n");          }/* end jk */ 
         }        }/* end i */ 
       }      } /* end i1 */
     }    } /* end k1 */
    }    
     /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/    /*free_vector(pp,1,nlstate);*/
      for(jk=1; jk <=m; jk++) {    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);  }  /* End of prevalence */
        if (ng==2)  
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");  /************* Waves Concatenation ***************/
        else  
          fprintf(ficgp,"\nset title \"Probability\"\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)
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);  {
        i=1;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        for(k2=1; k2<=nlstate; k2++) {       Death is a valid wave (if date is known).
          k3=i;       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
          for(k=1; k<=(nlstate+ndeath); k++) {       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
            if (k != k2){       and mw[mi+1][i]. dh depends on stepm.
              if(ng==2)       */
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);  
              else    int i, mi, m;
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
              ij=1;       double sum=0., jmean=0.;*/
              for(j=3; j <=ncovmodel; j++) {    int first;
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    int j, k=0,jk, ju, jl;
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    double sum=0.;
                  ij++;    first=0;
                }    jmin=1e+5;
                else    jmax=-1;
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    jmean=0.;
              }    for(i=1; i<=imx; i++){
              fprintf(ficgp,")/(1");      mi=0;
                    m=firstpass;
              for(k1=1; k1 <=nlstate; k1++){        while(s[m][i] <= nlstate){
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
                ij=1;          mw[++mi][i]=m;
                for(j=3; j <=ncovmodel; j++){        if(m >=lastpass)
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          break;
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        else
                    ij++;          m++;
                  }      }/* end while */
                  else      if (s[m][i] > nlstate){
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        mi++;     /* Death is another wave */
                }        /* if(mi==0)  never been interviewed correctly before death */
                fprintf(ficgp,")");           /* Only death is a correct wave */
              }        mw[mi][i]=m;
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);      }
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");  
              i=i+ncovmodel;      wav[i]=mi;
            }      if(mi==0){
          }        nbwarn++;
        }        if(first==0){
      }          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
    }          first=1;
    fclose(ficgp);        }
 }  /* end gnuplot */        if(first==1){
           fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
         }
 /*************** Moving average **************/      } /* end mi==0 */
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){    } /* End individuals */
   
   int i, cpt, cptcod;    for(i=1; i<=imx; i++){
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)      for(mi=1; mi<wav[i];mi++){
       for (i=1; i<=nlstate;i++)        if (stepm <=0)
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)          dh[mi][i]=1;
           mobaverage[(int)agedeb][i][cptcod]=0.;        else{
              if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){            if (agedc[i] < 2*AGESUP) {
       for (i=1; i<=nlstate;i++){              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              if(j==0) j=1;  /* Survives at least one month after exam */
           for (cpt=0;cpt<=4;cpt++){              else if(j<0){
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];                nberr++;
           }                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;                j=1; /* Temporary Dangerous patch */
         }                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
       }                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     }                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
                  }
 }              k=k+1;
               if (j >= jmax){
                 jmax=j;
 /************** Forecasting ******************/                ijmax=i;
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){              }
                if (j <= jmin){
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;                jmin=j;
   int *popage;                ijmin=i;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;              }
   double *popeffectif,*popcount;              sum=sum+j;
   double ***p3mat;              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   char fileresf[FILENAMELENGTH];              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
             }
  agelim=AGESUP;          }
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  /*        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]); */
    
              k=k+1;
   strcpy(fileresf,"f");            if (j >= jmax) {
   strcat(fileresf,fileres);              jmax=j;
   if((ficresf=fopen(fileresf,"w"))==NULL) {              ijmax=i;
     printf("Problem with forecast resultfile: %s\n", fileresf);            }
   }            else if (j <= jmin){
   printf("Computing forecasting: result on file '%s' \n", fileresf);              jmin=j;
               ijmin=i;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            }
             /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
   if (mobilav==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]);*/
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            if(j<0){
     movingaverage(agedeb, fage, ageminpar, mobaverage);              nberr++;
   }              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
               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]);
   stepsize=(int) (stepm+YEARM-1)/YEARM;            }
   if (stepm<=12) stepsize=1;            sum=sum+j;
            }
   agelim=AGESUP;          jk= j/stepm;
            jl= j -jk*stepm;
   hstepm=1;          ju= j -(jk+1)*stepm;
   hstepm=hstepm/stepm;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   yp1=modf(dateintmean,&yp);            if(jl==0){
   anprojmean=yp;              dh[mi][i]=jk;
   yp2=modf((yp1*12),&yp);              bh[mi][i]=0;
   mprojmean=yp;            }else{ /* We want a negative bias in order to only have interpolation ie
   yp1=modf((yp2*30.5),&yp);                    * to avoid the price of an extra matrix product in likelihood */
   jprojmean=yp;              dh[mi][i]=jk+1;
   if(jprojmean==0) jprojmean=1;              bh[mi][i]=ju;
   if(mprojmean==0) jprojmean=1;            }
            }else{
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);            if(jl <= -ju){
                dh[mi][i]=jk;
   for(cptcov=1;cptcov<=i2;cptcov++){              bh[mi][i]=jl;       /* bias is positive if real duration
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){                                   * is higher than the multiple of stepm and negative otherwise.
       k=k+1;                                   */
       fprintf(ficresf,"\n#******");            }
       for(j=1;j<=cptcoveff;j++) {            else{
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              dh[mi][i]=jk+1;
       }              bh[mi][i]=ju;
       fprintf(ficresf,"******\n");            }
       fprintf(ficresf,"# StartingAge FinalAge");            if(dh[mi][i]==0){
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);              dh[mi][i]=1; /* At least one step */
                    bh[mi][i]=ju; /* At least one step */
                    /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {            }
         fprintf(ficresf,"\n");          } /* end if mle */
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);          }
       } /* end wave */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    }
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    jmean=sum/k;
           nhstepm = nhstepm/hstepm;    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 %d) Max=%d (%d) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
           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);    /*********** Tricode ****************************/
          void tricode(int *Tvar, int **nbcode, int imx)
           for (h=0; h<=nhstepm; h++){  {
             if (h==(int) (calagedate+YEARM*cpt)) {    /* Uses cptcovn+2*cptcovprod as the number of covariates */
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
             }  
             for(j=1; j<=nlstate+ndeath;j++) {    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
               kk1=0.;kk2=0;    int modmaxcovj=0; /* Modality max of covariates j */
               for(i=1; i<=nlstate;i++) {                  cptcoveff=0; 
                 if (mobilav==1)   
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    for (k=0; k<maxncov; k++) Ndum[k]=0;
                 else {    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];  
                 }    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
                      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
               }                                 modality of this covariate Vj*/ 
               if (h==(int)(calagedate+12*cpt)){        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(ficresf," %.3f", kk1);                                        modality of the nth covariate of individual i. */
                                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);*/
             }        if (ij > modmaxcovj) modmaxcovj=ij; 
           }        /* getting the maximum value of the modality of the covariate
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
         }           female is 1, then modmaxcovj=1.*/
       }      }
     }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
   }      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
                if( Ndum[i] != 0 )
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          ncodemax[j]++; 
         /* Number of modalities of the j th covariate. In fact
   fclose(ficresf);           ncodemax[j]=2 (dichotom. variables only) but it could be more for
 }           historical reasons */
 /************** Forecasting ******************/      } /* Ndum[-1] number of undefined modalities */
 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){  
        /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      ij=1; 
   int *popage;      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;        for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
   double *popeffectif,*popcount;          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
   double ***p3mat,***tabpop,***tabpopprev;            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
   char filerespop[FILENAMELENGTH];                                       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; */
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            ij++;
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          }
   agelim=AGESUP;          if (ij > ncodemax[j]) break; 
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;        }  /* end of loop on */
        } /* end of loop on modality */ 
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
      
      for (k=0; k< maxncov; k++) Ndum[k]=0;
   strcpy(filerespop,"pop");    
   strcat(filerespop,fileres);    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
   if((ficrespop=fopen(filerespop,"w"))==NULL) {     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
     printf("Problem with forecast resultfile: %s\n", filerespop);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
   }     Ndum[ij]++;
   printf("Computing forecasting: result on file '%s' \n", filerespop);   }
   
   if (cptcoveff==0) ncodemax[cptcoveff]=1;   ij=1;
    for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   if (mobilav==1) {     if((Ndum[i]!=0) && (i<=ncovcol)){
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);       Tvaraff[ij]=i; /*For printing */
     movingaverage(agedeb, fage, ageminpar, mobaverage);       ij++;
   }     }
    }
   stepsize=(int) (stepm+YEARM-1)/YEARM;   ij--;
   if (stepm<=12) stepsize=1;   cptcoveff=ij; /*Number of simple covariates*/
    }
   agelim=AGESUP;  
    /*********** Health Expectancies ****************/
   hstepm=1;  
   hstepm=hstepm/stepm;  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
    
   if (popforecast==1) {  {
     if((ficpop=fopen(popfile,"r"))==NULL) {    /* Health expectancies, no variances */
       printf("Problem with population file : %s\n",popfile);exit(0);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
     }    int nhstepma, nstepma; /* Decreasing with age */
     popage=ivector(0,AGESUP);    double age, agelim, hf;
     popeffectif=vector(0,AGESUP);    double ***p3mat;
     popcount=vector(0,AGESUP);    double eip;
      
     i=1;      pstamp(ficreseij);
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    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");
     imx=i;    for(i=1; i<=nlstate;i++){
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];      for(j=1; j<=nlstate;j++){
   }        fprintf(ficreseij," e%1d%1d ",i,j);
       }
   for(cptcov=1;cptcov<=i2;cptcov++){      fprintf(ficreseij," e%1d. ",i);
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    }
       k=k+1;    fprintf(ficreseij,"\n");
       fprintf(ficrespop,"\n#******");  
       for(j=1;j<=cptcoveff;j++) {    
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    if(estepm < stepm){
       }      printf ("Problem %d lower than %d\n",estepm, stepm);
       fprintf(ficrespop,"******\n");    }
       fprintf(ficrespop,"# Age");    else  hstepm=estepm;   
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    /* We compute the life expectancy from trapezoids spaced every estepm months
       if (popforecast==1)  fprintf(ficrespop," [Population]");     * This is mainly to measure the difference between two models: for example
           * if stepm=24 months pijx are given only every 2 years and by summing them
       for (cpt=0; cpt<=0;cpt++) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);       * progression in between and thus overestimating or underestimating according
             * to the curvature of the survival function. If, for the same date, we 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     * estimate the model with stepm=1 month, we can keep estepm to 24 months
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);     * to compare the new estimate of Life expectancy with the same linear 
           nhstepm = nhstepm/hstepm;     * hypothesis. A more precise result, taking into account a more precise
               * curvature will be obtained if estepm is as small as stepm. */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;    /* For example we decided to compute the life expectancy with the smallest unit */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
               nhstepm is the number of hstepm from age to agelim 
           for (h=0; h<=nhstepm; h++){       nstepm is the number of stepm from age to agelin. 
             if (h==(int) (calagedate+YEARM*cpt)) {       Look at hpijx to understand the reason of that which relies in memory size
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);       and note for a fixed period like estepm months */
             }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             for(j=1; j<=nlstate+ndeath;j++) {       survival function given by stepm (the optimization length). Unfortunately it
               kk1=0.;kk2=0;       means that if the survival funtion is printed only each two years of age and if
               for(i=1; i<=nlstate;i++) {                     you sum them up and add 1 year (area under the trapezoids) you won't get the same 
                 if (mobilav==1)       results. So we changed our mind and took the option of the best precision.
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    */
                 else {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];  
                 }    agelim=AGESUP;
               }    /* If stepm=6 months */
               if (h==(int)(calagedate+12*cpt)){      /* Computed by stepm unit matrices, product of hstepm matrices, stored
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
                   /*fprintf(ficrespop," %.3f", kk1);      
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/  /* nhstepm age range expressed in number of stepm */
               }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             for(i=1; i<=nlstate;i++){    /* if (stepm >= YEARM) hstepm=1;*/
               kk1=0.;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
                 for(j=1; j<=nlstate;j++){    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];  
                 }    for (age=bage; age<=fage; age ++){ 
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);  
           }      /* If stepm=6 months */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
         }         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       }      
        hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   /******/      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {      
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        printf("%d|",(int)age);fflush(stdout);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      
           nhstepm = nhstepm/hstepm;      /* Computing expectancies */
                for(i=1; i<=nlstate;i++)
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(j=1; j<=nlstate;j++)
           oldm=oldms;savm=savms;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
           for (h=0; h<=nhstepm; h++){            
             if (h==(int) (calagedate+YEARM*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(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);  
             }          }
             for(j=1; j<=nlstate+ndeath;j++) {  
               kk1=0.;kk2=0;      fprintf(ficreseij,"%3.0f",age );
               for(i=1; i<=nlstate;i++) {                    for(i=1; i<=nlstate;i++){
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];            eip=0;
               }        for(j=1; j<=nlstate;j++){
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);          eip +=eij[i][j][(int)age];
             }          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
           }        }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficreseij,"%9.4f", eip );
         }      }
       }      fprintf(ficreseij,"\n");
    }      
   }    }
      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    printf("\n");
     fprintf(ficlog,"\n");
   if (popforecast==1) {    
     free_ivector(popage,0,AGESUP);  }
     free_vector(popeffectif,0,AGESUP);  
     free_vector(popcount,0,AGESUP);  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[] )
   }  
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  {
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /* Covariances of health expectancies eij and of total life expectancies according
   fclose(ficrespop);     to initial status i, ei. .
 }    */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
 /***********************************************/    int nhstepma, nstepma; /* Decreasing with age */
 /**************** Main Program *****************/    double age, agelim, hf;
 /***********************************************/    double ***p3matp, ***p3matm, ***varhe;
     double **dnewm,**doldm;
 int main(int argc, char *argv[])    double *xp, *xm;
 {    double **gp, **gm;
     double ***gradg, ***trgradg;
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    int theta;
   double agedeb, agefin,hf;  
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;    double eip, vip;
   
   double fret;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   double **xi,tmp,delta;    xp=vector(1,npar);
     xm=vector(1,npar);
   double dum; /* Dummy variable */    dnewm=matrix(1,nlstate*nlstate,1,npar);
   double ***p3mat;    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   int *indx;    
   char line[MAXLINE], linepar[MAXLINE];    pstamp(ficresstdeij);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   int firstobs=1, lastobs=10;    fprintf(ficresstdeij,"# Age");
   int sdeb, sfin; /* Status at beginning and end */    for(i=1; i<=nlstate;i++){
   int c,  h , cpt,l;      for(j=1; j<=nlstate;j++)
   int ju,jl, mi;        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      fprintf(ficresstdeij," e%1d. ",i);
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    }
   int mobilav=0,popforecast=0;    fprintf(ficresstdeij,"\n");
   int hstepm, nhstepm;  
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;    pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   double bage, fage, age, agelim, agebase;    fprintf(ficrescveij,"# Age");
   double ftolpl=FTOL;    for(i=1; i<=nlstate;i++)
   double **prlim;      for(j=1; j<=nlstate;j++){
   double *severity;        cptj= (j-1)*nlstate+i;
   double ***param; /* Matrix of parameters */        for(i2=1; i2<=nlstate;i2++)
   double  *p;          for(j2=1; j2<=nlstate;j2++){
   double **matcov; /* Matrix of covariance */            cptj2= (j2-1)*nlstate+i2;
   double ***delti3; /* Scale */            if(cptj2 <= cptj)
   double *delti; /* Scale */              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
   double ***eij, ***vareij;          }
   double **varpl; /* Variances of prevalence limits by age */      }
   double *epj, vepp;    fprintf(ficrescveij,"\n");
   double kk1, kk2;    
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    if(estepm < stepm){
        printf ("Problem %d lower than %d\n",estepm, stepm);
     }
   char *alph[]={"a","a","b","c","d","e"}, str[4];    else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
   char z[1]="c", occ;     * if stepm=24 months pijx are given only every 2 years and by summing them
 #include <sys/time.h>     * we are calculating an estimate of the Life Expectancy assuming a linear 
 #include <time.h>     * progression in between and thus overestimating or underestimating according
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];     * to the curvature of the survival function. If, for the same date, we 
       * estimate the model with stepm=1 month, we can keep estepm to 24 months
   /* long total_usecs;     * to compare the new estimate of Life expectancy with the same linear 
   struct timeval start_time, end_time;     * hypothesis. A more precise result, taking into account a more precise
       * curvature will be obtained if estepm is as small as stepm. */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   getcwd(pathcd, size);    /* 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. 
   printf("\n%s",version);       nhstepm is the number of hstepm from age to agelim 
   if(argc <=1){       nstepm is the number of stepm from age to agelin. 
     printf("\nEnter the parameter file name: ");       Look at hpijx to understand the reason of that which relies in memory size
     scanf("%s",pathtot);       and note for a fixed period like estepm months */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   else{       survival function given by stepm (the optimization length). Unfortunately it
     strcpy(pathtot,argv[1]);       means that if the survival funtion is printed only each two years of age and if
   }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/       results. So we changed our mind and took the option of the best precision.
   /*cygwin_split_path(pathtot,path,optionfile);    */
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   /* cutv(path,optionfile,pathtot,'\\');*/  
     /* If stepm=6 months */
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    /* nhstepm age range expressed in number of stepm */
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    agelim=AGESUP;
   chdir(path);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
   replace(pathc,path);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
 /*-------- arguments in the command line --------*/    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     
   strcpy(fileres,"r");    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   strcat(fileres, optionfilefiname);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   strcat(fileres,".txt");    /* Other files have txt extension */    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   /*---------arguments file --------*/    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     gm=matrix(0,nhstepm,1,nlstate*nlstate);
   if((ficpar=fopen(optionfile,"r"))==NULL)    {  
     printf("Problem with optionfile %s\n",optionfile);    for (age=bage; age<=fage; age ++){ 
     goto end;      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
   strcpy(filereso,"o");      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   strcat(filereso,fileres);  
   if((ficparo=fopen(filereso,"w"))==NULL) {      /* If stepm=6 months */
     printf("Problem with Output resultfile: %s\n", filereso);goto end;      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   }         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   /* Reads comments: lines beginning with '#' */      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);      /* Computing  Variances of health expectancies */
     fgets(line, MAXLINE, ficpar);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
     puts(line);         decrease memory allocation */
     fputs(line,ficparo);      for(theta=1; theta <=npar; theta++){
   }        for(i=1; i<=npar; i++){ 
   ungetc(c,ficpar);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);        }
   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);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   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);        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
 while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);        for(j=1; j<= nlstate; j++){
     fgets(line, MAXLINE, ficpar);          for(i=1; i<=nlstate; i++){
     puts(line);            for(h=0; h<=nhstepm-1; h++){
     fputs(line,ficparo);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   }              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   ungetc(c,ficpar);            }
            }
            }
   covar=matrix(0,NCOVMAX,1,n);       
   cptcovn=0;        for(ij=1; ij<= nlstate*nlstate; ij++)
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   ncovmodel=2+cptcovn;          }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      }/* End theta */
        
   /* Read guess parameters */      
   /* Reads comments: lines beginning with '#' */      for(h=0; h<=nhstepm-1; h++)
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate*nlstate;j++)
     ungetc(c,ficpar);          for(theta=1; theta <=npar; theta++)
     fgets(line, MAXLINE, ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
     puts(line);      
     fputs(line,ficparo);  
   }       for(ij=1;ij<=nlstate*nlstate;ij++)
   ungetc(c,ficpar);        for(ji=1;ji<=nlstate*nlstate;ji++)
            varhe[ij][ji][(int)age] =0.;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)       printf("%d|",(int)age);fflush(stdout);
     for(j=1; j <=nlstate+ndeath-1; j++){       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       fscanf(ficpar,"%1d%1d",&i1,&j1);       for(h=0;h<=nhstepm-1;h++){
       fprintf(ficparo,"%1d%1d",i1,j1);        for(k=0;k<=nhstepm-1;k++){
       printf("%1d%1d",i,j);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
       for(k=1; k<=ncovmodel;k++){          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
         fscanf(ficpar," %lf",&param[i][j][k]);          for(ij=1;ij<=nlstate*nlstate;ij++)
         printf(" %lf",param[i][j][k]);            for(ji=1;ji<=nlstate*nlstate;ji++)
         fprintf(ficparo," %lf",param[i][j][k]);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
       }        }
       fscanf(ficpar,"\n");      }
       printf("\n");  
       fprintf(ficparo,"\n");      /* Computing expectancies */
     }      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
        for(i=1; i<=nlstate;i++)
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   p=param[1][1];            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
              
   /* Reads comments: lines beginning with '#' */            /* 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]);*/
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);          }
     fgets(line, MAXLINE, ficpar);  
     puts(line);      fprintf(ficresstdeij,"%3.0f",age );
     fputs(line,ficparo);      for(i=1; i<=nlstate;i++){
   }        eip=0.;
   ungetc(c,ficpar);        vip=0.;
         for(j=1; j<=nlstate;j++){
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          eip += eij[i][j][(int)age];
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
   for(i=1; i <=nlstate; i++){            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
     for(j=1; j <=nlstate+ndeath-1; j++){          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
       fscanf(ficpar,"%1d%1d",&i1,&j1);        }
       printf("%1d%1d",i,j);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       fprintf(ficparo,"%1d%1d",i1,j1);      }
       for(k=1; k<=ncovmodel;k++){      fprintf(ficresstdeij,"\n");
         fscanf(ficpar,"%le",&delti3[i][j][k]);  
         printf(" %le",delti3[i][j][k]);      fprintf(ficrescveij,"%3.0f",age );
         fprintf(ficparo," %le",delti3[i][j][k]);      for(i=1; i<=nlstate;i++)
       }        for(j=1; j<=nlstate;j++){
       fscanf(ficpar,"\n");          cptj= (j-1)*nlstate+i;
       printf("\n");          for(i2=1; i2<=nlstate;i2++)
       fprintf(ficparo,"\n");            for(j2=1; j2<=nlstate;j2++){
     }              cptj2= (j2-1)*nlstate+i2;
   }              if(cptj2 <= cptj)
   delti=delti3[1][1];                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
              }
   /* Reads comments: lines beginning with '#' */        }
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficrescveij,"\n");
     ungetc(c,ficpar);     
     fgets(line, MAXLINE, ficpar);    }
     puts(line);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     fputs(line,ficparo);    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   }    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   ungetc(c,ficpar);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
      free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   matcov=matrix(1,npar,1,npar);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   for(i=1; i <=npar; i++){    printf("\n");
     fscanf(ficpar,"%s",&str);    fprintf(ficlog,"\n");
     printf("%s",str);  
     fprintf(ficparo,"%s",str);    free_vector(xm,1,npar);
     for(j=1; j <=i; j++){    free_vector(xp,1,npar);
       fscanf(ficpar," %le",&matcov[i][j]);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       printf(" %.5le",matcov[i][j]);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       fprintf(ficparo," %.5le",matcov[i][j]);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     }  }
     fscanf(ficpar,"\n");  
     printf("\n");  /************ Variance ******************/
     fprintf(ficparo,"\n");  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   }  {
   for(i=1; i <=npar; i++)    /* Variance of health expectancies */
     for(j=i+1;j<=npar;j++)    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
       matcov[i][j]=matcov[j][i];    /* double **newm;*/
        double **dnewm,**doldm;
   printf("\n");    double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
     int k, cptcode;
     /*-------- Rewriting paramater file ----------*/    double *xp;
      strcpy(rfileres,"r");    /* "Rparameterfile */    double **gp, **gm;  /* for var eij */
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/    double ***gradg, ***trgradg; /*for var eij */
      strcat(rfileres,".");    /* */    double **gradgp, **trgradgp; /* for var p point j */
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    double *gpp, *gmp; /* for var p point j */
     if((ficres =fopen(rfileres,"w"))==NULL) {    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    double ***p3mat;
     }    double age,agelim, hf;
     fprintf(ficres,"#%s\n",version);    double ***mobaverage;
        int theta;
     /*-------- data file ----------*/    char digit[4];
     if((fic=fopen(datafile,"r"))==NULL)    {    char digitp[25];
       printf("Problem with datafile: %s\n", datafile);goto end;  
     }    char fileresprobmorprev[FILENAMELENGTH];
   
     n= lastobs;    if(popbased==1){
     severity = vector(1,maxwav);      if(mobilav!=0)
     outcome=imatrix(1,maxwav+1,1,n);        strcpy(digitp,"-populbased-mobilav-");
     num=ivector(1,n);      else strcpy(digitp,"-populbased-nomobil-");
     moisnais=vector(1,n);    }
     annais=vector(1,n);    else 
     moisdc=vector(1,n);      strcpy(digitp,"-stablbased-");
     andc=vector(1,n);  
     agedc=vector(1,n);    if (mobilav!=0) {
     cod=ivector(1,n);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     weight=vector(1,n);      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
     mint=matrix(1,maxwav,1,n);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     anint=matrix(1,maxwav,1,n);      }
     s=imatrix(1,maxwav+1,1,n);    }
     adl=imatrix(1,maxwav+1,1,n);      
     tab=ivector(1,NCOVMAX);    strcpy(fileresprobmorprev,"prmorprev"); 
     ncodemax=ivector(1,8);    sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     i=1;    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     while (fgets(line, MAXLINE, fic) != NULL)    {    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
       if ((i >= firstobs) && (i <=lastobs)) {    strcat(fileresprobmorprev,fileres);
            if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
         for (j=maxwav;j>=1;j--){      printf("Problem with resultfile: %s\n", fileresprobmorprev);
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
           strcpy(line,stra);    }
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);   
         }    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
            pstamp(ficresprobmorprev);
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    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);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      fprintf(ficresprobmorprev," p.%-d SE",j);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    }  
         for (j=ncovcol;j>=1;j--){    fprintf(ficresprobmorprev,"\n");
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficgp,"\n# Routine varevsij");
         }    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
         num[i]=atol(stra);    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
            fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
         /*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;}*/    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pstamp(ficresvij);
         i=i+1;    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
       }    if(popbased==1)
     }      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
     /* printf("ii=%d", ij);    else
        scanf("%d",i);*/      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   imx=i-1; /* Number of individuals */    fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
   /* for (i=1; i<=imx; i++){      for(j=1; j<=nlstate;j++)
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    fprintf(ficresvij,"\n");
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;  
     }*/    xp=vector(1,npar);
    /*  for (i=1; i<=imx; i++){    dnewm=matrix(1,nlstate,1,npar);
      if (s[4][i]==9)  s[4][i]=-1;    doldm=matrix(1,nlstate,1,nlstate);
      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]));}*/    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
      doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
    
   /* Calculation of the number of parameter from char model*/    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   Tvar=ivector(1,15);    gpp=vector(nlstate+1,nlstate+ndeath);
   Tprod=ivector(1,15);    gmp=vector(nlstate+1,nlstate+ndeath);
   Tvaraff=ivector(1,15);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   Tvard=imatrix(1,15,1,2);    
   Tage=ivector(1,15);          if(estepm < stepm){
          printf ("Problem %d lower than %d\n",estepm, stepm);
   if (strlen(model) >1){    }
     j=0, j1=0, k1=1, k2=1;    else  hstepm=estepm;   
     j=nbocc(model,'+');    /* For example we decided to compute the life expectancy with the smallest unit */
     j1=nbocc(model,'*');    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     cptcovn=j+1;       nhstepm is the number of hstepm from age to agelim 
     cptcovprod=j1;       nstepm is the number of stepm from age to agelin. 
           Look at function hpijx to understand why (it is linked to memory size questions) */
     strcpy(modelsav,model);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){       survival function given by stepm (the optimization length). Unfortunately it
       printf("Error. Non available option model=%s ",model);       means that if the survival funtion is printed every two years of age and if
       goto end;       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(i=(j+1); i>=1;i--){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       cutv(stra,strb,modelsav,'+');    agelim = AGESUP;
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       /*scanf("%d",i);*/      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       if (strchr(strb,'*')) {      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         cutv(strd,strc,strb,'*');      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
         if (strcmp(strc,"age")==0) {      gp=matrix(0,nhstepm,1,nlstate);
           cptcovprod--;      gm=matrix(0,nhstepm,1,nlstate);
           cutv(strb,stre,strd,'V');  
           Tvar[i]=atoi(stre);  
           cptcovage++;      for(theta=1; theta <=npar; theta++){
             Tage[cptcovage]=i;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
             /*printf("stre=%s ", stre);*/          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }        }
         else if (strcmp(strd,"age")==0) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           cptcovprod--;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           cutv(strb,stre,strc,'V');  
           Tvar[i]=atoi(stre);        if (popbased==1) {
           cptcovage++;          if(mobilav ==0){
           Tage[cptcovage]=i;            for(i=1; i<=nlstate;i++)
         }              prlim[i][i]=probs[(int)age][i][ij];
         else {          }else{ /* mobilav */ 
           cutv(strb,stre,strc,'V');            for(i=1; i<=nlstate;i++)
           Tvar[i]=ncovcol+k1;              prlim[i][i]=mobaverage[(int)age][i][ij];
           cutv(strb,strc,strd,'V');          }
           Tprod[k1]=i;        }
           Tvard[k1][1]=atoi(strc);    
           Tvard[k1][2]=atoi(stre);        for(j=1; j<= nlstate; j++){
           Tvar[cptcovn+k2]=Tvard[k1][1];          for(h=0; h<=nhstepm; h++){
           Tvar[cptcovn+k2+1]=Tvard[k1][2];            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           for (k=1; k<=lastobs;k++)              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];          }
           k1++;        }
           k2=k2+2;        /* This for computing probability of death (h=1 means
         }           computed over hstepm matrices product = hstepm*stepm months) 
       }           as a weighted average of prlim.
       else {        */
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/        for(j=nlstate+1;j<=nlstate+ndeath;j++){
        /*  scanf("%d",i);*/          for(i=1,gpp[j]=0.; i<= nlstate; i++)
       cutv(strd,strc,strb,'V');            gpp[j] += prlim[i][i]*p3mat[i][j][1];
       Tvar[i]=atoi(strc);        }    
       }        /* end probability of death */
       strcpy(modelsav,stra);    
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
         scanf("%d",i);*/          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);
     
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);        if (popbased==1) {
   printf("cptcovprod=%d ", cptcovprod);          if(mobilav ==0){
   scanf("%d ",i);*/            for(i=1; i<=nlstate;i++)
     fclose(fic);              prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
     /*  if(mle==1){*/            for(i=1; i<=nlstate;i++)
     if (weightopt != 1) { /* Maximisation without weights*/              prlim[i][i]=mobaverage[(int)age][i][ij];
       for(i=1;i<=n;i++) weight[i]=1.0;          }
     }        }
     /*-calculation of age at interview from date of interview and age at death -*/  
     agev=matrix(1,maxwav,1,imx);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
           for(h=0; h<=nhstepm; h++){
     for (i=1; i<=imx; i++) {            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
       for(m=2; (m<= maxwav); m++) {              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){          }
          anint[m][i]=9999;        }
          s[m][i]=-1;        /* This for computing probability of death (h=1 means
        }           computed over hstepm matrices product = hstepm*stepm months) 
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;           as a weighted average of prlim.
       }        */
     }        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
     for (i=1; i<=imx; i++)  {           gmp[j] += prlim[i][i]*p3mat[i][j][1];
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        }    
       for(m=1; (m<= maxwav); m++){        /* end probability of death */
         if(s[m][i] >0){  
           if (s[m][i] >= nlstate+1) {        for(j=1; j<= nlstate; j++) /* vareij */
             if(agedc[i]>0)          for(h=0; h<=nhstepm; h++){
               if(moisdc[i]!=99 && andc[i]!=9999)            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
                 agev[m][i]=agedc[i];          }
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/  
            else {        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
               if (andc[i]!=9999){          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
               printf("Warning negative age at death: %d line:%d\n",num[i],i);        }
               agev[m][i]=-1;  
               }      } /* End theta */
             }  
           }      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
           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(h=0; h<=nhstepm; h++) /* veij */
             if(mint[m][i]==99 || anint[m][i]==9999)        for(j=1; j<=nlstate;j++)
               agev[m][i]=1;          for(theta=1; theta <=npar; theta++)
             else if(agev[m][i] <agemin){            trgradg[h][j][theta]=gradg[h][theta][j];
               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);*/      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
             }        for(theta=1; theta <=npar; theta++)
             else if(agev[m][i] >agemax){          trgradgp[j][theta]=gradgp[theta][j];
               agemax=agev[m][i];    
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/  
             }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
             /*agev[m][i]=anint[m][i]-annais[i];*/      for(i=1;i<=nlstate;i++)
             /*   agev[m][i] = age[i]+2*m;*/        for(j=1;j<=nlstate;j++)
           }          vareij[i][j][(int)age] =0.;
           else { /* =9 */  
             agev[m][i]=1;      for(h=0;h<=nhstepm;h++){
             s[m][i]=-1;        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]);
         else /*= 0 Unknown */          for(i=1;i<=nlstate;i++)
           agev[m][i]=1;            for(j=1;j<=nlstate;j++)
       }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
            }
     }      }
     for (i=1; i<=imx; i++)  {    
       for(m=1; (m<= maxwav); m++){      /* pptj */
         if (s[m][i] > (nlstate+ndeath)) {      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
           printf("Error: Wrong value in nlstate or ndeath\n");        matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
           goto end;      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 */
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     free_vector(severity,1,maxwav);   
     free_imatrix(outcome,1,maxwav+1,1,n);      if (popbased==1) {
     free_vector(moisnais,1,n);        if(mobilav ==0){
     free_vector(annais,1,n);          for(i=1; i<=nlstate;i++)
     /* free_matrix(mint,1,maxwav,1,n);            prlim[i][i]=probs[(int)age][i][ij];
        free_matrix(anint,1,maxwav,1,n);*/        }else{ /* mobilav */ 
     free_vector(moisdc,1,n);          for(i=1; i<=nlstate;i++)
     free_vector(andc,1,n);            prlim[i][i]=mobaverage[(int)age][i][ij];
         }
          }
     wav=ivector(1,imx);               
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      /* This for computing probability of death (h=1 means
     mw=imatrix(1,lastpass-firstpass+1,1,imx);         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
             as a weighted average of prlim.
     /* Concatenates waves */      */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      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]; 
       Tcode=ivector(1,100);      }    
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);      /* end probability of death */
       ncodemax[1]=1;  
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
            for(j=nlstate+1; j<=(nlstate+ndeath);j++){
    codtab=imatrix(1,100,1,10);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
    h=0;        for(i=1; i<=nlstate;i++){
    m=pow(2,cptcoveff);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
          }
    for(k=1;k<=cptcoveff; k++){      } 
      for(i=1; i <=(m/pow(2,k));i++){      fprintf(ficresprobmorprev,"\n");
        for(j=1; j <= ncodemax[k]; j++){  
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){      fprintf(ficresvij,"%.0f ",age );
            h++;      for(i=1; i<=nlstate;i++)
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;        for(j=1; j<=nlstate;j++){
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/          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);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       codtab[1][2]=1;codtab[2][2]=2; */      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
    /* for(i=1; i <=m ;i++){      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       for(k=1; k <=cptcovn; k++){    } /* End age */
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    free_vector(gpp,nlstate+1,nlstate+ndeath);
       }    free_vector(gmp,nlstate+1,nlstate+ndeath);
       printf("\n");    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
       }    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       scanf("%d",i);*/    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 */
    /* Calculates basic frequencies. Computes observed prevalence at single age    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
        and prints on file fileres'p'. */  /*   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 lt 2 ",subdirf(fileresprobmorprev));
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 3 ",subdirf(fileresprobmorprev));
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 3 ",subdirf(fileresprobmorprev));
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    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);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    /*  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);
        */
     /* For Powell, parameters are in a vector p[] starting at p[1]  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */  
     free_vector(xp,1,npar);
     if(mle==1){    free_matrix(doldm,1,nlstate,1,nlstate);
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    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);
     /*--------- results files --------------*/    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     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);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
      fclose(ficresprobmorprev);
     fflush(ficgp);
    jk=1;    fflush(fichtm); 
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");  }  /* end varevsij */
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");  
    for(i=1,jk=1; i <=nlstate; i++){  /************ Variance of prevlim ******************/
      for(k=1; k <=(nlstate+ndeath); k++){  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
        if (k != i)  {
          {    /* Variance of prevalence limit */
            printf("%d%d ",i,k);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
            fprintf(ficres,"%1d%1d ",i,k);    double **newm;
            for(j=1; j <=ncovmodel; j++){    double **dnewm,**doldm;
              printf("%f ",p[jk]);    int i, j, nhstepm, hstepm;
              fprintf(ficres,"%f ",p[jk]);    int k, cptcode;
              jk++;    double *xp;
            }    double *gp, *gm;
            printf("\n");    double **gradg, **trgradg;
            fprintf(ficres,"\n");    double age,agelim;
          }    int theta;
      }    
    }    pstamp(ficresvpl);
  if(mle==1){    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     /* Computing hessian and covariance matrix */    fprintf(ficresvpl,"# Age");
     ftolhess=ftol; /* Usually correct */    for(i=1; i<=nlstate;i++)
     hesscov(matcov, p, npar, delti, ftolhess, func);        fprintf(ficresvpl," %1d-%1d",i,i);
  }    fprintf(ficresvpl,"\n");
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");  
     printf("# Scales (for hessian or gradient estimation)\n");    xp=vector(1,npar);
      for(i=1,jk=1; i <=nlstate; i++){    dnewm=matrix(1,nlstate,1,npar);
       for(j=1; j <=nlstate+ndeath; j++){    doldm=matrix(1,nlstate,1,nlstate);
         if (j!=i) {    
           fprintf(ficres,"%1d%1d",i,j);    hstepm=1*YEARM; /* Every year of age */
           printf("%1d%1d",i,j);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
           for(k=1; k<=ncovmodel;k++){    agelim = AGESUP;
             printf(" %.5e",delti[jk]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
             fprintf(ficres," %.5e",delti[jk]);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             jk++;      if (stepm >= YEARM) hstepm=1;
           }      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
           printf("\n");      gradg=matrix(1,npar,1,nlstate);
           fprintf(ficres,"\n");      gp=vector(1,nlstate);
         }      gm=vector(1,nlstate);
       }  
      }      for(theta=1; theta <=npar; theta++){
            for(i=1; i<=npar; i++){ /* Computes gradient */
     k=1;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     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");        }
     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");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     for(i=1;i<=npar;i++){        for(i=1;i<=nlstate;i++)
       /*  if (k>nlstate) k=1;          gp[i] = prlim[i][i];
       i1=(i-1)/(ncovmodel*nlstate)+1;      
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        for(i=1; i<=npar; i++) /* Computes gradient */
       printf("%s%d%d",alph[k],i1,tab[i]);*/          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       fprintf(ficres,"%3d",i);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       printf("%3d",i);        for(i=1;i<=nlstate;i++)
       for(j=1; j<=i;j++){          gm[i] = prlim[i][i];
         fprintf(ficres," %.5e",matcov[i][j]);  
         printf(" %.5e",matcov[i][j]);        for(i=1;i<=nlstate;i++)
       }          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       fprintf(ficres,"\n");      } /* End theta */
       printf("\n");  
       k++;      trgradg =matrix(1,nlstate,1,npar);
     }  
          for(j=1; j<=nlstate;j++)
     while((c=getc(ficpar))=='#' && c!= EOF){        for(theta=1; theta <=npar; theta++)
       ungetc(c,ficpar);          trgradg[j][theta]=gradg[theta][j];
       fgets(line, MAXLINE, ficpar);  
       puts(line);      for(i=1;i<=nlstate;i++)
       fputs(line,ficparo);        varpl[i][(int)age] =0.;
     }      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
     ungetc(c,ficpar);      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
     estepm=0;      for(i=1;i<=nlstate;i++)
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     if (estepm==0 || estepm < stepm) estepm=stepm;  
     if (fage <= 2) {      fprintf(ficresvpl,"%.0f ",age );
       bage = ageminpar;      for(i=1; i<=nlstate;i++)
       fage = agemaxpar;        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     }      fprintf(ficresvpl,"\n");
          free_vector(gp,1,nlstate);
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");      free_vector(gm,1,nlstate);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);      free_matrix(gradg,1,npar,1,nlstate);
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);      free_matrix(trgradg,1,nlstate,1,npar);
      } /* End age */
     while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    free_vector(xp,1,npar);
     fgets(line, MAXLINE, ficpar);    free_matrix(doldm,1,nlstate,1,npar);
     puts(line);    free_matrix(dnewm,1,nlstate,1,nlstate);
     fputs(line,ficparo);  
   }  }
   ungetc(c,ficpar);  
    /************ Variance of one-step probabilities  ******************/
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);  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[])
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  {
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    int i, j=0,  i1, k1, l1, t, tj;
          int k2, l2, j1,  z1;
   while((c=getc(ficpar))=='#' && c!= EOF){    int k=0,l, cptcode;
     ungetc(c,ficpar);    int first=1, first1;
     fgets(line, MAXLINE, ficpar);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     puts(line);    double **dnewm,**doldm;
     fputs(line,ficparo);    double *xp;
   }    double *gp, *gm;
   ungetc(c,ficpar);    double **gradg, **trgradg;
      double **mu;
     double age,agelim, cov[NCOVMAX];
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    int theta;
     char fileresprob[FILENAMELENGTH];
   fscanf(ficpar,"pop_based=%d\n",&popbased);    char fileresprobcov[FILENAMELENGTH];
   fprintf(ficparo,"pop_based=%d\n",popbased);      char fileresprobcor[FILENAMELENGTH];
   fprintf(ficres,"pop_based=%d\n",popbased);    
      double ***varpij;
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    strcpy(fileresprob,"prob"); 
     fgets(line, MAXLINE, ficpar);    strcat(fileresprob,fileres);
     puts(line);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     fputs(line,ficparo);      printf("Problem with resultfile: %s\n", fileresprob);
   }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
   ungetc(c,ficpar);    }
     strcpy(fileresprobcov,"probcov"); 
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);    strcat(fileresprobcov,fileres);
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);      printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
 while((c=getc(ficpar))=='#' && c!= EOF){    strcpy(fileresprobcor,"probcor"); 
     ungetc(c,ficpar);    strcat(fileresprobcor,fileres);
     fgets(line, MAXLINE, ficpar);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
     puts(line);      printf("Problem with resultfile: %s\n", fileresprobcor);
     fputs(line,ficparo);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   }    }
   ungetc(c,ficpar);    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);
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    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);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
 /*------------ gnuplot -------------*/    fprintf(ficresprob,"# Age");
   strcpy(optionfilegnuplot,optionfilefiname);    pstamp(ficresprobcov);
   strcat(optionfilegnuplot,".gp");    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {    fprintf(ficresprobcov,"# Age");
     printf("Problem with file %s",optionfilegnuplot);    pstamp(ficresprobcor);
   }    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   fclose(ficgp);    fprintf(ficresprobcor,"# Age");
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);  
 /*--------- index.htm --------*/  
     for(i=1; i<=nlstate;i++)
   strcpy(optionfilehtm,optionfile);      for(j=1; j<=(nlstate+ndeath);j++){
   strcat(optionfilehtm,".htm");        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        fprintf(ficresprobcov," p%1d-%1d ",i,j);
     printf("Problem with %s \n",optionfilehtm), exit(0);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
   }      }  
    /* fprintf(ficresprob,"\n");
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    fprintf(ficresprobcov,"\n");
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n    fprintf(ficresprobcor,"\n");
 \n   */
 Total number of observations=%d <br>\n    xp=vector(1,npar);
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
 <hr  size=\"2\" color=\"#EC5E5E\">    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
  <ul><li>Parameter files<br>\n    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
  - Gnuplot file name: <a href=\"%s\">%s</a><br></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);    first=1;
   fclose(fichtm);    fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);    fprintf(fichtm,"\n");
    
 /*------------ free_vector  -------------*/    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
  chdir(path);    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
      file %s<br>\n",optionfilehtmcov);
  free_ivector(wav,1,imx);    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);  and drawn. It helps understanding how is the covariance between two incidences.\
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);     They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
  free_ivector(num,1,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. \
  free_vector(agedc,1,n);  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
  /*free_matrix(covar,1,NCOVMAX,1,n);*/  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
  fclose(ficparo);  standard deviations wide on each axis. <br>\
  fclose(ficres);   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");
   /*--------------- Prevalence limit --------------*/  
      cov[1]=1;
   strcpy(filerespl,"pl");    tj=cptcoveff;
   strcat(filerespl,fileres);    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    j1=0;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    for(t=1; t<=tj;t++){
   }      for(i1=1; i1<=ncodemax[t];i1++){ 
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);        j1++;
   fprintf(ficrespl,"#Prevalence limit\n");        if  (cptcovn>0) {
   fprintf(ficrespl,"#Age ");          fprintf(ficresprob, "\n#********** Variable "); 
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   fprintf(ficrespl,"\n");          fprintf(ficresprob, "**********\n#\n");
            fprintf(ficresprobcov, "\n#********** Variable "); 
   prlim=matrix(1,nlstate,1,nlstate);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresprobcov, "**********\n#\n");
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficgp, "\n#********** Variable "); 
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          fprintf(ficgp, "**********\n#\n");
   k=0;          
   agebase=ageminpar;          
   agelim=agemaxpar;          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   ftolpl=1.e-10;          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   i1=cptcoveff;          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   if (cptcovn < 1){i1=1;}          
           fprintf(ficresprobcor, "\n#********** Variable ");    
   for(cptcov=1;cptcov<=i1;cptcov++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          fprintf(ficresprobcor, "**********\n#");    
         k=k+1;        }
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/        
         fprintf(ficrespl,"\n#******");        for (age=bage; age<=fage; age ++){ 
         for(j=1;j<=cptcoveff;j++)          cov[2]=age;
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          for (k=1; k<=cptcovn;k++) {
         fprintf(ficrespl,"******\n");            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
                  }
         for (age=agebase; age<=agelim; age++){          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);          for (k=1; k<=cptcovprod;k++)
           fprintf(ficrespl,"%.0f",age );            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           for(i=1; i<=nlstate;i++)          
           fprintf(ficrespl," %.5f", prlim[i][i]);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           fprintf(ficrespl,"\n");          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
         }          gp=vector(1,(nlstate)*(nlstate+ndeath));
       }          gm=vector(1,(nlstate)*(nlstate+ndeath));
     }      
   fclose(ficrespl);          for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
   /*------------- h Pij x at various ages ------------*/              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
              
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {            
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;            k=0;
   }            for(i=1; i<= (nlstate); i++){
   printf("Computing pij: result on file '%s' \n", filerespij);              for(j=1; j<=(nlstate+ndeath);j++){
                  k=k+1;
   stepsize=(int) (stepm+YEARM-1)/YEARM;                gp[k]=pmmij[i][j];
   /*if (stepm<=24) stepsize=2;*/              }
             }
   agelim=AGESUP;            
   hstepm=stepsize*YEARM; /* Every year of age */            for(i=1; i<=npar; i++)
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
        
   k=0;            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   for(cptcov=1;cptcov<=i1;cptcov++){            k=0;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            for(i=1; i<=(nlstate); i++){
       k=k+1;              for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficrespij,"\n#****** ");                k=k+1;
         for(j=1;j<=cptcoveff;j++)                gm[k]=pmmij[i][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 */            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              for(theta=1; theta <=npar; theta++)
           fprintf(ficrespij,"# Age");              trgradg[j][theta]=gradg[theta][j];
           for(i=1; i<=nlstate;i++)          
             for(j=1; j<=nlstate+ndeath;j++)          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
               fprintf(ficrespij," %1d-%1d",i,j);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           fprintf(ficrespij,"\n");          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
            for (h=0; h<=nhstepm; h++){          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
             for(i=1; i<=nlstate;i++)          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
               for(j=1; j<=nlstate+ndeath;j++)  
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          pmij(pmmij,cov,ncovmodel,x,nlstate);
             fprintf(ficrespij,"\n");          
              }          k=0;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for(i=1; i<=(nlstate); i++){
           fprintf(ficrespij,"\n");            for(j=1; j<=(nlstate+ndeath);j++){
         }              k=k+1;
     }              mu[k][(int) age]=pmmij[i][j];
   }            }
           }
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
   fclose(ficrespij);              varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
   /*---------- Forecasting ------------------*/            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   if((stepm == 1) && (strcmp(model,".")==0)){            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);            }*/
   }  
   else{          fprintf(ficresprob,"\n%d ",(int)age);
     erreur=108;          fprintf(ficresprobcov,"\n%d ",(int)age);
     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(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]));
   /*---------- Health expectancies and variances ------------*/          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
   strcpy(filerest,"t");            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   strcat(filerest,fileres);          }
   if((ficrest=fopen(filerest,"w"))==NULL) {          i=0;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;          for (k=1; k<=(nlstate);k++){
   }            for (l=1; l<=(nlstate+ndeath);l++){ 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);              i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
   strcpy(filerese,"e");              for (j=1; j<=i;j++){
   strcat(filerese,fileres);                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
   if((ficreseij=fopen(filerese,"w"))==NULL) {                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);              }
   }            }
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);          }/* end of loop for state */
         } /* end of loop for age */
  strcpy(fileresv,"v");  
   strcat(fileresv,fileres);        /* Confidence intervalle of pij  */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {        /*
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);          fprintf(ficgp,"\nunset parametric;unset label");
   }          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
   calagedate=-1;          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);
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   k=0;          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
   for(cptcov=1;cptcov<=i1;cptcov++){        */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
       fprintf(ficrest,"\n#****** ");        first1=1;
       for(j=1;j<=cptcoveff;j++)        for (k2=1; k2<=(nlstate);k2++){
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
       fprintf(ficrest,"******\n");            if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
       fprintf(ficreseij,"\n#****** ");            for (k1=1; k1<=(nlstate);k1++){
       for(j=1;j<=cptcoveff;j++)              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                if(l1==k1) continue;
       fprintf(ficreseij,"******\n");                i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
       fprintf(ficresvij,"\n#****** ");                for (age=bage; age<=fage; age ++){ 
       for(j=1;j<=cptcoveff;j++)                  if ((int)age %5==0){
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
       fprintf(ficresvij,"******\n");                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    mu1=mu[i][(int) age]/stepm*YEARM ;
       oldm=oldms;savm=savms;                    mu2=mu[j][(int) age]/stepm*YEARM;
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);                      c12=cv12/sqrt(v1*v2);
                      /* Computing eigen value of matrix of covariance */
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       oldm=oldms;savm=savms;                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);                    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);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");                      lc2=fabs(lc2);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);                    }
       fprintf(ficrest,"\n");  
                     /* Eigen vectors */
       epj=vector(1,nlstate+1);                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       for(age=bage; age <=fage ;age++){                    /*v21=sqrt(1.-v11*v11); *//* error */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                    v21=(lc1-v1)/cv12*v11;
         if (popbased==1) {                    v12=-v21;
           for(i=1; i<=nlstate;i++)                    v22=v11;
             prlim[i][i]=probs[(int)age][i][k];                    tnalp=v21/v11;
         }                    if(first1==1){
                              first1=0;
         fprintf(ficrest," %4.0f",age);                      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);
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                    }
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                    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);
             epj[j] += prlim[i][i]*eij[i][j][(int)age];                    /*printf(fignu*/
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
           }                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
           epj[nlstate+1] +=epj[j];                    if(first==1){
         }                      first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
         for(i=1, vepp=0.;i <=nlstate;i++)                      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);
           for(j=1;j <=nlstate;j++)                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
             vepp += vareij[i][j][(int)age];                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
         for(j=1;j <=nlstate;j++){  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
         }                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         fprintf(ficrest,"\n");                      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);
 free_matrix(mint,1,maxwav,1,n);                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);                      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",\
     free_vector(weight,1,n);                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
   fclose(ficreseij);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
   fclose(ficresvij);                    }else{
   fclose(ficrest);                      first=0;
   fclose(ficpar);                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
   free_vector(epj,1,nlstate+1);                      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);
   /*------- Variance limit prevalence------*/                        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),\
   strcpy(fileresvpl,"vpl");                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
   strcat(fileresvpl,fileres);                    }/* if first */
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {                  } /* age mod 5 */
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);                } /* end loop age */
     exit(0);                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   }                first=1;
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);              } /*l12 */
             } /* k12 */
   k=0;          } /*l1 */
   for(cptcov=1;cptcov<=i1;cptcov++){        }/* k1 */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      } /* loop covariates */
       k=k+1;    }
       fprintf(ficresvpl,"\n#****** ");    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
       for(j=1;j<=cptcoveff;j++)    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
       fprintf(ficresvpl,"******\n");    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
          free_vector(xp,1,npar);
       varpl=matrix(1,nlstate,(int) bage, (int) fage);    fclose(ficresprob);
       oldm=oldms;savm=savms;    fclose(ficresprobcov);
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    fclose(ficresprobcor);
     }    fflush(ficgp);
  }    fflush(fichtmcov);
   }
   fclose(ficresvpl);  
   
   /*---------- End : free ----------------*/  /******************* Printing html file ***********/
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                      int lastpass, int stepm, int weightopt, char model[],\
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);                    int popforecast, int estepm ,\
                      double jprev1, double mprev1,double anprev1, \
                      double jprev2, double mprev2,double anprev2){
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);    int jj1, k1, i1, cpt;
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
    </ul>");
   free_matrix(matcov,1,npar,1,npar);     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
   free_vector(delti,1,npar);   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
   free_matrix(agev,1,maxwav,1,imx);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);     fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
   fprintf(fichtm,"\n</body>");             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
   fclose(fichtm);     fprintf(fichtm,"\
   fclose(ficgp);   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
               subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
   if(erreur >0)   - (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): \
     printf("End of Imach with error or warning %d\n",erreur);     <a href=\"%s\">%s</a> <br>\n",
   else   printf("End of Imach\n");             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */     fprintf(fichtm,"\
     - Population projections by age and states: \
   /* 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);*/     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   /*printf("Total time was %d uSec.\n", total_usecs);*/  
   /*------ End -----------*/  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
  end:   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
 #ifdef windows  
   /* chdir(pathcd);*/   jj1=0;
 #endif   for(k1=1; k1<=m;k1++){
  /*system("wgnuplot graph.plt");*/     for(i1=1; i1<=ncodemax[k1];i1++){
  /*system("../gp37mgw/wgnuplot graph.plt");*/       jj1++;
  /*system("cd ../gp37mgw");*/       if (cptcovn > 0) {
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
  strcpy(plotcmd,GNUPLOTPROGRAM);         for (cpt=1; cpt<=cptcoveff;cpt++) 
  strcat(plotcmd," ");           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
  strcat(plotcmd,optionfilegnuplot);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
  system(plotcmd);       }
        /* Pij */
 #ifdef windows       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> \
   while (z[0] != 'q') {  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
     /* chdir(path); */       /* Quasi-incidences */
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
     scanf("%s",z);   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> \
     if (z[0] == 'c') system("./imach");  <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
     else if (z[0] == 'e') system(optionfilehtm);         /* Period (stable) prevalence in each health state */
     else if (z[0] == 'g') system(plotcmd);         for(cpt=1; cpt<nlstate;cpt++){
     else if (z[0] == 'q') exit(0);           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);
 #endif         }
 }       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 lt 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\"95\%% CI\" w l lt 2,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l lt 2,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 3",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 lt 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)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l lt 1");
         else fprintf(ficgp,"\" t\"\" w l lt 1,");
       }
     }
     
     /*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;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /* Bug valgrind */
                    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 %d 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 %d 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 %d 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 %d 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 %d 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 %d 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 %d 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 %d 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 %d 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 %d 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 %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%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 '%ld' at line number %d 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 '%ld' at line number %d 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 '%ld' at line number %d 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 '%ld' at line number %d 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;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper 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++;
       fputs(line,stdout);
       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++;
       fputs(line, stdout);
       //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++;
         fputs(line,stdout);
         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++;
         fputs(line,stdout);
         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++;
         fputs(line,stdout);
         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); /* Gives the position of a product */
     /* 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); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * 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 <=pow(2,cptcoveff-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 ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); 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)  k
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     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");
       fprintf(ficgp,"set datafile 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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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=pow(2,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\n",cptcov, cptcod,codtab[cptcod][cptcov]);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           } /* Age */
           /* was end of cptcod */
       } /* cptcov */
       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); /*here or after loop ? */
       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 %ld 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 %ld 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.1.48  
changed lines
  Added in v.1.143


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