Diff for /imach/src/imach.c between versions 1.49 and 1.142

version 1.49, 2002/06/20 14:03:39 version 1.142, 2014/01/26 03:57:36
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.142  2014/01/26 03:57:36  brouard
      Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
   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  
   interviewed on their health status or degree of disability (in the    Revision 1.141  2014/01/26 02:42:01  brouard
   case of a health survey which is our main interest) -2- at least a    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   second wave of interviews ("longitudinal") which measure each change  
   (if any) in individual health status.  Health expectancies are    Revision 1.140  2011/09/02 10:37:54  brouard
   computed from the time spent in each health state according to a    Summary: times.h is ok with mingw32 now.
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.139  2010/06/14 07:50:17  brouard
   simplest model is the multinomial logistic model where pij is the    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   probability to be observed in state j at the second wave    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   conditional to be observed in state i at the first wave. Therefore  
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Revision 1.138  2010/04/30 18:19:40  brouard
   'age' is age and 'sex' is a covariate. If you want to have a more    *** empty log message ***
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.137  2010/04/29 18:11:38  brouard
   you to do it.  More covariates you add, slower the    (Module): Checking covariates for more complex models
   convergence.    than V1+V2. A lot of change to be done. Unstable.
   
   The advantage of this computer programme, compared to a simple    Revision 1.136  2010/04/26 20:30:53  brouard
   multinomial logistic model, is clear when the delay between waves is not    (Module): merging some libgsl code. Fixing computation
   identical for each individual. Also, if a individual missed an    of likelione (using inter/intrapolation if mle = 0) in order to
   intermediate interview, the information is lost, but taken into    get same likelihood as if mle=1.
   account using an interpolation or extrapolation.      Some cleaning of code and comments added.
   
   hPijx is the probability to be observed in state i at age x+h    Revision 1.135  2009/10/29 15:33:14  brouard
   conditional to the observed state i at age x. The delay 'h' can be    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.134  2009/10/29 13:18:53  brouard
   semester or year) is model as a multinomial logistic.  The hPx    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.133  2009/07/06 10:21:25  brouard
   hPijx.    just nforces
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.132  2009/07/06 08:22:05  brouard
   of the life expectancies. It also computes the prevalence limits.    Many tings
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.131  2009/06/20 16:22:47  brouard
            Institut national d'études démographiques, Paris.    Some dimensions resccaled
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.130  2009/05/26 06:44:34  brouard
   It is copyrighted identically to a GNU software product, ie programme and    (Module): Max Covariate is now set to 20 instead of 8. A
   software can be distributed freely for non commercial use. Latest version    lot of cleaning with variables initialized to 0. Trying to make
   can be accessed at http://euroreves.ined.fr/imach .    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   **********************************************************************/  
      Revision 1.129  2007/08/31 13:49:27  lievre
 #include <math.h>    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.128  2006/06/30 13:02:05  brouard
 #include <unistd.h>    (Module): Clarifications on computing e.j
   
 #define MAXLINE 256    Revision 1.127  2006/04/28 18:11:50  brouard
 #define GNUPLOTPROGRAM "gnuplot"    (Module): Yes the sum of survivors was wrong since
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    imach-114 because nhstepm was no more computed in the age
 #define FILENAMELENGTH 80    loop. Now we define nhstepma in the age loop.
 /*#define DEBUG*/    (Module): In order to speed up (in case of numerous covariates) we
 #define windows    compute health expectancies (without variances) in a first step
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    and then all the health expectancies with variances or standard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    deviation (needs data from the Hessian matrices) which slows the
     computation.
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    In the future we should be able to stop the program is only health
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    expectancies and graph are needed without standard deviations.
   
 #define NINTERVMAX 8    Revision 1.126  2006/04/28 17:23:28  brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    (Module): Yes the sum of survivors was wrong since
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    imach-114 because nhstepm was no more computed in the age
 #define NCOVMAX 8 /* Maximum number of covariates */    loop. Now we define nhstepma in the age loop.
 #define MAXN 20000    Version 0.98h
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.125  2006/04/04 15:20:31  lievre
 #define AGEBASE 40    Errors in calculation of health expectancies. Age was not initialized.
 #ifdef windows    Forecasting file added.
 #define DIRSEPARATOR '\\'  
 #else    Revision 1.124  2006/03/22 17:13:53  lievre
 #define DIRSEPARATOR '/'    Parameters are printed with %lf instead of %f (more numbers after the comma).
 #endif    The log-likelihood is printed in the log file
   
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    Revision 1.123  2006/03/20 10:52:43  brouard
 int erreur; /* Error number */    * imach.c (Module): <title> changed, corresponds to .htm file
 int nvar;    name. <head> headers where missing.
 int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    * imach.c (Module): Weights can have a decimal point as for
 int nlstate=2; /* Number of live states */    English (a comma might work with a correct LC_NUMERIC environment,
 int ndeath=1; /* Number of dead states */    otherwise the weight is truncated).
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Modification of warning when the covariates values are not 0 or
 int popbased=0;    1.
     Version 0.98g
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.122  2006/03/20 09:45:41  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    (Module): Weights can have a decimal point as for
 int mle, weightopt;    English (a comma might work with a correct LC_NUMERIC environment,
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    otherwise the weight is truncated).
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Modification of warning when the covariates values are not 0 or
 double jmean; /* Mean space between 2 waves */    1.
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Version 0.98g
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    Revision 1.121  2006/03/16 17:45:01  lievre
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    * imach.c (Module): Comments concerning covariates added
 FILE *fichtm; /* Html File */  
 FILE *ficreseij;    * imach.c (Module): refinements in the computation of lli if
 char filerese[FILENAMELENGTH];    status=-2 in order to have more reliable computation if stepm is
 FILE  *ficresvij;    not 1 month. Version 0.98f
 char fileresv[FILENAMELENGTH];  
 FILE  *ficresvpl;    Revision 1.120  2006/03/16 15:10:38  lievre
 char fileresvpl[FILENAMELENGTH];    (Module): refinements in the computation of lli if
 char title[MAXLINE];    status=-2 in order to have more reliable computation if stepm is
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    not 1 month. Version 0.98f
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];  
     Revision 1.119  2006/03/15 17:42:26  brouard
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 char filerest[FILENAMELENGTH];  
 char fileregp[FILENAMELENGTH];    Revision 1.118  2006/03/14 18:20:07  brouard
 char popfile[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 #define NR_END 1    (Module): Version 0.98d
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.117  2006/03/14 17:16:22  brouard
     (Module): varevsij Comments added explaining the second
 #define NRANSI    table of variances if popbased=1 .
 #define ITMAX 200    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 #define TOL 2.0e-4    (Module): Version 0.98d
   
 #define CGOLD 0.3819660    Revision 1.116  2006/03/06 10:29:27  brouard
 #define ZEPS 1.0e-10    (Module): Variance-covariance wrong links and
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    varian-covariance of ej. is needed (Saito).
   
 #define GOLD 1.618034    Revision 1.115  2006/02/27 12:17:45  brouard
 #define GLIMIT 100.0    (Module): One freematrix added in mlikeli! 0.98c
 #define TINY 1.0e-20  
     Revision 1.114  2006/02/26 12:57:58  brouard
 static double maxarg1,maxarg2;    (Module): Some improvements in processing parameter
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    filename with strsep.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.113  2006/02/24 14:20:24  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): Memory leaks checks with valgrind and:
 #define rint(a) floor(a+0.5)    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.112  2006/01/30 09:55:26  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   
 int imx;    Revision 1.111  2006/01/25 20:38:18  brouard
 int stepm;    (Module): Lots of cleaning and bugs added (Gompertz)
 /* Stepm, step in month: minimum step interpolation*/    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
 int estepm;  
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.109  2006/01/24 19:37:15  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    (Module): Comments (lines starting with a #) are allowed in data.
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.108  2006/01/19 18:05:42  lievre
     Gnuplot problem appeared...
 double *weight;    To be fixed
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.107  2006/01/19 16:20:37  brouard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    Test existence of gnuplot in imach path
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Revision 1.106  2006/01/19 13:24:36  brouard
 double ftolhess; /* Tolerance for computing hessian */    Some cleaning and links added in html output
   
 /**************** split *************************/    Revision 1.105  2006/01/05 20:23:19  lievre
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    *** empty log message ***
 {  
    char *s;                             /* pointer */    Revision 1.104  2005/09/30 16:11:43  lievre
    int  l1, l2;                         /* length counters */    (Module): sump fixed, loop imx fixed, and simplifications.
     (Module): If the status is missing at the last wave but we know
    l1 = strlen( path );                 /* length of path */    that the person is alive, then we can code his/her status as -2
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    (instead of missing=-1 in earlier versions) and his/her
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */    contributions to the likelihood is 1 - Prob of dying from last
    if ( s == NULL ) {                   /* no directory, so use current */    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 #if     defined(__bsd__)                /* get current working directory */    the healthy state at last known wave). Version is 0.98
       extern char       *getwd( );  
     Revision 1.103  2005/09/30 15:54:49  lievre
       if ( getwd( dirc ) == NULL ) {    (Module): sump fixed, loop imx fixed, and simplifications.
 #else  
       extern char       *getcwd( );    Revision 1.102  2004/09/15 17:31:30  brouard
     Add the possibility to read data file including tab characters.
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    Revision 1.101  2004/09/15 10:38:38  brouard
          return( GLOCK_ERROR_GETCWD );    Fix on curr_time
       }  
       strcpy( name, path );             /* we've got it */    Revision 1.100  2004/07/12 18:29:06  brouard
    } else {                             /* strip direcotry from path */    Add version for Mac OS X. Just define UNIX in Makefile
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.99  2004/06/05 08:57:40  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    *** empty log message ***
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.98  2004/05/16 15:05:56  brouard
       dirc[l1-l2] = 0;                  /* add zero */    New version 0.97 . First attempt to estimate force of mortality
    }    directly from the data i.e. without the need of knowing the health
    l1 = strlen( dirc );                 /* length of directory */    state at each age, but using a Gompertz model: log u =a + b*age .
 #ifdef windows    This is the basic analysis of mortality and should be done before any
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    other analysis, in order to test if the mortality estimated from the
 #else    cross-longitudinal survey is different from the mortality estimated
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    from other sources like vital statistic data.
 #endif  
    s = strrchr( name, '.' );            /* find last / */    The same imach parameter file can be used but the option for mle should be -3.
    s++;  
    strcpy(ext,s);                       /* save extension */    Agnès, who wrote this part of the code, tried to keep most of the
    l1= strlen( name);    former routines in order to include the new code within the former code.
    l2= strlen( s)+1;  
    strncpy( finame, name, l1-l2);    The output is very simple: only an estimate of the intercept and of
    finame[l1-l2]= 0;    the slope with 95% confident intervals.
    return( 0 );                         /* we're done */  
 }    Current limitations:
     A) Even if you enter covariates, i.e. with the
     model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 /******************************************/    B) There is no computation of Life Expectancy nor Life Table.
   
 void replace(char *s, char*t)    Revision 1.97  2004/02/20 13:25:42  lievre
 {    Version 0.96d. Population forecasting command line is (temporarily)
   int i;    suppressed.
   int lg=20;  
   i=0;    Revision 1.96  2003/07/15 15:38:55  brouard
   lg=strlen(t);    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   for(i=0; i<= lg; i++) {    rewritten within the same printf. Workaround: many printfs.
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.95  2003/07/08 07:54:34  brouard
   }    * imach.c (Repository):
 }    (Repository): Using imachwizard code to output a more meaningful covariance
     matrix (cov(a12,c31) instead of numbers.
 int nbocc(char *s, char occ)  
 {    Revision 1.94  2003/06/27 13:00:02  brouard
   int i,j=0;    Just cleaning
   int lg=20;  
   i=0;    Revision 1.93  2003/06/25 16:33:55  brouard
   lg=strlen(s);    (Module): On windows (cygwin) function asctime_r doesn't
   for(i=0; i<= lg; i++) {    exist so I changed back to asctime which exists.
   if  (s[i] == occ ) j++;    (Module): Version 0.96b
   }  
   return j;    Revision 1.92  2003/06/25 16:30:45  brouard
 }    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
 void cutv(char *u,char *v, char*t, char occ)  
 {    Revision 1.91  2003/06/25 15:30:29  brouard
   int i,lg,j,p=0;    * imach.c (Repository): Duplicated warning errors corrected.
   i=0;    (Repository): Elapsed time after each iteration is now output. It
   for(j=0; j<=strlen(t)-1; j++) {    helps to forecast when convergence will be reached. Elapsed time
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    is stamped in powell.  We created a new html file for the graphs
   }    concerning matrix of covariance. It has extension -cov.htm.
   
   lg=strlen(t);    Revision 1.90  2003/06/24 12:34:15  brouard
   for(j=0; j<p; j++) {    (Module): Some bugs corrected for windows. Also, when
     (u[j] = t[j]);    mle=-1 a template is output in file "or"mypar.txt with the design
   }    of the covariance matrix to be input.
      u[p]='\0';  
     Revision 1.89  2003/06/24 12:30:52  brouard
    for(j=0; j<= lg; j++) {    (Module): Some bugs corrected for windows. Also, when
     if (j>=(p+1))(v[j-p-1] = t[j]);    mle=-1 a template is output in file "or"mypar.txt with the design
   }    of the covariance matrix to be input.
 }  
     Revision 1.88  2003/06/23 17:54:56  brouard
 /********************** nrerror ********************/    * 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.
   
 void nrerror(char error_text[])    Revision 1.87  2003/06/18 12:26:01  brouard
 {    Version 0.96
   fprintf(stderr,"ERREUR ...\n");  
   fprintf(stderr,"%s\n",error_text);    Revision 1.86  2003/06/17 20:04:08  brouard
   exit(1);    (Module): Change position of html and gnuplot routines and added
 }    routine fileappend.
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    Revision 1.85  2003/06/17 13:12:43  brouard
 {    * imach.c (Repository): Check when date of death was earlier that
   double *v;    current date of interview. It may happen when the death was just
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    prior to the death. In this case, dh was negative and likelihood
   if (!v) nrerror("allocation failure in vector");    was wrong (infinity). We still send an "Error" but patch by
   return 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)
 /************************ free vector ******************/    we changed int to long in num[] and we added a new lvector for
 void free_vector(double*v, int nl, int nh)    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   free((FREE_ARG)(v+nl-NR_END));    (Repository): No more line truncation errors.
 }  
     Revision 1.84  2003/06/13 21:44:43  brouard
 /************************ivector *******************************/    * imach.c (Repository): Replace "freqsummary" at a correct
 int *ivector(long nl,long nh)    place. It differs from routine "prevalence" which may be called
 {    many times. Probs is memory consuming and must be used with
   int *v;    parcimony.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   if (!v) nrerror("allocation failure in ivector");  
   return v-nl+NR_END;    Revision 1.83  2003/06/10 13:39:11  lievre
 }    *** empty log message ***
   
 /******************free ivector **************************/    Revision 1.82  2003/06/05 15:57:20  brouard
 void free_ivector(int *v, long nl, long nh)    Add log in  imach.c and  fullversion number is now printed.
 {  
   free((FREE_ARG)(v+nl-NR_END));  */
 }  /*
      Interpolated Markov Chain
 /******************* imatrix *******************************/  
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Short summary of the programme:
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    
 {    This program computes Healthy Life Expectancies from
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   int **m;    first survey ("cross") where individuals from different ages are
      interviewed on their health status or degree of disability (in the
   /* allocate pointers to rows */    case of a health survey which is our main interest) -2- at least a
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    second wave of interviews ("longitudinal") which measure each change
   if (!m) nrerror("allocation failure 1 in matrix()");    (if any) in individual health status.  Health expectancies are
   m += NR_END;    computed from the time spent in each health state according to a
   m -= nrl;    model. More health states you consider, more time is necessary to reach the
      Maximum Likelihood of the parameters involved in the model.  The
      simplest model is the multinomial logistic model where pij is the
   /* allocate rows and set pointers to them */    probability to be observed in state j at the second wave
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    conditional to be observed in state i at the first wave. Therefore
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   m[nrl] += NR_END;    'age' is age and 'sex' is a covariate. If you want to have a more
   m[nrl] -= ncl;    complex model than "constant and age", you should modify the program
      where the markup *Covariates have to be included here again* invites
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    you to do it.  More covariates you add, slower the
      convergence.
   /* return pointer to array of pointers to rows */  
   return m;    The advantage of this computer programme, compared to a simple
 }    multinomial logistic model, is clear when the delay between waves is not
     identical for each individual. Also, if a individual missed an
 /****************** free_imatrix *************************/    intermediate interview, the information is lost, but taken into
 void free_imatrix(m,nrl,nrh,ncl,nch)    account using an interpolation or extrapolation.  
       int **m;  
       long nch,ncl,nrh,nrl;    hPijx is the probability to be observed in state i at age x+h
      /* free an int matrix allocated by imatrix() */    conditional to the observed state i at age x. The delay 'h' can be
 {    split into an exact number (nh*stepm) of unobserved intermediate
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    states. This elementary transition (by month, quarter,
   free((FREE_ARG) (m+nrl-NR_END));    semester or year) is modelled as a multinomial logistic.  The hPx
 }    matrix is simply the matrix product of nh*stepm elementary matrices
     and the contribution of each individual to the likelihood is simply
 /******************* matrix *******************************/    hPijx.
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {    Also this programme outputs the covariance matrix of the parameters but also
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    of the life expectancies. It also computes the period (stable) prevalence. 
   double **m;    
     Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));             Institut national d'études démographiques, Paris.
   if (!m) nrerror("allocation failure 1 in matrix()");    This software have been partly granted by Euro-REVES, a concerted action
   m += NR_END;    from the European Union.
   m -= nrl;    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    can be accessed at http://euroreves.ined.fr/imach .
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m[nrl] -= ncl;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    **********************************************************************/
   return m;  /*
 }    main
     read parameterfile
 /*************************free matrix ************************/    read datafile
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    concatwav
 {    freqsummary
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    if (mle >= 1)
   free((FREE_ARG)(m+nrl-NR_END));      mlikeli
 }    print results files
     if mle==1 
 /******************* ma3x *******************************/       computes hessian
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    read end of parameter file: agemin, agemax, bage, fage, estepm
 {        begin-prev-date,...
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    open gnuplot file
   double ***m;    open html file
     period (stable) prevalence
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));     for age prevalim()
   if (!m) nrerror("allocation failure 1 in matrix()");    h Pij x
   m += NR_END;    variance of p varprob
   m -= nrl;    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    Variance-covariance of DFLE
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    prevalence()
   m[nrl] += NR_END;     movingaverage()
   m[nrl] -= ncl;    varevsij() 
     if popbased==1 varevsij(,popbased)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    total life expectancies
     Variance of period (stable) prevalence
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));   end
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  */
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;   
    #include <math.h>
   for (i=nrl+1; i<=nrh; i++) {  #include <stdio.h>
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #include <stdlib.h>
     for (j=ncl+1; j<=nch; j++)  #include <string.h>
       m[i][j]=m[i][j-1]+nlay;  #include <unistd.h>
   }  
   return m;  #include <limits.h>
 }  #include <sys/types.h>
   #include <sys/stat.h>
 /*************************free ma3x ************************/  #include <errno.h>
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  extern int errno;
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #ifdef LINUX
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #include <time.h>
   free((FREE_ARG)(m+nrl-NR_END));  #include "timeval.h"
 }  #else
   #include <sys/time.h>
 /***************** f1dim *************************/  #endif
 extern int ncom;  
 extern double *pcom,*xicom;  #ifdef GSL
 extern double (*nrfunc)(double []);  #include <gsl/gsl_errno.h>
    #include <gsl/gsl_multimin.h>
 double f1dim(double x)  #endif
 {  
   int j;  /* #include <libintl.h> */
   double f;  /* #define _(String) gettext (String) */
   double *xt;  
    #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   xt=vector(1,ncom);  
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define GNUPLOTPROGRAM "gnuplot"
   f=(*nrfunc)(xt);  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   free_vector(xt,1,ncom);  #define FILENAMELENGTH 132
   return f;  
 }  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
 {  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   int iter;  
   double a,b,d,etemp;  #define NINTERVMAX 8
   double fu,fv,fw,fx;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   double ftemp;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #define NCOVMAX 20 /* Maximum number of covariates */
   double e=0.0;  #define MAXN 20000
    #define YEARM 12. /* Number of months per year */
   a=(ax < cx ? ax : cx);  #define AGESUP 130
   b=(ax > cx ? ax : cx);  #define AGEBASE 40
   x=w=v=bx;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   fw=fv=fx=(*f)(x);  #ifdef UNIX
   for (iter=1;iter<=ITMAX;iter++) {  #define DIRSEPARATOR '/'
     xm=0.5*(a+b);  #define CHARSEPARATOR "/"
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  #define ODIRSEPARATOR '\\'
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  #else
     printf(".");fflush(stdout);  #define DIRSEPARATOR '\\'
 #ifdef DEBUG  #define CHARSEPARATOR "\\"
     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 ODIRSEPARATOR '/'
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  #endif
 #endif  
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  /* $Id$ */
       *xmin=x;  /* $State$ */
       return fx;  
     }  char version[]="Imach version 0.98nR, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
     ftemp=fu;  char fullversion[]="$Revision$ $Date$"; 
     if (fabs(e) > tol1) {  char strstart[80];
       r=(x-w)*(fx-fv);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       q=(x-v)*(fx-fw);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       p=(x-v)*q-(x-w)*r;  int nvar=0, nforce=0; /* Number of variables, number of forces */
       q=2.0*(q-r);  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
       if (q > 0.0) p = -p;  int npar=NPARMAX;
       q=fabs(q);  int nlstate=2; /* Number of live states */
       etemp=e;  int ndeath=1; /* Number of dead states */
       e=d;  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  int popbased=0;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  
       else {  int *wav; /* Number of waves for this individuual 0 is possible */
         d=p/q;  int maxwav=0; /* Maxim number of waves */
         u=x+d;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
         if (u-a < tol2 || b-u < tol2)  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
           d=SIGN(tol1,xm-x);  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       }                     to the likelihood and the sum of weights (done by funcone)*/
     } else {  int mle=1, weightopt=0;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
     }  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
     fu=(*f)(u);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
     if (fu <= fx) {  double jmean=1; /* Mean space between 2 waves */
       if (u >= x) a=x; else b=x;  double **oldm, **newm, **savm; /* Working pointers to matrices */
       SHFT(v,w,x,u)  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
         SHFT(fv,fw,fx,fu)  /*FILE *fic ; */ /* Used in readdata only */
         } else {  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
           if (u < x) a=u; else b=u;  FILE *ficlog, *ficrespow;
           if (fu <= fw || w == x) {  int globpr=0; /* Global variable for printing or not */
             v=w;  double fretone; /* Only one call to likelihood */
             w=u;  long ipmx=0; /* Number of contributions */
             fv=fw;  double sw; /* Sum of weights */
             fw=fu;  char filerespow[FILENAMELENGTH];
           } else if (fu <= fv || v == x || v == w) {  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
             v=u;  FILE *ficresilk;
             fv=fu;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
           }  FILE *ficresprobmorprev;
         }  FILE *fichtm, *fichtmcov; /* Html File */
   }  FILE *ficreseij;
   nrerror("Too many iterations in brent");  char filerese[FILENAMELENGTH];
   *xmin=x;  FILE *ficresstdeij;
   return fx;  char fileresstde[FILENAMELENGTH];
 }  FILE *ficrescveij;
   char filerescve[FILENAMELENGTH];
 /****************** mnbrak ***********************/  FILE  *ficresvij;
   char fileresv[FILENAMELENGTH];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  FILE  *ficresvpl;
             double (*func)(double))  char fileresvpl[FILENAMELENGTH];
 {  char title[MAXLINE];
   double ulim,u,r,q, dum;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   double fu;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
    char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   *fa=(*func)(*ax);  char command[FILENAMELENGTH];
   *fb=(*func)(*bx);  int  outcmd=0;
   if (*fb > *fa) {  
     SHFT(dum,*ax,*bx,dum)  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
       SHFT(dum,*fb,*fa,dum)  
       }  char filelog[FILENAMELENGTH]; /* Log file */
   *cx=(*bx)+GOLD*(*bx-*ax);  char filerest[FILENAMELENGTH];
   *fc=(*func)(*cx);  char fileregp[FILENAMELENGTH];
   while (*fb > *fc) {  char popfile[FILENAMELENGTH];
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  struct timezone tzp;
     if ((*bx-u)*(u-*cx) > 0.0) {  extern int gettimeofday();
       fu=(*func)(u);  struct tm tmg, tm, tmf, *gmtime(), *localtime();
     } else if ((*cx-u)*(u-ulim) > 0.0) {  long time_value;
       fu=(*func)(u);  extern long time();
       if (fu < *fc) {  char strcurr[80], strfor[80];
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))  char *endptr;
           }  long lval;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  double dval;
       u=ulim;  
       fu=(*func)(u);  #define NR_END 1
     } else {  #define FREE_ARG char*
       u=(*cx)+GOLD*(*cx-*bx);  #define FTOL 1.0e-10
       fu=(*func)(u);  
     }  #define NRANSI 
     SHFT(*ax,*bx,*cx,u)  #define ITMAX 200 
       SHFT(*fa,*fb,*fc,fu)  
       }  #define TOL 2.0e-4 
 }  
   #define CGOLD 0.3819660 
 /*************** linmin ************************/  #define ZEPS 1.0e-10 
   #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 int ncom;  
 double *pcom,*xicom;  #define GOLD 1.618034 
 double (*nrfunc)(double []);  #define GLIMIT 100.0 
    #define TINY 1.0e-20 
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  static double maxarg1,maxarg2;
   double brent(double ax, double bx, double cx,  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
                double (*f)(double), double tol, double *xmin);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   double f1dim(double x);    
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
               double *fc, double (*func)(double));  #define rint(a) floor(a+0.5)
   int j;  
   double xx,xmin,bx,ax;  static double sqrarg;
   double fx,fb,fa;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
    #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   ncom=n;  int agegomp= AGEGOMP;
   pcom=vector(1,n);  
   xicom=vector(1,n);  int imx; 
   nrfunc=func;  int stepm=1;
   for (j=1;j<=n;j++) {  /* Stepm, step in month: minimum step interpolation*/
     pcom[j]=p[j];  
     xicom[j]=xi[j];  int estepm;
   }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   ax=0.0;  
   xx=1.0;  int m,nb;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  long *num;
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 #ifdef DEBUG  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  double **pmmij, ***probs;
 #endif  double *ageexmed,*agecens;
   for (j=1;j<=n;j++) {  double dateintmean=0;
     xi[j] *= xmin;  
     p[j] += xi[j];  double *weight;
   }  int **s; /* Status */
   free_vector(xicom,1,n);  double *agedc;
   free_vector(pcom,1,n);  double  **covar; /**< covar[i,j], value of jth covariate for individual i,
 }                    * covar=matrix(0,NCOVMAX,1,n); 
                     * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
 /*************** powell ************************/  double  idx; 
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
             double (*func)(double []))  int **codtab; /**< codtab=imatrix(1,100,1,10); */
 {  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
   void linmin(double p[], double xi[], int n, double *fret,  double *lsurv, *lpop, *tpop;
               double (*func)(double []));  
   int i,ibig,j;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   double del,t,*pt,*ptt,*xit;  double ftolhess; /* Tolerance for computing hessian */
   double fp,fptt;  
   double *xits;  /**************** split *************************/
   pt=vector(1,n);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   ptt=vector(1,n);  {
   xit=vector(1,n);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   xits=vector(1,n);       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   *fret=(*func)(p);    */ 
   for (j=1;j<=n;j++) pt[j]=p[j];    char  *ss;                            /* pointer */
   for (*iter=1;;++(*iter)) {    int   l1, l2;                         /* length counters */
     fp=(*fret);  
     ibig=0;    l1 = strlen(path );                   /* length of path */
     del=0.0;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     for (i=1;i<=n;i++)    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       printf(" %d %.12f",i, p[i]);      strcpy( name, path );               /* we got the fullname name because no directory */
     printf("\n");      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     for (i=1;i<=n;i++) {        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       for (j=1;j<=n;j++) xit[j]=xi[j][i];      /* get current working directory */
       fptt=(*fret);      /*    extern  char* getcwd ( char *buf , int len);*/
 #ifdef DEBUG      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       printf("fret=%lf \n",*fret);        return( GLOCK_ERROR_GETCWD );
 #endif      }
       printf("%d",i);fflush(stdout);      /* got dirc from getcwd*/
       linmin(p,xit,n,fret,func);      printf(" DIRC = %s \n",dirc);
       if (fabs(fptt-(*fret)) > del) {    } else {                              /* strip direcotry from path */
         del=fabs(fptt-(*fret));      ss++;                               /* after this, the filename */
         ibig=i;      l2 = strlen( ss );                  /* length of filename */
       }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 #ifdef DEBUG      strcpy( name, ss );         /* save file name */
       printf("%d %.12e",i,(*fret));      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       for (j=1;j<=n;j++) {      dirc[l1-l2] = 0;                    /* add zero */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      printf(" DIRC2 = %s \n",dirc);
         printf(" x(%d)=%.12e",j,xit[j]);    }
       }    /* We add a separator at the end of dirc if not exists */
       for(j=1;j<=n;j++)    l1 = strlen( dirc );                  /* length of directory */
         printf(" p=%.12e",p[j]);    if( dirc[l1-1] != DIRSEPARATOR ){
       printf("\n");      dirc[l1] =  DIRSEPARATOR;
 #endif      dirc[l1+1] = 0; 
     }      printf(" DIRC3 = %s \n",dirc);
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    }
 #ifdef DEBUG    ss = strrchr( name, '.' );            /* find last / */
       int k[2],l;    if (ss >0){
       k[0]=1;      ss++;
       k[1]=-1;      strcpy(ext,ss);                     /* save extension */
       printf("Max: %.12e",(*func)(p));      l1= strlen( name);
       for (j=1;j<=n;j++)      l2= strlen(ss)+1;
         printf(" %.12e",p[j]);      strncpy( finame, name, l1-l2);
       printf("\n");      finame[l1-l2]= 0;
       for(l=0;l<=1;l++) {    }
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    return( 0 );                          /* we're done */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  }
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  
       }  /******************************************/
 #endif  
   void replace_back_to_slash(char *s, char*t)
   {
       free_vector(xit,1,n);    int i;
       free_vector(xits,1,n);    int lg=0;
       free_vector(ptt,1,n);    i=0;
       free_vector(pt,1,n);    lg=strlen(t);
       return;    for(i=0; i<= lg; i++) {
     }      (s[i] = t[i]);
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");      if (t[i]== '\\') s[i]='/';
     for (j=1;j<=n;j++) {    }
       ptt[j]=2.0*p[j]-pt[j];  }
       xit[j]=p[j]-pt[j];  
       pt[j]=p[j];  char *trimbb(char *out, char *in)
     }  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
     fptt=(*func)(ptt);    char *s;
     if (fptt < fp) {    s=out;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    while (*in != '\0'){
       if (t < 0.0) {      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
         linmin(p,xit,n,fret,func);        in++;
         for (j=1;j<=n;j++) {      }
           xi[j][ibig]=xi[j][n];      *out++ = *in++;
           xi[j][n]=xit[j];    }
         }    *out='\0';
 #ifdef DEBUG    return s;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  }
         for(j=1;j<=n;j++)  
           printf(" %.12e",xit[j]);  char *cutv(char *blocc, char *alocc, char *in, char occ)
         printf("\n");  {
 #endif    /* 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')
     }       gives blocc="abcdef2ghi" and alocc="j".
   }       If occ is not found blocc is null and alocc is equal to in. Returns alocc
 }    */
     char *s, *t;
 /**** Prevalence limit ****************/    t=in;s=in;
     while (*in != '\0'){
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      while( *in == occ){
 {        *blocc++ = *in++;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit        s=in;
      matrix by transitions matrix until convergence is reached */      }
       *blocc++ = *in++;
   int i, ii,j,k;    }
   double min, max, maxmin, maxmax,sumnew=0.;    if (s == t) /* occ not found */
   double **matprod2();      *(blocc-(in-s))='\0';
   double **out, cov[NCOVMAX], **pmij();    else
   double **newm;      *(blocc-(in-s)-1)='\0';
   double agefin, delaymax=50 ; /* Max number of years to converge */    in=s;
     while ( *in != '\0'){
   for (ii=1;ii<=nlstate+ndeath;ii++)      *alocc++ = *in++;
     for (j=1;j<=nlstate+ndeath;j++){    }
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }    *alocc='\0';
     return s;
    cov[1]=1.;  }
    
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  int nbocc(char *s, char occ)
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  {
     newm=savm;    int i,j=0;
     /* Covariates have to be included here again */    int lg=20;
      cov[2]=agefin;    i=0;
      lg=strlen(s);
       for (k=1; k<=cptcovn;k++) {    for(i=0; i<= lg; i++) {
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if  (s[i] == occ ) j++;
         /*      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]]);*/    }
       }    return j;
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  }
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /* void cutv(char *u,char *v, char*t, char occ) */
   /* { */
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  /*      gives u="abcdef2ghi" and v="j" *\/ */
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  /*   int i,lg,j,p=0; */
   /*   i=0; */
     savm=oldm;  /*   lg=strlen(t); */
     oldm=newm;  /*   for(j=0; j<=lg-1; j++) { */
     maxmax=0.;  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
     for(j=1;j<=nlstate;j++){  /*   } */
       min=1.;  
       max=0.;  /*   for(j=0; j<p; j++) { */
       for(i=1; i<=nlstate; i++) {  /*     (u[j] = t[j]); */
         sumnew=0;  /*   } */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /*      u[p]='\0'; */
         prlim[i][j]= newm[i][j]/(1-sumnew);  
         max=FMAX(max,prlim[i][j]);  /*    for(j=0; j<= lg; j++) { */
         min=FMIN(min,prlim[i][j]);  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
       }  /*   } */
       maxmin=max-min;  /* } */
       maxmax=FMAX(maxmax,maxmin);  
     }  /********************** nrerror ********************/
     if(maxmax < ftolpl){  
       return prlim;  void nrerror(char error_text[])
     }  {
   }    fprintf(stderr,"ERREUR ...\n");
 }    fprintf(stderr,"%s\n",error_text);
     exit(EXIT_FAILURE);
 /*************** transition probabilities ***************/  }
   /*********************** vector *******************/
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  double *vector(int nl, int nh)
 {  {
   double s1, s2;    double *v;
   /*double t34;*/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   int i,j,j1, nc, ii, jj;    if (!v) nrerror("allocation failure in vector");
     return v-nl+NR_END;
     for(i=1; i<= nlstate; i++){  }
     for(j=1; j<i;j++){  
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  /************************ free vector ******************/
         /*s2 += param[i][j][nc]*cov[nc];*/  void free_vector(double*v, int nl, int nh)
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  {
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    free((FREE_ARG)(v+nl-NR_END));
       }  }
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  /************************ivector *******************************/
     }  int *ivector(long nl,long nh)
     for(j=i+1; j<=nlstate+ndeath;j++){  {
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    int *v;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    if (!v) nrerror("allocation failure in ivector");
       }    return v-nl+NR_END;
       ps[i][j]=s2;  }
     }  
   }  /******************free ivector **************************/
     /*ps[3][2]=1;*/  void free_ivector(int *v, long nl, long nh)
   {
   for(i=1; i<= nlstate; i++){    free((FREE_ARG)(v+nl-NR_END));
      s1=0;  }
     for(j=1; j<i; j++)  
       s1+=exp(ps[i][j]);  /************************lvector *******************************/
     for(j=i+1; j<=nlstate+ndeath; j++)  long *lvector(long nl,long nh)
       s1+=exp(ps[i][j]);  {
     ps[i][i]=1./(s1+1.);    long *v;
     for(j=1; j<i; j++)    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       ps[i][j]= exp(ps[i][j])*ps[i][i];    if (!v) nrerror("allocation failure in ivector");
     for(j=i+1; j<=nlstate+ndeath; j++)    return v-nl+NR_END;
       ps[i][j]= exp(ps[i][j])*ps[i][i];  }
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  
   } /* end i */  /******************free lvector **************************/
   void free_lvector(long *v, long nl, long nh)
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  {
     for(jj=1; jj<= nlstate+ndeath; jj++){    free((FREE_ARG)(v+nl-NR_END));
       ps[ii][jj]=0;  }
       ps[ii][ii]=1;  
     }  /******************* imatrix *******************************/
   }  int **imatrix(long nrl, long nrh, long ncl, long nch) 
        /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   { 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     for(jj=1; jj<= nlstate+ndeath; jj++){    int **m; 
      printf("%lf ",ps[ii][jj]);    
    }    /* allocate pointers to rows */ 
     printf("\n ");    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     }    if (!m) nrerror("allocation failure 1 in matrix()"); 
     printf("\n ");printf("%lf ",cov[2]);*/    m += NR_END; 
 /*    m -= nrl; 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    
   goto end;*/    
     return ps;    /* allocate rows and set pointers to them */ 
 }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 /**************** Product of 2 matrices ******************/    m[nrl] += NR_END; 
     m[nrl] -= ncl; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    
 {    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    /* return pointer to array of pointers to rows */ 
   /* in, b, out are matrice of pointers which should have been initialized    return m; 
      before: only the contents of out is modified. The function returns  } 
      a pointer to pointers identical to out */  
   long i, j, k;  /****************** free_imatrix *************************/
   for(i=nrl; i<= nrh; i++)  void free_imatrix(m,nrl,nrh,ncl,nch)
     for(k=ncolol; k<=ncoloh; k++)        int **m;
       for(j=ncl,out[i][k]=0.; j<=nch; j++)        long nch,ncl,nrh,nrl; 
         out[i][k] +=in[i][j]*b[j][k];       /* free an int matrix allocated by imatrix() */ 
   { 
   return out;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 }    free((FREE_ARG) (m+nrl-NR_END)); 
   } 
   
 /************* Higher Matrix Product ***************/  /******************* matrix *******************************/
   double **matrix(long nrl, long nrh, long ncl, long nch)
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  {
 {    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    double **m;
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    if (!m) nrerror("allocation failure 1 in matrix()");
      (typically every 2 years instead of every month which is too big).    m += NR_END;
      Model is determined by parameters x and covariates have to be    m -= nrl;
      included manually here.  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
      */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
   int i, j, d, h, k;    m[nrl] -= ncl;
   double **out, cov[NCOVMAX];  
   double **newm;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     return m;
   /* Hstepm could be zero and should return the unit matrix */    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
   for (i=1;i<=nlstate+ndeath;i++)     */
     for (j=1;j<=nlstate+ndeath;j++){  }
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);  /*************************free matrix ************************/
     }  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  {
   for(h=1; h <=nhstepm; h++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     for(d=1; d <=hstepm; d++){    free((FREE_ARG)(m+nrl-NR_END));
       newm=savm;  }
       /* Covariates have to be included here again */  
       cov[1]=1.;  /******************* ma3x *******************************/
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  {
       for (k=1; k<=cptcovage;k++)    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    double ***m;
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
     m += NR_END;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    m -= nrl;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       savm=oldm;    m[nrl] += NR_END;
       oldm=newm;    m[nrl] -= ncl;
     }  
     for(i=1; i<=nlstate+ndeath; i++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       for(j=1;j<=nlstate+ndeath;j++) {  
         po[i][j][h]=newm[i][j];    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
          */    m[nrl][ncl] += NR_END;
       }    m[nrl][ncl] -= nll;
   } /* end h */    for (j=ncl+1; j<=nch; j++) 
   return po;      m[nrl][j]=m[nrl][j-1]+nlay;
 }    
     for (i=nrl+1; i<=nrh; i++) {
       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
 /*************** log-likelihood *************/      for (j=ncl+1; j<=nch; j++) 
 double func( double *x)        m[i][j]=m[i][j-1]+nlay;
 {    }
   int i, ii, j, k, mi, d, kk;    return m; 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   double **out;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   double sw; /* Sum of weights */    */
   double lli; /* Individual log likelihood */  }
   long ipmx;  
   /*extern weight */  /*************************free ma3x ************************/
   /* We are differentiating ll according to initial status */  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  {
   /*for(i=1;i<imx;i++)    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     printf(" %d\n",s[4][i]);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   */    free((FREE_ARG)(m+nrl-NR_END));
   cov[1]=1.;  }
   
   for(k=1; k<=nlstate; k++) ll[k]=0.;  /*************** function subdirf ***********/
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){  char *subdirf(char fileres[])
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  {
     for(mi=1; mi<= wav[i]-1; mi++){    /* Caution optionfilefiname is hidden */
       for (ii=1;ii<=nlstate+ndeath;ii++)    strcpy(tmpout,optionfilefiname);
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    strcat(tmpout,"/"); /* Add to the right */
       for(d=0; d<dh[mi][i]; d++){    strcat(tmpout,fileres);
         newm=savm;    return tmpout;
         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];  /*************** function subdirf2 ***********/
         }  char *subdirf2(char fileres[], char *preop)
          {
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    /* Caution optionfilefiname is hidden */
         savm=oldm;    strcpy(tmpout,optionfilefiname);
         oldm=newm;    strcat(tmpout,"/");
            strcat(tmpout,preop);
            strcat(tmpout,fileres);
       } /* end mult */    return tmpout;
        }
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  /*************** function subdirf3 ***********/
       ipmx +=1;  char *subdirf3(char fileres[], char *preop, char *preop2)
       sw += weight[i];  {
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    
     } /* end of wave */    /* Caution optionfilefiname is hidden */
   } /* end of individual */    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    strcat(tmpout,preop);
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    strcat(tmpout,preop2);
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    strcat(tmpout,fileres);
   return -l;    return tmpout;
 }  }
   
   /***************** f1dim *************************/
 /*********** Maximum Likelihood Estimation ***************/  extern int ncom; 
   extern double *pcom,*xicom;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  extern double (*nrfunc)(double []); 
 {   
   int i,j, iter;  double f1dim(double x) 
   double **xi,*delti;  { 
   double fret;    int j; 
   xi=matrix(1,npar,1,npar);    double f;
   for (i=1;i<=npar;i++)    double *xt; 
     for (j=1;j<=npar;j++)   
       xi[i][j]=(i==j ? 1.0 : 0.0);    xt=vector(1,ncom); 
   printf("Powell\n");    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   powell(p,xi,npar,ftol,&iter,&fret,func);    f=(*nrfunc)(xt); 
     free_vector(xt,1,ncom); 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    return f; 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));  } 
   
 }  /*****************brent *************************/
   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
 /**** Computes Hessian and covariance matrix ***/  { 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    int iter; 
 {    double a,b,d,etemp;
   double  **a,**y,*x,pd;    double fu,fv,fw,fx;
   double **hess;    double ftemp;
   int i, j,jk;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   int *indx;    double e=0.0; 
    
   double hessii(double p[], double delta, int theta, double delti[]);    a=(ax < cx ? ax : cx); 
   double hessij(double p[], double delti[], int i, int j);    b=(ax > cx ? ax : cx); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    x=w=v=bx; 
   void ludcmp(double **a, int npar, int *indx, double *d) ;    fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
   hess=matrix(1,npar,1,npar);      xm=0.5*(a+b); 
       tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   printf("\nCalculation of the hessian matrix. Wait...\n");      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   for (i=1;i<=npar;i++){      printf(".");fflush(stdout);
     printf("%d",i);fflush(stdout);      fprintf(ficlog,".");fflush(ficlog);
     hess[i][i]=hessii(p,ftolhess,i,delti);  #ifdef DEBUG
     /*printf(" %f ",p[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(" %lf ",hess[i][i]);*/      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);
   }      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
    #endif
   for (i=1;i<=npar;i++) {      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     for (j=1;j<=npar;j++)  {        *xmin=x; 
       if (j>i) {        return fx; 
         printf(".%d%d",i,j);fflush(stdout);      } 
         hess[i][j]=hessij(p,delti,i,j);      ftemp=fu;
         hess[j][i]=hess[i][j];          if (fabs(e) > tol1) { 
         /*printf(" %lf ",hess[i][j]);*/        r=(x-w)*(fx-fv); 
       }        q=(x-v)*(fx-fw); 
     }        p=(x-v)*q-(x-w)*r; 
   }        q=2.0*(q-r); 
   printf("\n");        if (q > 0.0) p = -p; 
         q=fabs(q); 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        etemp=e; 
          e=d; 
   a=matrix(1,npar,1,npar);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   y=matrix(1,npar,1,npar);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   x=vector(1,npar);        else { 
   indx=ivector(1,npar);          d=p/q; 
   for (i=1;i<=npar;i++)          u=x+d; 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];          if (u-a < tol2 || b-u < tol2) 
   ludcmp(a,npar,indx,&pd);            d=SIGN(tol1,xm-x); 
         } 
   for (j=1;j<=npar;j++) {      } else { 
     for (i=1;i<=npar;i++) x[i]=0;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     x[j]=1;      } 
     lubksb(a,npar,indx,x);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     for (i=1;i<=npar;i++){      fu=(*f)(u); 
       matcov[i][j]=x[i];      if (fu <= fx) { 
     }        if (u >= x) a=x; else b=x; 
   }        SHFT(v,w,x,u) 
           SHFT(fv,fw,fx,fu) 
   printf("\n#Hessian matrix#\n");          } else { 
   for (i=1;i<=npar;i++) {            if (u < x) a=u; else b=u; 
     for (j=1;j<=npar;j++) {            if (fu <= fw || w == x) { 
       printf("%.3e ",hess[i][j]);              v=w; 
     }              w=u; 
     printf("\n");              fv=fw; 
   }              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
   /* Recompute Inverse */              v=u; 
   for (i=1;i<=npar;i++)              fv=fu; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];            } 
   ludcmp(a,npar,indx,&pd);          } 
     } 
   /*  printf("\n#Hessian matrix recomputed#\n");    nrerror("Too many iterations in brent"); 
     *xmin=x; 
   for (j=1;j<=npar;j++) {    return fx; 
     for (i=1;i<=npar;i++) x[i]=0;  } 
     x[j]=1;  
     lubksb(a,npar,indx,x);  /****************** mnbrak ***********************/
     for (i=1;i<=npar;i++){  
       y[i][j]=x[i];  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       printf("%.3e ",y[i][j]);              double (*func)(double)) 
     }  { 
     printf("\n");    double ulim,u,r,q, dum;
   }    double fu; 
   */   
     *fa=(*func)(*ax); 
   free_matrix(a,1,npar,1,npar);    *fb=(*func)(*bx); 
   free_matrix(y,1,npar,1,npar);    if (*fb > *fa) { 
   free_vector(x,1,npar);      SHFT(dum,*ax,*bx,dum) 
   free_ivector(indx,1,npar);        SHFT(dum,*fb,*fa,dum) 
   free_matrix(hess,1,npar,1,npar);        } 
     *cx=(*bx)+GOLD*(*bx-*ax); 
     *fc=(*func)(*cx); 
 }    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
 /*************** hessian matrix ****************/      q=(*bx-*cx)*(*fb-*fa); 
 double hessii( double x[], double delta, int theta, double delti[])      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
 {        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   int i;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
   int l=1, lmax=20;      if ((*bx-u)*(u-*cx) > 0.0) { 
   double k1,k2;        fu=(*func)(u); 
   double p2[NPARMAX+1];      } else if ((*cx-u)*(u-ulim) > 0.0) { 
   double res;        fu=(*func)(u); 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        if (fu < *fc) { 
   double fx;          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   int k=0,kmax=10;            SHFT(*fb,*fc,fu,(*func)(u)) 
   double l1;            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   fx=func(x);        u=ulim; 
   for (i=1;i<=npar;i++) p2[i]=x[i];        fu=(*func)(u); 
   for(l=0 ; l <=lmax; l++){      } else { 
     l1=pow(10,l);        u=(*cx)+GOLD*(*cx-*bx); 
     delts=delt;        fu=(*func)(u); 
     for(k=1 ; k <kmax; k=k+1){      } 
       delt = delta*(l1*k);      SHFT(*ax,*bx,*cx,u) 
       p2[theta]=x[theta] +delt;        SHFT(*fa,*fb,*fc,fu) 
       k1=func(p2)-fx;        } 
       p2[theta]=x[theta]-delt;  } 
       k2=func(p2)-fx;  
       /*res= (k1-2.0*fx+k2)/delt/delt; */  /*************** linmin ************************/
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  
        int ncom; 
 #ifdef DEBUG  double *pcom,*xicom;
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);  double (*nrfunc)(double []); 
 #endif   
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  { 
         k=kmax;    double brent(double ax, double bx, double cx, 
       }                 double (*f)(double), double tol, double *xmin); 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    double f1dim(double x); 
         k=kmax; l=lmax*10.;    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       }                double *fc, double (*func)(double)); 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    int j; 
         delts=delt;    double xx,xmin,bx,ax; 
       }    double fx,fb,fa;
     }   
   }    ncom=n; 
   delti[theta]=delts;    pcom=vector(1,n); 
   return res;    xicom=vector(1,n); 
      nrfunc=func; 
 }    for (j=1;j<=n;j++) { 
       pcom[j]=p[j]; 
 double hessij( double x[], double delti[], int thetai,int thetaj)      xicom[j]=xi[j]; 
 {    } 
   int i;    ax=0.0; 
   int l=1, l1, lmax=20;    xx=1.0; 
   double k1,k2,k3,k4,res,fx;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   double p2[NPARMAX+1];    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   int k;  #ifdef DEBUG
     printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   fx=func(x);    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   for (k=1; k<=2; k++) {  #endif
     for (i=1;i<=npar;i++) p2[i]=x[i];    for (j=1;j<=n;j++) { 
     p2[thetai]=x[thetai]+delti[thetai]/k;      xi[j] *= xmin; 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      p[j] += xi[j]; 
     k1=func(p2)-fx;    } 
      free_vector(xicom,1,n); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    free_vector(pcom,1,n); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  } 
     k2=func(p2)-fx;  
    char *asc_diff_time(long time_sec, char ascdiff[])
     p2[thetai]=x[thetai]-delti[thetai]/k;  {
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    long sec_left, days, hours, minutes;
     k3=func(p2)-fx;    days = (time_sec) / (60*60*24);
      sec_left = (time_sec) % (60*60*24);
     p2[thetai]=x[thetai]-delti[thetai]/k;    hours = (sec_left) / (60*60) ;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    sec_left = (sec_left) %(60*60);
     k4=func(p2)-fx;    minutes = (sec_left) /60;
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    sec_left = (sec_left) % (60);
 #ifdef DEBUG    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     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);    return ascdiff;
 #endif  }
   }  
   return res;  /*************** powell ************************/
 }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
               double (*func)(double [])) 
 /************** Inverse of matrix **************/  { 
 void ludcmp(double **a, int n, int *indx, double *d)    void linmin(double p[], double xi[], int n, double *fret, 
 {                double (*func)(double [])); 
   int i,imax,j,k;    int i,ibig,j; 
   double big,dum,sum,temp;    double del,t,*pt,*ptt,*xit;
   double *vv;    double fp,fptt;
      double *xits;
   vv=vector(1,n);    int niterf, itmp;
   *d=1.0;  
   for (i=1;i<=n;i++) {    pt=vector(1,n); 
     big=0.0;    ptt=vector(1,n); 
     for (j=1;j<=n;j++)    xit=vector(1,n); 
       if ((temp=fabs(a[i][j])) > big) big=temp;    xits=vector(1,n); 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    *fret=(*func)(p); 
     vv[i]=1.0/big;    for (j=1;j<=n;j++) pt[j]=p[j]; 
   }    for (*iter=1;;++(*iter)) { 
   for (j=1;j<=n;j++) {      fp=(*fret); 
     for (i=1;i<j;i++) {      ibig=0; 
       sum=a[i][j];      del=0.0; 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];      last_time=curr_time;
       a[i][j]=sum;      (void) gettimeofday(&curr_time,&tzp);
     }      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
     big=0.0;      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
     for (i=j;i<=n;i++) {  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       sum=a[i][j];     for (i=1;i<=n;i++) {
       for (k=1;k<j;k++)        printf(" %d %.12f",i, p[i]);
         sum -= a[i][k]*a[k][j];        fprintf(ficlog," %d %.12lf",i, p[i]);
       a[i][j]=sum;        fprintf(ficrespow," %.12lf", p[i]);
       if ( (dum=vv[i]*fabs(sum)) >= big) {      }
         big=dum;      printf("\n");
         imax=i;      fprintf(ficlog,"\n");
       }      fprintf(ficrespow,"\n");fflush(ficrespow);
     }      if(*iter <=3){
     if (j != imax) {        tm = *localtime(&curr_time.tv_sec);
       for (k=1;k<=n;k++) {        strcpy(strcurr,asctime(&tm));
         dum=a[imax][k];  /*       asctime_r(&tm,strcurr); */
         a[imax][k]=a[j][k];        forecast_time=curr_time; 
         a[j][k]=dum;        itmp = strlen(strcurr);
       }        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       *d = -(*d);          strcurr[itmp-1]='\0';
       vv[imax]=vv[j];        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);
     indx[j]=imax;        for(niterf=10;niterf<=30;niterf+=10){
     if (a[j][j] == 0.0) a[j][j]=TINY;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     if (j != n) {          tmf = *localtime(&forecast_time.tv_sec);
       dum=1.0/(a[j][j]);  /*      asctime_r(&tmf,strfor); */
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          strcpy(strfor,asctime(&tmf));
     }          itmp = strlen(strfor);
   }          if(strfor[itmp-1]=='\n')
   free_vector(vv,1,n);  /* Doesn't work */          strfor[itmp-1]='\0';
 ;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
 }          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);
         }
 void lubksb(double **a, int n, int *indx, double b[])      }
 {      for (i=1;i<=n;i++) { 
   int i,ii=0,ip,j;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   double sum;        fptt=(*fret); 
    #ifdef DEBUG
   for (i=1;i<=n;i++) {        printf("fret=%lf \n",*fret);
     ip=indx[i];        fprintf(ficlog,"fret=%lf \n",*fret);
     sum=b[ip];  #endif
     b[ip]=b[i];        printf("%d",i);fflush(stdout);
     if (ii)        fprintf(ficlog,"%d",i);fflush(ficlog);
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        linmin(p,xit,n,fret,func); 
     else if (sum) ii=i;        if (fabs(fptt-(*fret)) > del) { 
     b[i]=sum;          del=fabs(fptt-(*fret)); 
   }          ibig=i; 
   for (i=n;i>=1;i--) {        } 
     sum=b[i];  #ifdef DEBUG
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        printf("%d %.12e",i,(*fret));
     b[i]=sum/a[i][i];        fprintf(ficlog,"%d %.12e",i,(*fret));
   }        for (j=1;j<=n;j++) {
 }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           printf(" x(%d)=%.12e",j,xit[j]);
 /************ Frequencies ********************/          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
 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)        }
 {  /* Some frequencies */        for(j=1;j<=n;j++) {
            printf(" p=%.12e",p[j]);
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;          fprintf(ficlog," p=%.12e",p[j]);
   double ***freq; /* Frequencies */        }
   double *pp;        printf("\n");
   double pos, k2, dateintsum=0,k2cpt=0;        fprintf(ficlog,"\n");
   FILE *ficresp;  #endif
   char fileresp[FILENAMELENGTH];      } 
        if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   pp=vector(1,nlstate);  #ifdef DEBUG
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        int k[2],l;
   strcpy(fileresp,"p");        k[0]=1;
   strcat(fileresp,fileres);        k[1]=-1;
   if((ficresp=fopen(fileresp,"w"))==NULL) {        printf("Max: %.12e",(*func)(p));
     printf("Problem with prevalence resultfile: %s\n", fileresp);        fprintf(ficlog,"Max: %.12e",(*func)(p));
     exit(0);        for (j=1;j<=n;j++) {
   }          printf(" %.12e",p[j]);
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          fprintf(ficlog," %.12e",p[j]);
   j1=0;        }
          printf("\n");
   j=cptcoveff;        fprintf(ficlog,"\n");
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for(l=0;l<=1;l++) {
            for (j=1;j<=n;j++) {
   for(k1=1; k1<=j;k1++){            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     for(i1=1; i1<=ncodemax[k1];i1++){            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       j1++;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          }
         scanf("%d", i);*/          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       for (i=-1; i<=nlstate+ndeath; i++)            fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         for (jk=-1; jk<=nlstate+ndeath; jk++)          }
           for(m=agemin; m <= agemax+3; m++)  #endif
             freq[i][jk][m]=0;  
        
       dateintsum=0;        free_vector(xit,1,n); 
       k2cpt=0;        free_vector(xits,1,n); 
       for (i=1; i<=imx; i++) {        free_vector(ptt,1,n); 
         bool=1;        free_vector(pt,1,n); 
         if  (cptcovn>0) {        return; 
           for (z1=1; z1<=cptcoveff; z1++)      } 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
               bool=0;      for (j=1;j<=n;j++) { 
         }        ptt[j]=2.0*p[j]-pt[j]; 
         if (bool==1) {        xit[j]=p[j]-pt[j]; 
           for(m=firstpass; m<=lastpass; m++){        pt[j]=p[j]; 
             k2=anint[m][i]+(mint[m][i]/12.);      } 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      fptt=(*func)(ptt); 
               if(agev[m][i]==0) agev[m][i]=agemax+1;      if (fptt < fp) { 
               if(agev[m][i]==1) agev[m][i]=agemax+2;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
               if (m<lastpass) {        if (t < 0.0) { 
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          linmin(p,xit,n,fret,func); 
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          for (j=1;j<=n;j++) { 
               }            xi[j][ibig]=xi[j][n]; 
                          xi[j][n]=xit[j]; 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {          }
                 dateintsum=dateintsum+k2;  #ifdef DEBUG
                 k2cpt++;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
               }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
             }          for(j=1;j<=n;j++){
           }            printf(" %.12e",xit[j]);
         }            fprintf(ficlog," %.12e",xit[j]);
       }          }
                  printf("\n");
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          fprintf(ficlog,"\n");
   #endif
       if  (cptcovn>0) {        }
         fprintf(ficresp, "\n#********** Variable ");      } 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    } 
         fprintf(ficresp, "**********\n#");  } 
       }  
       for(i=1; i<=nlstate;i++)  /**** Prevalence limit (stable or period prevalence)  ****************/
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  
       fprintf(ficresp, "\n");  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
        {
       for(i=(int)agemin; i <= (int)agemax+3; i++){    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
         if(i==(int)agemax+3)       matrix by transitions matrix until convergence is reached */
           printf("Total");  
         else    int i, ii,j,k;
           printf("Age %d", i);    double min, max, maxmin, maxmax,sumnew=0.;
         for(jk=1; jk <=nlstate ; jk++){    double **matprod2();
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    double **out, cov[NCOVMAX+1], **pmij();
             pp[jk] += freq[jk][m][i];    double **newm;
         }    double agefin, delaymax=50 ; /* Max number of years to converge */
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pos=0; m <=0 ; m++)    for (ii=1;ii<=nlstate+ndeath;ii++)
             pos += freq[jk][m][i];      for (j=1;j<=nlstate+ndeath;j++){
           if(pp[jk]>=1.e-10)        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);      }
           else  
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);     cov[1]=1.;
         }   
    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         for(jk=1; jk <=nlstate ; jk++){    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      newm=savm;
             pp[jk] += freq[jk][m][i];      /* Covariates have to be included here again */
         }      cov[2]=agefin;
       
         for(jk=1,pos=0; jk <=nlstate ; jk++)      for (k=1; k<=cptcovn;k++) {
           pos += pp[jk];        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         for(jk=1; jk <=nlstate ; jk++){        /*        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]]);*/
           if(pos>=1.e-5)      }
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           else      for (k=1; k<=cptcovprod;k++)
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           if( i <= (int) agemax){      
             if(pos>=1.e-5){      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
               probs[i][jk][j1]= pp[jk]/pos;      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
             }      
             else      savm=oldm;
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      oldm=newm;
           }      maxmax=0.;
         }      for(j=1;j<=nlstate;j++){
                min=1.;
         for(jk=-1; jk <=nlstate+ndeath; jk++)        max=0.;
           for(m=-1; m <=nlstate+ndeath; m++)        for(i=1; i<=nlstate; i++) {
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          sumnew=0;
         if(i <= (int) agemax)          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
           fprintf(ficresp,"\n");          prlim[i][j]= newm[i][j]/(1-sumnew);
         printf("\n");          max=FMAX(max,prlim[i][j]);
       }          min=FMIN(min,prlim[i][j]);
     }        }
   }        maxmin=max-min;
   dateintmean=dateintsum/k2cpt;        maxmax=FMAX(maxmax,maxmin);
        }
   fclose(ficresp);      if(maxmax < ftolpl){
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        return prlim;
   free_vector(pp,1,nlstate);      }
      }
   /* End of Freq */  }
 }  
   /*************** transition probabilities ***************/ 
 /************ Prevalence ********************/  
 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)  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
 {  /* Some frequencies */  {
      /* According to parameters values stored in x and the covariate's values stored in cov,
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;       computes the probability to be observed in state j being in state i by appying the
   double ***freq; /* Frequencies */       model to the ncovmodel covariates (including constant and age).
   double *pp;       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
   double pos, k2;       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:
   pp=vector(1,nlstate);       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
         Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
   j1=0;       Outputs ps[i][j] the probability to be observed in j being in j according to
         the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
   j=cptcoveff;    */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    double s1, lnpijopii;
      /*double t34;*/
   for(k1=1; k1<=j;k1++){    int i,j,j1, nc, ii, jj;
     for(i1=1; i1<=ncodemax[k1];i1++){  
       j1++;      for(i=1; i<= nlstate; i++){
              for(j=1; j<i;j++){
       for (i=-1; i<=nlstate+ndeath; i++)            for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
         for (jk=-1; jk<=nlstate+ndeath; jk++)              /*lnpijopii += param[i][j][nc]*cov[nc];*/
           for(m=agemin; m <= agemax+3; m++)            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
             freq[i][jk][m]=0;  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
                }
       for (i=1; i<=imx; i++) {          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         bool=1;  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
         if  (cptcovn>0) {        }
           for (z1=1; z1<=cptcoveff; z1++)        for(j=i+1; j<=nlstate+ndeath;j++){
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
               bool=0;            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
         }            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
         if (bool==1) {  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
           for(m=firstpass; m<=lastpass; m++){          }
             k2=anint[m][i]+(mint[m][i]/12.);          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        }
               if(agev[m][i]==0) agev[m][i]=agemax+1;      }
               if(agev[m][i]==1) agev[m][i]=agemax+2;      
               if (m<lastpass) {      for(i=1; i<= nlstate; i++){
                 if (calagedate>0)        s1=0;
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];        for(j=1; j<i; j++){
                 else          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];        }
               }        for(j=i+1; j<=nlstate+ndeath; j++){
             }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
           }          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }        }
       }        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
       for(i=(int)agemin; i <= (int)agemax+3; i++){        ps[i][i]=1./(s1+1.);
         for(jk=1; jk <=nlstate ; jk++){        /* Computing other pijs */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        for(j=1; j<i; j++)
             pp[jk] += freq[jk][m][i];          ps[i][j]= exp(ps[i][j])*ps[i][i];
         }        for(j=i+1; j<=nlstate+ndeath; j++)
         for(jk=1; jk <=nlstate ; jk++){          ps[i][j]= exp(ps[i][j])*ps[i][i];
           for(m=-1, pos=0; m <=0 ; m++)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
             pos += freq[jk][m][i];      } /* end i */
         }      
              for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         for(jk=1; jk <=nlstate ; jk++){        for(jj=1; jj<= nlstate+ndeath; jj++){
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          ps[ii][jj]=0;
             pp[jk] += freq[jk][m][i];          ps[ii][ii]=1;
         }        }
              }
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];      
          
         for(jk=1; jk <=nlstate ; jk++){      /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
           if( i <= (int) agemax){  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
             if(pos>=1.e-5){  /*         printf("ddd %lf ",ps[ii][jj]); */
               probs[i][jk][j1]= pp[jk]/pos;  /*       } */
             }  /*       printf("\n "); */
           }  /*        } */
         }  /*        printf("\n ");printf("%lf ",cov[2]); */
                 /*
       }        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     }        goto end;*/
   }      return ps;
   }
    
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  /**************** Product of 2 matrices ******************/
   free_vector(pp,1,nlstate);  
    double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
 }  /* End of Freq */  {
     /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
 /************* Waves Concatenation ***************/       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     /* in, b, out are matrice of pointers which should have been initialized 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)       before: only the contents of out is modified. The function returns
 {       a pointer to pointers identical to out */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    long i, j, k;
      Death is a valid wave (if date is known).    for(i=nrl; i<= nrh; i++)
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i      for(k=ncolol; k<=ncoloh; k++)
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        for(j=ncl,out[i][k]=0.; j<=nch; j++)
      and mw[mi+1][i]. dh depends on stepm.          out[i][k] +=in[i][j]*b[j][k];
      */  
     return out;
   int i, mi, m;  }
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  
      double sum=0., jmean=0.;*/  
   /************* Higher Matrix Product ***************/
   int j, k=0,jk, ju, jl;  
   double sum=0.;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   jmin=1e+5;  {
   jmax=-1;    /* Computes the transition matrix starting at age 'age' over 
   jmean=0.;       'nhstepm*hstepm*stepm' months (i.e. until
   for(i=1; i<=imx; i++){       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     mi=0;       nhstepm*hstepm matrices. 
     m=firstpass;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     while(s[m][i] <= nlstate){       (typically every 2 years instead of every month which is too big 
       if(s[m][i]>=1)       for the memory).
         mw[++mi][i]=m;       Model is determined by parameters x and covariates have to be 
       if(m >=lastpass)       included manually here. 
         break;  
       else       */
         m++;  
     }/* end while */    int i, j, d, h, k;
     if (s[m][i] > nlstate){    double **out, cov[NCOVMAX+1];
       mi++;     /* Death is another wave */    double **newm;
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */    /* Hstepm could be zero and should return the unit matrix */
       mw[mi][i]=m;    for (i=1;i<=nlstate+ndeath;i++)
     }      for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
     wav[i]=mi;        po[i][j][0]=(i==j ? 1.0 : 0.0);
     if(mi==0)      }
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   }    for(h=1; h <=nhstepm; h++){
       for(d=1; d <=hstepm; d++){
   for(i=1; i<=imx; i++){        newm=savm;
     for(mi=1; mi<wav[i];mi++){        /* Covariates have to be included here again */
       if (stepm <=0)        cov[1]=1.;
         dh[mi][i]=1;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
       else{        for (k=1; k<=cptcovn;k++) 
         if (s[mw[mi+1][i]][i] > nlstate) {          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           if (agedc[i] < 2*AGESUP) {        for (k=1; k<=cptcovage;k++)
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           if(j==0) j=1;  /* Survives at least one month after exam */        for (k=1; k<=cptcovprod;k++)
           k=k+1;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           if (j >= jmax) jmax=j;  
           if (j <= jmin) jmin=j;  
           sum=sum+j;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
           /*if (j<0) printf("j=%d num=%d \n",j,i); */        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           }        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
         }                     pmij(pmmij,cov,ncovmodel,x,nlstate));
         else{        savm=oldm;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        oldm=newm;
           k=k+1;      }
           if (j >= jmax) jmax=j;      for(i=1; i<=nlstate+ndeath; i++)
           else if (j <= jmin)jmin=j;        for(j=1;j<=nlstate+ndeath;j++) {
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */          po[i][j][h]=newm[i][j];
           sum=sum+j;          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
         }        }
         jk= j/stepm;      /*printf("h=%d ",h);*/
         jl= j -jk*stepm;    } /* end h */
         ju= j -(jk+1)*stepm;  /*     printf("\n H=%d \n",h); */
         if(jl <= -ju)    return po;
           dh[mi][i]=jk;  }
         else  
           dh[mi][i]=jk+1;  
         if(dh[mi][i]==0)  /*************** log-likelihood *************/
           dh[mi][i]=1; /* At least one step */  double func( double *x)
       }  {
     }    int i, ii, j, k, mi, d, kk;
   }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   jmean=sum/k;    double **out;
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);    double sw; /* Sum of weights */
  }    double lli; /* Individual log likelihood */
 /*********** Tricode ****************************/    int s1, s2;
 void tricode(int *Tvar, int **nbcode, int imx)    double bbh, survp;
 {    long ipmx;
   int Ndum[20],ij=1, k, j, i;    /*extern weight */
   int cptcode=0;    /* We are differentiating ll according to initial status */
   cptcoveff=0;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
      /*for(i=1;i<imx;i++) 
   for (k=0; k<19; k++) Ndum[k]=0;      printf(" %d\n",s[4][i]);
   for (k=1; k<=7; k++) ncodemax[k]=0;    */
     cov[1]=1.;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {  
     for (i=1; i<=imx; i++) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
       ij=(int)(covar[Tvar[j]][i]);  
       Ndum[ij]++;    if(mle==1){
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       if (ij > cptcode) cptcode=ij;        /* 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=0; i<=cptcode; i++) {           to be observed in j being in i according to the model.
       if(Ndum[i]!=0) ncodemax[j]++;         */
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     ij=1;        /* 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] 
            has been calculated etc */
     for (i=1; i<=ncodemax[j]; i++) {        for(mi=1; mi<= wav[i]-1; mi++){
       for (k=0; k<=19; k++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
         if (Ndum[k] != 0) {            for (j=1;j<=nlstate+ndeath;j++){
           nbcode[Tvar[j]][ij]=k;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                        savm[ii][j]=(ii==j ? 1.0 : 0.0);
           ij++;            }
         }          for(d=0; d<dh[mi][i]; d++){
         if (ij > ncodemax[j]) break;            newm=savm;
       }              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     }            for (kk=1; kk<=cptcovage;kk++) {
   }                cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
             }
  for (k=0; k<19; k++) Ndum[k]=0;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
  for (i=1; i<=ncovmodel-2; i++) {            savm=oldm;
       ij=Tvar[i];            oldm=newm;
       Ndum[ij]++;          } /* end mult */
     }        
           /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
  ij=1;          /* But now since version 0.9 we anticipate for bias at large stepm.
  for (i=1; i<=10; i++) {           * If stepm is larger than one month (smallest stepm) and if the exact delay 
    if((Ndum[i]!=0) && (i<=ncovcol)){           * (in months) between two waves is not a multiple of stepm, we rounded to 
      Tvaraff[ij]=i;           * the nearest (and in case of equal distance, to the lowest) interval but now
      ij++;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
    }           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
  }           * probability in order to take into account the bias as a fraction of the way
             * from savm to out if bh is negative or even beyond if bh is positive. bh varies
     cptcoveff=ij-1;           * -stepm/2 to stepm/2 .
 }           * For stepm=1 the results are the same as for previous versions of Imach.
            * For stepm > 1 the results are less biased than in previous versions. 
 /*********** Health Expectancies ****************/           */
           s1=s[mw[mi][i]][i];
 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 )          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
 {          /* bias bh is positive if real duration
   /* Health expectancies */           * is higher than the multiple of stepm and negative otherwise.
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;           */
   double age, agelim, hf;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   double ***p3mat,***varhe;          if( s2 > nlstate){ 
   double **dnewm,**doldm;            /* i.e. if s2 is a death state and if the date of death is known 
   double *xp;               then the contribution to the likelihood is the probability to 
   double **gp, **gm;               die between last step unit time and current  step unit time, 
   double ***gradg, ***trgradg;               which is also equal to probability to die before dh 
   int theta;               minus probability to die before dh-stepm . 
                In version up to 0.92 likelihood was computed
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          as if date of death was unknown. Death was treated as any other
   xp=vector(1,npar);          health state: the date of the interview describes the actual state
   dnewm=matrix(1,nlstate*2,1,npar);          and not the date of a change in health state. The former idea was
   doldm=matrix(1,nlstate*2,1,nlstate*2);          to consider that at each interview the state was recorded
            (healthy, disable or death) and IMaCh was corrected; but when we
   fprintf(ficreseij,"# Health expectancies\n");          introduced the exact date of death then we should have modified
   fprintf(ficreseij,"# Age");          the contribution of an exact death to the likelihood. This new
   for(i=1; i<=nlstate;i++)          contribution is smaller and very dependent of the step unit
     for(j=1; j<=nlstate;j++)          stepm. It is no more the probability to die between last interview
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          and month of death but the probability to survive from last
   fprintf(ficreseij,"\n");          interview up to one month before death multiplied by the
           probability to die within a month. Thanks to Chris
   if(estepm < stepm){          Jackson for correcting this bug.  Former versions increased
     printf ("Problem %d lower than %d\n",estepm, stepm);          mortality artificially. The bad side is that we add another loop
   }          which slows down the processing. The difference can be up to 10%
   else  hstepm=estepm;            lower mortality.
   /* We compute the life expectancy from trapezoids spaced every estepm months            */
    * This is mainly to measure the difference between two models: for example            lli=log(out[s1][s2] - savm[s1][s2]);
    * if stepm=24 months pijx are given only every 2 years and by summing them  
    * we are calculating an estimate of the Life Expectancy assuming a linear  
    * progression inbetween and thus overestimating or underestimating according          } else if  (s2==-2) {
    * to the curvature of the survival function. If, for the same date, we            for (j=1,survp=0. ; j<=nlstate; j++) 
    * estimate the model with stepm=1 month, we can keep estepm to 24 months              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
    * to compare the new estimate of Life expectancy with the same linear            /*survp += out[s1][j]; */
    * hypothesis. A more precise result, taking into account a more precise            lli= log(survp);
    * curvature will be obtained if estepm is as small as stepm. */          }
           
   /* For example we decided to compute the life expectancy with the smallest unit */          else if  (s2==-4) { 
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            for (j=3,survp=0. ; j<=nlstate; j++)  
      nhstepm is the number of hstepm from age to agelim              survp += (1.+bbh)*out[s1][j]- bbh*savm[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==-5) { 
      survival function given by stepm (the optimization length). Unfortunately it            for (j=1,survp=0. ; j<=2; 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{
             lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   agelim=AGESUP;            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          } 
     /* nhstepm age range expressed in number of stepm */          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          /*if(lli ==000.0)*/
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
     /* if (stepm >= YEARM) hstepm=1;*/          ipmx +=1;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          sw += weight[i];
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);        } /* end of wave */
     gp=matrix(0,nhstepm,1,nlstate*2);      } /* end of individual */
     gm=matrix(0,nhstepm,1,nlstate*2);    }  else if(mle==2){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */        for(mi=1; mi<= wav[i]-1; mi++){
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            for (ii=1;ii<=nlstate+ndeath;ii++)
              for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
     /* Computing Variances of health expectancies */          for(d=0; d<=dh[mi][i]; d++){
             newm=savm;
      for(theta=1; theta <=npar; theta++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(i=1; i<=npar; i++){            for (kk=1; kk<=cptcovage;kk++) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       cptj=0;            savm=oldm;
       for(j=1; j<= nlstate; j++){            oldm=newm;
         for(i=1; i<=nlstate; i++){          } /* end mult */
           cptj=cptj+1;        
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          s1=s[mw[mi][i]][i];
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;          s2=s[mw[mi+1][i]][i];
           }          bbh=(double)bh[mi][i]/(double)stepm; 
         }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       }          ipmx +=1;
                sw += weight[i];
                ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1; i<=npar; i++)        } /* end of wave */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      } /* end of individual */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      }  else if(mle==3){  /* exponential inter-extrapolation */
            for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       cptj=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1; j<= nlstate; j++){        for(mi=1; mi<= wav[i]-1; mi++){
         for(i=1;i<=nlstate;i++){          for (ii=1;ii<=nlstate+ndeath;ii++)
           cptj=cptj+1;            for (j=1;j<=nlstate+ndeath;j++){
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }            }
         }          for(d=0; d<dh[mi][i]; d++){
       }            newm=savm;
       for(j=1; j<= nlstate*2; j++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         for(h=0; h<=nhstepm-1; h++){            for (kk=1; kk<=cptcovage;kk++) {
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];              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));
 /* End theta */            savm=oldm;
             oldm=newm;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          } /* end mult */
         
      for(h=0; h<=nhstepm-1; h++)          s1=s[mw[mi][i]][i];
       for(j=1; j<=nlstate*2;j++)          s2=s[mw[mi+1][i]][i];
         for(theta=1; theta <=npar; theta++)          bbh=(double)bh[mi][i]/(double)stepm; 
           trgradg[h][j][theta]=gradg[h][theta][j];          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
                ipmx +=1;
           sw += weight[i];
      for(i=1;i<=nlstate*2;i++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(j=1;j<=nlstate*2;j++)        } /* end of wave */
         varhe[i][j][(int)age] =0.;      } /* end of individual */
     }else if (mle==4){  /* ml=4 no inter-extrapolation */
      printf("%d|",(int)age);fflush(stdout);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      for(h=0;h<=nhstepm-1;h++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(k=0;k<=nhstepm-1;k++){        for(mi=1; mi<= wav[i]-1; mi++){
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);          for (ii=1;ii<=nlstate+ndeath;ii++)
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);            for (j=1;j<=nlstate+ndeath;j++){
         for(i=1;i<=nlstate*2;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(j=1;j<=nlstate*2;j++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;            }
       }          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
     /* Computing expectancies */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(i=1; i<=nlstate;i++)            for (kk=1; kk<=cptcovage;kk++) {
       for(j=1; j<=nlstate;j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){            }
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          
                      out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 /* 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]);*/                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
         }            oldm=newm;
           } /* end mult */
     fprintf(ficreseij,"%3.0f",age );        
     cptj=0;          s1=s[mw[mi][i]][i];
     for(i=1; i<=nlstate;i++)          s2=s[mw[mi+1][i]][i];
       for(j=1; j<=nlstate;j++){          if( s2 > nlstate){ 
         cptj++;            lli=log(out[s1][s2] - savm[s1][s2]);
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          }else{
       }            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     fprintf(ficreseij,"\n");          }
              ipmx +=1;
     free_matrix(gm,0,nhstepm,1,nlstate*2);          sw += weight[i];
     free_matrix(gp,0,nhstepm,1,nlstate*2);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);  /*      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_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);        } /* end of wave */
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      } /* end of individual */
   }    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   printf("\n");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   free_vector(xp,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
   free_matrix(dnewm,1,nlstate*2,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);            for (j=1;j<=nlstate+ndeath;j++){
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
 /************ Variance ******************/          for(d=0; d<dh[mi][i]; d++){
 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)            newm=savm;
 {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* Variance of health expectancies */            for (kk=1; kk<=cptcovage;kk++) {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double **newm;            }
   double **dnewm,**doldm;          
   int i, j, nhstepm, hstepm, h, nstepm ;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int k, cptcode;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double *xp;            savm=oldm;
   double **gp, **gm;            oldm=newm;
   double ***gradg, ***trgradg;          } /* end mult */
   double ***p3mat;        
   double age,agelim, hf;          s1=s[mw[mi][i]][i];
   int theta;          s2=s[mw[mi+1][i]][i];
           lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   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");          ipmx +=1;
   fprintf(ficresvij,"# Age");          sw += weight[i];
   for(i=1; i<=nlstate;i++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for(j=1; j<=nlstate;j++)          /*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]);*/
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        } /* end of wave */
   fprintf(ficresvij,"\n");      } /* end of individual */
     } /* End of if */
   xp=vector(1,npar);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   dnewm=matrix(1,nlstate,1,npar);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   doldm=matrix(1,nlstate,1,nlstate);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
      return -l;
   if(estepm < stepm){  }
     printf ("Problem %d lower than %d\n",estepm, stepm);  
   }  /*************** log-likelihood *************/
   else  hstepm=estepm;    double funcone( double *x)
   /* 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.    /* Same as likeli but slower because of a lot of printf and if */
      nhstepm is the number of hstepm from age to agelim    int i, ii, j, k, mi, d, kk;
      nstepm is the number of stepm from age to agelin.    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
      Look at hpijx to understand the reason of that which relies in memory size    double **out;
      and note for a fixed period like k years */    double lli; /* Individual log likelihood */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    double llt;
      survival function given by stepm (the optimization length). Unfortunately it    int s1, s2;
      means that if the survival funtion is printed only each two years of age and if    double bbh, survp;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    /*extern weight */
      results. So we changed our mind and took the option of the best precision.    /* We are differentiating ll according to initial status */
   */    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    /*for(i=1;i<imx;i++) 
   agelim = AGESUP;      printf(" %d\n",s[4][i]);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    */
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    cov[1]=1.;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(k=1; k<=nlstate; k++) ll[k]=0.;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  
     gp=matrix(0,nhstepm,1,nlstate);    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     gm=matrix(0,nhstepm,1,nlstate);      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(mi=1; mi<= wav[i]-1; mi++){
     for(theta=1; theta <=npar; theta++){        for (ii=1;ii<=nlstate+ndeath;ii++)
       for(i=1; i<=npar; i++){ /* Computes gradient */          for (j=1;j<=nlstate+ndeath;j++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            savm[ii][j]=(ii==j ? 1.0 : 0.0);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
       if (popbased==1) {          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         for(i=1; i<=nlstate;i++)          for (kk=1; kk<=cptcovage;kk++) {
           prlim[i][i]=probs[(int)age][i][ij];            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }          }
            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       for(j=1; j<= nlstate; j++){                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(h=0; h<=nhstepm; h++){          savm=oldm;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          oldm=newm;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        } /* end mult */
         }        
       }        s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
       for(i=1; i<=npar; i++) /* Computes gradient */        bbh=(double)bh[mi][i]/(double)stepm; 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        /* bias is positive if real duration
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);           * is higher than the multiple of stepm and negative otherwise.
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);         */
          if( s2 > nlstate && (mle <5) ){  /* Jackson */
       if (popbased==1) {          lli=log(out[s1][s2] - savm[s1][s2]);
         for(i=1; i<=nlstate;i++)        } else if  (s2==-2) {
           prlim[i][i]=probs[(int)age][i][ij];          for (j=1,survp=0. ; j<=nlstate; j++) 
       }            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           lli= log(survp);
       for(j=1; j<= nlstate; j++){        }else if (mle==1){
         for(h=0; h<=nhstepm; h++){          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        } else if(mle==2){
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         }        } else if(mle==3){  /* exponential inter-extrapolation */
       }          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
         } else if (mle==4){  /* mle=4 no inter-extrapolation */
       for(j=1; j<= nlstate; j++)          lli=log(out[s1][s2]); /* Original formula */
         for(h=0; h<=nhstepm; h++){        } else{  /* mle=0 back to 1 */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         }          /*lli=log(out[s1][s2]); */ /* Original formula */
     } /* End theta */        } /* End of if */
         ipmx +=1;
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        sw += weight[i];
         ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for(h=0; h<=nhstepm; h++)        /*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){
         for(theta=1; theta <=npar; theta++)          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
           trgradg[h][j][theta]=gradg[h][theta][j];   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
     for(i=1;i<=nlstate;i++)          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       for(j=1;j<=nlstate;j++)            llt +=ll[k]*gipmx/gsw;
         vareij[i][j][(int)age] =0.;            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           }
     for(h=0;h<=nhstepm;h++){          fprintf(ficresilk," %10.6f\n", -llt);
       for(k=0;k<=nhstepm;k++){        }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);      } /* end of wave */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    } /* end of individual */
         for(i=1;i<=nlstate;i++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
           for(j=1;j<=nlstate;j++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       }    if(globpr==0){ /* First time we count the contributions and weights */
     }      gipmx=ipmx;
       gsw=sw;
     fprintf(ficresvij,"%.0f ",age );    }
     for(i=1; i<=nlstate;i++)    return -l;
       for(j=1; j<=nlstate;j++){  }
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);  
       }  
     fprintf(ficresvij,"\n");  /*************** function likelione ***********/
     free_matrix(gp,0,nhstepm,1,nlstate);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
     free_matrix(gm,0,nhstepm,1,nlstate);  {
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    /* This routine should help understanding what is done with 
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);       the selection of individuals/waves and
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       to check the exact contribution to the likelihood.
   } /* End age */       Plotting could be done.
       */
   free_vector(xp,1,npar);    int k;
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    if(*globpri !=0){ /* Just counts and sums, no printings */
       strcpy(fileresilk,"ilk"); 
 }      strcat(fileresilk,fileres);
       if((ficresilk=fopen(fileresilk,"w"))==NULL) {
 /************ Variance of prevlim ******************/        printf("Problem with resultfile: %s\n", fileresilk);
 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)        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
 {      }
   /* Variance of prevalence limit */      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 **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   double **newm;      /*  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 **dnewm,**doldm;      for(k=1; k<=nlstate; k++) 
   int i, j, nhstepm, hstepm;        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   int k, cptcode;      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   double *xp;    }
   double *gp, *gm;  
   double **gradg, **trgradg;    *fretone=(*funcone)(p);
   double age,agelim;    if(*globpri !=0){
   int theta;      fclose(ficresilk);
          fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");      fflush(fichtm); 
   fprintf(ficresvpl,"# Age");    } 
   for(i=1; i<=nlstate;i++)    return;
       fprintf(ficresvpl," %1d-%1d",i,i);  }
   fprintf(ficresvpl,"\n");  
   
   xp=vector(1,npar);  /*********** Maximum Likelihood Estimation ***************/
   dnewm=matrix(1,nlstate,1,npar);  
   doldm=matrix(1,nlstate,1,nlstate);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
    {
   hstepm=1*YEARM; /* Every year of age */    int i,j, iter;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    double **xi;
   agelim = AGESUP;    double fret;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    double fretone; /* Only one call to likelihood */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    /*  char filerespow[FILENAMELENGTH];*/
     if (stepm >= YEARM) hstepm=1;    xi=matrix(1,npar,1,npar);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    for (i=1;i<=npar;i++)
     gradg=matrix(1,npar,1,nlstate);      for (j=1;j<=npar;j++)
     gp=vector(1,nlstate);        xi[i][j]=(i==j ? 1.0 : 0.0);
     gm=vector(1,nlstate);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow"); 
     for(theta=1; theta <=npar; theta++){    strcat(filerespow,fileres);
       for(i=1; i<=npar; i++){ /* Computes gradient */    if((ficrespow=fopen(filerespow,"w"))==NULL) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      printf("Problem with resultfile: %s\n", filerespow);
       }      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");
         gp[i] = prlim[i][i];    for (i=1;i<=nlstate;i++)
          for(j=1;j<=nlstate+ndeath;j++)
       for(i=1; i<=npar; i++) /* Computes gradient */        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    fprintf(ficrespow,"\n");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)    powell(p,xi,npar,ftol,&iter,&fret,func);
         gm[i] = prlim[i][i];  
     free_matrix(xi,1,npar,1,npar);
       for(i=1;i<=nlstate;i++)    fclose(ficrespow);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     } /* End theta */    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));
     trgradg =matrix(1,nlstate,1,npar);  
   }
     for(j=1; j<=nlstate;j++)  
       for(theta=1; theta <=npar; theta++)  /**** Computes Hessian and covariance matrix ***/
         trgradg[j][theta]=gradg[theta][j];  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   {
     for(i=1;i<=nlstate;i++)    double  **a,**y,*x,pd;
       varpl[i][(int)age] =0.;    double **hess;
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    int i, j,jk;
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    int *indx;
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     fprintf(ficresvpl,"%.0f ",age );    void lubksb(double **a, int npar, int *indx, double b[]) ;
     for(i=1; i<=nlstate;i++)    void ludcmp(double **a, int npar, int *indx, double *d) ;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    double gompertz(double p[]);
     fprintf(ficresvpl,"\n");    hess=matrix(1,npar,1,npar);
     free_vector(gp,1,nlstate);  
     free_vector(gm,1,nlstate);    printf("\nCalculation of the hessian matrix. Wait...\n");
     free_matrix(gradg,1,npar,1,nlstate);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     free_matrix(trgradg,1,nlstate,1,npar);    for (i=1;i<=npar;i++){
   } /* End age */      printf("%d",i);fflush(stdout);
       fprintf(ficlog,"%d",i);fflush(ficlog);
   free_vector(xp,1,npar);     
   free_matrix(doldm,1,nlstate,1,npar);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   free_matrix(dnewm,1,nlstate,1,nlstate);      
       /*  printf(" %f ",p[i]);
 }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
 /************ 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)    for (i=1;i<=npar;i++) {
 {      for (j=1;j<=npar;j++)  {
   int i, j=0,  i1, k1, l1, t, tj;        if (j>i) { 
   int k2, l2, j1,  z1;          printf(".%d%d",i,j);fflush(stdout);
   int k=0,l, cptcode;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   int first=1;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;          
   double **dnewm,**doldm;          hess[j][i]=hess[i][j];    
   double *xp;          /*printf(" %lf ",hess[i][j]);*/
   double *gp, *gm;        }
   double **gradg, **trgradg;      }
   double **mu;    }
   double age,agelim, cov[NCOVMAX];    printf("\n");
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */    fprintf(ficlog,"\n");
   int theta;  
   char fileresprob[FILENAMELENGTH];    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   char fileresprobcov[FILENAMELENGTH];    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   char fileresprobcor[FILENAMELENGTH];    
     a=matrix(1,npar,1,npar);
   double ***varpij;    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
   strcpy(fileresprob,"prob");    indx=ivector(1,npar);
   strcat(fileresprob,fileres);    for (i=1;i<=npar;i++)
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     printf("Problem with resultfile: %s\n", fileresprob);    ludcmp(a,npar,indx,&pd);
   }  
   strcpy(fileresprobcov,"probcov");    for (j=1;j<=npar;j++) {
   strcat(fileresprobcov,fileres);      for (i=1;i<=npar;i++) x[i]=0;
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {      x[j]=1;
     printf("Problem with resultfile: %s\n", fileresprobcov);      lubksb(a,npar,indx,x);
   }      for (i=1;i<=npar;i++){ 
   strcpy(fileresprobcor,"probcor");        matcov[i][j]=x[i];
   strcat(fileresprobcor,fileres);      }
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {    }
     printf("Problem with resultfile: %s\n", fileresprobcor);  
   }    printf("\n#Hessian matrix#\n");
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    fprintf(ficlog,"\n#Hessian matrix#\n");
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    for (i=1;i<=npar;i++) { 
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      for (j=1;j<=npar;j++) { 
          printf("%.3e ",hess[i][j]);
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");        fprintf(ficlog,"%.3e ",hess[i][j]);
   fprintf(ficresprob,"# Age");      }
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");      printf("\n");
   fprintf(ficresprobcov,"# Age");      fprintf(ficlog,"\n");
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    }
   fprintf(ficresprobcov,"# Age");  
     /* Recompute Inverse */
     for (i=1;i<=npar;i++)
   for(i=1; i<=nlstate;i++)      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     for(j=1; j<=(nlstate+ndeath);j++){    ludcmp(a,npar,indx,&pd);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);  
       fprintf(ficresprobcov," p%1d-%1d ",i,j);    /*  printf("\n#Hessian matrix recomputed#\n");
       fprintf(ficresprobcor," p%1d-%1d ",i,j);  
     }      for (j=1;j<=npar;j++) {
   fprintf(ficresprob,"\n");      for (i=1;i<=npar;i++) x[i]=0;
   fprintf(ficresprobcov,"\n");      x[j]=1;
   fprintf(ficresprobcor,"\n");      lubksb(a,npar,indx,x);
   xp=vector(1,npar);      for (i=1;i<=npar;i++){ 
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);        y[i][j]=x[i];
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));        printf("%.3e ",y[i][j]);
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);        fprintf(ficlog,"%.3e ",y[i][j]);
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);      }
   first=1;      printf("\n");
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      fprintf(ficlog,"\n");
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    }
     exit(0);    */
   }  
   else{    free_matrix(a,1,npar,1,npar);
     fprintf(ficgp,"\n# Routine varprob");    free_matrix(y,1,npar,1,npar);
   }    free_vector(x,1,npar);
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    free_ivector(indx,1,npar);
     printf("Problem with html file: %s\n", optionfilehtm);    free_matrix(hess,1,npar,1,npar);
     exit(0);  
   }  
   else{  }
     fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");  
     fprintf(fichtm,"\nWe 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");  /*************** hessian matrix ****************/
     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");  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   {
   }    int i;
     int l=1, lmax=20;
      double k1,k2;
   cov[1]=1;    double p2[MAXPARM+1]; /* identical to x */
   tj=cptcoveff;    double res;
   if (cptcovn<1) {tj=1;ncodemax[1]=1;}    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   j1=0;    double fx;
   for(t=1; t<=tj;t++){    int k=0,kmax=10;
     for(i1=1; i1<=ncodemax[t];i1++){    double l1;
       j1++;  
          fx=func(x);
       if  (cptcovn>0) {    for (i=1;i<=npar;i++) p2[i]=x[i];
         fprintf(ficresprob, "\n#********** Variable ");    for(l=0 ; l <=lmax; l++){
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      l1=pow(10,l);
         fprintf(ficresprob, "**********\n#");      delts=delt;
         fprintf(ficresprobcov, "\n#********** Variable ");      for(k=1 ; k <kmax; k=k+1){
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        delt = delta*(l1*k);
         fprintf(ficresprobcov, "**********\n#");        p2[theta]=x[theta] +delt;
                k1=func(p2)-fx;
         fprintf(ficgp, "\n#********** Variable ");        p2[theta]=x[theta]-delt;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        k2=func(p2)-fx;
         fprintf(ficgp, "**********\n#");        /*res= (k1-2.0*fx+k2)/delt/delt; */
                res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
                
         fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable ");  #ifdef DEBUGHESS
         for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
         fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
          #endif
         fprintf(ficresprobcor, "\n#********** Variable ");            /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
         fprintf(ficgp, "**********\n#");              k=kmax;
       }        }
              else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       for (age=bage; age<=fage; age ++){          k=kmax; l=lmax*10.;
         cov[2]=age;        }
         for (k=1; k<=cptcovn;k++) {        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];          delts=delt;
         }        }
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      }
         for (k=1; k<=cptcovprod;k++)    }
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    delti[theta]=delts;
            return res; 
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));    
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);  }
         gp=vector(1,(nlstate)*(nlstate+ndeath));  
         gm=vector(1,(nlstate)*(nlstate+ndeath));  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
      {
         for(theta=1; theta <=npar; theta++){    int i;
           for(i=1; i<=npar; i++)    int l=1, l1, lmax=20;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    double k1,k2,k3,k4,res,fx;
              double p2[MAXPARM+1];
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    int k;
            
           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;
               gp[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<=npar; i++)      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);      k2=func(p2)-fx;
        
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      p2[thetai]=x[thetai]-delti[thetai]/k;
           k=0;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           for(i=1; i<=(nlstate); i++){      k3=func(p2)-fx;
             for(j=1; j<=(nlstate+ndeath);j++){    
               k=k+1;      p2[thetai]=x[thetai]-delti[thetai]/k;
               gm[k]=pmmij[i][j];      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
             }      k4=func(p2)-fx;
           }      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
        #ifdef DEBUG
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)      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);
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         }  #endif
     }
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)    return res;
           for(theta=1; theta <=npar; theta++)  }
             trgradg[j][theta]=gradg[theta][j];  
          /************** Inverse of matrix **************/
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);  void ludcmp(double **a, int n, int *indx, double *d) 
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);  { 
            int i,imax,j,k; 
         pmij(pmmij,cov,ncovmodel,x,nlstate);    double big,dum,sum,temp; 
            double *vv; 
         k=0;   
         for(i=1; i<=(nlstate); i++){    vv=vector(1,n); 
           for(j=1; j<=(nlstate+ndeath);j++){    *d=1.0; 
             k=k+1;    for (i=1;i<=n;i++) { 
             mu[k][(int) age]=pmmij[i][j];      big=0.0; 
           }      for (j=1;j<=n;j++) 
         }        if ((temp=fabs(a[i][j])) > big) big=temp; 
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)      vv[i]=1.0/big; 
             varpij[i][j][(int)age] = doldm[i][j];    } 
     for (j=1;j<=n;j++) { 
         /*printf("\n%d ",(int)age);      for (i=1;i<j;i++) { 
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){        sum=a[i][j]; 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
      }*/        a[i][j]=sum; 
       } 
         fprintf(ficresprob,"\n%d ",(int)age);      big=0.0; 
         fprintf(ficresprobcov,"\n%d ",(int)age);      for (i=j;i<=n;i++) { 
         fprintf(ficresprobcor,"\n%d ",(int)age);        sum=a[i][j]; 
         for (k=1;k<j;k++) 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)          sum -= a[i][k]*a[k][j]; 
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));        a[i][j]=sum; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){        if ( (dum=vv[i]*fabs(sum)) >= big) { 
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);          big=dum; 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);          imax=i; 
         }        } 
         i=0;      } 
         for (k=1; k<=(nlstate);k++){      if (j != imax) { 
           for (l=1; l<=(nlstate+ndeath);l++){        for (k=1;k<=n;k++) { 
             i=i++;          dum=a[imax][k]; 
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);          a[imax][k]=a[j][k]; 
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);          a[j][k]=dum; 
             for (j=1; j<=i;j++){        } 
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);        *d = -(*d); 
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));        vv[imax]=vv[j]; 
             }      } 
           }      indx[j]=imax; 
         }/* end of loop for state */      if (a[j][j] == 0.0) a[j][j]=TINY; 
       } /* end of loop for age */      if (j != n) { 
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/        dum=1.0/(a[j][j]); 
       for (k1=1; k1<=(nlstate);k1++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         for (l1=1; l1<=(nlstate+ndeath);l1++){      } 
           if(l1==k1) continue;    } 
           i=(k1-1)*(nlstate+ndeath)+l1;    free_vector(vv,1,n);  /* Doesn't work */
           for (k2=1; k2<=(nlstate);k2++){  ;
             for (l2=1; l2<=(nlstate+ndeath);l2++){  } 
               if(l2==k2) continue;  
               j=(k2-1)*(nlstate+ndeath)+l2;  void lubksb(double **a, int n, int *indx, double b[]) 
               if(j<=i) continue;  { 
               for (age=bage; age<=fage; age ++){    int i,ii=0,ip,j; 
                 if ((int)age %5==0){    double sum; 
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;   
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;    for (i=1;i<=n;i++) { 
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;      ip=indx[i]; 
                   mu1=mu[i][(int) age]/stepm*YEARM ;      sum=b[ip]; 
                   mu2=mu[j][(int) age]/stepm*YEARM;      b[ip]=b[i]; 
                   /* Computing eigen value of matrix of covariance */      if (ii) 
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));      else if (sum) ii=i; 
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);      b[i]=sum; 
                   /* Eigen vectors */    } 
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));    for (i=n;i>=1;i--) { 
                   v21=sqrt(1.-v11*v11);      sum=b[i]; 
                   v12=-v21;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                   v22=v11;      b[i]=sum/a[i][i]; 
                   /*printf(fignu*/    } 
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */  } 
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */  
                   if(first==1){  void pstamp(FILE *fichier)
                     first=0;  {
                     fprintf(ficgp,"\nset parametric;set nolabel");    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
                     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);  }
                     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%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1);  /************ Frequencies ********************/
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k2,l2,k1,l1);  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[])
                     fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k2,l2,k1,l1);  {  /* Some frequencies */
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);    
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    int i, m, jk, k1,i1, j1, bool, z1,j;
                     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\"",\    int first;
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    double ***freq; /* Frequencies */
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    double *pp, **prop;
                   }else{    double pos,posprop, k2, dateintsum=0,k2cpt=0;
                     first=0;    char fileresp[FILENAMELENGTH];
                     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);    pp=vector(1,nlstate);
                     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\"",\    prop=matrix(1,nlstate,iagemin,iagemax+3);
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    strcpy(fileresp,"p");
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    strcat(fileresp,fileres);
                   }/* if first */    if((ficresp=fopen(fileresp,"w"))==NULL) {
                 } /* age mod 5 */      printf("Problem with prevalence resultfile: %s\n", fileresp);
               } /* end loop age */      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
               fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k2,l2,k1,l1);      exit(0);
               first=1;    }
             } /*l12 */    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
           } /* k12 */    j1=0;
         } /*l1 */    
       }/* k1 */    j=cptcoveff;
     } /* loop covariates */    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);  
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    first=1;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));  
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);    for(k1=1; k1<=j;k1++){
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      for(i1=1; i1<=ncodemax[k1];i1++){
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        j1++;
   }        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   free_vector(xp,1,npar);          scanf("%d", i);*/
   fclose(ficresprob);        for (i=-5; i<=nlstate+ndeath; i++)  
   fclose(ficresprobcov);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
   fclose(ficresprobcor);            for(m=iagemin; m <= iagemax+3; m++)
   fclose(ficgp);              freq[i][jk][m]=0;
   fclose(fichtm);  
 }      for (i=1; i<=nlstate; i++)  
         for(m=iagemin; m <= iagemax+3; m++)
           prop[i][m]=0;
 /******************* Printing html file ***********/        
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        dateintsum=0;
                   int lastpass, int stepm, int weightopt, char model[],\        k2cpt=0;
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\        for (i=1; i<=imx; i++) {
                   int popforecast, int estepm ,\          bool=1;
                   double jprev1, double mprev1,double anprev1, \          if  (cptcovn>0) {
                   double jprev2, double mprev2,double anprev2){            for (z1=1; z1<=cptcoveff; z1++) 
   int jj1, k1, i1, cpt;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   /*char optionfilehtm[FILENAMELENGTH];*/                bool=0;
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {          }
     printf("Problem with %s \n",optionfilehtm), exit(0);          if (bool==1){
   }            for(m=firstpass; m<=lastpass; m++){
               k2=anint[m][i]+(mint[m][i]/12.);
    fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
  - 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                if(agev[m][i]==0) agev[m][i]=iagemax+1;
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n                if(agev[m][i]==1) agev[m][i]=iagemax+2;
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
  - Life expectancies by age and initial health status (estepm=%2d months):                if (m<lastpass) {
    <a href=\"e%s\">e%s</a> <br>\n</li>", \                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                 }
  fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n                
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n                  dateintsum=dateintsum+k2;
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n                  k2cpt++;
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n                }
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n                /*}*/
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n            }
  - 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(popforecast==1) fprintf(fichtm,"\n         
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n        pstamp(ficresp);
         <br>",fileres,fileres,fileres,fileres);        if  (cptcovn>0) {
  else          fprintf(ficresp, "\n#********** Variable "); 
    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);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 fprintf(fichtm," <li><b>Graphs</b></li><p>");          fprintf(ficresp, "**********\n#");
         }
  m=cptcoveff;        for(i=1; i<=nlstate;i++) 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
  jj1=0;        
  for(k1=1; k1<=m;k1++){        for(i=iagemin; i <= iagemax+3; i++){
    for(i1=1; i1<=ncodemax[k1];i1++){          if(i==iagemax+3){
      jj1++;            fprintf(ficlog,"Total");
      if (cptcovn > 0) {          }else{
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");            if(first==1){
        for (cpt=1; cpt<=cptcoveff;cpt++)              first=0;
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);              printf("See log file for details...\n");
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");            }
      }            fprintf(ficlog,"Age %d", i);
      /* Pij */          }
      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>          for(jk=1; jk <=nlstate ; jk++){
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
      /* Quasi-incidences */              pp[jk] += freq[jk][m][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>          }
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          for(jk=1; jk <=nlstate ; jk++){
        /* Stable prevalence in each health state */            for(m=-1, pos=0; m <=0 ; m++)
        for(cpt=1; cpt<nlstate;cpt++){              pos += freq[jk][m][i];
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>            if(pp[jk]>=1.e-10){
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              if(first==1){
        }                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     for(cpt=1; cpt<=nlstate;cpt++) {              }
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 interval) in state (%d): v%s%d%d.png <br>            }else{
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                if(first==1)
      }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
      for(cpt=1; cpt<=nlstate;cpt++) {              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>            }
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          }
      }  
      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=0, pp[jk]=0; m <=nlstate+ndeath; m++)
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              pp[jk] += freq[jk][m][i];
    }          }       
  }          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
 fclose(fichtm);            pos += pp[jk];
 }            posprop += prop[jk][i];
           }
 /******************* Gnuplot file **************/          for(jk=1; jk <=nlstate ; jk++){
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){            if(pos>=1.e-5){
               if(first==1)
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   int ng;              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {            }else{
     printf("Problem with file %s",optionfilegnuplot);              if(first==1)
   }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 #ifdef windows            }
     fprintf(ficgp,"cd \"%s\" \n",pathc);            if( i <= iagemax){
 #endif              if(pos>=1.e-5){
 m=pow(2,cptcoveff);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                  /*probs[i][jk][j1]= pp[jk]/pos;*/
  /* 1eme*/                /*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 (cpt=1; cpt<= nlstate ; cpt ++) {              }
    for (k1=1; k1<= m ; k1 ++) {              else
                 fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
 #ifdef windows            }
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          }
      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);          
 #endif          for(jk=-1; jk <=nlstate+ndeath; jk++)
 #ifdef unix            for(m=-1; m <=nlstate+ndeath; m++)
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              if(freq[jk][m][i] !=0 ) {
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);              if(first==1)
 #endif                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                 fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 for (i=1; i<= nlstate ; i ++) {              }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          if(i <= iagemax)
   else fprintf(ficgp," \%%*lf (\%%*lf)");            fprintf(ficresp,"\n");
 }          if(first==1)
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            printf("Others in log...\n");
     for (i=1; i<= nlstate ; i ++) {          fprintf(ficlog,"\n");
   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*$3) \"\%%lf",fileres,k1-1,k1-1);    dateintmean=dateintsum/k2cpt; 
      for (i=1; i<= nlstate ; i ++) {   
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    fclose(ficresp);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 }      free_vector(pp,1,nlstate);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
 #ifdef unix    /* End of Freq */
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");  }
 #endif  
    }  /************ Prevalence ********************/
   }  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   /*2 eme*/  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   for (k1=1; k1<= m ; k1 ++) {       in each health status at the date of interview (if between dateprev1 and dateprev2).
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);       We still use firstpass and lastpass as another selection.
     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 ++) {    int i, m, jk, k1, i1, j1, bool, z1,j;
       k=2*i;    double ***freq; /* Frequencies */
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    double *pp, **prop;
       for (j=1; j<= nlstate+1 ; j ++) {    double pos,posprop; 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    double  y2; /* in fractional years */
   else fprintf(ficgp," \%%*lf (\%%*lf)");    int iagemin, iagemax;
 }    
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    iagemin= (int) agemin;
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    iagemax= (int) agemax;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    /*pp=vector(1,nlstate);*/
       for (j=1; j<= nlstate+1 ; j ++) {    prop=matrix(1,nlstate,iagemin,iagemax+3); 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
         else fprintf(ficgp," \%%*lf (\%%*lf)");    j1=0;
 }      
       fprintf(ficgp,"\" t\"\" w l 0,");    j=cptcoveff;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       for (j=1; j<= nlstate+1 ; j ++) {    
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    for(k1=1; k1<=j;k1++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");      for(i1=1; i1<=ncodemax[k1];i1++){
 }          j1++;
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        
       else fprintf(ficgp,"\" t\"\" w l 0,");        for (i=1; i<=nlstate; i++)  
     }          for(m=iagemin; m <= iagemax+3; m++)
   }            prop[i][m]=0.0;
         
   /*3eme*/        for (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
   for (k1=1; k1<= m ; k1 ++) {          if  (cptcovn>0) {
     for (cpt=1; cpt<= nlstate ; cpt ++) {            for (z1=1; z1<=cptcoveff; z1++) 
       k=2+nlstate*(2*cpt-2);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);                bool=0;
       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);          if (bool==1) { 
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");                if(agev[m][i]==0) agev[m][i]=iagemax+1;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);                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); 
 */                if (s[m][i]>0 && s[m][i]<=nlstate) { 
       for (i=1; i< nlstate ; i ++) {                  /*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," ,\"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);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
                   prop[s[m][i]][iagemax+3] += weight[i]; 
       }                } 
     }              }
   }            } /* end selection of waves */
            }
   /* CV preval stat */        }
     for (k1=1; k1<= m ; k1 ++) {        for(i=iagemin; i <= iagemax+3; i++){  
     for (cpt=1; cpt<nlstate ; cpt ++) {          
       k=3;          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            posprop += prop[jk][i]; 
       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);          } 
   
       for (i=1; i< nlstate ; i ++)          for(jk=1; jk <=nlstate ; jk++){     
         fprintf(ficgp,"+$%d",k+i+1);            if( i <=  iagemax){ 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);              if(posprop>=1.e-5){ 
                      probs[i][jk][j1]= prop[jk][i]/posprop;
       l=3+(nlstate+ndeath)*cpt;              } else
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
       for (i=1; i< nlstate ; i ++) {            } 
         l=3+(nlstate+ndeath)*cpt;          }/* end jk */ 
         fprintf(ficgp,"+$%d",l+i+1);        }/* end i */ 
       }      } /* end i1 */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      } /* end k1 */
     }    
   }      /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
      /*free_vector(pp,1,nlstate);*/
   /* proba elementaires */    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
    for(i=1,jk=1; i <=nlstate; i++){  }  /* End of prevalence */
     for(k=1; k <=(nlstate+ndeath); k++){  
       if (k != i) {  /************* Waves Concatenation ***************/
         for(j=1; j <=ncovmodel; j++){  
          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,"p%d=%f ",jk,p[jk]);  {
           jk++;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           fprintf(ficgp,"\n");       Death is a valid wave (if date is known).
         }       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
     }       and mw[mi+1][i]. dh depends on stepm.
    }       */
   
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/    int i, mi, m;
      for(jk=1; jk <=m; jk++) {    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);       double sum=0., jmean=0.;*/
        if (ng==2)    int first;
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");    int j, k=0,jk, ju, jl;
        else    double sum=0.;
          fprintf(ficgp,"\nset title \"Probability\"\n");    first=0;
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);    jmin=1e+5;
        i=1;    jmax=-1;
        for(k2=1; k2<=nlstate; k2++) {    jmean=0.;
          k3=i;    for(i=1; i<=imx; i++){
          for(k=1; k<=(nlstate+ndeath); k++) {      mi=0;
            if (k != k2){      m=firstpass;
              if(ng==2)      while(s[m][i] <= nlstate){
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
              else          mw[++mi][i]=m;
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);        if(m >=lastpass)
              ij=1;          break;
              for(j=3; j <=ncovmodel; j++) {        else
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          m++;
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);      }/* end while */
                  ij++;      if (s[m][i] > nlstate){
                }        mi++;     /* Death is another wave */
                else        /* if(mi==0)  never been interviewed correctly before death */
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);           /* Only death is a correct wave */
              }        mw[mi][i]=m;
              fprintf(ficgp,")/(1");      }
                
              for(k1=1; k1 <=nlstate; k1++){        wav[i]=mi;
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);      if(mi==0){
                ij=1;        nbwarn++;
                for(j=3; j <=ncovmodel; j++){        if(first==0){
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          first=1;
                    ij++;        }
                  }        if(first==1){
                  else          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        }
                }      } /* end mi==0 */
                fprintf(ficgp,")");    } /* End individuals */
              }  
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);    for(i=1; i<=imx; i++){
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      for(mi=1; mi<wav[i];mi++){
              i=i+ncovmodel;        if (stepm <=0)
            }          dh[mi][i]=1;
          }        else{
        }          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
      }            if (agedc[i] < 2*AGESUP) {
    }              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
    fclose(ficgp);              if(j==0) j=1;  /* Survives at least one month after exam */
 }  /* end gnuplot */              else if(j<0){
                 nberr++;
                 printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
 /*************** Moving average **************/                j=1; /* Temporary Dangerous patch */
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){                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]);
   int i, cpt, cptcod;                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)              }
       for (i=1; i<=nlstate;i++)              k=k+1;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)              if (j >= jmax){
           mobaverage[(int)agedeb][i][cptcod]=0.;                jmax=j;
                    ijmax=i;
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){              }
       for (i=1; i<=nlstate;i++){              if (j <= jmin){
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){                jmin=j;
           for (cpt=0;cpt<=4;cpt++){                ijmin=i;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];              }
           }              sum=sum+j;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
         }              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       }            }
     }          }
              else{
 }            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   /*        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]); */
   
 /************** Forecasting ******************/            k=k+1;
 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 >= jmax) {
                jmax=j;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;              ijmax=i;
   int *popage;            }
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;            else if (j <= jmin){
   double *popeffectif,*popcount;              jmin=j;
   double ***p3mat;              ijmin=i;
   char fileresf[FILENAMELENGTH];            }
             /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
  agelim=AGESUP;            /*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]);*/
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;            if(j<0){
               nberr++;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              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]);
              }
   strcpy(fileresf,"f");            sum=sum+j;
   strcat(fileresf,fileres);          }
   if((ficresf=fopen(fileresf,"w"))==NULL) {          jk= j/stepm;
     printf("Problem with forecast resultfile: %s\n", fileresf);          jl= j -jk*stepm;
   }          ju= j -(jk+1)*stepm;
   printf("Computing forecasting: result on file '%s' \n", fileresf);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
             if(jl==0){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;              dh[mi][i]=jk;
               bh[mi][i]=0;
   if (mobilav==1) {            }else{ /* We want a negative bias in order to only have interpolation ie
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                    * to avoid the price of an extra matrix product in likelihood */
     movingaverage(agedeb, fage, ageminpar, mobaverage);              dh[mi][i]=jk+1;
   }              bh[mi][i]=ju;
             }
   stepsize=(int) (stepm+YEARM-1)/YEARM;          }else{
   if (stepm<=12) stepsize=1;            if(jl <= -ju){
                dh[mi][i]=jk;
   agelim=AGESUP;              bh[mi][i]=jl;       /* bias is positive if real duration
                                     * is higher than the multiple of stepm and negative otherwise.
   hstepm=1;                                   */
   hstepm=hstepm/stepm;            }
   yp1=modf(dateintmean,&yp);            else{
   anprojmean=yp;              dh[mi][i]=jk+1;
   yp2=modf((yp1*12),&yp);              bh[mi][i]=ju;
   mprojmean=yp;            }
   yp1=modf((yp2*30.5),&yp);            if(dh[mi][i]==0){
   jprojmean=yp;              dh[mi][i]=1; /* At least one step */
   if(jprojmean==0) jprojmean=1;              bh[mi][i]=ju; /* At least one step */
   if(mprojmean==0) jprojmean=1;              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
              }
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);          } /* end if mle */
          }
   for(cptcov=1;cptcov<=i2;cptcov++){      } /* end wave */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    }
       k=k+1;    jmean=sum/k;
       fprintf(ficresf,"\n#******");    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
       for(j=1;j<=cptcoveff;j++) {    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);
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   }
       }  
       fprintf(ficresf,"******\n");  /*********** Tricode ****************************/
       fprintf(ficresf,"# StartingAge FinalAge");  void tricode(int *Tvar, int **nbcode, int imx)
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  {
          /* Uses cptcovn+2*cptcovprod as the number of covariates */
          /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {  
         fprintf(ficresf,"\n");    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      int modmaxcovj=0; /* Modality max of covariates j */
     cptcoveff=0; 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){   
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    for (k=0; k<maxncov; k++) Ndum[k]=0;
           nhstepm = nhstepm/hstepm;    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
            
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
           oldm=oldms;savm=savms;      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                                   modality of this covariate Vj*/ 
                ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
           for (h=0; h<=nhstepm; h++){                                        modality of the nth covariate of individual i. */
             if (h==(int) (calagedate+YEARM*cpt)) {        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
             }        if (ij > modmaxcovj) modmaxcovj=ij; 
             for(j=1; j<=nlstate+ndeath;j++) {        /* getting the maximum value of the modality of the covariate
               kk1=0.;kk2=0;           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
               for(i=1; i<=nlstate;i++) {                         female is 1, then modmaxcovj=1.*/
                 if (mobilav==1)      }
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
                 else {      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];        if( Ndum[i] != 0 )
                 }          ncodemax[j]++; 
                        /* Number of modalities of the j th covariate. In fact
               }           ncodemax[j]=2 (dichotom. variables only) but it could be more for
               if (h==(int)(calagedate+12*cpt)){           historical reasons */
                 fprintf(ficresf," %.3f", kk1);      } /* Ndum[-1] number of undefined modalities */
                          
               }      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
             }      ij=1; 
           }      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
         }          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
       }            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
     }                                       k is a modality. If we have model=V1+V1*sex 
   }                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
                    ij++;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          }
           if (ij > ncodemax[j]) break; 
   fclose(ficresf);        }  /* end of loop on */
 }      } /* end of loop on modality */ 
 /************** Forecasting ******************/    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
 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){    
      for (k=0; k< maxncov; k++) Ndum[k]=0;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    
   int *popage;    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   double *popeffectif,*popcount;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
   double ***p3mat,***tabpop,***tabpopprev;     Ndum[ij]++;
   char filerespop[FILENAMELENGTH];   }
   
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);   ij=1;
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   agelim=AGESUP;     if((Ndum[i]!=0) && (i<=ncovcol)){
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;       Tvaraff[ij]=i; /*For printing */
         ij++;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);     }
     }
     ij--;
   strcpy(filerespop,"pop");   cptcoveff=ij; /*Number of simple covariates*/
   strcat(filerespop,fileres);  }
   if((ficrespop=fopen(filerespop,"w"))==NULL) {  
     printf("Problem with forecast resultfile: %s\n", filerespop);  /*********** Health Expectancies ****************/
   }  
   printf("Computing forecasting: result on file '%s' \n", filerespop);  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 (cptcoveff==0) ncodemax[cptcoveff]=1;  {
     /* Health expectancies, no variances */
   if (mobilav==1) {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    int nhstepma, nstepma; /* Decreasing with age */
     movingaverage(agedeb, fage, ageminpar, mobaverage);    double age, agelim, hf;
   }    double ***p3mat;
     double eip;
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=12) stepsize=1;    pstamp(ficreseij);
      fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   agelim=AGESUP;    fprintf(ficreseij,"# Age");
      for(i=1; i<=nlstate;i++){
   hstepm=1;      for(j=1; j<=nlstate;j++){
   hstepm=hstepm/stepm;        fprintf(ficreseij," e%1d%1d ",i,j);
        }
   if (popforecast==1) {      fprintf(ficreseij," e%1d. ",i);
     if((ficpop=fopen(popfile,"r"))==NULL) {    }
       printf("Problem with population file : %s\n",popfile);exit(0);    fprintf(ficreseij,"\n");
     }  
     popage=ivector(0,AGESUP);    
     popeffectif=vector(0,AGESUP);    if(estepm < stepm){
     popcount=vector(0,AGESUP);      printf ("Problem %d lower than %d\n",estepm, stepm);
        }
     i=1;      else  hstepm=estepm;   
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    /* We compute the life expectancy from trapezoids spaced every estepm months
         * This is mainly to measure the difference between two models: for example
     imx=i;     * if stepm=24 months pijx are given only every 2 years and by summing them
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];     * we are calculating an estimate of the Life Expectancy assuming a linear 
   }     * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
   for(cptcov=1;cptcov<=i2;cptcov++){     * estimate the model with stepm=1 month, we can keep estepm to 24 months
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){     * to compare the new estimate of Life expectancy with the same linear 
       k=k+1;     * hypothesis. A more precise result, taking into account a more precise
       fprintf(ficrespop,"\n#******");     * curvature will be obtained if estepm is as small as stepm. */
       for(j=1;j<=cptcoveff;j++) {  
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    /* 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. 
       fprintf(ficrespop,"******\n");       nhstepm is the number of hstepm from age to agelim 
       fprintf(ficrespop,"# Age");       nstepm is the number of stepm from age to agelin. 
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);       Look at hpijx to understand the reason of that which relies in memory size
       if (popforecast==1)  fprintf(ficrespop," [Population]");       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 (cpt=0; cpt<=0;cpt++) {       survival function given by stepm (the optimization length). Unfortunately it
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);         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 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){       results. So we changed our mind and took the option of the best precision.
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    */
           nhstepm = nhstepm/hstepm;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
            
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    agelim=AGESUP;
           oldm=oldms;savm=savms;    /* If stepm=6 months */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        /* Computed by stepm unit matrices, product of hstepm matrices, stored
                 in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
           for (h=0; h<=nhstepm; h++){      
             if (h==(int) (calagedate+YEARM*cpt)) {  /* nhstepm age range expressed in number of stepm */
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             for(j=1; j<=nlstate+ndeath;j++) {    /* if (stepm >= YEARM) hstepm=1;*/
               kk1=0.;kk2=0;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
               for(i=1; i<=nlstate;i++) {                  p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                 if (mobilav==1)  
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    for (age=bage; age<=fage; age ++){ 
                 else {      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
                 }      /* if (stepm >= YEARM) hstepm=1;*/
               }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
               if (h==(int)(calagedate+12*cpt)){  
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;      /* If stepm=6 months */
                   /*fprintf(ficrespop," %.3f", kk1);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
               }      
             }      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
             for(i=1; i<=nlstate;i++){      
               kk1=0.;      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
                 for(j=1; j<=nlstate;j++){      
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];      printf("%d|",(int)age);fflush(stdout);
                 }      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];      
             }      /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)        for(j=1; j<=nlstate;j++)
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);          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;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            
         }            /* 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(ficreseij,"%3.0f",age );
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {      for(i=1; i<=nlstate;i++){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);          eip=0;
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        for(j=1; j<=nlstate;j++){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          eip +=eij[i][j][(int)age];
           nhstepm = nhstepm/hstepm;          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
                  }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficreseij,"%9.4f", eip );
           oldm=oldms;savm=savms;      }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        fprintf(ficreseij,"\n");
           for (h=0; h<=nhstepm; h++){      
             if (h==(int) (calagedate+YEARM*cpt)) {    }
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             }    printf("\n");
             for(j=1; j<=nlstate+ndeath;j++) {    fprintf(ficlog,"\n");
               kk1=0.;kk2=0;    
               for(i=1; i<=nlstate;i++) {                }
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];      
               }  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[] )
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);  
             }  {
           }    /* Covariances of health expectancies eij and of total life expectancies according
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     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 */
   }    double age, agelim, hf;
      double ***p3matp, ***p3matm, ***varhe;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    double **dnewm,**doldm;
     double *xp, *xm;
   if (popforecast==1) {    double **gp, **gm;
     free_ivector(popage,0,AGESUP);    double ***gradg, ***trgradg;
     free_vector(popeffectif,0,AGESUP);    int theta;
     free_vector(popcount,0,AGESUP);  
   }    double eip, vip;
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   fclose(ficrespop);    xp=vector(1,npar);
 }    xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
 /***********************************************/    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
 /**************** Main Program *****************/    
 /***********************************************/    pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
 int main(int argc, char *argv[])    fprintf(ficresstdeij,"# Age");
 {    for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++)
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   double agedeb, agefin,hf;      fprintf(ficresstdeij," e%1d. ",i);
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;    }
     fprintf(ficresstdeij,"\n");
   double fret;  
   double **xi,tmp,delta;    pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   double dum; /* Dummy variable */    fprintf(ficrescveij,"# Age");
   double ***p3mat;    for(i=1; i<=nlstate;i++)
   int *indx;      for(j=1; j<=nlstate;j++){
   char line[MAXLINE], linepar[MAXLINE];        cptj= (j-1)*nlstate+i;
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        for(i2=1; i2<=nlstate;i2++)
   int firstobs=1, lastobs=10;          for(j2=1; j2<=nlstate;j2++){
   int sdeb, sfin; /* Status at beginning and end */            cptj2= (j2-1)*nlstate+i2;
   int c,  h , cpt,l;            if(cptj2 <= cptj)
   int ju,jl, mi;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;          }
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      }
   int mobilav=0,popforecast=0;    fprintf(ficrescveij,"\n");
   int hstepm, nhstepm;    
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
   double bage, fage, age, agelim, agebase;    }
   double ftolpl=FTOL;    else  hstepm=estepm;   
   double **prlim;    /* We compute the life expectancy from trapezoids spaced every estepm months
   double *severity;     * This is mainly to measure the difference between two models: for example
   double ***param; /* Matrix of parameters */     * if stepm=24 months pijx are given only every 2 years and by summing them
   double  *p;     * we are calculating an estimate of the Life Expectancy assuming a linear 
   double **matcov; /* Matrix of covariance */     * progression in between and thus overestimating or underestimating according
   double ***delti3; /* Scale */     * to the curvature of the survival function. If, for the same date, we 
   double *delti; /* Scale */     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   double ***eij, ***vareij;     * to compare the new estimate of Life expectancy with the same linear 
   double **varpl; /* Variances of prevalence limits by age */     * hypothesis. A more precise result, taking into account a more precise
   double *epj, vepp;     * curvature will be obtained if estepm is as small as stepm. */
   double kk1, kk2;  
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    /* For example we decided to compute the life expectancy with the smallest unit */
      /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
   char *alph[]={"a","a","b","c","d","e"}, str[4];       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like estepm months */
   char z[1]="c", occ;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
 #include <sys/time.h>       survival function given by stepm (the optimization length). Unfortunately it
 #include <time.h>       means that if the survival funtion is printed only each two years of age and if
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];       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.
   /* long total_usecs;    */
   struct timeval start_time, end_time;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
    
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    /* If stepm=6 months */
   getcwd(pathcd, size);    /* nhstepm age range expressed in number of stepm */
     agelim=AGESUP;
   printf("\n%s",version);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
   if(argc <=1){    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     printf("\nEnter the parameter file name: ");    /* if (stepm >= YEARM) hstepm=1;*/
     scanf("%s",pathtot);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }    
   else{    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     strcpy(pathtot,argv[1]);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   /*cygwin_split_path(pathtot,path,optionfile);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   /* cutv(path,optionfile,pathtot,'\\');*/  
     for (age=bage; age<=fage; age ++){ 
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   chdir(path);      /* if (stepm >= YEARM) hstepm=1;*/
   replace(pathc,path);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
 /*-------- arguments in the command line --------*/      /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
   strcpy(fileres,"r");         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   strcat(fileres, optionfilefiname);      
   strcat(fileres,".txt");    /* Other files have txt extension */      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
   /*---------arguments file --------*/      /* Computing  Variances of health expectancies */
       /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   if((ficpar=fopen(optionfile,"r"))==NULL)    {         decrease memory allocation */
     printf("Problem with optionfile %s\n",optionfile);      for(theta=1; theta <=npar; theta++){
     goto end;        for(i=1; i<=npar; i++){ 
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
   strcpy(filereso,"o");        }
   strcat(filereso,fileres);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   if((ficparo=fopen(filereso,"w"))==NULL) {        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    
   }        for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate; i++){
   /* Reads comments: lines beginning with '#' */            for(h=0; h<=nhstepm-1; h++){
   while((c=getc(ficpar))=='#' && c!= EOF){              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
     ungetc(c,ficpar);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
     fgets(line, MAXLINE, ficpar);            }
     puts(line);          }
     fputs(line,ficparo);        }
   }       
   ungetc(c,ficpar);        for(ij=1; ij<= nlstate*nlstate; ij++)
           for(h=0; h<=nhstepm-1; h++){
   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);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   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);      }/* End theta */
 while((c=getc(ficpar))=='#' && c!= EOF){      
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      for(h=0; h<=nhstepm-1; h++)
     puts(line);        for(j=1; j<=nlstate*nlstate;j++)
     fputs(line,ficparo);          for(theta=1; theta <=npar; theta++)
   }            trgradg[h][j][theta]=gradg[h][theta][j];
   ungetc(c,ficpar);      
    
           for(ij=1;ij<=nlstate*nlstate;ij++)
   covar=matrix(0,NCOVMAX,1,n);        for(ji=1;ji<=nlstate*nlstate;ji++)
   cptcovn=0;          varhe[ij][ji][(int)age] =0.;
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;  
        printf("%d|",(int)age);fflush(stdout);
   ncovmodel=2+cptcovn;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */       for(h=0;h<=nhstepm-1;h++){
          for(k=0;k<=nhstepm-1;k++){
   /* Read guess parameters */          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   /* Reads comments: lines beginning with '#' */          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   while((c=getc(ficpar))=='#' && c!= EOF){          for(ij=1;ij<=nlstate*nlstate;ij++)
     ungetc(c,ficpar);            for(ji=1;ji<=nlstate*nlstate;ji++)
     fgets(line, MAXLINE, ficpar);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     puts(line);        }
     fputs(line,ficparo);      }
   }  
   ungetc(c,ficpar);      /* Computing expectancies */
        hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      for(i=1; i<=nlstate;i++)
     for(i=1; i <=nlstate; i++)        for(j=1; j<=nlstate;j++)
     for(j=1; j <=nlstate+ndeath-1; j++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       fscanf(ficpar,"%1d%1d",&i1,&j1);            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
       fprintf(ficparo,"%1d%1d",i1,j1);            
       printf("%1d%1d",i,j);            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
       for(k=1; k<=ncovmodel;k++){  
         fscanf(ficpar," %lf",&param[i][j][k]);          }
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);      fprintf(ficresstdeij,"%3.0f",age );
       }      for(i=1; i<=nlstate;i++){
       fscanf(ficpar,"\n");        eip=0.;
       printf("\n");        vip=0.;
       fprintf(ficparo,"\n");        for(j=1; j<=nlstate;j++){
     }          eip += eij[i][j][(int)age];
            for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
   p=param[1][1];        }
          fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
   /* Reads comments: lines beginning with '#' */      }
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficresstdeij,"\n");
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);      fprintf(ficrescveij,"%3.0f",age );
     puts(line);      for(i=1; i<=nlstate;i++)
     fputs(line,ficparo);        for(j=1; j<=nlstate;j++){
   }          cptj= (j-1)*nlstate+i;
   ungetc(c,ficpar);          for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);              cptj2= (j2-1)*nlstate+i2;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */              if(cptj2 <= cptj)
   for(i=1; i <=nlstate; i++){                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
     for(j=1; j <=nlstate+ndeath-1; j++){            }
       fscanf(ficpar,"%1d%1d",&i1,&j1);        }
       printf("%1d%1d",i,j);      fprintf(ficrescveij,"\n");
       fprintf(ficparo,"%1d%1d",i1,j1);     
       for(k=1; k<=ncovmodel;k++){    }
         fscanf(ficpar,"%le",&delti3[i][j][k]);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         printf(" %le",delti3[i][j][k]);    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
         fprintf(ficparo," %le",delti3[i][j][k]);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       }    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       fscanf(ficpar,"\n");    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       printf("\n");    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficparo,"\n");    printf("\n");
     }    fprintf(ficlog,"\n");
   }  
   delti=delti3[1][1];    free_vector(xm,1,npar);
      free_vector(xp,1,npar);
   /* Reads comments: lines beginning with '#' */    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     ungetc(c,ficpar);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     fgets(line, MAXLINE, ficpar);  }
     puts(line);  
     fputs(line,ficparo);  /************ Variance ******************/
   }  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   ungetc(c,ficpar);  {
      /* Variance of health expectancies */
   matcov=matrix(1,npar,1,npar);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   for(i=1; i <=npar; i++){    /* double **newm;*/
     fscanf(ficpar,"%s",&str);    double **dnewm,**doldm;
     printf("%s",str);    double **dnewmp,**doldmp;
     fprintf(ficparo,"%s",str);    int i, j, nhstepm, hstepm, h, nstepm ;
     for(j=1; j <=i; j++){    int k, cptcode;
       fscanf(ficpar," %le",&matcov[i][j]);    double *xp;
       printf(" %.5le",matcov[i][j]);    double **gp, **gm;  /* for var eij */
       fprintf(ficparo," %.5le",matcov[i][j]);    double ***gradg, ***trgradg; /*for var eij */
     }    double **gradgp, **trgradgp; /* for var p point j */
     fscanf(ficpar,"\n");    double *gpp, *gmp; /* for var p point j */
     printf("\n");    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     fprintf(ficparo,"\n");    double ***p3mat;
   }    double age,agelim, hf;
   for(i=1; i <=npar; i++)    double ***mobaverage;
     for(j=i+1;j<=npar;j++)    int theta;
       matcov[i][j]=matcov[j][i];    char digit[4];
        char digitp[25];
   printf("\n");  
     char fileresprobmorprev[FILENAMELENGTH];
   
     /*-------- Rewriting paramater file ----------*/    if(popbased==1){
      strcpy(rfileres,"r");    /* "Rparameterfile */      if(mobilav!=0)
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/        strcpy(digitp,"-populbased-mobilav-");
      strcat(rfileres,".");    /* */      else strcpy(digitp,"-populbased-nomobil-");
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    }
     if((ficres =fopen(rfileres,"w"))==NULL) {    else 
       printf("Problem writing new parameter file: %s\n", fileres);goto end;      strcpy(digitp,"-stablbased-");
     }  
     fprintf(ficres,"#%s\n",version);    if (mobilav!=0) {
          mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     /*-------- data file ----------*/      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
     if((fic=fopen(datafile,"r"))==NULL)    {        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
       printf("Problem with datafile: %s\n", datafile);goto end;        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     }      }
     }
     n= lastobs;  
     severity = vector(1,maxwav);    strcpy(fileresprobmorprev,"prmorprev"); 
     outcome=imatrix(1,maxwav+1,1,n);    sprintf(digit,"%-d",ij);
     num=ivector(1,n);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     moisnais=vector(1,n);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     annais=vector(1,n);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     moisdc=vector(1,n);    strcat(fileresprobmorprev,fileres);
     andc=vector(1,n);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     agedc=vector(1,n);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     cod=ivector(1,n);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     weight=vector(1,n);    }
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     mint=matrix(1,maxwav,1,n);   
     anint=matrix(1,maxwav,1,n);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     s=imatrix(1,maxwav+1,1,n);    pstamp(ficresprobmorprev);
     adl=imatrix(1,maxwav+1,1,n);        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);
     tab=ivector(1,NCOVMAX);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     ncodemax=ivector(1,8);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
     i=1;      for(i=1; i<=nlstate;i++)
     while (fgets(line, MAXLINE, fic) != NULL)    {        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
       if ((i >= firstobs) && (i <=lastobs)) {    }  
            fprintf(ficresprobmorprev,"\n");
         for (j=maxwav;j>=1;j--){    fprintf(ficgp,"\n# Routine varevsij");
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
           strcpy(line,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");
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);  /*   } */
         }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
            pstamp(ficresvij);
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    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);
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    else
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    for(i=1; i<=nlstate;i++)
         for (j=ncovcol;j>=1;j--){      for(j=1; j<=nlstate;j++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
         }    fprintf(ficresvij,"\n");
         num[i]=atol(stra);  
            xp=vector(1,npar);
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    dnewm=matrix(1,nlstate,1,npar);
           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;}*/    doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
         i=i+1;    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       }  
     }    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     /* printf("ii=%d", ij);    gpp=vector(nlstate+1,nlstate+ndeath);
        scanf("%d",i);*/    gmp=vector(nlstate+1,nlstate+ndeath);
   imx=i-1; /* Number of individuals */    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
   /* for (i=1; i<=imx; i++){    if(estepm < stepm){
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      printf ("Problem %d lower than %d\n",estepm, stepm);
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    }
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    else  hstepm=estepm;   
     }*/    /* For example we decided to compute the life expectancy with the smallest unit */
    /*  for (i=1; i<=imx; i++){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
      if (s[4][i]==9)  s[4][i]=-1;       nhstepm is the number of hstepm from age to agelim 
      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]));}*/       nstepm is the number of stepm from age to agelin. 
         Look at function hpijx to understand why (it is linked to memory size questions) */
      /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   /* Calculation of the number of parameter from char model*/       survival function given by stepm (the optimization length). Unfortunately it
   Tvar=ivector(1,15);       means that if the survival funtion is printed every two years of age and if
   Tprod=ivector(1,15);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   Tvaraff=ivector(1,15);       results. So we changed our mind and took the option of the best precision.
   Tvard=imatrix(1,15,1,2);    */
   Tage=ivector(1,15);          hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
        agelim = AGESUP;
   if (strlen(model) >1){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     j=0, j1=0, k1=1, k2=1;      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     j=nbocc(model,'+');      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     j1=nbocc(model,'*');      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     cptcovn=j+1;      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
     cptcovprod=j1;      gp=matrix(0,nhstepm,1,nlstate);
          gm=matrix(0,nhstepm,1,nlstate);
     strcpy(modelsav,model);  
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);      for(theta=1; theta <=npar; theta++){
       goto end;        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
            }
     for(i=(j+1); i>=1;i--){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       cutv(stra,strb,modelsav,'+');        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);  
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        if (popbased==1) {
       /*scanf("%d",i);*/          if(mobilav ==0){
       if (strchr(strb,'*')) {            for(i=1; i<=nlstate;i++)
         cutv(strd,strc,strb,'*');              prlim[i][i]=probs[(int)age][i][ij];
         if (strcmp(strc,"age")==0) {          }else{ /* mobilav */ 
           cptcovprod--;            for(i=1; i<=nlstate;i++)
           cutv(strb,stre,strd,'V');              prlim[i][i]=mobaverage[(int)age][i][ij];
           Tvar[i]=atoi(stre);          }
           cptcovage++;        }
             Tage[cptcovage]=i;    
             /*printf("stre=%s ", stre);*/        for(j=1; j<= nlstate; j++){
         }          for(h=0; h<=nhstepm; h++){
         else if (strcmp(strd,"age")==0) {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           cptcovprod--;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           cutv(strb,stre,strc,'V');          }
           Tvar[i]=atoi(stre);        }
           cptcovage++;        /* This for computing probability of death (h=1 means
           Tage[cptcovage]=i;           computed over hstepm matrices product = hstepm*stepm months) 
         }           as a weighted average of prlim.
         else {        */
           cutv(strb,stre,strc,'V');        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           Tvar[i]=ncovcol+k1;          for(i=1,gpp[j]=0.; i<= nlstate; i++)
           cutv(strb,strc,strd,'V');            gpp[j] += prlim[i][i]*p3mat[i][j][1];
           Tprod[k1]=i;        }    
           Tvard[k1][1]=atoi(strc);        /* end probability of death */
           Tvard[k1][2]=atoi(stre);  
           Tvar[cptcovn+k2]=Tvard[k1][1];        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           Tvar[cptcovn+k2+1]=Tvard[k1][2];          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           for (k=1; k<=lastobs;k++)        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           k1++;   
           k2=k2+2;        if (popbased==1) {
         }          if(mobilav ==0){
       }            for(i=1; i<=nlstate;i++)
       else {              prlim[i][i]=probs[(int)age][i][ij];
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          }else{ /* mobilav */ 
        /*  scanf("%d",i);*/            for(i=1; i<=nlstate;i++)
       cutv(strd,strc,strb,'V');              prlim[i][i]=mobaverage[(int)age][i][ij];
       Tvar[i]=atoi(strc);          }
       }        }
       strcpy(modelsav,stra);    
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
         scanf("%d",i);*/          for(h=0; h<=nhstepm; h++){
     }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
 }              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
            }
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);        }
   printf("cptcovprod=%d ", cptcovprod);        /* This for computing probability of death (h=1 means
   scanf("%d ",i);*/           computed over hstepm matrices product = hstepm*stepm months) 
     fclose(fic);           as a weighted average of prlim.
         */
     /*  if(mle==1){*/        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     if (weightopt != 1) { /* Maximisation without weights*/          for(i=1,gmp[j]=0.; i<= nlstate; i++)
       for(i=1;i<=n;i++) weight[i]=1.0;           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     }        }    
     /*-calculation of age at interview from date of interview and age at death -*/        /* end probability of death */
     agev=matrix(1,maxwav,1,imx);  
         for(j=1; j<= nlstate; j++) /* vareij */
     for (i=1; i<=imx; i++) {          for(h=0; h<=nhstepm; h++){
       for(m=2; (m<= maxwav); m++) {            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){          }
          anint[m][i]=9999;  
          s[m][i]=-1;        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
        }          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;        }
       }  
     }      } /* End theta */
   
     for (i=1; i<=imx; i++)  {      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  
       for(m=1; (m<= maxwav); m++){      for(h=0; h<=nhstepm; h++) /* veij */
         if(s[m][i] >0){        for(j=1; j<=nlstate;j++)
           if (s[m][i] >= nlstate+1) {          for(theta=1; theta <=npar; theta++)
             if(agedc[i]>0)            trgradg[h][j][theta]=gradg[h][theta][j];
               if(moisdc[i]!=99 && andc[i]!=9999)  
                 agev[m][i]=agedc[i];      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/        for(theta=1; theta <=npar; theta++)
            else {          trgradgp[j][theta]=gradgp[theta][j];
               if (andc[i]!=9999){    
               printf("Warning negative age at death: %d line:%d\n",num[i],i);  
               agev[m][i]=-1;      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
               }      for(i=1;i<=nlstate;i++)
             }        for(j=1;j<=nlstate;j++)
           }          vareij[i][j][(int)age] =0.;
           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++){
             if(mint[m][i]==99 || anint[m][i]==9999)        for(k=0;k<=nhstepm;k++){
               agev[m][i]=1;          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
             else if(agev[m][i] <agemin){          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
               agemin=agev[m][i];          for(i=1;i<=nlstate;i++)
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/            for(j=1;j<=nlstate;j++)
             }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
             else if(agev[m][i] >agemax){        }
               agemax=agev[m][i];      }
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    
             }      /* pptj */
             /*agev[m][i]=anint[m][i]-annais[i];*/      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
             /*   agev[m][i] = age[i]+2*m;*/      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
           }      for(j=nlstate+1;j<=nlstate+ndeath;j++)
           else { /* =9 */        for(i=nlstate+1;i<=nlstate+ndeath;i++)
             agev[m][i]=1;          varppt[j][i]=doldmp[j][i];
             s[m][i]=-1;      /* end ppptj */
           }      /*  x centered again */
         }      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
         else /*= 0 Unknown */      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
           agev[m][i]=1;   
       }      if (popbased==1) {
            if(mobilav ==0){
     }          for(i=1; i<=nlstate;i++)
     for (i=1; i<=imx; i++)  {            prlim[i][i]=probs[(int)age][i][ij];
       for(m=1; (m<= maxwav); m++){        }else{ /* mobilav */ 
         if (s[m][i] > (nlstate+ndeath)) {          for(i=1; i<=nlstate;i++)
           printf("Error: Wrong value in nlstate or ndeath\n");              prlim[i][i]=mobaverage[(int)age][i][ij];
           goto end;        }
         }      }
       }               
     }      /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);         as a weighted average of prlim.
       */
     free_vector(severity,1,maxwav);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
     free_imatrix(outcome,1,maxwav+1,1,n);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     free_vector(moisnais,1,n);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     free_vector(annais,1,n);      }    
     /* free_matrix(mint,1,maxwav,1,n);      /* end probability of death */
        free_matrix(anint,1,maxwav,1,n);*/  
     free_vector(moisdc,1,n);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     free_vector(andc,1,n);      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
            for(i=1; i<=nlstate;i++){
     wav=ivector(1,imx);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);        }
     mw=imatrix(1,lastpass-firstpass+1,1,imx);      } 
          fprintf(ficresprobmorprev,"\n");
     /* Concatenates waves */  
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
       Tcode=ivector(1,100);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);        }
       ncodemax[1]=1;      fprintf(ficresvij,"\n");
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      free_matrix(gp,0,nhstepm,1,nlstate);
            free_matrix(gm,0,nhstepm,1,nlstate);
    codtab=imatrix(1,100,1,10);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
    h=0;      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
    m=pow(2,cptcoveff);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      } /* End age */
    for(k=1;k<=cptcoveff; k++){    free_vector(gpp,nlstate+1,nlstate+ndeath);
      for(i=1; i <=(m/pow(2,k));i++){    free_vector(gmp,nlstate+1,nlstate+ndeath);
        for(j=1; j <= ncodemax[k]; j++){    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
            h++;    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
          }  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
        }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
      }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
    }    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 2 ",subdirf(fileresprobmorprev));
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 3 ",subdirf(fileresprobmorprev));
       codtab[1][2]=1;codtab[2][2]=2; */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 3 ",subdirf(fileresprobmorprev));
    /* for(i=1; i <=m ;i++){    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
       for(k=1; k <=cptcovn; k++){    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);
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    /*  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);
       }  */
       printf("\n");  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
       }    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
       scanf("%d",i);*/  
        free_vector(xp,1,npar);
    /* Calculates basic frequencies. Computes observed prevalence at single age    free_matrix(doldm,1,nlstate,1,nlstate);
        and prints on file fileres'p'. */    free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
        free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
        free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fclose(ficresprobmorprev);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fflush(ficgp);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fflush(fichtm); 
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  }  /* end varevsij */
        
     /* For Powell, parameters are in a vector p[] starting at p[1]  /************ Variance of prevlim ******************/
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */  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[])
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */  {
     /* Variance of prevalence limit */
     if(mle==1){    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    double **newm;
     }    double **dnewm,**doldm;
        int i, j, nhstepm, hstepm;
     /*--------- results files --------------*/    int k, cptcode;
     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);    double *xp;
      double *gp, *gm;
     double **gradg, **trgradg;
    jk=1;    double age,agelim;
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    int theta;
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    
    for(i=1,jk=1; i <=nlstate; i++){    pstamp(ficresvpl);
      for(k=1; k <=(nlstate+ndeath); k++){    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
        if (k != i)    fprintf(ficresvpl,"# Age");
          {    for(i=1; i<=nlstate;i++)
            printf("%d%d ",i,k);        fprintf(ficresvpl," %1d-%1d",i,i);
            fprintf(ficres,"%1d%1d ",i,k);    fprintf(ficresvpl,"\n");
            for(j=1; j <=ncovmodel; j++){  
              printf("%f ",p[jk]);    xp=vector(1,npar);
              fprintf(ficres,"%f ",p[jk]);    dnewm=matrix(1,nlstate,1,npar);
              jk++;    doldm=matrix(1,nlstate,1,nlstate);
            }    
            printf("\n");    hstepm=1*YEARM; /* Every year of age */
            fprintf(ficres,"\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
          }    agelim = AGESUP;
      }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
    }      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
  if(mle==1){      if (stepm >= YEARM) hstepm=1;
     /* Computing hessian and covariance matrix */      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
     ftolhess=ftol; /* Usually correct */      gradg=matrix(1,npar,1,nlstate);
     hesscov(matcov, p, npar, delti, ftolhess, func);      gp=vector(1,nlstate);
  }      gm=vector(1,nlstate);
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");  
     printf("# Scales (for hessian or gradient estimation)\n");      for(theta=1; theta <=npar; theta++){
      for(i=1,jk=1; i <=nlstate; i++){        for(i=1; i<=npar; i++){ /* Computes gradient */
       for(j=1; j <=nlstate+ndeath; j++){          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         if (j!=i) {        }
           fprintf(ficres,"%1d%1d",i,j);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           printf("%1d%1d",i,j);        for(i=1;i<=nlstate;i++)
           for(k=1; k<=ncovmodel;k++){          gp[i] = prlim[i][i];
             printf(" %.5e",delti[jk]);      
             fprintf(ficres," %.5e",delti[jk]);        for(i=1; i<=npar; i++) /* Computes gradient */
             jk++;          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           printf("\n");        for(i=1;i<=nlstate;i++)
           fprintf(ficres,"\n");          gm[i] = prlim[i][i];
         }  
       }        for(i=1;i<=nlstate;i++)
      }          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
          } /* End theta */
     k=1;  
     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");      trgradg =matrix(1,nlstate,1,npar);
     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");  
     for(i=1;i<=npar;i++){      for(j=1; j<=nlstate;j++)
       /*  if (k>nlstate) k=1;        for(theta=1; theta <=npar; theta++)
       i1=(i-1)/(ncovmodel*nlstate)+1;          trgradg[j][theta]=gradg[theta][j];
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);  
       printf("%s%d%d",alph[k],i1,tab[i]);*/      for(i=1;i<=nlstate;i++)
       fprintf(ficres,"%3d",i);        varpl[i][(int)age] =0.;
       printf("%3d",i);      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       for(j=1; j<=i;j++){      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
         fprintf(ficres," %.5e",matcov[i][j]);      for(i=1;i<=nlstate;i++)
         printf(" %.5e",matcov[i][j]);        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
       }  
       fprintf(ficres,"\n");      fprintf(ficresvpl,"%.0f ",age );
       printf("\n");      for(i=1; i<=nlstate;i++)
       k++;        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     }      fprintf(ficresvpl,"\n");
          free_vector(gp,1,nlstate);
     while((c=getc(ficpar))=='#' && c!= EOF){      free_vector(gm,1,nlstate);
       ungetc(c,ficpar);      free_matrix(gradg,1,npar,1,nlstate);
       fgets(line, MAXLINE, ficpar);      free_matrix(trgradg,1,nlstate,1,npar);
       puts(line);    } /* End age */
       fputs(line,ficparo);  
     }    free_vector(xp,1,npar);
     ungetc(c,ficpar);    free_matrix(doldm,1,nlstate,1,npar);
     estepm=0;    free_matrix(dnewm,1,nlstate,1,nlstate);
     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;  /************ Variance of one-step probabilities  ******************/
       fage = agemaxpar;  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
     }  {
        int i, j=0,  i1, k1, l1, t, tj;
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    int k2, l2, j1,  z1;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    int k=0,l, cptcode;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    int first=1, first1;
      double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     while((c=getc(ficpar))=='#' && c!= EOF){    double **dnewm,**doldm;
     ungetc(c,ficpar);    double *xp;
     fgets(line, MAXLINE, ficpar);    double *gp, *gm;
     puts(line);    double **gradg, **trgradg;
     fputs(line,ficparo);    double **mu;
   }    double age,agelim, cov[NCOVMAX];
   ungetc(c,ficpar);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
      int theta;
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    char fileresprob[FILENAMELENGTH];
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    char fileresprobcov[FILENAMELENGTH];
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    char fileresprobcor[FILENAMELENGTH];
        
   while((c=getc(ficpar))=='#' && c!= EOF){    double ***varpij;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    strcpy(fileresprob,"prob"); 
     puts(line);    strcat(fileresprob,fileres);
     fputs(line,ficparo);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   }      printf("Problem with resultfile: %s\n", fileresprob);
   ungetc(c,ficpar);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
      }
     strcpy(fileresprobcov,"probcov"); 
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    strcat(fileresprobcov,fileres);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
   fscanf(ficpar,"pop_based=%d\n",&popbased);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   fprintf(ficparo,"pop_based=%d\n",popbased);      }
   fprintf(ficres,"pop_based=%d\n",popbased);      strcpy(fileresprobcor,"probcor"); 
      strcat(fileresprobcor,fileres);
   while((c=getc(ficpar))=='#' && c!= EOF){    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
     ungetc(c,ficpar);      printf("Problem with resultfile: %s\n", fileresprobcor);
     fgets(line, MAXLINE, ficpar);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     puts(line);    }
     fputs(line,ficparo);    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);
   ungetc(c,ficpar);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   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);    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
 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);    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
 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);    pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
 while((c=getc(ficpar))=='#' && c!= EOF){    pstamp(ficresprobcov);
     ungetc(c,ficpar);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprobcov,"# Age");
     puts(line);    pstamp(ficresprobcor);
     fputs(line,ficparo);    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   }    fprintf(ficresprobcor,"# Age");
   ungetc(c,ficpar);  
   
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    for(i=1; i<=nlstate;i++)
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      for(j=1; j<=(nlstate+ndeath);j++){
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
 /*------------ gnuplot -------------*/   /* fprintf(ficresprob,"\n");
   strcpy(optionfilegnuplot,optionfilefiname);    fprintf(ficresprobcov,"\n");
   strcat(optionfilegnuplot,".gp");    fprintf(ficresprobcor,"\n");
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {   */
     printf("Problem with file %s",optionfilegnuplot);    xp=vector(1,npar);
   }    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   fclose(ficgp);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
 /*--------- index.htm --------*/    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
   strcpy(optionfilehtm,optionfile);    fprintf(ficgp,"\n# Routine varprob");
   strcat(optionfilehtm,".htm");    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    fprintf(fichtm,"\n");
     printf("Problem with %s \n",optionfilehtm), exit(0);  
   }    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    file %s<br>\n",optionfilehtmcov);
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
 \n  and drawn. It helps understanding how is the covariance between two incidences.\
 Total number of observations=%d <br>\n   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
 <hr  size=\"2\" color=\"#EC5E5E\">  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
  <ul><li><h4>Parameter files</h4>\n  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n  standard deviations wide on each axis. <br>\
  - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
   fclose(fichtm);   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");
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);  
      cov[1]=1;
 /*------------ free_vector  -------------*/    tj=cptcoveff;
  chdir(path);    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
      j1=0;
  free_ivector(wav,1,imx);    for(t=1; t<=tj;t++){
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      for(i1=1; i1<=ncodemax[t];i1++){ 
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          j1++;
  free_ivector(num,1,n);        if  (cptcovn>0) {
  free_vector(agedc,1,n);          fprintf(ficresprob, "\n#********** Variable "); 
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  fclose(ficparo);          fprintf(ficresprob, "**********\n#\n");
  fclose(ficres);          fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
   /*--------------- Prevalence limit --------------*/          
            fprintf(ficgp, "\n#********** Variable "); 
   strcpy(filerespl,"pl");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcat(filerespl,fileres);          fprintf(ficgp, "**********\n#\n");
   if((ficrespl=fopen(filerespl,"w"))==NULL) {          
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;          
   }          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   fprintf(ficrespl,"#Prevalence limit\n");          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   fprintf(ficrespl,"#Age ");          
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          fprintf(ficresprobcor, "\n#********** Variable ");    
   fprintf(ficrespl,"\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprobcor, "**********\n#");    
   prlim=matrix(1,nlstate,1,nlstate);        }
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for (age=bage; age<=fage; age ++){ 
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          cov[2]=age;
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for (k=1; k<=cptcovn;k++) {
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   k=0;          }
   agebase=ageminpar;          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   agelim=agemaxpar;          for (k=1; k<=cptcovprod;k++)
   ftolpl=1.e-10;            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   i1=cptcoveff;          
   if (cptcovn < 1){i1=1;}          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   for(cptcov=1;cptcov<=i1;cptcov++){          gp=vector(1,(nlstate)*(nlstate+ndeath));
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          gm=vector(1,(nlstate)*(nlstate+ndeath));
         k=k+1;      
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/          for(theta=1; theta <=npar; theta++){
         fprintf(ficrespl,"\n#******");            for(i=1; i<=npar; i++)
         for(j=1;j<=cptcoveff;j++)              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            
         fprintf(ficrespl,"******\n");            pmij(pmmij,cov,ncovmodel,xp,nlstate);
                    
         for (age=agebase; age<=agelim; age++){            k=0;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            for(i=1; i<= (nlstate); i++){
           fprintf(ficrespl,"%.0f",age );              for(j=1; j<=(nlstate+ndeath);j++){
           for(i=1; i<=nlstate;i++)                k=k+1;
           fprintf(ficrespl," %.5f", prlim[i][i]);                gp[k]=pmmij[i][j];
           fprintf(ficrespl,"\n");              }
         }            }
       }            
     }            for(i=1; i<=npar; i++)
   fclose(ficrespl);              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
   /*------------- h Pij x at various ages ------------*/            pmij(pmmij,cov,ncovmodel,xp,nlstate);
              k=0;
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);            for(i=1; i<=(nlstate); i++){
   if((ficrespij=fopen(filerespij,"w"))==NULL) {              for(j=1; j<=(nlstate+ndeath);j++){
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;                k=k+1;
   }                gm[k]=pmmij[i][j];
   printf("Computing pij: result on file '%s' \n", filerespij);              }
              }
   stepsize=(int) (stepm+YEARM-1)/YEARM;       
   /*if (stepm<=24) stepsize=2;*/            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
   agelim=AGESUP;          }
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
   /* hstepm=1;   aff par mois*/              trgradg[j][theta]=gradg[theta][j];
           
   k=0;          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
   for(cptcov=1;cptcov<=i1;cptcov++){          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
       k=k+1;          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
         fprintf(ficrespij,"\n#****** ");          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         for(j=1;j<=cptcoveff;j++)          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
         fprintf(ficrespij,"******\n");          pmij(pmmij,cov,ncovmodel,x,nlstate);
                  
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */          k=0;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          for(i=1; i<=(nlstate); i++){
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
           /*      nhstepm=nhstepm*YEARM; aff par mois*/              mu[k][(int) age]=pmmij[i][j];
             }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          }
           oldm=oldms;savm=savms;          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
           fprintf(ficrespij,"# Age");              varpij[i][j][(int)age] = doldm[i][j];
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)          /*printf("\n%d ",(int)age);
               fprintf(ficrespij," %1d-%1d",i,j);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
           fprintf(ficrespij,"\n");            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
            for (h=0; h<=nhstepm; h++){            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );            }*/
             for(i=1; i<=nlstate;i++)  
               for(j=1; j<=nlstate+ndeath;j++)          fprintf(ficresprob,"\n%d ",(int)age);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          fprintf(ficresprobcov,"\n%d ",(int)age);
             fprintf(ficrespij,"\n");          fprintf(ficresprobcor,"\n%d ",(int)age);
              }  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
           fprintf(ficrespij,"\n");            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
         }          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     }            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
   }            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);          i=0;
           for (k=1; k<=(nlstate);k++){
   fclose(ficrespij);            for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
   /*---------- Forecasting ------------------*/              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
   if((stepm == 1) && (strcmp(model,".")==0)){              for (j=1; j<=i;j++){
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
   }              }
   else{            }
     erreur=108;          }/* end of loop for state */
     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);        } /* end of loop for age */
   }  
          /* Confidence intervalle of pij  */
         /*
   /*---------- Health expectancies and variances ------------*/          fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   strcpy(filerest,"t");          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
   strcat(filerest,fileres);          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);
   if((ficrest=fopen(filerest,"w"))==NULL) {          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   }          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);        */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
   strcpy(filerese,"e");        first1=1;
   strcat(filerese,fileres);        for (k2=1; k2<=(nlstate);k2++){
   if((ficreseij=fopen(filerese,"w"))==NULL) {          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);            if(l2==k2) continue;
   }            j=(k2-1)*(nlstate+ndeath)+l2;
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);            for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
  strcpy(fileresv,"v");                if(l1==k1) continue;
   strcat(fileresv,fileres);                i=(k1-1)*(nlstate+ndeath)+l1;
   if((ficresvij=fopen(fileresv,"w"))==NULL) {                if(i<=j) continue;
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);                for (age=bage; age<=fage; age ++){ 
   }                  if ((int)age %5==0){
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
   calagedate=-1;                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
   k=0;                    mu2=mu[j][(int) age]/stepm*YEARM;
   for(cptcov=1;cptcov<=i1;cptcov++){                    c12=cv12/sqrt(v1*v2);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                    /* Computing eigen value of matrix of covariance */
       k=k+1;                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       fprintf(ficrest,"\n#****** ");                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       for(j=1;j<=cptcoveff;j++)                    if ((lc2 <0) || (lc1 <0) ){
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      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(ficrest,"******\n");                      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(ficreseij,"\n#****** ");                      lc2=fabs(lc2);
       for(j=1;j<=cptcoveff;j++)                    }
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficreseij,"******\n");                    /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       fprintf(ficresvij,"\n#****** ");                    /*v21=sqrt(1.-v11*v11); *//* error */
       for(j=1;j<=cptcoveff;j++)                    v21=(lc1-v1)/cv12*v11;
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    v12=-v21;
       fprintf(ficresvij,"******\n");                    v22=v11;
                     tnalp=v21/v11;
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    if(first1==1){
       oldm=oldms;savm=savms;                      first1=0;
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);                        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);
                      }
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    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);
       oldm=oldms;savm=savms;                    /*printf(fignu*/
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                        /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                        first=0;
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");                      fprintf(ficgp,"\nset parametric;unset label");
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",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);
       fprintf(ficrest,"\n");                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
       epj=vector(1,nlstate+1);   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
       for(age=bage; age <=fage ;age++){  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
         if (popbased==1) {                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
           for(i=1; i<=nlstate;i++)                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
             prlim[i][i]=probs[(int)age][i][k];                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
         }                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                              fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
         fprintf(ficrest," %4.0f",age);                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                      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",\
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
             epj[j] += prlim[i][i]*eij[i][j][(int)age];                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/                    }else{
           }                      first=0;
           epj[nlstate+1] +=epj[j];                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
         }                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
         for(i=1, vepp=0.;i <=nlstate;i++)                      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",\
           for(j=1;j <=nlstate;j++)                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
             vepp += vareij[i][j][(int)age];                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));                    }/* if first */
         for(j=1;j <=nlstate;j++){                  } /* age mod 5 */
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));                } /* end loop age */
         }                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         fprintf(ficrest,"\n");                first=1;
       }              } /*l12 */
     }            } /* k12 */
   }          } /*l1 */
 free_matrix(mint,1,maxwav,1,n);        }/* k1 */
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);      } /* loop covariates */
     free_vector(weight,1,n);    }
   fclose(ficreseij);    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
   fclose(ficresvij);    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
   fclose(ficrest);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   fclose(ficpar);    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   free_vector(epj,1,nlstate+1);    free_vector(xp,1,npar);
      fclose(ficresprob);
   /*------- Variance limit prevalence------*/      fclose(ficresprobcov);
     fclose(ficresprobcor);
   strcpy(fileresvpl,"vpl");    fflush(ficgp);
   strcat(fileresvpl,fileres);    fflush(fichtmcov);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {  }
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);  
     exit(0);  
   }  /******************* Printing html file ***********/
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
   k=0;                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
   for(cptcov=1;cptcov<=i1;cptcov++){                    int popforecast, int estepm ,\
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                    double jprev1, double mprev1,double anprev1, \
       k=k+1;                    double jprev2, double mprev2,double anprev2){
       fprintf(ficresvpl,"\n#****** ");    int jj1, k1, i1, cpt;
       for(j=1;j<=cptcoveff;j++)  
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
       fprintf(ficresvpl,"******\n");     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
        </ul>");
       varpl=matrix(1,nlstate,(int) bage, (int) fage);     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
       oldm=oldms;savm=savms;   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
     }     fprintf(fichtm,"\
  }   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
   fclose(ficresvpl);     fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
   /*---------- End : free ----------------*/             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);     fprintf(fichtm,"\
     - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);     <a href=\"%s\">%s</a> <br>\n",
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
       fprintf(fichtm,"\
     - Population projections by age and states: \
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);  
     m=cptcoveff;
   free_matrix(matcov,1,npar,1,npar);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   free_vector(delti,1,npar);  
   free_matrix(agev,1,maxwav,1,imx);   jj1=0;
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);   for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
   fprintf(fichtm,"\n</body>");       jj1++;
   fclose(fichtm);       if (cptcovn > 0) {
   fclose(ficgp);         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]]);
   if(erreur >0)         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
     printf("End of Imach with error or warning %d\n",erreur);       }
   else   printf("End of Imach\n");       /* Pij */
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
    <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
   /* 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);*/       /* Quasi-incidences */
   /*printf("Total time was %d uSec.\n", total_usecs);*/       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
   /*------ End -----------*/   before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
  end:         for(cpt=1; cpt<nlstate;cpt++){
 #ifdef windows           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   /* chdir(pathcd);*/  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
 #endif         }
  /*system("wgnuplot graph.plt");*/       for(cpt=1; cpt<=nlstate;cpt++) {
  /*system("../gp37mgw/wgnuplot graph.plt");*/          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> \
  /*system("cd ../gp37mgw");*/  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/       }
  strcpy(plotcmd,GNUPLOTPROGRAM);     } /* end i1 */
  strcat(plotcmd," ");   }/* End k1 */
  strcat(plotcmd,optionfilegnuplot);   fprintf(fichtm,"</ul>");
  system(plotcmd);  
   
 #ifdef windows   fprintf(fichtm,"\
   while (z[0] != 'q') {  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
     /* chdir(path); */   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");  
     scanf("%s",z);   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     if (z[0] == 'c') system("./imach");           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
     else if (z[0] == 'e') system(optionfilehtm);   fprintf(fichtm,"\
     else if (z[0] == 'g') system(plotcmd);   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     else if (z[0] == 'q') exit(0);           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   }  
 #endif   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 <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             codtab[h][k]=j;
             codtab[h][Tvar[k]]=j;
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       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=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*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.1.49  
changed lines
  Added in v.1.142


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