Diff for /imach/src/imach.c between versions 1.41 and 1.143

version 1.41, 2002/05/07 15:53:01 version 1.143, 2014/01/26 09:45:38
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.143  2014/01/26 09:45:38  brouard
      Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   first survey ("cross") where individuals from different ages are    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.142  2014/01/26 03:57:36  brouard
   second wave of interviews ("longitudinal") which measure each change    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
   (if any) in individual health status.  Health expectancies are  
   computed from the time spent in each health state according to a    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.141  2014/01/26 02:42:01  brouard
   simplest model is the multinomial logistic model where pij is the    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.140  2011/09/02 10:37:54  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Summary: times.h is ok with mingw32 now.
   'age' is age and 'sex' is a covariate. If you want to have a more  
   complex model than "constant and age", you should modify the program    Revision 1.139  2010/06/14 07:50:17  brouard
   where the markup *Covariates have to be included here again* invites    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   you to do it.  More covariates you add, slower the    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   convergence.  
     Revision 1.138  2010/04/30 18:19:40  brouard
   The advantage of this computer programme, compared to a simple    *** empty log message ***
   multinomial logistic model, is clear when the delay between waves is not  
   identical for each individual. Also, if a individual missed an    Revision 1.137  2010/04/29 18:11:38  brouard
   intermediate interview, the information is lost, but taken into    (Module): Checking covariates for more complex models
   account using an interpolation or extrapolation.      than V1+V2. A lot of change to be done. Unstable.
   
   hPijx is the probability to be observed in state i at age x+h    Revision 1.136  2010/04/26 20:30:53  brouard
   conditional to the observed state i at age x. The delay 'h' can be    (Module): merging some libgsl code. Fixing computation
   split into an exact number (nh*stepm) of unobserved intermediate    of likelione (using inter/intrapolation if mle = 0) in order to
   states. This elementary transition (by month or quarter trimester,    get same likelihood as if mle=1.
   semester or year) is model as a multinomial logistic.  The hPx    Some cleaning of code and comments added.
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.135  2009/10/29 15:33:14  brouard
   hPijx.    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.134  2009/10/29 13:18:53  brouard
   of the life expectancies. It also computes the prevalence limits.    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.133  2009/07/06 10:21:25  brouard
            Institut national d'études démographiques, Paris.    just nforces
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.132  2009/07/06 08:22:05  brouard
   It is copyrighted identically to a GNU software product, ie programme and    Many tings
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.131  2009/06/20 16:22:47  brouard
   **********************************************************************/    Some dimensions resccaled
    
 #include <math.h>    Revision 1.130  2009/05/26 06:44:34  brouard
 #include <stdio.h>    (Module): Max Covariate is now set to 20 instead of 8. A
 #include <stdlib.h>    lot of cleaning with variables initialized to 0. Trying to make
 #include <unistd.h>    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   
 #define MAXLINE 256    Revision 1.129  2007/08/31 13:49:27  lievre
 #define GNUPLOTPROGRAM "wgnuplot"    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/  
 #define FILENAMELENGTH 80    Revision 1.128  2006/06/30 13:02:05  brouard
 /*#define DEBUG*/    (Module): Clarifications on computing e.j
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.127  2006/04/28 18:11:50  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    loop. Now we define nhstepma in the age loop.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    (Module): In order to speed up (in case of numerous covariates) we
     compute health expectancies (without variances) in a first step
 #define NINTERVMAX 8    and then all the health expectancies with variances or standard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    deviation (needs data from the Hessian matrices) which slows the
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    computation.
 #define NCOVMAX 8 /* Maximum number of covariates */    In the future we should be able to stop the program is only health
 #define MAXN 20000    expectancies and graph are needed without standard deviations.
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.126  2006/04/28 17:23:28  brouard
 #define AGEBASE 40    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
     loop. Now we define nhstepma in the age loop.
 int erreur; /* Error number */    Version 0.98h
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Revision 1.125  2006/04/04 15:20:31  lievre
 int npar=NPARMAX;    Errors in calculation of health expectancies. Age was not initialized.
 int nlstate=2; /* Number of live states */    Forecasting file added.
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.124  2006/03/22 17:13:53  lievre
 int popbased=0;    Parameters are printed with %lf instead of %f (more numbers after the comma).
     The log-likelihood is printed in the log file
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.123  2006/03/20 10:52:43  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    * imach.c (Module): <title> changed, corresponds to .htm file
 int mle, weightopt;    name. <head> headers where missing.
 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 */    * imach.c (Module): Weights can have a decimal point as for
 double jmean; /* Mean space between 2 waves */    English (a comma might work with a correct LC_NUMERIC environment,
 double **oldm, **newm, **savm; /* Working pointers to matrices */    otherwise the weight is truncated).
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Modification of warning when the covariates values are not 0 or
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    1.
 FILE *ficgp,*ficresprob,*ficpop;    Version 0.98g
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Revision 1.122  2006/03/20 09:45:41  brouard
  FILE  *ficresvij;    (Module): Weights can have a decimal point as for
   char fileresv[FILENAMELENGTH];    English (a comma might work with a correct LC_NUMERIC environment,
  FILE  *ficresvpl;    otherwise the weight is truncated).
   char fileresvpl[FILENAMELENGTH];    Modification of warning when the covariates values are not 0 or
     1.
 #define NR_END 1    Version 0.98g
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.121  2006/03/16 17:45:01  lievre
     * imach.c (Module): Comments concerning covariates added
 #define NRANSI  
 #define ITMAX 200    * imach.c (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
 #define TOL 2.0e-4    not 1 month. Version 0.98f
   
 #define CGOLD 0.3819660    Revision 1.120  2006/03/16 15:10:38  lievre
 #define ZEPS 1.0e-10    (Module): refinements in the computation of lli if
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.119  2006/03/15 17:42:26  brouard
 #define TINY 1.0e-20    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.118  2006/03/14 18:20:07  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    (Module): varevsij Comments added explaining the second
      table of variances if popbased=1 .
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define rint(a) floor(a+0.5)    (Module): Function pstamp added
     (Module): Version 0.98d
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.117  2006/03/14 17:16:22  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 int imx;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 int stepm;    (Module): Function pstamp added
 /* Stepm, step in month: minimum step interpolation*/    (Module): Version 0.98d
   
 int estepm;    Revision 1.116  2006/03/06 10:29:27  brouard
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.115  2006/02/27 12:17:45  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    (Module): One freematrix added in mlikeli! 0.98c
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 double *weight;    filename with strsep.
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.113  2006/02/24 14:20:24  brouard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    (Module): Memory leaks checks with valgrind and:
     datafile was not closed, some imatrix were not freed and on matrix
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    allocation too.
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.112  2006/01/30 09:55:26  brouard
 /**************** split *************************/    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.111  2006/01/25 20:38:18  brouard
    char *s;                             /* pointer */    (Module): Lots of cleaning and bugs added (Gompertz)
    int  l1, l2;                         /* length counters */    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.110  2006/01/25 00:51:50  brouard
 #ifdef windows    (Module): Lots of cleaning and bugs added (Gompertz)
    s = strrchr( path, '\\' );           /* find last / */  
 #else    Revision 1.109  2006/01/24 19:37:15  brouard
    s = strrchr( path, '/' );            /* find last / */    (Module): Comments (lines starting with a #) are allowed in data.
 #endif  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.108  2006/01/19 18:05:42  lievre
 #if     defined(__bsd__)                /* get current working directory */    Gnuplot problem appeared...
       extern char       *getwd( );    To be fixed
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.107  2006/01/19 16:20:37  brouard
 #else    Test existence of gnuplot in imach path
       extern char       *getcwd( );  
     Revision 1.106  2006/01/19 13:24:36  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Some cleaning and links added in html output
 #endif  
          return( GLOCK_ERROR_GETCWD );    Revision 1.105  2006/01/05 20:23:19  lievre
       }    *** empty log message ***
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Revision 1.104  2005/09/30 16:11:43  lievre
       s++;                              /* after this, the filename */    (Module): sump fixed, loop imx fixed, and simplifications.
       l2 = strlen( s );                 /* length of filename */    (Module): If the status is missing at the last wave but we know
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    that the person is alive, then we can code his/her status as -2
       strcpy( name, s );                /* save file name */    (instead of missing=-1 in earlier versions) and his/her
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    contributions to the likelihood is 1 - Prob of dying from last
       dirc[l1-l2] = 0;                  /* add zero */    health status (= 1-p13= p11+p12 in the easiest case of somebody in
    }    the healthy state at last known wave). Version is 0.98
    l1 = strlen( dirc );                 /* length of directory */  
 #ifdef windows    Revision 1.103  2005/09/30 15:54:49  lievre
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    (Module): sump fixed, loop imx fixed, and simplifications.
 #else  
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    Revision 1.102  2004/09/15 17:31:30  brouard
 #endif    Add the possibility to read data file including tab characters.
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Revision 1.101  2004/09/15 10:38:38  brouard
    strcpy(ext,s);                       /* save extension */    Fix on curr_time
    l1= strlen( name);  
    l2= strlen( s)+1;    Revision 1.100  2004/07/12 18:29:06  brouard
    strncpy( finame, name, l1-l2);    Add version for Mac OS X. Just define UNIX in Makefile
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    Revision 1.99  2004/06/05 08:57:40  brouard
 }    *** empty log message ***
   
     Revision 1.98  2004/05/16 15:05:56  brouard
 /******************************************/    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 void replace(char *s, char*t)    state at each age, but using a Gompertz model: log u =a + b*age .
 {    This is the basic analysis of mortality and should be done before any
   int i;    other analysis, in order to test if the mortality estimated from the
   int lg=20;    cross-longitudinal survey is different from the mortality estimated
   i=0;    from other sources like vital statistic data.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    The same imach parameter file can be used but the option for mle should be -3.
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Agnès, who wrote this part of the code, tried to keep most of the
   }    former routines in order to include the new code within the former code.
 }  
     The output is very simple: only an estimate of the intercept and of
 int nbocc(char *s, char occ)    the slope with 95% confident intervals.
 {  
   int i,j=0;    Current limitations:
   int lg=20;    A) Even if you enter covariates, i.e. with the
   i=0;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   lg=strlen(s);    B) There is no computation of Life Expectancy nor Life Table.
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Revision 1.97  2004/02/20 13:25:42  lievre
   }    Version 0.96d. Population forecasting command line is (temporarily)
   return j;    suppressed.
 }  
     Revision 1.96  2003/07/15 15:38:55  brouard
 void cutv(char *u,char *v, char*t, char occ)    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 {    rewritten within the same printf. Workaround: many printfs.
   int i,lg,j,p=0;  
   i=0;    Revision 1.95  2003/07/08 07:54:34  brouard
   for(j=0; j<=strlen(t)-1; j++) {    * imach.c (Repository):
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    (Repository): Using imachwizard code to output a more meaningful covariance
   }    matrix (cov(a12,c31) instead of numbers.
   
   lg=strlen(t);    Revision 1.94  2003/06/27 13:00:02  brouard
   for(j=0; j<p; j++) {    Just cleaning
     (u[j] = t[j]);  
   }    Revision 1.93  2003/06/25 16:33:55  brouard
      u[p]='\0';    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
    for(j=0; j<= lg; j++) {    (Module): Version 0.96b
     if (j>=(p+1))(v[j-p-1] = t[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.
 /********************** nrerror ********************/  
     Revision 1.91  2003/06/25 15:30:29  brouard
 void nrerror(char error_text[])    * imach.c (Repository): Duplicated warning errors corrected.
 {    (Repository): Elapsed time after each iteration is now output. It
   fprintf(stderr,"ERREUR ...\n");    helps to forecast when convergence will be reached. Elapsed time
   fprintf(stderr,"%s\n",error_text);    is stamped in powell.  We created a new html file for the graphs
   exit(1);    concerning matrix of covariance. It has extension -cov.htm.
 }  
 /*********************** vector *******************/    Revision 1.90  2003/06/24 12:34:15  brouard
 double *vector(int nl, int nh)    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   double *v;    of the covariance matrix to be input.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Revision 1.89  2003/06/24 12:30:52  brouard
   return v-nl+NR_END;    (Module): Some bugs corrected for windows. Also, when
 }    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 /************************ free vector ******************/  
 void free_vector(double*v, int nl, int nh)    Revision 1.88  2003/06/23 17:54:56  brouard
 {    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.87  2003/06/18 12:26:01  brouard
     Version 0.96
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Revision 1.86  2003/06/17 20:04:08  brouard
 {    (Module): Change position of html and gnuplot routines and added
   int *v;    routine fileappend.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Revision 1.85  2003/06/17 13:12:43  brouard
   return v-nl+NR_END;    * imach.c (Repository): Check when date of death was earlier that
 }    current date of interview. It may happen when the death was just
     prior to the death. In this case, dh was negative and likelihood
 /******************free ivector **************************/    was wrong (infinity). We still send an "Error" but patch by
 void free_ivector(int *v, long nl, long nh)    assuming that the date of death was just one stepm after the
 {    interview.
   free((FREE_ARG)(v+nl-NR_END));    (Repository): Because some people have very long ID (first column)
 }    we changed int to long in num[] and we added a new lvector for
     memory allocation. But we also truncated to 8 characters (left
 /******************* imatrix *******************************/    truncation)
 int **imatrix(long nrl, long nrh, long ncl, long nch)    (Repository): No more line truncation errors.
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {    Revision 1.84  2003/06/13 21:44:43  brouard
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    * imach.c (Repository): Replace "freqsummary" at a correct
   int **m;    place. It differs from routine "prevalence" which may be called
      many times. Probs is memory consuming and must be used with
   /* allocate pointers to rows */    parcimony.
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.83  2003/06/10 13:39:11  lievre
   m -= nrl;    *** empty log message ***
    
      Revision 1.82  2003/06/05 15:57:20  brouard
   /* allocate rows and set pointers to them */    Add log in  imach.c and  fullversion number is now printed.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  */
   m[nrl] += NR_END;  /*
   m[nrl] -= ncl;     Interpolated Markov Chain
    
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    Short summary of the programme:
      
   /* return pointer to array of pointers to rows */    This program computes Healthy Life Expectancies from
   return m;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 }    first survey ("cross") where individuals from different ages are
     interviewed on their health status or degree of disability (in the
 /****************** free_imatrix *************************/    case of a health survey which is our main interest) -2- at least a
 void free_imatrix(m,nrl,nrh,ncl,nch)    second wave of interviews ("longitudinal") which measure each change
       int **m;    (if any) in individual health status.  Health expectancies are
       long nch,ncl,nrh,nrl;    computed from the time spent in each health state according to a
      /* free an int matrix allocated by imatrix() */    model. More health states you consider, more time is necessary to reach the
 {    Maximum Likelihood of the parameters involved in the model.  The
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    simplest model is the multinomial logistic model where pij is the
   free((FREE_ARG) (m+nrl-NR_END));    probability to be observed in state j at the second wave
 }    conditional to be observed in state i at the first wave. Therefore
     the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 /******************* matrix *******************************/    'age' is age and 'sex' is a covariate. If you want to have a more
 double **matrix(long nrl, long nrh, long ncl, long nch)    complex model than "constant and age", you should modify the program
 {    where the markup *Covariates have to be included here again* invites
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    you to do it.  More covariates you add, slower the
   double **m;    convergence.
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    The advantage of this computer programme, compared to a simple
   if (!m) nrerror("allocation failure 1 in matrix()");    multinomial logistic model, is clear when the delay between waves is not
   m += NR_END;    identical for each individual. Also, if a individual missed an
   m -= nrl;    intermediate interview, the information is lost, but taken into
     account using an interpolation or extrapolation.  
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    hPijx is the probability to be observed in state i at age x+h
   m[nrl] += NR_END;    conditional to the observed state i at age x. The delay 'h' can be
   m[nrl] -= ncl;    split into an exact number (nh*stepm) of unobserved intermediate
     states. This elementary transition (by month, quarter,
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    semester or year) is modelled as a multinomial logistic.  The hPx
   return m;    matrix is simply the matrix product of nh*stepm elementary matrices
 }    and the contribution of each individual to the likelihood is simply
     hPijx.
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    Also this programme outputs the covariance matrix of the parameters but also
 {    of the life expectancies. It also computes the period (stable) prevalence. 
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    
   free((FREE_ARG)(m+nrl-NR_END));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 }             Institut national d'études démographiques, Paris.
     This software have been partly granted by Euro-REVES, a concerted action
 /******************* ma3x *******************************/    from the European Union.
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    It is copyrighted identically to a GNU software product, ie programme and
 {    software can be distributed freely for non commercial use. Latest version
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    can be accessed at http://euroreves.ined.fr/imach .
   double ***m;  
     Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   if (!m) nrerror("allocation failure 1 in matrix()");    
   m += NR_END;    **********************************************************************/
   m -= nrl;  /*
     main
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    read parameterfile
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    read datafile
   m[nrl] += NR_END;    concatwav
   m[nrl] -= ncl;    freqsummary
     if (mle >= 1)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;      mlikeli
     print results files
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    if mle==1 
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");       computes hessian
   m[nrl][ncl] += NR_END;    read end of parameter file: agemin, agemax, bage, fage, estepm
   m[nrl][ncl] -= nll;        begin-prev-date,...
   for (j=ncl+1; j<=nch; j++)    open gnuplot file
     m[nrl][j]=m[nrl][j-1]+nlay;    open html file
      period (stable) prevalence
   for (i=nrl+1; i<=nrh; i++) {     for age prevalim()
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    h Pij x
     for (j=ncl+1; j<=nch; j++)    variance of p varprob
       m[i][j]=m[i][j-1]+nlay;    forecasting if prevfcast==1 prevforecast call prevalence()
   }    health expectancies
   return m;    Variance-covariance of DFLE
 }    prevalence()
      movingaverage()
 /*************************free ma3x ************************/    varevsij() 
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    if popbased==1 varevsij(,popbased)
 {    total life expectancies
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    Variance of period (stable) prevalence
   free((FREE_ARG)(m[nrl]+ncl-NR_END));   end
   free((FREE_ARG)(m+nrl-NR_END));  */
 }  
   
 /***************** f1dim *************************/  
 extern int ncom;   
 extern double *pcom,*xicom;  #include <math.h>
 extern double (*nrfunc)(double []);  #include <stdio.h>
    #include <stdlib.h>
 double f1dim(double x)  #include <string.h>
 {  #include <unistd.h>
   int j;  
   double f;  #include <limits.h>
   double *xt;  #include <sys/types.h>
    #include <sys/stat.h>
   xt=vector(1,ncom);  #include <errno.h>
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  extern int errno;
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  #ifdef LINUX
   return f;  #include <time.h>
 }  #include "timeval.h"
   #else
 /*****************brent *************************/  #include <sys/time.h>
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #endif
 {  
   int iter;  #ifdef GSL
   double a,b,d,etemp;  #include <gsl/gsl_errno.h>
   double fu,fv,fw,fx;  #include <gsl/gsl_multimin.h>
   double ftemp;  #endif
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;  /* #include <libintl.h> */
    /* #define _(String) gettext (String) */
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);  #define GNUPLOTPROGRAM "gnuplot"
   for (iter=1;iter<=ITMAX;iter++) {  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
     xm=0.5*(a+b);  #define FILENAMELENGTH 132
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
     printf(".");fflush(stdout);  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 #ifdef DEBUG  
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 #endif  
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  #define NINTERVMAX 8
       *xmin=x;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
       return fx;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
     }  #define NCOVMAX 20 /* Maximum number of covariates */
     ftemp=fu;  #define MAXN 20000
     if (fabs(e) > tol1) {  #define YEARM 12. /* Number of months per year */
       r=(x-w)*(fx-fv);  #define AGESUP 130
       q=(x-v)*(fx-fw);  #define AGEBASE 40
       p=(x-v)*q-(x-w)*r;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
       q=2.0*(q-r);  #ifdef UNIX
       if (q > 0.0) p = -p;  #define DIRSEPARATOR '/'
       q=fabs(q);  #define CHARSEPARATOR "/"
       etemp=e;  #define ODIRSEPARATOR '\\'
       e=d;  #else
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #define DIRSEPARATOR '\\'
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define CHARSEPARATOR "\\"
       else {  #define ODIRSEPARATOR '/'
         d=p/q;  #endif
         u=x+d;  
         if (u-a < tol2 || b-u < tol2)  /* $Id$ */
           d=SIGN(tol1,xm-x);  /* $State$ */
       }  
     } else {  char version[]="Imach version 0.98nR2, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  char fullversion[]="$Revision$ $Date$"; 
     }  char strstart[80];
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     fu=(*f)(u);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
     if (fu <= fx) {  int nvar=0, nforce=0; /* Number of variables, number of forces */
       if (u >= x) a=x; else b=x;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
       SHFT(v,w,x,u)  int npar=NPARMAX;
         SHFT(fv,fw,fx,fu)  int nlstate=2; /* Number of live states */
         } else {  int ndeath=1; /* Number of dead states */
           if (u < x) a=u; else b=u;  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
           if (fu <= fw || w == x) {  int popbased=0;
             v=w;  
             w=u;  int *wav; /* Number of waves for this individuual 0 is possible */
             fv=fw;  int maxwav=0; /* Maxim number of waves */
             fw=fu;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
           } else if (fu <= fv || v == x || v == w) {  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
             v=u;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
             fv=fu;                     to the likelihood and the sum of weights (done by funcone)*/
           }  int mle=1, weightopt=0;
         }  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 */
   nrerror("Too many iterations in brent");  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   *xmin=x;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   return fx;  double jmean=1; /* Mean space between 2 waves */
 }  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 /****************** mnbrak ***********************/  /*FILE *fic ; */ /* Used in readdata only */
   FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  FILE *ficlog, *ficrespow;
             double (*func)(double))  int globpr=0; /* Global variable for printing or not */
 {  double fretone; /* Only one call to likelihood */
   double ulim,u,r,q, dum;  long ipmx=0; /* Number of contributions */
   double fu;  double sw; /* Sum of weights */
    char filerespow[FILENAMELENGTH];
   *fa=(*func)(*ax);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   *fb=(*func)(*bx);  FILE *ficresilk;
   if (*fb > *fa) {  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
     SHFT(dum,*ax,*bx,dum)  FILE *ficresprobmorprev;
       SHFT(dum,*fb,*fa,dum)  FILE *fichtm, *fichtmcov; /* Html File */
       }  FILE *ficreseij;
   *cx=(*bx)+GOLD*(*bx-*ax);  char filerese[FILENAMELENGTH];
   *fc=(*func)(*cx);  FILE *ficresstdeij;
   while (*fb > *fc) {  char fileresstde[FILENAMELENGTH];
     r=(*bx-*ax)*(*fb-*fc);  FILE *ficrescveij;
     q=(*bx-*cx)*(*fb-*fa);  char filerescve[FILENAMELENGTH];
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  FILE  *ficresvij;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  char fileresv[FILENAMELENGTH];
     ulim=(*bx)+GLIMIT*(*cx-*bx);  FILE  *ficresvpl;
     if ((*bx-u)*(u-*cx) > 0.0) {  char fileresvpl[FILENAMELENGTH];
       fu=(*func)(u);  char title[MAXLINE];
     } else if ((*cx-u)*(u-ulim) > 0.0) {  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       fu=(*func)(u);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       if (fu < *fc) {  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  char command[FILENAMELENGTH];
           SHFT(*fb,*fc,fu,(*func)(u))  int  outcmd=0;
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
       u=ulim;  
       fu=(*func)(u);  char filelog[FILENAMELENGTH]; /* Log file */
     } else {  char filerest[FILENAMELENGTH];
       u=(*cx)+GOLD*(*cx-*bx);  char fileregp[FILENAMELENGTH];
       fu=(*func)(u);  char popfile[FILENAMELENGTH];
     }  
     SHFT(*ax,*bx,*cx,u)  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       SHFT(*fa,*fb,*fc,fu)  
       }  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
 }  struct timezone tzp;
   extern int gettimeofday();
 /*************** linmin ************************/  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   long time_value;
 int ncom;  extern long time();
 double *pcom,*xicom;  char strcurr[80], strfor[80];
 double (*nrfunc)(double []);  
    char *endptr;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  long lval;
 {  double dval;
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  #define NR_END 1
   double f1dim(double x);  #define FREE_ARG char*
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define FTOL 1.0e-10
               double *fc, double (*func)(double));  
   int j;  #define NRANSI 
   double xx,xmin,bx,ax;  #define ITMAX 200 
   double fx,fb,fa;  
    #define TOL 2.0e-4 
   ncom=n;  
   pcom=vector(1,n);  #define CGOLD 0.3819660 
   xicom=vector(1,n);  #define ZEPS 1.0e-10 
   nrfunc=func;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  #define GOLD 1.618034 
     xicom[j]=xi[j];  #define GLIMIT 100.0 
   }  #define TINY 1.0e-20 
   ax=0.0;  
   xx=1.0;  static double maxarg1,maxarg2;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 #ifdef DEBUG    
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 #endif  #define rint(a) floor(a+0.5)
   for (j=1;j<=n;j++) {  
     xi[j] *= xmin;  static double sqrarg;
     p[j] += xi[j];  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   free_vector(xicom,1,n);  int agegomp= AGEGOMP;
   free_vector(pcom,1,n);  
 }  int imx; 
   int stepm=1;
 /*************** powell ************************/  /* Stepm, step in month: minimum step interpolation*/
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  
             double (*func)(double []))  int estepm;
 {  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   void linmin(double p[], double xi[], int n, double *fret,  
               double (*func)(double []));  int m,nb;
   int i,ibig,j;  long *num;
   double del,t,*pt,*ptt,*xit;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   double fp,fptt;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double *xits;  double **pmmij, ***probs;
   pt=vector(1,n);  double *ageexmed,*agecens;
   ptt=vector(1,n);  double dateintmean=0;
   xit=vector(1,n);  
   xits=vector(1,n);  double *weight;
   *fret=(*func)(p);  int **s; /* Status */
   for (j=1;j<=n;j++) pt[j]=p[j];  double *agedc;
   for (*iter=1;;++(*iter)) {  double  **covar; /**< covar[i,j], value of jth covariate for individual i,
     fp=(*fret);                    * covar=matrix(0,NCOVMAX,1,n); 
     ibig=0;                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
     del=0.0;  double  idx; 
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
     for (i=1;i<=n;i++)  int **codtab; /**< codtab=imatrix(1,100,1,10); */
       printf(" %d %.12f",i, p[i]);  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
     printf("\n");  double *lsurv, *lpop, *tpop;
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
       fptt=(*fret);  double ftolhess; /**< Tolerance for computing hessian */
 #ifdef DEBUG  
       printf("fret=%lf \n",*fret);  /**************** split *************************/
 #endif  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
       printf("%d",i);fflush(stdout);  {
       linmin(p,xit,n,fret,func);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       if (fabs(fptt-(*fret)) > del) {       the name of the file (name), its extension only (ext) and its first part of the name (finame)
         del=fabs(fptt-(*fret));    */ 
         ibig=i;    char  *ss;                            /* pointer */
       }    int   l1, l2;                         /* length counters */
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));    l1 = strlen(path );                   /* length of path */
       for (j=1;j<=n;j++) {    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
         printf(" x(%d)=%.12e",j,xit[j]);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       }      strcpy( name, path );               /* we got the fullname name because no directory */
       for(j=1;j<=n;j++)      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
         printf(" p=%.12e",p[j]);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       printf("\n");      /* get current working directory */
 #endif      /*    extern  char* getcwd ( char *buf , int len);*/
     }      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {        return( GLOCK_ERROR_GETCWD );
 #ifdef DEBUG      }
       int k[2],l;      /* got dirc from getcwd*/
       k[0]=1;      printf(" DIRC = %s \n",dirc);
       k[1]=-1;    } else {                              /* strip direcotry from path */
       printf("Max: %.12e",(*func)(p));      ss++;                               /* after this, the filename */
       for (j=1;j<=n;j++)      l2 = strlen( ss );                  /* length of filename */
         printf(" %.12e",p[j]);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       printf("\n");      strcpy( name, ss );         /* save file name */
       for(l=0;l<=1;l++) {      strncpy( dirc, path, l1 - l2 );     /* now the directory */
         for (j=1;j<=n;j++) {      dirc[l1-l2] = 0;                    /* add zero */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      printf(" DIRC2 = %s \n",dirc);
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    }
         }    /* We add a separator at the end of dirc if not exists */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    l1 = strlen( dirc );                  /* length of directory */
       }    if( dirc[l1-1] != DIRSEPARATOR ){
 #endif      dirc[l1] =  DIRSEPARATOR;
       dirc[l1+1] = 0; 
       printf(" DIRC3 = %s \n",dirc);
       free_vector(xit,1,n);    }
       free_vector(xits,1,n);    ss = strrchr( name, '.' );            /* find last / */
       free_vector(ptt,1,n);    if (ss >0){
       free_vector(pt,1,n);      ss++;
       return;      strcpy(ext,ss);                     /* save extension */
     }      l1= strlen( name);
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");      l2= strlen(ss)+1;
     for (j=1;j<=n;j++) {      strncpy( finame, name, l1-l2);
       ptt[j]=2.0*p[j]-pt[j];      finame[l1-l2]= 0;
       xit[j]=p[j]-pt[j];    }
       pt[j]=p[j];  
     }    return( 0 );                          /* we're done */
     fptt=(*func)(ptt);  }
     if (fptt < fp) {  
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  
       if (t < 0.0) {  /******************************************/
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {  void replace_back_to_slash(char *s, char*t)
           xi[j][ibig]=xi[j][n];  {
           xi[j][n]=xit[j];    int i;
         }    int lg=0;
 #ifdef DEBUG    i=0;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    lg=strlen(t);
         for(j=1;j<=n;j++)    for(i=0; i<= lg; i++) {
           printf(" %.12e",xit[j]);      (s[i] = t[i]);
         printf("\n");      if (t[i]== '\\') s[i]='/';
 #endif    }
       }  }
     }  
   }  char *trimbb(char *out, char *in)
 }  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
     char *s;
 /**** Prevalence limit ****************/    s=out;
     while (*in != '\0'){
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
 {        in++;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit      }
      matrix by transitions matrix until convergence is reached */      *out++ = *in++;
     }
   int i, ii,j,k;    *out='\0';
   double min, max, maxmin, maxmax,sumnew=0.;    return s;
   double **matprod2();  }
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  char *cutv(char *blocc, char *alocc, char *in, char occ)
   double agefin, delaymax=50 ; /* Max number of years to converge */  {
     /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
   for (ii=1;ii<=nlstate+ndeath;ii++)       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
     for (j=1;j<=nlstate+ndeath;j++){       gives blocc="abcdef2ghi" and alocc="j".
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);       If occ is not found blocc is null and alocc is equal to in. Returns alocc
     }    */
     char *s, *t;
    cov[1]=1.;    t=in;s=in;
      while (*in != '\0'){
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */      while( *in == occ){
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){        *blocc++ = *in++;
     newm=savm;        s=in;
     /* Covariates have to be included here again */      }
      cov[2]=agefin;      *blocc++ = *in++;
      }
       for (k=1; k<=cptcovn;k++) {    if (s == t) /* occ not found */
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      *(blocc-(in-s))='\0';
         /*      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]]);*/    else
       }      *(blocc-(in-s)-1)='\0';
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    in=s;
       for (k=1; k<=cptcovprod;k++)    while ( *in != '\0'){
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      *alocc++ = *in++;
     }
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    *alocc='\0';
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    return s;
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  }
   
     savm=oldm;  int nbocc(char *s, char occ)
     oldm=newm;  {
     maxmax=0.;    int i,j=0;
     for(j=1;j<=nlstate;j++){    int lg=20;
       min=1.;    i=0;
       max=0.;    lg=strlen(s);
       for(i=1; i<=nlstate; i++) {    for(i=0; i<= lg; i++) {
         sumnew=0;    if  (s[i] == occ ) j++;
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    }
         prlim[i][j]= newm[i][j]/(1-sumnew);    return j;
         max=FMAX(max,prlim[i][j]);  }
         min=FMIN(min,prlim[i][j]);  
       }  /* void cutv(char *u,char *v, char*t, char occ) */
       maxmin=max-min;  /* { */
       maxmax=FMAX(maxmax,maxmin);  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
     }  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
     if(maxmax < ftolpl){  /*      gives u="abcdef2ghi" and v="j" *\/ */
       return prlim;  /*   int i,lg,j,p=0; */
     }  /*   i=0; */
   }  /*   lg=strlen(t); */
 }  /*   for(j=0; j<=lg-1; j++) { */
   /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
 /*************** transition probabilities ***************/  /*   } */
   
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  /*   for(j=0; j<p; j++) { */
 {  /*     (u[j] = t[j]); */
   double s1, s2;  /*   } */
   /*double t34;*/  /*      u[p]='\0'; */
   int i,j,j1, nc, ii, jj;  
   /*    for(j=0; j<= lg; j++) { */
     for(i=1; i<= nlstate; i++){  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
     for(j=1; j<i;j++){  /*   } */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  /* } */
         /*s2 += param[i][j][nc]*cov[nc];*/  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  /********************** nrerror ********************/
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  
       }  void nrerror(char error_text[])
       ps[i][j]=s2;  {
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    fprintf(stderr,"ERREUR ...\n");
     }    fprintf(stderr,"%s\n",error_text);
     for(j=i+1; j<=nlstate+ndeath;j++){    exit(EXIT_FAILURE);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  }
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  /*********************** vector *******************/
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  double *vector(int nl, int nh)
       }  {
       ps[i][j]=s2;    double *v;
     }    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   }    if (!v) nrerror("allocation failure in vector");
     /*ps[3][2]=1;*/    return v-nl+NR_END;
   }
   for(i=1; i<= nlstate; i++){  
      s1=0;  /************************ free vector ******************/
     for(j=1; j<i; j++)  void free_vector(double*v, int nl, int nh)
       s1+=exp(ps[i][j]);  {
     for(j=i+1; j<=nlstate+ndeath; j++)    free((FREE_ARG)(v+nl-NR_END));
       s1+=exp(ps[i][j]);  }
     ps[i][i]=1./(s1+1.);  
     for(j=1; j<i; j++)  /************************ivector *******************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  int *ivector(long nl,long nh)
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    int *v;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   } /* end i */    if (!v) nrerror("allocation failure in ivector");
     return v-nl+NR_END;
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
       ps[ii][jj]=0;  /******************free ivector **************************/
       ps[ii][ii]=1;  void free_ivector(int *v, long nl, long nh)
     }  {
   }    free((FREE_ARG)(v+nl-NR_END));
   }
   
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  /************************lvector *******************************/
     for(jj=1; jj<= nlstate+ndeath; jj++){  long *lvector(long nl,long nh)
      printf("%lf ",ps[ii][jj]);  {
    }    long *v;
     printf("\n ");    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     }    if (!v) nrerror("allocation failure in ivector");
     printf("\n ");printf("%lf ",cov[2]);*/    return v-nl+NR_END;
 /*  }
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  
   goto end;*/  /******************free lvector **************************/
     return ps;  void free_lvector(long *v, long nl, long nh)
 }  {
     free((FREE_ARG)(v+nl-NR_END));
 /**************** Product of 2 matrices ******************/  }
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  /******************* imatrix *******************************/
 {  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  { 
   /* in, b, out are matrice of pointers which should have been initialized    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
      before: only the contents of out is modified. The function returns    int **m; 
      a pointer to pointers identical to out */    
   long i, j, k;    /* allocate pointers to rows */ 
   for(i=nrl; i<= nrh; i++)    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     for(k=ncolol; k<=ncoloh; k++)    if (!m) nrerror("allocation failure 1 in matrix()"); 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    m += NR_END; 
         out[i][k] +=in[i][j]*b[j][k];    m -= nrl; 
     
   return out;    
 }    /* 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()"); 
 /************* Higher Matrix Product ***************/    m[nrl] += NR_END; 
     m[nrl] -= ncl; 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    
 {    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    
      duration (i.e. until    /* return pointer to array of pointers to rows */ 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    return m; 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  } 
      (typically every 2 years instead of every month which is too big).  
      Model is determined by parameters x and covariates have to be  /****************** free_imatrix *************************/
      included manually here.  void free_imatrix(m,nrl,nrh,ncl,nch)
         int **m;
      */        long nch,ncl,nrh,nrl; 
        /* free an int matrix allocated by imatrix() */ 
   int i, j, d, h, k;  { 
   double **out, cov[NCOVMAX];    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   double **newm;    free((FREE_ARG) (m+nrl-NR_END)); 
   } 
   /* Hstepm could be zero and should return the unit matrix */  
   for (i=1;i<=nlstate+ndeath;i++)  /******************* matrix *******************************/
     for (j=1;j<=nlstate+ndeath;j++){  double **matrix(long nrl, long nrh, long ncl, long nch)
       oldm[i][j]=(i==j ? 1.0 : 0.0);  {
       po[i][j][0]=(i==j ? 1.0 : 0.0);    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     }    double **m;
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(h=1; h <=nhstepm; h++){    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     for(d=1; d <=hstepm; d++){    if (!m) nrerror("allocation failure 1 in matrix()");
       newm=savm;    m += NR_END;
       /* Covariates have to be included here again */    m -= nrl;
       cov[1]=1.;  
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for (k=1; k<=cptcovage;k++)    m[nrl] += NR_END;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m[nrl] -= ncl;
       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]]];    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     return m;
     /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/     */
       /*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));  /*************************free matrix ************************/
       savm=oldm;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       oldm=newm;  {
     }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     for(i=1; i<=nlstate+ndeath; i++)    free((FREE_ARG)(m+nrl-NR_END));
       for(j=1;j<=nlstate+ndeath;j++) {  }
         po[i][j][h]=newm[i][j];  
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  /******************* ma3x *******************************/
          */  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       }  {
   } /* end h */    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   return po;    double ***m;
 }  
     m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
 /*************** log-likelihood *************/    m += NR_END;
 double func( double *x)    m -= nrl;
 {  
   int i, ii, j, k, mi, d, kk;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double **out;    m[nrl] += NR_END;
   double sw; /* Sum of weights */    m[nrl] -= ncl;
   double lli; /* Individual log likelihood */  
   long ipmx;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   /*extern weight */  
   /* We are differentiating ll according to initial status */    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   /*for(i=1;i<imx;i++)    m[nrl][ncl] += NR_END;
     printf(" %d\n",s[4][i]);    m[nrl][ncl] -= nll;
   */    for (j=ncl+1; j<=nch; j++) 
   cov[1]=1.;      m[nrl][j]=m[nrl][j-1]+nlay;
     
   for(k=1; k<=nlstate; k++) ll[k]=0.;    for (i=nrl+1; i<=nrh; i++) {
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];      for (j=ncl+1; j<=nch; j++) 
     for(mi=1; mi<= wav[i]-1; mi++){        m[i][j]=m[i][j-1]+nlay;
       for (ii=1;ii<=nlstate+ndeath;ii++)    }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    return m; 
       for(d=0; d<dh[mi][i]; d++){    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
         newm=savm;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
         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];  
         }  /*************************free ma3x ************************/
          void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  {
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
         savm=oldm;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         oldm=newm;    free((FREE_ARG)(m+nrl-NR_END));
          }
          
       } /* end mult */  /*************** function subdirf ***********/
        char *subdirf(char fileres[])
       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]]);*/    /* Caution optionfilefiname is hidden */
       ipmx +=1;    strcpy(tmpout,optionfilefiname);
       sw += weight[i];    strcat(tmpout,"/"); /* Add to the right */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    strcat(tmpout,fileres);
     } /* end of wave */    return tmpout;
   } /* end of individual */  }
   
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  /*************** function subdirf2 ***********/
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  char *subdirf2(char fileres[], char *preop)
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  {
   return -l;    
 }    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
 /*********** Maximum Likelihood Estimation ***************/    strcat(tmpout,preop);
     strcat(tmpout,fileres);
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    return tmpout;
 {  }
   int i,j, iter;  
   double **xi,*delti;  /*************** function subdirf3 ***********/
   double fret;  char *subdirf3(char fileres[], char *preop, char *preop2)
   xi=matrix(1,npar,1,npar);  {
   for (i=1;i<=npar;i++)    
     for (j=1;j<=npar;j++)    /* Caution optionfilefiname is hidden */
       xi[i][j]=(i==j ? 1.0 : 0.0);    strcpy(tmpout,optionfilefiname);
   printf("Powell\n");    strcat(tmpout,"/");
   powell(p,xi,npar,ftol,&iter,&fret,func);    strcat(tmpout,preop);
     strcat(tmpout,preop2);
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    strcat(tmpout,fileres);
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    return tmpout;
   }
 }  
   /***************** f1dim *************************/
 /**** Computes Hessian and covariance matrix ***/  extern int ncom; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  extern double *pcom,*xicom;
 {  extern double (*nrfunc)(double []); 
   double  **a,**y,*x,pd;   
   double **hess;  double f1dim(double x) 
   int i, j,jk;  { 
   int *indx;    int j; 
     double f;
   double hessii(double p[], double delta, int theta, double delti[]);    double *xt; 
   double hessij(double p[], double delti[], int i, int j);   
   void lubksb(double **a, int npar, int *indx, double b[]) ;    xt=vector(1,ncom); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
   hess=matrix(1,npar,1,npar);    free_vector(xt,1,ncom); 
     return f; 
   printf("\nCalculation of the hessian matrix. Wait...\n");  } 
   for (i=1;i<=npar;i++){  
     printf("%d",i);fflush(stdout);  /*****************brent *************************/
     hess[i][i]=hessii(p,ftolhess,i,delti);  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     /*printf(" %f ",p[i]);*/  { 
     /*printf(" %lf ",hess[i][i]);*/    int iter; 
   }    double a,b,d,etemp;
      double fu,fv,fw,fx;
   for (i=1;i<=npar;i++) {    double ftemp;
     for (j=1;j<=npar;j++)  {    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       if (j>i) {    double e=0.0; 
         printf(".%d%d",i,j);fflush(stdout);   
         hess[i][j]=hessij(p,delti,i,j);    a=(ax < cx ? ax : cx); 
         hess[j][i]=hess[i][j];        b=(ax > cx ? ax : cx); 
         /*printf(" %lf ",hess[i][j]);*/    x=w=v=bx; 
       }    fw=fv=fx=(*f)(x); 
     }    for (iter=1;iter<=ITMAX;iter++) { 
   }      xm=0.5*(a+b); 
   printf("\n");      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");      printf(".");fflush(stdout);
        fprintf(ficlog,".");fflush(ficlog);
   a=matrix(1,npar,1,npar);  #ifdef DEBUG
   y=matrix(1,npar,1,npar);      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);
   x=vector(1,npar);      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);
   indx=ivector(1,npar);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   for (i=1;i<=npar;i++)  #endif
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   ludcmp(a,npar,indx,&pd);        *xmin=x; 
         return fx; 
   for (j=1;j<=npar;j++) {      } 
     for (i=1;i<=npar;i++) x[i]=0;      ftemp=fu;
     x[j]=1;      if (fabs(e) > tol1) { 
     lubksb(a,npar,indx,x);        r=(x-w)*(fx-fv); 
     for (i=1;i<=npar;i++){        q=(x-v)*(fx-fw); 
       matcov[i][j]=x[i];        p=(x-v)*q-(x-w)*r; 
     }        q=2.0*(q-r); 
   }        if (q > 0.0) p = -p; 
         q=fabs(q); 
   printf("\n#Hessian matrix#\n");        etemp=e; 
   for (i=1;i<=npar;i++) {        e=d; 
     for (j=1;j<=npar;j++) {        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
       printf("%.3e ",hess[i][j]);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     }        else { 
     printf("\n");          d=p/q; 
   }          u=x+d; 
           if (u-a < tol2 || b-u < tol2) 
   /* Recompute Inverse */            d=SIGN(tol1,xm-x); 
   for (i=1;i<=npar;i++)        } 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      } else { 
   ludcmp(a,npar,indx,&pd);        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
   /*  printf("\n#Hessian matrix recomputed#\n");      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*f)(u); 
   for (j=1;j<=npar;j++) {      if (fu <= fx) { 
     for (i=1;i<=npar;i++) x[i]=0;        if (u >= x) a=x; else b=x; 
     x[j]=1;        SHFT(v,w,x,u) 
     lubksb(a,npar,indx,x);          SHFT(fv,fw,fx,fu) 
     for (i=1;i<=npar;i++){          } else { 
       y[i][j]=x[i];            if (u < x) a=u; else b=u; 
       printf("%.3e ",y[i][j]);            if (fu <= fw || w == x) { 
     }              v=w; 
     printf("\n");              w=u; 
   }              fv=fw; 
   */              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
   free_matrix(a,1,npar,1,npar);              v=u; 
   free_matrix(y,1,npar,1,npar);              fv=fu; 
   free_vector(x,1,npar);            } 
   free_ivector(indx,1,npar);          } 
   free_matrix(hess,1,npar,1,npar);    } 
     nrerror("Too many iterations in brent"); 
     *xmin=x; 
 }    return fx; 
   } 
 /*************** hessian matrix ****************/  
 double hessii( double x[], double delta, int theta, double delti[])  /****************** mnbrak ***********************/
 {  
   int i;  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   int l=1, lmax=20;              double (*func)(double)) 
   double k1,k2;  { 
   double p2[NPARMAX+1];    double ulim,u,r,q, dum;
   double res;    double fu; 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;   
   double fx;    *fa=(*func)(*ax); 
   int k=0,kmax=10;    *fb=(*func)(*bx); 
   double l1;    if (*fb > *fa) { 
       SHFT(dum,*ax,*bx,dum) 
   fx=func(x);        SHFT(dum,*fb,*fa,dum) 
   for (i=1;i<=npar;i++) p2[i]=x[i];        } 
   for(l=0 ; l <=lmax; l++){    *cx=(*bx)+GOLD*(*bx-*ax); 
     l1=pow(10,l);    *fc=(*func)(*cx); 
     delts=delt;    while (*fb > *fc) { 
     for(k=1 ; k <kmax; k=k+1){      r=(*bx-*ax)*(*fb-*fc); 
       delt = delta*(l1*k);      q=(*bx-*cx)*(*fb-*fa); 
       p2[theta]=x[theta] +delt;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       k1=func(p2)-fx;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       p2[theta]=x[theta]-delt;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       k2=func(p2)-fx;      if ((*bx-u)*(u-*cx) > 0.0) { 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        fu=(*func)(u); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      } else if ((*cx-u)*(u-ulim) > 0.0) { 
              fu=(*func)(u); 
 #ifdef DEBUG        if (fu < *fc) { 
       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);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
 #endif            SHFT(*fb,*fc,fu,(*func)(u)) 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */            } 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
         k=kmax;        u=ulim; 
       }        fu=(*func)(u); 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */      } else { 
         k=kmax; l=lmax*10.;        u=(*cx)+GOLD*(*cx-*bx); 
       }        fu=(*func)(u); 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){      } 
         delts=delt;      SHFT(*ax,*bx,*cx,u) 
       }        SHFT(*fa,*fb,*fc,fu) 
     }        } 
   }  } 
   delti[theta]=delts;  
   return res;  /*************** linmin ************************/
    
 }  int ncom; 
   double *pcom,*xicom;
 double hessij( double x[], double delti[], int thetai,int thetaj)  double (*nrfunc)(double []); 
 {   
   int i;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   int l=1, l1, lmax=20;  { 
   double k1,k2,k3,k4,res,fx;    double brent(double ax, double bx, double cx, 
   double p2[NPARMAX+1];                 double (*f)(double), double tol, double *xmin); 
   int k;    double f1dim(double x); 
     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   fx=func(x);                double *fc, double (*func)(double)); 
   for (k=1; k<=2; k++) {    int j; 
     for (i=1;i<=npar;i++) p2[i]=x[i];    double xx,xmin,bx,ax; 
     p2[thetai]=x[thetai]+delti[thetai]/k;    double fx,fb,fa;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;   
     k1=func(p2)-fx;    ncom=n; 
      pcom=vector(1,n); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    xicom=vector(1,n); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    nrfunc=func; 
     k2=func(p2)-fx;    for (j=1;j<=n;j++) { 
        pcom[j]=p[j]; 
     p2[thetai]=x[thetai]-delti[thetai]/k;      xicom[j]=xi[j]; 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    } 
     k3=func(p2)-fx;    ax=0.0; 
      xx=1.0; 
     p2[thetai]=x[thetai]-delti[thetai]/k;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     k4=func(p2)-fx;  #ifdef DEBUG
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 #ifdef DEBUG    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     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);  #endif
 #endif    for (j=1;j<=n;j++) { 
   }      xi[j] *= xmin; 
   return res;      p[j] += xi[j]; 
 }    } 
     free_vector(xicom,1,n); 
 /************** Inverse of matrix **************/    free_vector(pcom,1,n); 
 void ludcmp(double **a, int n, int *indx, double *d)  } 
 {  
   int i,imax,j,k;  char *asc_diff_time(long time_sec, char ascdiff[])
   double big,dum,sum,temp;  {
   double *vv;    long sec_left, days, hours, minutes;
      days = (time_sec) / (60*60*24);
   vv=vector(1,n);    sec_left = (time_sec) % (60*60*24);
   *d=1.0;    hours = (sec_left) / (60*60) ;
   for (i=1;i<=n;i++) {    sec_left = (sec_left) %(60*60);
     big=0.0;    minutes = (sec_left) /60;
     for (j=1;j<=n;j++)    sec_left = (sec_left) % (60);
       if ((temp=fabs(a[i][j])) > big) big=temp;    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    return ascdiff;
     vv[i]=1.0/big;  }
   }  
   for (j=1;j<=n;j++) {  /*************** powell ************************/
     for (i=1;i<j;i++) {  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       sum=a[i][j];              double (*func)(double [])) 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  { 
       a[i][j]=sum;    void linmin(double p[], double xi[], int n, double *fret, 
     }                double (*func)(double [])); 
     big=0.0;    int i,ibig,j; 
     for (i=j;i<=n;i++) {    double del,t,*pt,*ptt,*xit;
       sum=a[i][j];    double fp,fptt;
       for (k=1;k<j;k++)    double *xits;
         sum -= a[i][k]*a[k][j];    int niterf, itmp;
       a[i][j]=sum;  
       if ( (dum=vv[i]*fabs(sum)) >= big) {    pt=vector(1,n); 
         big=dum;    ptt=vector(1,n); 
         imax=i;    xit=vector(1,n); 
       }    xits=vector(1,n); 
     }    *fret=(*func)(p); 
     if (j != imax) {    for (j=1;j<=n;j++) pt[j]=p[j]; 
       for (k=1;k<=n;k++) {    for (*iter=1;;++(*iter)) { 
         dum=a[imax][k];      fp=(*fret); 
         a[imax][k]=a[j][k];      ibig=0; 
         a[j][k]=dum;      del=0.0; 
       }      last_time=curr_time;
       *d = -(*d);      (void) gettimeofday(&curr_time,&tzp);
       vv[imax]=vv[j];      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
     }      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);
     indx[j]=imax;  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
     if (a[j][j] == 0.0) a[j][j]=TINY;     for (i=1;i<=n;i++) {
     if (j != n) {        printf(" %d %.12f",i, p[i]);
       dum=1.0/(a[j][j]);        fprintf(ficlog," %d %.12lf",i, p[i]);
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        fprintf(ficrespow," %.12lf", p[i]);
     }      }
   }      printf("\n");
   free_vector(vv,1,n);  /* Doesn't work */      fprintf(ficlog,"\n");
 ;      fprintf(ficrespow,"\n");fflush(ficrespow);
 }      if(*iter <=3){
         tm = *localtime(&curr_time.tv_sec);
 void lubksb(double **a, int n, int *indx, double b[])        strcpy(strcurr,asctime(&tm));
 {  /*       asctime_r(&tm,strcurr); */
   int i,ii=0,ip,j;        forecast_time=curr_time; 
   double sum;        itmp = strlen(strcurr);
          if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   for (i=1;i<=n;i++) {          strcurr[itmp-1]='\0';
     ip=indx[i];        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     sum=b[ip];        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     b[ip]=b[i];        for(niterf=10;niterf<=30;niterf+=10){
     if (ii)          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          tmf = *localtime(&forecast_time.tv_sec);
     else if (sum) ii=i;  /*      asctime_r(&tmf,strfor); */
     b[i]=sum;          strcpy(strfor,asctime(&tmf));
   }          itmp = strlen(strfor);
   for (i=n;i>=1;i--) {          if(strfor[itmp-1]=='\n')
     sum=b[i];          strfor[itmp-1]='\0';
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          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);
     b[i]=sum/a[i][i];          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   }        }
 }      }
       for (i=1;i<=n;i++) { 
 /************ Frequencies ********************/        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 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)        fptt=(*fret); 
 {  /* Some frequencies */  #ifdef DEBUG
          printf("fret=%lf \n",*fret);
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;        fprintf(ficlog,"fret=%lf \n",*fret);
   double ***freq; /* Frequencies */  #endif
   double *pp;        printf("%d",i);fflush(stdout);
   double pos, k2, dateintsum=0,k2cpt=0;        fprintf(ficlog,"%d",i);fflush(ficlog);
   FILE *ficresp;        linmin(p,xit,n,fret,func); 
   char fileresp[FILENAMELENGTH];        if (fabs(fptt-(*fret)) > del) { 
            del=fabs(fptt-(*fret)); 
   pp=vector(1,nlstate);          ibig=i; 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        } 
   strcpy(fileresp,"p");  #ifdef DEBUG
   strcat(fileresp,fileres);        printf("%d %.12e",i,(*fret));
   if((ficresp=fopen(fileresp,"w"))==NULL) {        fprintf(ficlog,"%d %.12e",i,(*fret));
     printf("Problem with prevalence resultfile: %s\n", fileresp);        for (j=1;j<=n;j++) {
     exit(0);          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   }          printf(" x(%d)=%.12e",j,xit[j]);
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   j1=0;        }
          for(j=1;j<=n;j++) {
   j=cptcoveff;          printf(" p=%.12e",p[j]);
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          fprintf(ficlog," p=%.12e",p[j]);
          }
   for(k1=1; k1<=j;k1++){        printf("\n");
     for(i1=1; i1<=ncodemax[k1];i1++){        fprintf(ficlog,"\n");
       j1++;  #endif
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      } 
         scanf("%d", i);*/      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       for (i=-1; i<=nlstate+ndeath; i++)    #ifdef DEBUG
         for (jk=-1; jk<=nlstate+ndeath; jk++)          int k[2],l;
           for(m=agemin; m <= agemax+3; m++)        k[0]=1;
             freq[i][jk][m]=0;        k[1]=-1;
              printf("Max: %.12e",(*func)(p));
       dateintsum=0;        fprintf(ficlog,"Max: %.12e",(*func)(p));
       k2cpt=0;        for (j=1;j<=n;j++) {
       for (i=1; i<=imx; i++) {          printf(" %.12e",p[j]);
         bool=1;          fprintf(ficlog," %.12e",p[j]);
         if  (cptcovn>0) {        }
           for (z1=1; z1<=cptcoveff; z1++)        printf("\n");
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        fprintf(ficlog,"\n");
               bool=0;        for(l=0;l<=1;l++) {
         }          for (j=1;j<=n;j++) {
         if (bool==1) {            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
           for(m=firstpass; m<=lastpass; m++){            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             k2=anint[m][i]+(mint[m][i]/12.);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          }
               if(agev[m][i]==0) agev[m][i]=agemax+1;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
               if(agev[m][i]==1) agev[m][i]=agemax+2;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
               if (m<lastpass) {        }
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  #endif
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  
               }  
                      free_vector(xit,1,n); 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        free_vector(xits,1,n); 
                 dateintsum=dateintsum+k2;        free_vector(ptt,1,n); 
                 k2cpt++;        free_vector(pt,1,n); 
               }        return; 
             }      } 
           }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
         }      for (j=1;j<=n;j++) { 
       }        ptt[j]=2.0*p[j]-pt[j]; 
                xit[j]=p[j]-pt[j]; 
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        pt[j]=p[j]; 
       } 
       if  (cptcovn>0) {      fptt=(*func)(ptt); 
         fprintf(ficresp, "\n#********** Variable ");      if (fptt < fp) { 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         fprintf(ficresp, "**********\n#");        if (t < 0.0) { 
       }          linmin(p,xit,n,fret,func); 
       for(i=1; i<=nlstate;i++)          for (j=1;j<=n;j++) { 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);            xi[j][ibig]=xi[j][n]; 
       fprintf(ficresp, "\n");            xi[j][n]=xit[j]; 
                }
       for(i=(int)agemin; i <= (int)agemax+3; i++){  #ifdef DEBUG
         if(i==(int)agemax+3)          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           printf("Total");          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         else          for(j=1;j<=n;j++){
           printf("Age %d", i);            printf(" %.12e",xit[j]);
         for(jk=1; jk <=nlstate ; jk++){            fprintf(ficlog," %.12e",xit[j]);
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          }
             pp[jk] += freq[jk][m][i];          printf("\n");
         }          fprintf(ficlog,"\n");
         for(jk=1; jk <=nlstate ; jk++){  #endif
           for(m=-1, pos=0; m <=0 ; m++)        }
             pos += freq[jk][m][i];      } 
           if(pp[jk]>=1.e-10)    } 
             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);  /**** Prevalence limit (stable or period prevalence)  ****************/
         }  
   double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
         for(jk=1; jk <=nlstate ; jk++){  {
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
             pp[jk] += freq[jk][m][i];       matrix by transitions matrix until convergence is reached */
         }  
     int i, ii,j,k;
         for(jk=1,pos=0; jk <=nlstate ; jk++)    double min, max, maxmin, maxmax,sumnew=0.;
           pos += pp[jk];    double **matprod2();
         for(jk=1; jk <=nlstate ; jk++){    double **out, cov[NCOVMAX+1], **pmij();
           if(pos>=1.e-5)    double **newm;
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    double agefin, delaymax=50 ; /* Max number of years to converge */
           else  
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    for (ii=1;ii<=nlstate+ndeath;ii++)
           if( i <= (int) agemax){      for (j=1;j<=nlstate+ndeath;j++){
             if(pos>=1.e-5){        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      }
               probs[i][jk][j1]= pp[jk]/pos;  
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/     cov[1]=1.;
             }   
             else   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           }      newm=savm;
         }      /* Covariates have to be included here again */
              cov[2]=agefin;
         for(jk=-1; jk <=nlstate+ndeath; jk++)      
           for(m=-1; m <=nlstate+ndeath; m++)      for (k=1; k<=cptcovn;k++) {
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         if(i <= (int) agemax)        /*        printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
           fprintf(ficresp,"\n");      }
         printf("\n");      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]]];
   }      
   dateintmean=dateintsum/k2cpt;      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   fclose(ficresp);      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
   free_vector(pp,1,nlstate);      
        savm=oldm;
   /* End of Freq */      oldm=newm;
 }      maxmax=0.;
       for(j=1;j<=nlstate;j++){
 /************ Prevalence ********************/        min=1.;
 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)        max=0.;
 {  /* Some frequencies */        for(i=1; i<=nlstate; i++) {
            sumnew=0;
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   double ***freq; /* Frequencies */          prlim[i][j]= newm[i][j]/(1-sumnew);
   double *pp;          max=FMAX(max,prlim[i][j]);
   double pos, k2;          min=FMIN(min,prlim[i][j]);
         }
   pp=vector(1,nlstate);        maxmin=max-min;
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        maxmax=FMAX(maxmax,maxmin);
        }
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      if(maxmax < ftolpl){
   j1=0;        return prlim;
        }
   j=cptcoveff;    }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  }
    
  for(k1=1; k1<=j;k1++){  /*************** transition probabilities ***************/ 
     for(i1=1; i1<=ncodemax[k1];i1++){  
       j1++;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
    {
       for (i=-1; i<=nlstate+ndeath; i++)      /* According to parameters values stored in x and the covariate's values stored in cov,
         for (jk=-1; jk<=nlstate+ndeath; jk++)         computes the probability to be observed in state j being in state i by appying the
           for(m=agemin; m <= agemax+3; m++)       model to the ncovmodel covariates (including constant and age).
             freq[i][jk][m]=0;       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
             and, according on how parameters are entered, the position of the coefficient xij(nc) of the
       for (i=1; i<=imx; i++) {       ncth covariate in the global vector x is given by the formula:
         bool=1;       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
         if  (cptcovn>0) {       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
           for (z1=1; z1<=cptcoveff; z1++)       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
               bool=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]
         if (bool==1) {    */
           for(m=firstpass; m<=lastpass; m++){    double s1, lnpijopii;
             k2=anint[m][i]+(mint[m][i]/12.);    /*double t34;*/
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    int i,j,j1, nc, ii, jj;
               if(agev[m][i]==0) agev[m][i]=agemax+1;  
               if(agev[m][i]==1) agev[m][i]=agemax+2;      for(i=1; i<= nlstate; i++){
               if (m<lastpass)        for(j=1; j<i;j++){
                 if (calagedate>0) freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
               else            /*lnpijopii += param[i][j][nc]*cov[nc];*/
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
                freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
             }          }
           }          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         }  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
       }        }
         for(i=(int)agemin; i <= (int)agemax+3; i++){        for(j=i+1; j<=nlstate+ndeath;j++){
           for(jk=1; jk <=nlstate ; jk++){          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
               pp[jk] += freq[jk][m][i];            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
           }  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
           for(jk=1; jk <=nlstate ; jk++){          }
             for(m=-1, pos=0; m <=0 ; m++)          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
             pos += freq[jk][m][i];        }
         }      }
              
          for(jk=1; jk <=nlstate ; jk++){      for(i=1; i<= nlstate; i++){
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        s1=0;
              pp[jk] += freq[jk][m][i];        for(j=1; j<i; j++){
          }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
                    /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        }
         for(j=i+1; j<=nlstate+ndeath; j++){
          for(jk=1; jk <=nlstate ; jk++){                    s1+=exp(ps[i][j]); /* In fact sums pij/pii */
            if( i <= (int) agemax){          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
              if(pos>=1.e-5){        }
                probs[i][jk][j1]= pp[jk]/pos;        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
              }        ps[i][i]=1./(s1+1.);
            }        /* Computing other pijs */
          }        for(j=1; j<i; j++)
                    ps[i][j]= exp(ps[i][j])*ps[i][i];
         }        for(j=i+1; j<=nlstate+ndeath; j++)
     }          ps[i][j]= exp(ps[i][j])*ps[i][i];
   }        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
       } /* end i */
        
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   free_vector(pp,1,nlstate);        for(jj=1; jj<= nlstate+ndeath; jj++){
            ps[ii][jj]=0;
 }  /* End of Freq */          ps[ii][ii]=1;
         }
 /************* Waves Concatenation ***************/      }
       
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)  
 {  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
      Death is a valid wave (if date is known).  /*         printf("ddd %lf ",ps[ii][jj]); */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i  /*       } */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]  /*       printf("\n "); */
      and mw[mi+1][i]. dh depends on stepm.  /*        } */
      */  /*        printf("\n ");printf("%lf ",cov[2]); */
          /*
   int i, mi, m;        for(i=1; i<= npar; i++) printf("%f ",x[i]);
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        goto end;*/
      double sum=0., jmean=0.;*/      return ps;
   }
   int j, k=0,jk, ju, jl;  
   double sum=0.;  /**************** Product of 2 matrices ******************/
   jmin=1e+5;  
   jmax=-1;  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   jmean=0.;  {
   for(i=1; i<=imx; i++){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     mi=0;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     m=firstpass;    /* in, b, out are matrice of pointers which should have been initialized 
     while(s[m][i] <= nlstate){       before: only the contents of out is modified. The function returns
       if(s[m][i]>=1)       a pointer to pointers identical to out */
         mw[++mi][i]=m;    long i, j, k;
       if(m >=lastpass)    for(i=nrl; i<= nrh; i++)
         break;      for(k=ncolol; k<=ncoloh; k++)
       else        for(j=ncl,out[i][k]=0.; j<=nch; j++)
         m++;          out[i][k] +=in[i][j]*b[j][k];
     }/* end while */  
     if (s[m][i] > nlstate){    return out;
       mi++;     /* Death is another wave */  }
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */  
       mw[mi][i]=m;  /************* Higher Matrix Product ***************/
     }  
   double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     wav[i]=mi;  {
     if(mi==0)    /* Computes the transition matrix starting at age 'age' over 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);       'nhstepm*hstepm*stepm' months (i.e. until
   }       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
   for(i=1; i<=imx; i++){       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     for(mi=1; mi<wav[i];mi++){       (typically every 2 years instead of every month which is too big 
       if (stepm <=0)       for the memory).
         dh[mi][i]=1;       Model is determined by parameters x and covariates have to be 
       else{       included manually here. 
         if (s[mw[mi+1][i]][i] > nlstate) {  
           if (agedc[i] < 2*AGESUP) {       */
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);  
           if(j==0) j=1;  /* Survives at least one month after exam */    int i, j, d, h, k;
           k=k+1;    double **out, cov[NCOVMAX+1];
           if (j >= jmax) jmax=j;    double **newm;
           if (j <= jmin) jmin=j;  
           sum=sum+j;    /* Hstepm could be zero and should return the unit matrix */
           /*if (j<0) printf("j=%d num=%d \n",j,i); */    for (i=1;i<=nlstate+ndeath;i++)
           }      for (j=1;j<=nlstate+ndeath;j++){
         }        oldm[i][j]=(i==j ? 1.0 : 0.0);
         else{        po[i][j][0]=(i==j ? 1.0 : 0.0);
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));      }
           k=k+1;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           if (j >= jmax) jmax=j;    for(h=1; h <=nhstepm; h++){
           else if (j <= jmin)jmin=j;      for(d=1; d <=hstepm; d++){
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */        newm=savm;
           sum=sum+j;        /* Covariates have to be included here again */
         }        cov[1]=1.;
         jk= j/stepm;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         jl= j -jk*stepm;        for (k=1; k<=cptcovn;k++) 
         ju= j -(jk+1)*stepm;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         if(jl <= -ju)        for (k=1; k<=cptcovage;k++)
           dh[mi][i]=jk;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         else        for (k=1; k<=cptcovprod;k++)
           dh[mi][i]=jk+1;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         if(dh[mi][i]==0)  
           dh[mi][i]=1; /* At least one step */  
       }        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
     }        /*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, 
   jmean=sum/k;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        savm=oldm;
  }        oldm=newm;
 /*********** Tricode ****************************/      }
 void tricode(int *Tvar, int **nbcode, int imx)      for(i=1; i<=nlstate+ndeath; i++)
 {        for(j=1;j<=nlstate+ndeath;j++) {
   int Ndum[20],ij=1, k, j, i;          po[i][j][h]=newm[i][j];
   int cptcode=0;          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
   cptcoveff=0;        }
        /*printf("h=%d ",h);*/
   for (k=0; k<19; k++) Ndum[k]=0;    } /* end h */
   for (k=1; k<=7; k++) ncodemax[k]=0;  /*     printf("\n H=%d \n",h); */
     return po;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {  }
     for (i=1; i<=imx; i++) {  
       ij=(int)(covar[Tvar[j]][i]);  
       Ndum[ij]++;  /*************** log-likelihood *************/
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/  double func( double *x)
       if (ij > cptcode) cptcode=ij;  {
     }    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     for (i=0; i<=cptcode; i++) {    double **out;
       if(Ndum[i]!=0) ncodemax[j]++;    double sw; /* Sum of weights */
     }    double lli; /* Individual log likelihood */
     ij=1;    int s1, s2;
     double bbh, survp;
     long ipmx;
     for (i=1; i<=ncodemax[j]; i++) {    /*extern weight */
       for (k=0; k<=19; k++) {    /* We are differentiating ll according to initial status */
         if (Ndum[k] != 0) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
           nbcode[Tvar[j]][ij]=k;    /*for(i=1;i<imx;i++) 
                printf(" %d\n",s[4][i]);
           ij++;    */
         }    cov[1]=1.;
         if (ij > ncodemax[j]) break;  
       }      for(k=1; k<=nlstate; k++) ll[k]=0.;
     }  
   }      if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
  for (k=0; k<19; k++) Ndum[k]=0;        /* 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[]
  for (i=1; i<=ncovmodel-2; i++) {           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
       ij=Tvar[i];           to be observed in j being in i according to the model.
       Ndum[ij]++;         */
     }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
  ij=1;           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
  for (i=1; i<=10; i++) {           has been calculated etc */
    if((Ndum[i]!=0) && (i<=ncovcol)){        for(mi=1; mi<= wav[i]-1; mi++){
      Tvaraff[ij]=i;          for (ii=1;ii<=nlstate+ndeath;ii++)
      ij++;            for (j=1;j<=nlstate+ndeath;j++){
    }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
              }
     cptcoveff=ij-1;          for(d=0; d<dh[mi][i]; d++){
 }            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 /*********** Health Expectancies ****************/            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 */
 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 )            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* Health expectancies */            savm=oldm;
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;            oldm=newm;
   double age, agelim, hf;          } /* end mult */
   double ***p3mat,***varhe;        
   double **dnewm,**doldm;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   double *xp;          /* But now since version 0.9 we anticipate for bias at large stepm.
   double **gp, **gm;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   double ***gradg, ***trgradg;           * (in months) between two waves is not a multiple of stepm, we rounded to 
   int theta;           * the nearest (and in case of equal distance, to the lowest) interval but now
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
   xp=vector(1,npar);           * probability in order to take into account the bias as a fraction of the way
   dnewm=matrix(1,nlstate*2,1,npar);           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   doldm=matrix(1,nlstate*2,1,nlstate*2);           * -stepm/2 to stepm/2 .
             * For stepm=1 the results are the same as for previous versions of Imach.
   fprintf(ficreseij,"# Health expectancies\n");           * For stepm > 1 the results are less biased than in previous versions. 
   fprintf(ficreseij,"# Age");           */
   for(i=1; i<=nlstate;i++)          s1=s[mw[mi][i]][i];
     for(j=1; j<=nlstate;j++)          s2=s[mw[mi+1][i]][i];
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficreseij,"\n");          /* bias bh is positive if real duration
            * is higher than the multiple of stepm and negative otherwise.
   if(estepm < stepm){           */
     printf ("Problem %d lower than %d\n",estepm, stepm);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   }          if( s2 > nlstate){ 
   else  hstepm=estepm;              /* i.e. if s2 is a death state and if the date of death is known 
   /* We compute the life expectancy from trapezoids spaced every estepm months               then the contribution to the likelihood is the probability to 
    * This is mainly to measure the difference between two models: for example               die between last step unit time and current  step unit time, 
    * if stepm=24 months pijx are given only every 2 years and by summing them               which is also equal to probability to die before dh 
    * we are calculating an estimate of the Life Expectancy assuming a linear               minus probability to die before dh-stepm . 
    * progression inbetween and thus overestimating or underestimating according               In version up to 0.92 likelihood was computed
    * to the curvature of the survival function. If, for the same date, we          as if date of death was unknown. Death was treated as any other
    * estimate the model with stepm=1 month, we can keep estepm to 24 months          health state: the date of the interview describes the actual state
    * to compare the new estimate of Life expectancy with the same linear          and not the date of a change in health state. The former idea was
    * hypothesis. A more precise result, taking into account a more precise          to consider that at each interview the state was recorded
    * curvature will be obtained if estepm is as small as stepm. */          (healthy, disable or death) and IMaCh was corrected; but when we
           introduced the exact date of death then we should have modified
   /* For example we decided to compute the life expectancy with the smallest unit */          the contribution of an exact death to the likelihood. This new
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          contribution is smaller and very dependent of the step unit
      nhstepm is the number of hstepm from age to agelim          stepm. It is no more the probability to die between last interview
      nstepm is the number of stepm from age to agelin.          and month of death but the probability to survive from last
      Look at hpijx to understand the reason of that which relies in memory size          interview up to one month before death multiplied by the
      and note for a fixed period like estepm months */          probability to die within a month. Thanks to Chris
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          Jackson for correcting this bug.  Former versions increased
      survival function given by stepm (the optimization length). Unfortunately it          mortality artificially. The bad side is that we add another loop
      means that if the survival funtion is printed only each two years of age and if          which slows down the processing. The difference can be up to 10%
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          lower mortality.
      results. So we changed our mind and took the option of the best precision.            */
   */            lli=log(out[s1][s2] - savm[s1][s2]);
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */  
   
   agelim=AGESUP;          } else if  (s2==-2) {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            for (j=1,survp=0. ; j<=nlstate; j++) 
     /* nhstepm age range expressed in number of stepm */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     nstepm=(int) rint((agelim-age)*YEARM/stepm);            /*survp += out[s1][j]; */
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */            lli= log(survp);
     /* if (stepm >= YEARM) hstepm=1;*/          }
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          else if  (s2==-4) { 
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);            for (j=3,survp=0. ; j<=nlstate; j++)  
     gp=matrix(0,nhstepm,1,nlstate*2);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     gm=matrix(0,nhstepm,1,nlstate*2);            lli= log(survp); 
           } 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored  
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          else if  (s2==-5) { 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              for (j=1,survp=0. ; j<=2; j++)  
                survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             lli= log(survp); 
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          } 
           
     /* Computing Variances of health expectancies */          else{
             lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
      for(theta=1; theta <=npar; theta++){            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
       for(i=1; i<=npar; i++){          } 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       }          /*if(lli ==000.0)*/
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
            ipmx +=1;
       cptj=0;          sw += weight[i];
       for(j=1; j<= nlstate; j++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(i=1; i<=nlstate; i++){        } /* end of wave */
           cptj=cptj+1;      } /* end of individual */
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){    }  else if(mle==2){
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
       }          for (ii=1;ii<=nlstate+ndeath;ii++)
                  for (j=1;j<=nlstate+ndeath;j++){
                    oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(i=1; i<=npar; i++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for(d=0; d<=dh[mi][i]; d++){
                  newm=savm;
       cptj=0;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(j=1; j<= nlstate; j++){            for (kk=1; kk<=cptcovage;kk++) {
         for(i=1;i<=nlstate;i++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           cptj=cptj+1;            }
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           }            savm=oldm;
         }            oldm=newm;
       }          } /* end mult */
              
              s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
       for(j=1; j<= nlstate*2; j++)          bbh=(double)bh[mi][i]/(double)stepm; 
         for(h=0; h<=nhstepm-1; 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 */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          ipmx +=1;
         }          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      }        } /* end of wave */
          } /* end of individual */
 /* End theta */    }  else if(mle==3){  /* exponential inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
      for(h=0; h<=nhstepm-1; h++)          for (ii=1;ii<=nlstate+ndeath;ii++)
       for(j=1; j<=nlstate*2;j++)            for (j=1;j<=nlstate+ndeath;j++){
         for(theta=1; theta <=npar; theta++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         trgradg[h][j][theta]=gradg[h][theta][j];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
           for(d=0; d<dh[mi][i]; d++){
      for(i=1;i<=nlstate*2;i++)            newm=savm;
       for(j=1;j<=nlstate*2;j++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         varhe[i][j][(int)age] =0.;            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(h=0;h<=nhstepm-1;h++){            }
       for(k=0;k<=nhstepm-1;k++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);            savm=oldm;
         for(i=1;i<=nlstate*2;i++)            oldm=newm;
           for(j=1;j<=nlstate*2;j++)          } /* end mult */
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;        
       }          s1=s[mw[mi][i]][i];
     }          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
                lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
     /* Computing expectancies */          ipmx +=1;
     for(i=1; i<=nlstate;i++)          sw += weight[i];
       for(j=1; j<=nlstate;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){        } /* end of wave */
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;      } /* end of individual */
              }else if (mle==4){  /* ml=4 no inter-extrapolation */
 /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
     fprintf(ficreseij,"%3.0f",age );            for (j=1;j<=nlstate+ndeath;j++){
     cptj=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i=1; i<=nlstate;i++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate;j++){            }
         cptj++;          for(d=0; d<dh[mi][i]; d++){
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );            newm=savm;
       }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     fprintf(ficreseij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     free_matrix(gm,0,nhstepm,1,nlstate*2);            }
     free_matrix(gp,0,nhstepm,1,nlstate*2);          
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            savm=oldm;
   }            oldm=newm;
   free_vector(xp,1,npar);          } /* end mult */
   free_matrix(dnewm,1,nlstate*2,1,npar);        
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);          s1=s[mw[mi][i]][i];
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);          s2=s[mw[mi+1][i]][i];
 }          if( s2 > nlstate){ 
             lli=log(out[s1][s2] - savm[s1][s2]);
 /************ Variance ******************/          }else{
 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)            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 {          }
   /* Variance of health expectancies */          ipmx +=1;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          sw += weight[i];
   double **newm;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **dnewm,**doldm;  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   int i, j, nhstepm, hstepm, h, nstepm ;        } /* end of wave */
   int k, cptcode;      } /* end of individual */
   double *xp;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   double **gp, **gm;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***gradg, ***trgradg;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double ***p3mat;        for(mi=1; mi<= wav[i]-1; mi++){
   double age,agelim, hf;          for (ii=1;ii<=nlstate+ndeath;ii++)
   int theta;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
    fprintf(ficresvij,"# Covariances of life expectancies\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficresvij,"# Age");            }
   for(i=1; i<=nlstate;i++)          for(d=0; d<dh[mi][i]; d++){
     for(j=1; j<=nlstate;j++)            newm=savm;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficresvij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   xp=vector(1,npar);            }
   dnewm=matrix(1,nlstate,1,npar);          
   doldm=matrix(1,nlstate,1,nlstate);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   if(estepm < stepm){            savm=oldm;
     printf ("Problem %d lower than %d\n",estepm, stepm);            oldm=newm;
   }          } /* end mult */
   else  hstepm=estepm;          
   /* For example we decided to compute the life expectancy with the smallest unit */          s1=s[mw[mi][i]][i];
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          s2=s[mw[mi+1][i]][i];
      nhstepm is the number of hstepm from age to agelim          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
      nstepm is the number of stepm from age to agelin.          ipmx +=1;
      Look at hpijx to understand the reason of that which relies in memory size          sw += weight[i];
      and note for a fixed period like k years */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          /*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]);*/
      survival function given by stepm (the optimization length). Unfortunately it        } /* end of wave */
      means that if the survival funtion is printed only each two years of age and if      } /* end of individual */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    } /* End of if */
      results. So we changed our mind and took the option of the best precision.    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   */    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   agelim = AGESUP;    return -l;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  }
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  /*************** log-likelihood *************/
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  double funcone( double *x)
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  {
     gp=matrix(0,nhstepm,1,nlstate);    /* Same as likeli but slower because of a lot of printf and if */
     gm=matrix(0,nhstepm,1,nlstate);    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     for(theta=1; theta <=npar; theta++){    double **out;
       for(i=1; i<=npar; i++){ /* Computes gradient */    double lli; /* Individual log likelihood */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    double llt;
       }    int s1, s2;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      double bbh, survp;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    /*extern weight */
     /* We are differentiating ll according to initial status */
       if (popbased==1) {    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         for(i=1; i<=nlstate;i++)    /*for(i=1;i<imx;i++) 
           prlim[i][i]=probs[(int)age][i][ij];      printf(" %d\n",s[4][i]);
       }    */
      cov[1]=1.;
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){    for(k=1; k<=nlstate; k++) ll[k]=0.;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)  
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }      for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
       for(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);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          }
          for(d=0; d<dh[mi][i]; d++){
       if (popbased==1) {          newm=savm;
         for(i=1; i<=nlstate;i++)          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           prlim[i][i]=probs[(int)age][i][ij];          for (kk=1; kk<=cptcovage;kk++) {
       }            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }
       for(j=1; j<= nlstate; j++){          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(h=0; h<=nhstepm; h++){                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          savm=oldm;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          oldm=newm;
         }        } /* end mult */
       }        
         s1=s[mw[mi][i]][i];
       for(j=1; j<= nlstate; j++)        s2=s[mw[mi+1][i]][i];
         for(h=0; h<=nhstepm; h++){        bbh=(double)bh[mi][i]/(double)stepm; 
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        /* bias is positive if real duration
         }         * is higher than the multiple of stepm and negative otherwise.
     } /* End theta */         */
         if( s2 > nlstate && (mle <5) ){  /* Jackson */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          lli=log(out[s1][s2] - savm[s1][s2]);
         } else if  (s2==-2) {
     for(h=0; h<=nhstepm; h++)          for (j=1,survp=0. ; j<=nlstate; j++) 
       for(j=1; j<=nlstate;j++)            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
         for(theta=1; theta <=npar; theta++)          lli= log(survp);
           trgradg[h][j][theta]=gradg[h][theta][j];        }else if (mle==1){
           lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */        } else if(mle==2){
     for(i=1;i<=nlstate;i++)          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(j=1;j<=nlstate;j++)        } else if(mle==3){  /* exponential inter-extrapolation */
         vareij[i][j][(int)age] =0.;          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(h=0;h<=nhstepm;h++){          lli=log(out[s1][s2]); /* Original formula */
       for(k=0;k<=nhstepm;k++){        } else{  /* mle=0 back to 1 */
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          /*lli=log(out[s1][s2]); */ /* Original formula */
         for(i=1;i<=nlstate;i++)        } /* End of if */
           for(j=1;j<=nlstate;j++)        ipmx +=1;
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;        sw += weight[i];
       }        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         if(globpr){
     fprintf(ficresvij,"%.0f ",age );          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     for(i=1; i<=nlstate;i++)   %11.6f %11.6f %11.6f ", \
       for(j=1; j<=nlstate;j++){                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     fprintf(ficresvij,"\n");            llt +=ll[k]*gipmx/gsw;
     free_matrix(gp,0,nhstepm,1,nlstate);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
     free_matrix(gm,0,nhstepm,1,nlstate);          }
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);          fprintf(ficresilk," %10.6f\n", -llt);
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      } /* end of wave */
   } /* End age */    } /* end of individual */
      for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   free_vector(xp,1,npar);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   free_matrix(doldm,1,nlstate,1,npar);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   free_matrix(dnewm,1,nlstate,1,nlstate);    if(globpr==0){ /* First time we count the contributions and weights */
       gipmx=ipmx;
 }      gsw=sw;
     }
 /************ Variance of prevlim ******************/    return -l;
 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)  }
 {  
   /* Variance of prevalence limit */  
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  /*************** function likelione ***********/
   double **newm;  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   double **dnewm,**doldm;  {
   int i, j, nhstepm, hstepm;    /* This routine should help understanding what is done with 
   int k, cptcode;       the selection of individuals/waves and
   double *xp;       to check the exact contribution to the likelihood.
   double *gp, *gm;       Plotting could be done.
   double **gradg, **trgradg;     */
   double age,agelim;    int k;
   int theta;  
        if(*globpri !=0){ /* Just counts and sums, no printings */
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      strcpy(fileresilk,"ilk"); 
   fprintf(ficresvpl,"# Age");      strcat(fileresilk,fileres);
   for(i=1; i<=nlstate;i++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
       fprintf(ficresvpl," %1d-%1d",i,i);        printf("Problem with resultfile: %s\n", fileresilk);
   fprintf(ficresvpl,"\n");        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
   xp=vector(1,npar);      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");
   dnewm=matrix(1,nlstate,1,npar);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   doldm=matrix(1,nlstate,1,nlstate);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
        for(k=1; k<=nlstate; k++) 
   hstepm=1*YEARM; /* Every year of age */        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   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 */    *fretone=(*funcone)(p);
     if (stepm >= YEARM) hstepm=1;    if(*globpri !=0){
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      fclose(ficresilk);
     gradg=matrix(1,npar,1,nlstate);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
     gp=vector(1,nlstate);      fflush(fichtm); 
     gm=vector(1,nlstate);    } 
     return;
     for(theta=1; theta <=npar; theta++){  }
       for(i=1; i<=npar; i++){ /* Computes gradient */  
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }  /*********** Maximum Likelihood Estimation ***************/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
         gp[i] = prlim[i][i];  {
        int i,j, iter;
       for(i=1; i<=npar; i++) /* Computes gradient */    double **xi;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double fret;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double fretone; /* Only one call to likelihood */
       for(i=1;i<=nlstate;i++)    /*  char filerespow[FILENAMELENGTH];*/
         gm[i] = prlim[i][i];    xi=matrix(1,npar,1,npar);
     for (i=1;i<=npar;i++)
       for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++)
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        xi[i][j]=(i==j ? 1.0 : 0.0);
     } /* End theta */    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow"); 
     trgradg =matrix(1,nlstate,1,npar);    strcat(filerespow,fileres);
     if((ficrespow=fopen(filerespow,"w"))==NULL) {
     for(j=1; j<=nlstate;j++)      printf("Problem with resultfile: %s\n", filerespow);
       for(theta=1; theta <=npar; theta++)      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
         trgradg[j][theta]=gradg[theta][j];    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
     for(i=1;i<=nlstate;i++)    for (i=1;i<=nlstate;i++)
       varpl[i][(int)age] =0.;      for(j=1;j<=nlstate+ndeath;j++)
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    fprintf(ficrespow,"\n");
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    powell(p,xi,npar,ftol,&iter,&fret,func);
   
     fprintf(ficresvpl,"%.0f ",age );    free_matrix(xi,1,npar,1,npar);
     for(i=1; i<=nlstate;i++)    fclose(ficrespow);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficresvpl,"\n");    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     free_vector(gp,1,nlstate);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     free_vector(gm,1,nlstate);  
     free_matrix(gradg,1,npar,1,nlstate);  }
     free_matrix(trgradg,1,nlstate,1,npar);  
   } /* End age */  /**** Computes Hessian and covariance matrix ***/
   void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   free_vector(xp,1,npar);  {
   free_matrix(doldm,1,nlstate,1,npar);    double  **a,**y,*x,pd;
   free_matrix(dnewm,1,nlstate,1,nlstate);    double **hess;
     int i, j,jk;
 }    int *indx;
   
 /************ Variance of one-step probabilities  ******************/    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
 {    void lubksb(double **a, int npar, int *indx, double b[]) ;
   int i, j, i1, k1, j1, z1;    void ludcmp(double **a, int npar, int *indx, double *d) ;
   int k=0, cptcode;    double gompertz(double p[]);
   double **dnewm,**doldm;    hess=matrix(1,npar,1,npar);
   double *xp;  
   double *gp, *gm;    printf("\nCalculation of the hessian matrix. Wait...\n");
   double **gradg, **trgradg;    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   double age,agelim, cov[NCOVMAX];    for (i=1;i<=npar;i++){
   int theta;      printf("%d",i);fflush(stdout);
   char fileresprob[FILENAMELENGTH];      fprintf(ficlog,"%d",i);fflush(ficlog);
      
   strcpy(fileresprob,"prob");       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   strcat(fileresprob,fileres);      
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {      /*  printf(" %f ",p[i]);
     printf("Problem with resultfile: %s\n", fileresprob);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   }    }
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    
      for (i=1;i<=npar;i++) {
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");      for (j=1;j<=npar;j++)  {
   fprintf(ficresprob,"# Age");        if (j>i) { 
   for(i=1; i<=nlstate;i++)          printf(".%d%d",i,j);fflush(stdout);
     for(j=1; j<=(nlstate+ndeath);j++)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);          hess[i][j]=hessij(p,delti,i,j,func,npar);
           
           hess[j][i]=hess[i][j];    
   fprintf(ficresprob,"\n");          /*printf(" %lf ",hess[i][j]);*/
         }
       }
   xp=vector(1,npar);    }
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    printf("\n");
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    fprintf(ficlog,"\n");
    
   cov[1]=1;    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   j=cptcoveff;    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    
   j1=0;    a=matrix(1,npar,1,npar);
   for(k1=1; k1<=1;k1++){    y=matrix(1,npar,1,npar);
     for(i1=1; i1<=ncodemax[k1];i1++){    x=vector(1,npar);
     j1++;    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
     if  (cptcovn>0) {      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
       fprintf(ficresprob, "\n#********** Variable ");    ludcmp(a,npar,indx,&pd);
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  
       fprintf(ficresprob, "**********\n#");    for (j=1;j<=npar;j++) {
     }      for (i=1;i<=npar;i++) x[i]=0;
          x[j]=1;
       for (age=bage; age<=fage; age ++){      lubksb(a,npar,indx,x);
         cov[2]=age;      for (i=1;i<=npar;i++){ 
         for (k=1; k<=cptcovn;k++) {        matcov[i][j]=x[i];
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];      }
              }
         }  
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    printf("\n#Hessian matrix#\n");
         for (k=1; k<=cptcovprod;k++)    fprintf(ficlog,"\n#Hessian matrix#\n");
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for (i=1;i<=npar;i++) { 
              for (j=1;j<=npar;j++) { 
         gradg=matrix(1,npar,1,9);        printf("%.3e ",hess[i][j]);
         trgradg=matrix(1,9,1,npar);        fprintf(ficlog,"%.3e ",hess[i][j]);
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));      }
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));      printf("\n");
          fprintf(ficlog,"\n");
         for(theta=1; theta <=npar; theta++){    }
           for(i=1; i<=npar; i++)  
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    /* Recompute Inverse */
              for (i=1;i<=npar;i++)
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
              ludcmp(a,npar,indx,&pd);
           k=0;  
           for(i=1; i<= (nlstate+ndeath); i++){    /*  printf("\n#Hessian matrix recomputed#\n");
             for(j=1; j<=(nlstate+ndeath);j++){  
               k=k+1;    for (j=1;j<=npar;j++) {
               gp[k]=pmmij[i][j];      for (i=1;i<=npar;i++) x[i]=0;
             }      x[j]=1;
           }      lubksb(a,npar,indx,x);
                for (i=1;i<=npar;i++){ 
           for(i=1; i<=npar; i++)        y[i][j]=x[i];
             xp[i] = x[i] - (i==theta ?delti[theta]:0);        printf("%.3e ",y[i][j]);
            fprintf(ficlog,"%.3e ",y[i][j]);
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      }
           k=0;      printf("\n");
           for(i=1; i<=(nlstate+ndeath); i++){      fprintf(ficlog,"\n");
             for(j=1; j<=(nlstate+ndeath);j++){    }
               k=k+1;    */
               gm[k]=pmmij[i][j];  
             }    free_matrix(a,1,npar,1,npar);
           }    free_matrix(y,1,npar,1,npar);
          free_vector(x,1,npar);
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)    free_ivector(indx,1,npar);
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      free_matrix(hess,1,npar,1,npar);
         }  
   
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)  }
           for(theta=1; theta <=npar; theta++)  
             trgradg[j][theta]=gradg[theta][j];  /*************** hessian matrix ****************/
          double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);  {
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    int i;
            int l=1, lmax=20;
         pmij(pmmij,cov,ncovmodel,x,nlstate);    double k1,k2;
            double p2[MAXPARM+1]; /* identical to x */
         k=0;    double res;
         for(i=1; i<=(nlstate+ndeath); i++){    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
           for(j=1; j<=(nlstate+ndeath);j++){    double fx;
             k=k+1;    int k=0,kmax=10;
             gm[k]=pmmij[i][j];    double l1;
           }  
         }    fx=func(x);
          for (i=1;i<=npar;i++) p2[i]=x[i];
      /*printf("\n%d ",(int)age);    for(l=0 ; l <=lmax; l++){
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      l1=pow(10,l);
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      delts=delt;
      }*/      for(k=1 ; k <kmax; k=k+1){
         delt = delta*(l1*k);
         fprintf(ficresprob,"\n%d ",(int)age);        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)        p2[theta]=x[theta]-delt;
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));        k2=func(p2)-fx;
          /*res= (k1-2.0*fx+k2)/delt/delt; */
       }        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     }        
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));  #ifdef DEBUGHESS
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));        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);
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        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);
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  #endif
   }        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   free_vector(xp,1,npar);        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   fclose(ficresprob);          k=kmax;
          }
 }        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
           k=kmax; l=lmax*10.;
 /******************* Printing html file ***********/        }
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
  int lastpass, int stepm, int weightopt, char model[],\          delts=delt;
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \        }
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\      }
  char version[], int popforecast, int estepm ){    }
   int jj1, k1, i1, cpt;    delti[theta]=delts;
   FILE *fichtm;    return res; 
   /*char optionfilehtm[FILENAMELENGTH];*/    
   }
   strcpy(optionfilehtm,optionfile);  
   strcat(optionfilehtm,".htm");  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {  {
     printf("Problem with %s \n",optionfilehtm), exit(0);    int i;
   }    int l=1, l1, lmax=20;
     double k1,k2,k3,k4,res,fx;
  fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    double p2[MAXPARM+1];
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n    int k;
 \n  
 Total number of observations=%d <br>\n    fx=func(x);
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    for (k=1; k<=2; k++) {
 <hr  size=\"2\" color=\"#EC5E5E\">      for (i=1;i<=npar;i++) p2[i]=x[i];
  <ul><li>Outputs files<br>\n      p2[thetai]=x[thetai]+delti[thetai]/k;
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n      k1=func(p2)-fx;
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n      p2[thetai]=x[thetai]+delti[thetai]/k;
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
  - Life expectancies by age and initial health status (estepm=%2d months): <a href=\"e%s\">e%s</a> <br>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot,fileres,fileres,fileres,fileres,fileres,fileres,estepm,fileres,fileres);      k2=func(p2)-fx;
     
  fprintf(fichtm,"\n      p2[thetai]=x[thetai]-delti[thetai]/k;
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n      k3=func(p2)-fx;
  - Variances 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: <a href=\"t%s\">t%s</a> <br>\n      p2[thetai]=x[thetai]-delti[thetai]/k;
  - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k4=func(p2)-fx;
  if(popforecast==1) fprintf(fichtm,"\n      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n  #ifdef DEBUG
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         <br>",fileres,fileres,fileres,fileres);      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);
  else  #endif
    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);    }
 fprintf(fichtm," <li>Graphs</li><p>");    return res;
   }
  m=cptcoveff;  
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  /************** Inverse of matrix **************/
   void ludcmp(double **a, int n, int *indx, double *d) 
  jj1=0;  { 
  for(k1=1; k1<=m;k1++){    int i,imax,j,k; 
    for(i1=1; i1<=ncodemax[k1];i1++){    double big,dum,sum,temp; 
        jj1++;    double *vv; 
        if (cptcovn > 0) {   
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    vv=vector(1,n); 
          for (cpt=1; cpt<=cptcoveff;cpt++)    *d=1.0; 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);    for (i=1;i<=n;i++) { 
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      big=0.0; 
        }      for (j=1;j<=n;j++) 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>        if ((temp=fabs(a[i][j])) > big) big=temp; 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
        for(cpt=1; cpt<nlstate;cpt++){      vv[i]=1.0/big; 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    } 
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    for (j=1;j<=n;j++) { 
        }      for (i=1;i<j;i++) { 
     for(cpt=1; cpt<=nlstate;cpt++) {        sum=a[i][j]; 
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
 interval) in state (%d): v%s%d%d.gif <br>        a[i][j]=sum; 
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);        } 
      }      big=0.0; 
      for(cpt=1; cpt<=nlstate;cpt++) {      for (i=j;i<=n;i++) { 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>        sum=a[i][j]; 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);        for (k=1;k<j;k++) 
      }          sum -= a[i][k]*a[k][j]; 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and        a[i][j]=sum; 
 health expectancies in states (1) and (2): e%s%d.gif<br>        if ( (dum=vv[i]*fabs(sum)) >= big) { 
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          big=dum; 
 fprintf(fichtm,"\n</body>");          imax=i; 
    }        } 
    }      } 
 fclose(fichtm);      if (j != imax) { 
 }        for (k=1;k<=n;k++) { 
           dum=a[imax][k]; 
 /******************* Gnuplot file **************/          a[imax][k]=a[j][k]; 
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){          a[j][k]=dum; 
         } 
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;        *d = -(*d); 
         vv[imax]=vv[j]; 
   strcpy(optionfilegnuplot,optionfilefiname);      } 
   strcat(optionfilegnuplot,".gp.txt");      indx[j]=imax; 
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {      if (a[j][j] == 0.0) a[j][j]=TINY; 
     printf("Problem with file %s",optionfilegnuplot);      if (j != n) { 
   }        dum=1.0/(a[j][j]); 
         for (i=j+1;i<=n;i++) a[i][j] *= dum; 
 #ifdef windows      } 
     fprintf(ficgp,"cd \"%s\" \n",pathc);    } 
 #endif    free_vector(vv,1,n);  /* Doesn't work */
 m=pow(2,cptcoveff);  ;
    } 
  /* 1eme*/  
   for (cpt=1; cpt<= nlstate ; cpt ++) {  void lubksb(double **a, int n, int *indx, double b[]) 
    for (k1=1; k1<= m ; k1 ++) {  { 
     int i,ii=0,ip,j; 
 #ifdef windows    double sum; 
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);   
 #endif    for (i=1;i<=n;i++) { 
 #ifdef unix      ip=indx[i]; 
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);      sum=b[ip]; 
 #endif      b[ip]=b[i]; 
       if (ii) 
 for (i=1; i<= nlstate ; i ++) {        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      else if (sum) ii=i; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      b[i]=sum; 
 }    } 
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    for (i=n;i>=1;i--) { 
     for (i=1; i<= nlstate ; i ++) {      sum=b[i]; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      b[i]=sum/a[i][i]; 
 }    } 
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  } 
      for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  void pstamp(FILE *fichier)
   else fprintf(ficgp," \%%*lf (\%%*lf)");  {
 }      fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));  }
 #ifdef unix  
 fprintf(ficgp,"\nset ter gif small size 400,300");  /************ Frequencies ********************/
 #endif  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 \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  {  /* Some frequencies */
    }    
   }    int i, m, jk, k1,i1, j1, bool, z1,j;
   /*2 eme*/    int first;
     double ***freq; /* Frequencies */
   for (k1=1; k1<= m ; k1 ++) {    double *pp, **prop;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",ageminpar,fage);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
        char fileresp[FILENAMELENGTH];
     for (i=1; i<= nlstate+1 ; i ++) {    
       k=2*i;    pp=vector(1,nlstate);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    prop=matrix(1,nlstate,iagemin,iagemax+3);
       for (j=1; j<= nlstate+1 ; j ++) {    strcpy(fileresp,"p");
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    strcat(fileresp,fileres);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    if((ficresp=fopen(fileresp,"w"))==NULL) {
 }        printf("Problem with prevalence resultfile: %s\n", fileresp);
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);      exit(0);
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    }
       for (j=1; j<= nlstate+1 ; j ++) {    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    j1=0;
         else fprintf(ficgp," \%%*lf (\%%*lf)");    
 }      j=cptcoveff;
       fprintf(ficgp,"\" t\"\" w l 0,");    if (cptcovn<1) {j=1;ncodemax[1]=1;}
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);  
       for (j=1; j<= nlstate+1 ; j ++) {    first=1;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for(k1=1; k1<=j;k1++){   /* Loop on covariates */
 }        for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        j1++;
       else fprintf(ficgp,"\" t\"\" w l 0,");        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
     }          scanf("%d", i);*/
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);        for (i=-5; i<=nlstate+ndeath; i++)  
   }          for (jk=-5; jk<=nlstate+ndeath; jk++)  
              for(m=iagemin; m <= iagemax+3; m++)
   /*3eme*/              freq[i][jk][m]=0;
         
   for (k1=1; k1<= m ; k1 ++) {        for (i=1; i<=nlstate; i++)  
     for (cpt=1; cpt<= nlstate ; cpt ++) {          for(m=iagemin; m <= iagemax+3; m++)
       k=2+nlstate*(2*cpt-2);            prop[i][m]=0;
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",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);        dateintsum=0;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");        k2cpt=0;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);        for (i=1; i<=imx; i++) {
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          bool=1;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          if  (cptcovn>0) {
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
 */                bool=0;
       for (i=1; i< nlstate ; i ++) {          }
         fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);          if (bool==1){
             for(m=firstpass; m<=lastpass; m++){
       }              k2=anint[m][i]+(mint[m][i]/12.);
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                  if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   /* CV preval stat */                if (m<lastpass) {
     for (k1=1; k1<= m ; k1 ++) {                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     for (cpt=1; cpt<nlstate ; cpt ++) {                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
       k=3;                }
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);                
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
       for (i=1; i< nlstate ; i ++)                  dateintsum=dateintsum+k2;
         fprintf(ficgp,"+$%d",k+i+1);                  k2cpt++;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);                }
                      /*}*/
       l=3+(nlstate+ndeath)*cpt;            }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);          }
       for (i=1; i< nlstate ; i ++) {        }
         l=3+(nlstate+ndeath)*cpt;         
         fprintf(ficgp,"+$%d",l+i+1);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       }        pstamp(ficresp);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);          if  (cptcovn>0) {
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          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#");
            fprintf(ficlog, "\n#********** Variable "); 
   /* proba elementaires */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    for(i=1,jk=1; i <=nlstate; i++){          fprintf(ficlog, "**********\n#");
     for(k=1; k <=(nlstate+ndeath); k++){        }
       if (k != i) {        for(i=1; i<=nlstate;i++) 
         for(j=1; j <=ncovmodel; j++){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
                fprintf(ficresp, "\n");
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);        
           jk++;        for(i=iagemin; i <= iagemax+3; i++){
           fprintf(ficgp,"\n");          if(i==iagemax+3){
         }            fprintf(ficlog,"Total");
       }          }else{
     }            if(first==1){
     }              first=0;
               printf("See log file for details...\n");
     for(jk=1; jk <=m; jk++) {            }
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);            fprintf(ficlog,"Age %d", i);
    i=1;          }
    for(k2=1; k2<=nlstate; k2++) {          for(jk=1; jk <=nlstate ; jk++){
      k3=i;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
      for(k=1; k<=(nlstate+ndeath); k++) {              pp[jk] += freq[jk][m][i]; 
        if (k != k2){          }
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          for(jk=1; jk <=nlstate ; jk++){
 ij=1;            for(m=-1, pos=0; m <=0 ; m++)
         for(j=3; j <=ncovmodel; j++) {              pos += freq[jk][m][i];
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {            if(pp[jk]>=1.e-10){
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);              if(first==1){
             ij++;                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           }              }
           else              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);            }else{
         }              if(first==1)
           fprintf(ficgp,")/(1");                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                      fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
         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++){          for(jk=1; jk <=nlstate ; jk++){
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);              pp[jk] += freq[jk][m][i];
             ij++;          }       
           }          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
           else            pos += pp[jk];
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);            posprop += prop[jk][i];
           }          }
           fprintf(ficgp,")");          for(jk=1; jk <=nlstate ; jk++){
         }            if(pos>=1.e-5){
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);              if(first==1)
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         i=i+ncovmodel;              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
        }            }else{
      }              if(first==1)
    }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
    }            }
                if( i <= iagemax){
   fclose(ficgp);              if(pos>=1.e-5){
 }  /* end gnuplot */                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                 /*probs[i][jk][j1]= pp[jk]/pos;*/
                 /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
 /*************** Moving average **************/              }
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){              else
                 fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   int i, cpt, cptcod;            }
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)          }
       for (i=1; i<=nlstate;i++)          
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)          for(jk=-1; jk <=nlstate+ndeath; jk++)
           mobaverage[(int)agedeb][i][cptcod]=0.;            for(m=-1; m <=nlstate+ndeath; m++)
                  if(freq[jk][m][i] !=0 ) {
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){              if(first==1)
       for (i=1; i<=nlstate;i++){                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
           for (cpt=0;cpt<=4;cpt++){              }
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];          if(i <= iagemax)
           }            fprintf(ficresp,"\n");
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;          if(first==1)
         }            printf("Others in log...\n");
       }          fprintf(ficlog,"\n");
     }        }
          }
 }    }
     dateintmean=dateintsum/k2cpt; 
    
 /************** Forecasting ******************/    fclose(ficresp);
 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){    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
      free_vector(pp,1,nlstate);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
   int *popage;    /* End of Freq */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  }
   double *popeffectif,*popcount;  
   double ***p3mat;  /************ Prevalence ********************/
   char fileresf[FILENAMELENGTH];  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)
   {  
  agelim=AGESUP;    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;       in each health status at the date of interview (if between dateprev1 and dateprev2).
        We still use firstpass and lastpass as another selection.
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    */
     
      int i, m, jk, k1, i1, j1, bool, z1,j;
   strcpy(fileresf,"f");    double ***freq; /* Frequencies */
   strcat(fileresf,fileres);    double *pp, **prop;
   if((ficresf=fopen(fileresf,"w"))==NULL) {    double pos,posprop; 
     printf("Problem with forecast resultfile: %s\n", fileresf);    double  y2; /* in fractional years */
   }    int iagemin, iagemax;
   printf("Computing forecasting: result on file '%s' \n", fileresf);  
     iagemin= (int) agemin;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    iagemax= (int) agemax;
     /*pp=vector(1,nlstate);*/
   if (mobilav==1) {    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     movingaverage(agedeb, fage, ageminpar, mobaverage);    j1=0;
   }    
     j=cptcoveff;
   stepsize=(int) (stepm+YEARM-1)/YEARM;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   if (stepm<=12) stepsize=1;    
      for(k1=1; k1<=j;k1++){
   agelim=AGESUP;      for(i1=1; i1<=ncodemax[k1];i1++){
          j1++;
   hstepm=1;        
   hstepm=hstepm/stepm;        for (i=1; i<=nlstate; i++)  
   yp1=modf(dateintmean,&yp);          for(m=iagemin; m <= iagemax+3; m++)
   anprojmean=yp;            prop[i][m]=0.0;
   yp2=modf((yp1*12),&yp);       
   mprojmean=yp;        for (i=1; i<=imx; i++) { /* Each individual */
   yp1=modf((yp2*30.5),&yp);          bool=1;
   jprojmean=yp;          if  (cptcovn>0) {
   if(jprojmean==0) jprojmean=1;            for (z1=1; z1<=cptcoveff; z1++) 
   if(mprojmean==0) jprojmean=1;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                  bool=0;
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);          } 
            if (bool==1) { 
   for(cptcov=1;cptcov<=i2;cptcov++){            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       k=k+1;              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
       fprintf(ficresf,"\n#******");                if(agev[m][i]==0) agev[m][i]=iagemax+1;
       for(j=1;j<=cptcoveff;j++) {                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
       }                if (s[m][i]>0 && s[m][i]<=nlstate) { 
       fprintf(ficresf,"******\n");                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
       fprintf(ficresf,"# StartingAge FinalAge");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);                  prop[s[m][i]][iagemax+3] += weight[i]; 
                      } 
                    }
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {            } /* end selection of waves */
         fprintf(ficresf,"\n");          }
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);          }
         for(i=iagemin; i <= iagemax+3; i++){  
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){          
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
           nhstepm = nhstepm/hstepm;            posprop += prop[jk][i]; 
                    } 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;          for(jk=1; jk <=nlstate ; jk++){     
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              if( i <=  iagemax){ 
                      if(posprop>=1.e-5){ 
           for (h=0; h<=nhstepm; h++){                probs[i][jk][j1]= prop[jk][i]/posprop;
             if (h==(int) (calagedate+YEARM*cpt)) {              } else
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
             }            } 
             for(j=1; j<=nlstate+ndeath;j++) {          }/* end jk */ 
               kk1=0.;kk2=0;        }/* end i */ 
               for(i=1; i<=nlstate;i++) {                    } /* end i1 */
                 if (mobilav==1)    } /* end k1 */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    
                 else {    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    /*free_vector(pp,1,nlstate);*/
                 }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
                  }  /* End of prevalence */
               }  
               if (h==(int)(calagedate+12*cpt)){  /************* Waves Concatenation ***************/
                 fprintf(ficresf," %.3f", kk1);  
                          void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
               }  {
             }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           }       Death is a valid wave (if date is known).
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       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.
     }       */
   }  
            int i, mi, m;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
   fclose(ficresf);    int first;
 }    int j, k=0,jk, ju, jl;
 /************** Forecasting ******************/    double sum=0.;
 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){    first=0;
      jmin=1e+5;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    jmax=-1;
   int *popage;    jmean=0.;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    for(i=1; i<=imx; i++){
   double *popeffectif,*popcount;      mi=0;
   double ***p3mat,***tabpop,***tabpopprev;      m=firstpass;
   char filerespop[FILENAMELENGTH];      while(s[m][i] <= nlstate){
         if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          mw[++mi][i]=m;
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        if(m >=lastpass)
   agelim=AGESUP;          break;
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;        else
            m++;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      }/* end while */
        if (s[m][i] > nlstate){
          mi++;     /* Death is another wave */
   strcpy(filerespop,"pop");        /* if(mi==0)  never been interviewed correctly before death */
   strcat(filerespop,fileres);           /* Only death is a correct wave */
   if((ficrespop=fopen(filerespop,"w"))==NULL) {        mw[mi][i]=m;
     printf("Problem with forecast resultfile: %s\n", filerespop);      }
   }  
   printf("Computing forecasting: result on file '%s' \n", filerespop);      wav[i]=mi;
       if(mi==0){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        nbwarn++;
         if(first==0){
   if (mobilav==1) {          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          first=1;
     movingaverage(agedeb, fage, ageminpar, mobaverage);        }
   }        if(first==1){
           fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
   stepsize=(int) (stepm+YEARM-1)/YEARM;        }
   if (stepm<=12) stepsize=1;      } /* end mi==0 */
      } /* End individuals */
   agelim=AGESUP;  
      for(i=1; i<=imx; i++){
   hstepm=1;      for(mi=1; mi<wav[i];mi++){
   hstepm=hstepm/stepm;        if (stepm <=0)
            dh[mi][i]=1;
   if (popforecast==1) {        else{
     if((ficpop=fopen(popfile,"r"))==NULL) {          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       printf("Problem with population file : %s\n",popfile);exit(0);            if (agedc[i] < 2*AGESUP) {
     }              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     popage=ivector(0,AGESUP);              if(j==0) j=1;  /* Survives at least one month after exam */
     popeffectif=vector(0,AGESUP);              else if(j<0){
     popcount=vector(0,AGESUP);                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]);
     i=1;                  j=1; /* Temporary Dangerous patch */
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;                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]);
     imx=i;                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];              }
   }              k=k+1;
               if (j >= jmax){
   for(cptcov=1;cptcov<=i2;cptcov++){                jmax=j;
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){                ijmax=i;
       k=k+1;              }
       fprintf(ficrespop,"\n#******");              if (j <= jmin){
       for(j=1;j<=cptcoveff;j++) {                jmin=j;
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                ijmin=i;
       }              }
       fprintf(ficrespop,"******\n");              sum=sum+j;
       fprintf(ficrespop,"# Age");              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       if (popforecast==1)  fprintf(ficrespop," [Population]");            }
                }
       for (cpt=0; cpt<=0;cpt++) {          else{
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);              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]); */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            k=k+1;
           nhstepm = nhstepm/hstepm;            if (j >= jmax) {
                        jmax=j;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              ijmax=i;
           oldm=oldms;savm=savms;            }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              else if (j <= jmin){
                      jmin=j;
           for (h=0; h<=nhstepm; h++){              ijmin=i;
             if (h==(int) (calagedate+YEARM*cpt)) {            }
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             }            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
             for(j=1; j<=nlstate+ndeath;j++) {            if(j<0){
               kk1=0.;kk2=0;              nberr++;
               for(i=1; i<=nlstate;i++) {                            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]);
                 if (mobilav==1)              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]);
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];            }
                 else {            sum=sum+j;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];          }
                 }          jk= j/stepm;
               }          jl= j -jk*stepm;
               if (h==(int)(calagedate+12*cpt)){          ju= j -(jk+1)*stepm;
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
                   /*fprintf(ficrespop," %.3f", kk1);            if(jl==0){
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/              dh[mi][i]=jk;
               }              bh[mi][i]=0;
             }            }else{ /* We want a negative bias in order to only have interpolation ie
             for(i=1; i<=nlstate;i++){                    * to avoid the price of an extra matrix product in likelihood */
               kk1=0.;              dh[mi][i]=jk+1;
                 for(j=1; j<=nlstate;j++){              bh[mi][i]=ju;
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];            }
                 }          }else{
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];            if(jl <= -ju){
             }              dh[mi][i]=jk;
               bh[mi][i]=jl;       /* bias is positive if real duration
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)                                   * is higher than the multiple of stepm and negative otherwise.
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);                                   */
           }            }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            else{
         }              dh[mi][i]=jk+1;
       }              bh[mi][i]=ju;
              }
   /******/            if(dh[mi][i]==0){
               dh[mi][i]=1; /* At least one step */
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {              bh[mi][i]=ju; /* At least one step */
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);                /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){            }
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          } /* end if mle */
           nhstepm = nhstepm/hstepm;        }
                } /* end wave */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    }
           oldm=oldms;savm=savms;    jmean=sum/k;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
           for (h=0; h<=nhstepm; h++){    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);
             if (h==(int) (calagedate+YEARM*cpt)) {   }
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);  
             }  /*********** Tricode ****************************/
             for(j=1; j<=nlstate+ndeath;j++) {  void tricode(int *Tvar, int **nbcode, int imx)
               kk1=0.;kk2=0;  {
               for(i=1; i<=nlstate;i++) {                  /* Uses cptcovn+2*cptcovprod as the number of covariates */
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
               }  
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
             }    int modmaxcovj=0; /* Modality max of covariates j */
           }    cptcoveff=0; 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);   
         }    for (k=0; k<maxncov; k++) Ndum[k]=0;
       }    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
    }  
   }    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
        for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                                 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
   if (popforecast==1) {                                        modality of the nth covariate of individual i. */
     free_ivector(popage,0,AGESUP);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
     free_vector(popeffectif,0,AGESUP);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     free_vector(popcount,0,AGESUP);        if (ij > modmaxcovj) modmaxcovj=ij; 
   }        /* getting the maximum value of the modality of the covariate
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);           female is 1, then modmaxcovj=1.*/
   fclose(ficrespop);      }
 }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
       for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
 /***********************************************/        if( Ndum[i] != 0 )
 /**************** Main Program *****************/          ncodemax[j]++; 
 /***********************************************/        /* Number of modalities of the j th covariate. In fact
            ncodemax[j]=2 (dichotom. variables only) but it could be more for
 int main(int argc, char *argv[])           historical reasons */
 {      } /* Ndum[-1] number of undefined modalities */
   
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
   double agedeb, agefin,hf;      ij=1; 
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
         for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
   double fret;          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
   double **xi,tmp,delta;            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
                                        k is a modality. If we have model=V1+V1*sex 
   double dum; /* Dummy variable */                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   double ***p3mat;            ij++;
   int *indx;          }
   char line[MAXLINE], linepar[MAXLINE];          if (ij > ncodemax[j]) break; 
   char title[MAXLINE];        }  /* end of loop on */
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];      } /* end of loop on modality */ 
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
      
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    for (k=0; k< maxncov; k++) Ndum[k]=0;
     
   char filerest[FILENAMELENGTH];    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
   char fileregp[FILENAMELENGTH];     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   char popfile[FILENAMELENGTH];     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];     Ndum[ij]++;
   int firstobs=1, lastobs=10;   }
   int sdeb, sfin; /* Status at beginning and end */  
   int c,  h , cpt,l;   ij=1;
   int ju,jl, mi;   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;     if((Ndum[i]!=0) && (i<=ncovcol)){
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;       Tvaraff[ij]=i; /*For printing */
   int mobilav=0,popforecast=0;       ij++;
   int hstepm, nhstepm;     }
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;   }
    ij--;
   double bage, fage, age, agelim, agebase;   cptcoveff=ij; /*Number of simple covariates*/
   double ftolpl=FTOL;  }
   double **prlim;  
   double *severity;  /*********** Health Expectancies ****************/
   double ***param; /* Matrix of parameters */  
   double  *p;  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   double **matcov; /* Matrix of covariance */  
   double ***delti3; /* Scale */  {
   double *delti; /* Scale */    /* Health expectancies, no variances */
   double ***eij, ***vareij;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
   double **varpl; /* Variances of prevalence limits by age */    int nhstepma, nstepma; /* Decreasing with age */
   double *epj, vepp;    double age, agelim, hf;
   double kk1, kk2;    double ***p3mat;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    double eip;
    
     pstamp(ficreseij);
   char version[80]="Imach version 0.8a, May 2002, INED-EUROREVES ";    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   char *alph[]={"a","a","b","c","d","e"}, str[4];    fprintf(ficreseij,"# Age");
     for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++){
   char z[1]="c", occ;        fprintf(ficreseij," e%1d%1d ",i,j);
 #include <sys/time.h>      }
 #include <time.h>      fprintf(ficreseij," e%1d. ",i);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    }
      fprintf(ficreseij,"\n");
   /* long total_usecs;  
   struct timeval start_time, end_time;    
      if(estepm < stepm){
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      printf ("Problem %d lower than %d\n",estepm, stepm);
   getcwd(pathcd, size);    }
     else  hstepm=estepm;   
   printf("\n%s",version);    /* We compute the life expectancy from trapezoids spaced every estepm months
   if(argc <=1){     * This is mainly to measure the difference between two models: for example
     printf("\nEnter the parameter file name: ");     * if stepm=24 months pijx are given only every 2 years and by summing them
     scanf("%s",pathtot);     * we are calculating an estimate of the Life Expectancy assuming a linear 
   }     * progression in between and thus overestimating or underestimating according
   else{     * to the curvature of the survival function. If, for the same date, we 
     strcpy(pathtot,argv[1]);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   }     * to compare the new estimate of Life expectancy with the same linear 
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/     * hypothesis. A more precise result, taking into account a more precise
   /*cygwin_split_path(pathtot,path,optionfile);     * curvature will be obtained if estepm is as small as stepm. */
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/  
   /* cutv(path,optionfile,pathtot,'\\');*/    /* 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. 
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);       nhstepm is the number of hstepm from age to agelim 
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);       nstepm is the number of stepm from age to agelin. 
   chdir(path);       Look at hpijx to understand the reason of that which relies in memory size
   replace(pathc,path);       and note for a fixed period like estepm months */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
 /*-------- arguments in the command line --------*/       survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed only each two years of age and if
   strcpy(fileres,"r");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   strcat(fileres, optionfilefiname);       results. So we changed our mind and took the option of the best precision.
   strcat(fileres,".txt");    /* Other files have txt extension */    */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   /*---------arguments file --------*/  
     agelim=AGESUP;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    /* If stepm=6 months */
     printf("Problem with optionfile %s\n",optionfile);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
     goto end;         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   }      
   /* nhstepm age range expressed in number of stepm */
   strcpy(filereso,"o");    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   strcat(filereso,fileres);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   if((ficparo=fopen(filereso,"w"))==NULL) {    /* if (stepm >= YEARM) hstepm=1;*/
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   
   /* Reads comments: lines beginning with '#' */    for (age=bage; age<=fage; age ++){ 
   while((c=getc(ficpar))=='#' && c!= EOF){      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
     ungetc(c,ficpar);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     fgets(line, MAXLINE, ficpar);      /* if (stepm >= YEARM) hstepm=1;*/
     puts(line);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     fputs(line,ficparo);  
   }      /* If stepm=6 months */
   ungetc(c,ficpar);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);      
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);      
 while((c=getc(ficpar))=='#' && c!= EOF){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      printf("%d|",(int)age);fflush(stdout);
     puts(line);      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     fputs(line,ficparo);      
   }      /* Computing expectancies */
   ungetc(c,ficpar);      for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++)
              for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   covar=matrix(0,NCOVMAX,1,n);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
   cptcovn=0;            
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;            /* 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]);*/
   
   ncovmodel=2+cptcovn;          }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */  
        fprintf(ficreseij,"%3.0f",age );
   /* Read guess parameters */      for(i=1; i<=nlstate;i++){
   /* Reads comments: lines beginning with '#' */        eip=0;
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate;j++){
     ungetc(c,ficpar);          eip +=eij[i][j][(int)age];
     fgets(line, MAXLINE, ficpar);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
     puts(line);        }
     fputs(line,ficparo);        fprintf(ficreseij,"%9.4f", eip );
   }      }
   ungetc(c,ficpar);      fprintf(ficreseij,"\n");
        
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    }
     for(i=1; i <=nlstate; i++)    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for(j=1; j <=nlstate+ndeath-1; j++){    printf("\n");
       fscanf(ficpar,"%1d%1d",&i1,&j1);    fprintf(ficlog,"\n");
       fprintf(ficparo,"%1d%1d",i1,j1);    
       printf("%1d%1d",i,j);  }
       for(k=1; k<=ncovmodel;k++){  
         fscanf(ficpar," %lf",&param[i][j][k]);  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[] )
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);  {
       }    /* Covariances of health expectancies eij and of total life expectancies according
       fscanf(ficpar,"\n");     to initial status i, ei. .
       printf("\n");    */
       fprintf(ficparo,"\n");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
     }    int nhstepma, nstepma; /* Decreasing with age */
      double age, agelim, hf;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    double ***p3matp, ***p3matm, ***varhe;
     double **dnewm,**doldm;
   p=param[1][1];    double *xp, *xm;
      double **gp, **gm;
   /* Reads comments: lines beginning with '#' */    double ***gradg, ***trgradg;
   while((c=getc(ficpar))=='#' && c!= EOF){    int theta;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    double eip, vip;
     puts(line);  
     fputs(line,ficparo);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   }    xp=vector(1,npar);
   ungetc(c,ficpar);    xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    
   for(i=1; i <=nlstate; i++){    pstamp(ficresstdeij);
     for(j=1; j <=nlstate+ndeath-1; j++){    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
       fscanf(ficpar,"%1d%1d",&i1,&j1);    fprintf(ficresstdeij,"# Age");
       printf("%1d%1d",i,j);    for(i=1; i<=nlstate;i++){
       fprintf(ficparo,"%1d%1d",i1,j1);      for(j=1; j<=nlstate;j++)
       for(k=1; k<=ncovmodel;k++){        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
         fscanf(ficpar,"%le",&delti3[i][j][k]);      fprintf(ficresstdeij," e%1d. ",i);
         printf(" %le",delti3[i][j][k]);    }
         fprintf(ficparo," %le",delti3[i][j][k]);    fprintf(ficresstdeij,"\n");
       }  
       fscanf(ficpar,"\n");    pstamp(ficrescveij);
       printf("\n");    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
       fprintf(ficparo,"\n");    fprintf(ficrescveij,"# Age");
     }    for(i=1; i<=nlstate;i++)
   }      for(j=1; j<=nlstate;j++){
   delti=delti3[1][1];        cptj= (j-1)*nlstate+i;
          for(i2=1; i2<=nlstate;i2++)
   /* Reads comments: lines beginning with '#' */          for(j2=1; j2<=nlstate;j2++){
   while((c=getc(ficpar))=='#' && c!= EOF){            cptj2= (j2-1)*nlstate+i2;
     ungetc(c,ficpar);            if(cptj2 <= cptj)
     fgets(line, MAXLINE, ficpar);              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
     puts(line);          }
     fputs(line,ficparo);      }
   }    fprintf(ficrescveij,"\n");
   ungetc(c,ficpar);    
      if(estepm < stepm){
   matcov=matrix(1,npar,1,npar);      printf ("Problem %d lower than %d\n",estepm, stepm);
   for(i=1; i <=npar; i++){    }
     fscanf(ficpar,"%s",&str);    else  hstepm=estepm;   
     printf("%s",str);    /* We compute the life expectancy from trapezoids spaced every estepm months
     fprintf(ficparo,"%s",str);     * This is mainly to measure the difference between two models: for example
     for(j=1; j <=i; j++){     * if stepm=24 months pijx are given only every 2 years and by summing them
       fscanf(ficpar," %le",&matcov[i][j]);     * we are calculating an estimate of the Life Expectancy assuming a linear 
       printf(" %.5le",matcov[i][j]);     * progression in between and thus overestimating or underestimating according
       fprintf(ficparo," %.5le",matcov[i][j]);     * to the curvature of the survival function. If, for the same date, we 
     }     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     fscanf(ficpar,"\n");     * to compare the new estimate of Life expectancy with the same linear 
     printf("\n");     * hypothesis. A more precise result, taking into account a more precise
     fprintf(ficparo,"\n");     * curvature will be obtained if estepm is as small as stepm. */
   }  
   for(i=1; i <=npar; i++)    /* For example we decided to compute the life expectancy with the smallest unit */
     for(j=i+1;j<=npar;j++)    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       matcov[i][j]=matcov[j][i];       nhstepm is the number of hstepm from age to agelim 
           nstepm is the number of stepm from age to agelin. 
   printf("\n");       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
     /*-------- Rewriting paramater file ----------*/       survival function given by stepm (the optimization length). Unfortunately it
      strcpy(rfileres,"r");    /* "Rparameterfile */       means that if the survival funtion is printed only each two years of age and if
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
      strcat(rfileres,".");    /* */       results. So we changed our mind and took the option of the best precision.
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    */
     if((ficres =fopen(rfileres,"w"))==NULL) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       printf("Problem writing new parameter file: %s\n", fileres);goto end;  
     }    /* If stepm=6 months */
     fprintf(ficres,"#%s\n",version);    /* nhstepm age range expressed in number of stepm */
        agelim=AGESUP;
     /*-------- data file ----------*/    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     if((fic=fopen(datafile,"r"))==NULL)    {    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       printf("Problem with datafile: %s\n", datafile);goto end;    /* if (stepm >= YEARM) hstepm=1;*/
     }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     
     n= lastobs;    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     severity = vector(1,maxwav);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     outcome=imatrix(1,maxwav+1,1,n);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     num=ivector(1,n);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     moisnais=vector(1,n);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     annais=vector(1,n);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
     moisdc=vector(1,n);  
     andc=vector(1,n);    for (age=bage; age<=fage; age ++){ 
     agedc=vector(1,n);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
     cod=ivector(1,n);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     weight=vector(1,n);      /* if (stepm >= YEARM) hstepm=1;*/
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     mint=matrix(1,maxwav,1,n);  
     anint=matrix(1,maxwav,1,n);      /* If stepm=6 months */
     s=imatrix(1,maxwav+1,1,n);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     adl=imatrix(1,maxwav+1,1,n);             in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     tab=ivector(1,NCOVMAX);      
     ncodemax=ivector(1,8);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
     i=1;      /* Computing  Variances of health expectancies */
     while (fgets(line, MAXLINE, fic) != NULL)    {      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
       if ((i >= firstobs) && (i <=lastobs)) {         decrease memory allocation */
              for(theta=1; theta <=npar; theta++){
         for (j=maxwav;j>=1;j--){        for(i=1; i<=npar; i++){ 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           strcpy(line,stra);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        }
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         }        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
            
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        for(j=1; j<= nlstate; j++){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
             }
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);          }
         for (j=ncovcol;j>=1;j--){        }
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);       
         }        for(ij=1; ij<= nlstate*nlstate; ij++)
         num[i]=atol(stra);          for(h=0; h<=nhstepm-1; h++){
                    gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){          }
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/      }/* End theta */
       
         i=i+1;      
       }      for(h=0; h<=nhstepm-1; h++)
     }        for(j=1; j<=nlstate*nlstate;j++)
     /* printf("ii=%d", ij);          for(theta=1; theta <=npar; theta++)
        scanf("%d",i);*/            trgradg[h][j][theta]=gradg[h][theta][j];
   imx=i-1; /* Number of individuals */      
   
   /* for (i=1; i<=imx; i++){       for(ij=1;ij<=nlstate*nlstate;ij++)
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;        for(ji=1;ji<=nlstate*nlstate;ji++)
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;          varhe[ij][ji][(int)age] =0.;
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;  
     }*/       printf("%d|",(int)age);fflush(stdout);
    /*  for (i=1; i<=imx; i++){       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
      if (s[4][i]==9)  s[4][i]=-1;       for(h=0;h<=nhstepm-1;h++){
      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]));}*/        for(k=0;k<=nhstepm-1;k++){
            matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
            matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   /* Calculation of the number of parameter from char model*/          for(ij=1;ij<=nlstate*nlstate;ij++)
   Tvar=ivector(1,15);            for(ji=1;ji<=nlstate*nlstate;ji++)
   Tprod=ivector(1,15);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   Tvaraff=ivector(1,15);        }
   Tvard=imatrix(1,15,1,2);      }
   Tage=ivector(1,15);        
          /* Computing expectancies */
   if (strlen(model) >1){      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     j=0, j1=0, k1=1, k2=1;      for(i=1; i<=nlstate;i++)
     j=nbocc(model,'+');        for(j=1; j<=nlstate;j++)
     j1=nbocc(model,'*');          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     cptcovn=j+1;            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     cptcovprod=j1;            
                /* 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]);*/
     strcpy(modelsav,model);  
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          }
       printf("Error. Non available option model=%s ",model);  
       goto end;      fprintf(ficresstdeij,"%3.0f",age );
     }      for(i=1; i<=nlstate;i++){
            eip=0.;
     for(i=(j+1); i>=1;i--){        vip=0.;
       cutv(stra,strb,modelsav,'+');        for(j=1; j<=nlstate;j++){
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          eip += eij[i][j][(int)age];
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
       /*scanf("%d",i);*/            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
       if (strchr(strb,'*')) {          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         cutv(strd,strc,strb,'*');        }
         if (strcmp(strc,"age")==0) {        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
           cptcovprod--;      }
           cutv(strb,stre,strd,'V');      fprintf(ficresstdeij,"\n");
           Tvar[i]=atoi(stre);  
           cptcovage++;      fprintf(ficrescveij,"%3.0f",age );
             Tage[cptcovage]=i;      for(i=1; i<=nlstate;i++)
             /*printf("stre=%s ", stre);*/        for(j=1; j<=nlstate;j++){
         }          cptj= (j-1)*nlstate+i;
         else if (strcmp(strd,"age")==0) {          for(i2=1; i2<=nlstate;i2++)
           cptcovprod--;            for(j2=1; j2<=nlstate;j2++){
           cutv(strb,stre,strc,'V');              cptj2= (j2-1)*nlstate+i2;
           Tvar[i]=atoi(stre);              if(cptj2 <= cptj)
           cptcovage++;                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
           Tage[cptcovage]=i;            }
         }        }
         else {      fprintf(ficrescveij,"\n");
           cutv(strb,stre,strc,'V');     
           Tvar[i]=ncovcol+k1;    }
           cutv(strb,strc,strd,'V');    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
           Tprod[k1]=i;    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
           Tvard[k1][1]=atoi(strc);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
           Tvard[k1][2]=atoi(stre);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
           Tvar[cptcovn+k2]=Tvard[k1][1];    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           for (k=1; k<=lastobs;k++)    printf("\n");
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    fprintf(ficlog,"\n");
           k1++;  
           k2=k2+2;    free_vector(xm,1,npar);
         }    free_vector(xp,1,npar);
       }    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       else {    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
        /*  scanf("%d",i);*/  }
       cutv(strd,strc,strb,'V');  
       Tvar[i]=atoi(strc);  /************ 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[])
       strcpy(modelsav,stra);    {
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    /* Variance of health expectancies */
         scanf("%d",i);*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     }    /* double **newm;*/
 }    double **dnewm,**doldm;
      double **dnewmp,**doldmp;
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    int i, j, nhstepm, hstepm, h, nstepm ;
   printf("cptcovprod=%d ", cptcovprod);    int k, cptcode;
   scanf("%d ",i);*/    double *xp;
     fclose(fic);    double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     /*  if(mle==1){*/    double **gradgp, **trgradgp; /* for var p point j */
     if (weightopt != 1) { /* Maximisation without weights*/    double *gpp, *gmp; /* for var p point j */
       for(i=1;i<=n;i++) weight[i]=1.0;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     }    double ***p3mat;
     /*-calculation of age at interview from date of interview and age at death -*/    double age,agelim, hf;
     agev=matrix(1,maxwav,1,imx);    double ***mobaverage;
     int theta;
     for (i=1; i<=imx; i++) {    char digit[4];
       for(m=2; (m<= maxwav); m++) {    char digitp[25];
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){  
          anint[m][i]=9999;    char fileresprobmorprev[FILENAMELENGTH];
          s[m][i]=-1;  
        }    if(popbased==1){
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;      if(mobilav!=0)
       }        strcpy(digitp,"-populbased-mobilav-");
     }      else strcpy(digitp,"-populbased-nomobil-");
     }
     for (i=1; i<=imx; i++)  {    else 
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);      strcpy(digitp,"-stablbased-");
       for(m=1; (m<= maxwav); m++){  
         if(s[m][i] >0){    if (mobilav!=0) {
           if (s[m][i] >= nlstate+1) {      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
             if(agedc[i]>0)      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
               if(moisdc[i]!=99 && andc[i]!=9999)        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
                 agev[m][i]=agedc[i];        printf(" Error in movingaverage mobilav=%d\n",mobilav);
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/      }
            else {    }
               if (andc[i]!=9999){  
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    strcpy(fileresprobmorprev,"prmorprev"); 
               agev[m][i]=-1;    sprintf(digit,"%-d",ij);
               }    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
             }    strcat(fileresprobmorprev,digit); /* Tvar to be done */
           }    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
           else if(s[m][i] !=9){ /* Should no more exist */    strcat(fileresprobmorprev,fileres);
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
             if(mint[m][i]==99 || anint[m][i]==9999)      printf("Problem with resultfile: %s\n", fileresprobmorprev);
               agev[m][i]=1;      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
             else if(agev[m][i] <agemin){    }
               agemin=agev[m][i];    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/   
             }    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
             else if(agev[m][i] >agemax){    pstamp(ficresprobmorprev);
               agemax=agev[m][i];    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
             }    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
             /*agev[m][i]=anint[m][i]-annais[i];*/      fprintf(ficresprobmorprev," p.%-d SE",j);
             /*   agev[m][i] = age[i]+2*m;*/      for(i=1; i<=nlstate;i++)
           }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           else { /* =9 */    }  
             agev[m][i]=1;    fprintf(ficresprobmorprev,"\n");
             s[m][i]=-1;    fprintf(ficgp,"\n# Routine varevsij");
           }    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
         }    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
         else /*= 0 Unknown */    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           agev[m][i]=1;  /*   } */
       }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
        pstamp(ficresvij);
     }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     for (i=1; i<=imx; i++)  {    if(popbased==1)
       for(m=1; (m<= maxwav); m++){      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);
         if (s[m][i] > (nlstate+ndeath)) {    else
           printf("Error: Wrong value in nlstate or ndeath\n");        fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
           goto end;    fprintf(ficresvij,"# Age");
         }    for(i=1; i<=nlstate;i++)
       }      for(j=1; j<=nlstate;j++)
     }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  
     xp=vector(1,npar);
     free_vector(severity,1,maxwav);    dnewm=matrix(1,nlstate,1,npar);
     free_imatrix(outcome,1,maxwav+1,1,n);    doldm=matrix(1,nlstate,1,nlstate);
     free_vector(moisnais,1,n);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     free_vector(annais,1,n);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     /* free_matrix(mint,1,maxwav,1,n);  
        free_matrix(anint,1,maxwav,1,n);*/    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     free_vector(moisdc,1,n);    gpp=vector(nlstate+1,nlstate+ndeath);
     free_vector(andc,1,n);    gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
        
     wav=ivector(1,imx);    if(estepm < stepm){
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      printf ("Problem %d lower than %d\n",estepm, stepm);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    }
        else  hstepm=estepm;   
     /* Concatenates waves */    /* For example we decided to compute the life expectancy with the smallest unit */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
       Tcode=ivector(1,100);       Look at function hpijx to understand why (it is linked to memory size questions) */
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       ncodemax[1]=1;       survival function given by stepm (the optimization length). Unfortunately it
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);       means that if the survival funtion is printed every two years of age and if
             you sum them up and add 1 year (area under the trapezoids) you won't get the same 
    codtab=imatrix(1,100,1,10);       results. So we changed our mind and took the option of the best precision.
    h=0;    */
    m=pow(2,cptcoveff);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
      agelim = AGESUP;
    for(k=1;k<=cptcoveff; k++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      for(i=1; i <=(m/pow(2,k));i++){      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
        for(j=1; j <= ncodemax[k]; j++){      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
            h++;      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;      gp=matrix(0,nhstepm,1,nlstate);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/      gm=matrix(0,nhstepm,1,nlstate);
          }  
        }  
      }      for(theta=1; theta <=npar; theta++){
    }        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       codtab[1][2]=1;codtab[2][2]=2; */        }
    /* for(i=1; i <=m ;i++){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       for(k=1; k <=cptcovn; k++){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);  
       }        if (popbased==1) {
       printf("\n");          if(mobilav ==0){
       }            for(i=1; i<=nlstate;i++)
       scanf("%d",i);*/              prlim[i][i]=probs[(int)age][i][ij];
              }else{ /* mobilav */ 
    /* Calculates basic frequencies. Computes observed prevalence at single age            for(i=1; i<=nlstate;i++)
        and prints on file fileres'p'. */              prlim[i][i]=mobaverage[(int)age][i][ij];
           }
            }
        
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(j=1; j<= nlstate; j++){
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(h=0; h<=nhstepm; h++){
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          }
              }
     /* For Powell, parameters are in a vector p[] starting at p[1]        /* This for computing probability of death (h=1 means
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */           computed over hstepm matrices product = hstepm*stepm months) 
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */           as a weighted average of prlim.
         */
     if(mle==1){        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
     }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
            }    
     /*--------- results files --------------*/        /* end probability of death */
     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);  
          for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
    jk=1;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");   
    for(i=1,jk=1; i <=nlstate; i++){        if (popbased==1) {
      for(k=1; k <=(nlstate+ndeath); k++){          if(mobilav ==0){
        if (k != i)            for(i=1; i<=nlstate;i++)
          {              prlim[i][i]=probs[(int)age][i][ij];
            printf("%d%d ",i,k);          }else{ /* mobilav */ 
            fprintf(ficres,"%1d%1d ",i,k);            for(i=1; i<=nlstate;i++)
            for(j=1; j <=ncovmodel; j++){              prlim[i][i]=mobaverage[(int)age][i][ij];
              printf("%f ",p[jk]);          }
              fprintf(ficres,"%f ",p[jk]);        }
              jk++;  
            }        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
            printf("\n");          for(h=0; h<=nhstepm; h++){
            fprintf(ficres,"\n");            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
          }              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
      }          }
    }        }
  if(mle==1){        /* This for computing probability of death (h=1 means
     /* Computing hessian and covariance matrix */           computed over hstepm matrices product = hstepm*stepm months) 
     ftolhess=ftol; /* Usually correct */           as a weighted average of prlim.
     hesscov(matcov, p, npar, delti, ftolhess, func);        */
  }        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     printf("# Scales (for hessian or gradient estimation)\n");           gmp[j] += prlim[i][i]*p3mat[i][j][1];
      for(i=1,jk=1; i <=nlstate; i++){        }    
       for(j=1; j <=nlstate+ndeath; j++){        /* end probability of death */
         if (j!=i) {  
           fprintf(ficres,"%1d%1d",i,j);        for(j=1; j<= nlstate; j++) /* vareij */
           printf("%1d%1d",i,j);          for(h=0; h<=nhstepm; h++){
           for(k=1; k<=ncovmodel;k++){            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
             printf(" %.5e",delti[jk]);          }
             fprintf(ficres," %.5e",delti[jk]);  
             jk++;        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           }          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
           printf("\n");        }
           fprintf(ficres,"\n");  
         }      } /* End theta */
       }  
      }      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
      
     k=1;      for(h=0; h<=nhstepm; h++) /* veij */
     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");        for(j=1; j<=nlstate;j++)
     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(theta=1; theta <=npar; theta++)
     for(i=1;i<=npar;i++){            trgradg[h][j][theta]=gradg[h][theta][j];
       /*  if (k>nlstate) k=1;  
       i1=(i-1)/(ncovmodel*nlstate)+1;      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        for(theta=1; theta <=npar; theta++)
       printf("%s%d%d",alph[k],i1,tab[i]);*/          trgradgp[j][theta]=gradgp[theta][j];
       fprintf(ficres,"%3d",i);    
       printf("%3d",i);  
       for(j=1; j<=i;j++){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         fprintf(ficres," %.5e",matcov[i][j]);      for(i=1;i<=nlstate;i++)
         printf(" %.5e",matcov[i][j]);        for(j=1;j<=nlstate;j++)
       }          vareij[i][j][(int)age] =0.;
       fprintf(ficres,"\n");  
       printf("\n");      for(h=0;h<=nhstepm;h++){
       k++;        for(k=0;k<=nhstepm;k++){
     }          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
              matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
     while((c=getc(ficpar))=='#' && c!= EOF){          for(i=1;i<=nlstate;i++)
       ungetc(c,ficpar);            for(j=1;j<=nlstate;j++)
       fgets(line, MAXLINE, ficpar);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
       puts(line);        }
       fputs(line,ficparo);      }
     }    
     ungetc(c,ficpar);      /* pptj */
     estepm=0;      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
     if (estepm==0 || estepm < stepm) estepm=stepm;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
     if (fage <= 2) {        for(i=nlstate+1;i<=nlstate+ndeath;i++)
       bage = ageminpar;          varppt[j][i]=doldmp[j][i];
       fage = agemaxpar;      /* end ppptj */
     }      /*  x centered again */
          hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     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);      if (popbased==1) {
          if(mobilav ==0){
     while((c=getc(ficpar))=='#' && c!= EOF){          for(i=1; i<=nlstate;i++)
     ungetc(c,ficpar);            prlim[i][i]=probs[(int)age][i][ij];
     fgets(line, MAXLINE, ficpar);        }else{ /* mobilav */ 
     puts(line);          for(i=1; i<=nlstate;i++)
     fputs(line,ficparo);            prlim[i][i]=mobaverage[(int)age][i][ij];
   }        }
   ungetc(c,ficpar);      }
                 
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);      /* This for computing probability of death (h=1 means
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);         as a weighted average of prlim.
            */
   while((c=getc(ficpar))=='#' && c!= EOF){      for(j=nlstate+1;j<=nlstate+ndeath;j++){
     ungetc(c,ficpar);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     fgets(line, MAXLINE, ficpar);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     puts(line);      }    
     fputs(line,ficparo);      /* end probability of death */
   }  
   ungetc(c,ficpar);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
        for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
    dateprev1=anprev1+mprev1/12.+jprev1/365.;        for(i=1; i<=nlstate;i++){
    dateprev2=anprev2+mprev2/12.+jprev2/365.;          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
   fscanf(ficpar,"pop_based=%d\n",&popbased);      } 
   fprintf(ficparo,"pop_based=%d\n",popbased);        fprintf(ficresprobmorprev,"\n");
   fprintf(ficres,"pop_based=%d\n",popbased);    
        fprintf(ficresvij,"%.0f ",age );
   while((c=getc(ficpar))=='#' && c!= EOF){      for(i=1; i<=nlstate;i++)
     ungetc(c,ficpar);        for(j=1; j<=nlstate;j++){
     fgets(line, MAXLINE, ficpar);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
     puts(line);        }
     fputs(line,ficparo);      fprintf(ficresvij,"\n");
   }      free_matrix(gp,0,nhstepm,1,nlstate);
   ungetc(c,ficpar);      free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   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);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
 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);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 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);    } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
 while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     ungetc(c,ficpar);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fgets(line, MAXLINE, ficpar);    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
     puts(line);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fputs(line,ficparo);    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); */
   ungetc(c,ficpar);  /*   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); */
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 2 ",subdirf(fileresprobmorprev));
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 3 ",subdirf(fileresprobmorprev));
   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(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 3 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
 /*------------ gnuplot -------------*/  */
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
      fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
 /*------------ free_vector  -------------*/  
  chdir(path);    free_vector(xp,1,npar);
      free_matrix(doldm,1,nlstate,1,nlstate);
  free_ivector(wav,1,imx);    free_matrix(dnewm,1,nlstate,1,npar);
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
  free_ivector(num,1,n);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
  free_vector(agedc,1,n);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
  /*free_matrix(covar,1,NCOVMAX,1,n);*/    fclose(ficresprobmorprev);
  fclose(ficparo);    fflush(ficgp);
  fclose(ficres);    fflush(fichtm); 
   }  /* end varevsij */
 /*--------- index.htm --------*/  
   /************ Variance of prevlim ******************/
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
      /* Variance of prevalence limit */
   /*--------------- Prevalence limit --------------*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
      double **newm;
   strcpy(filerespl,"pl");    double **dnewm,**doldm;
   strcat(filerespl,fileres);    int i, j, nhstepm, hstepm;
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    int k, cptcode;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    double *xp;
   }    double *gp, *gm;
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    double **gradg, **trgradg;
   fprintf(ficrespl,"#Prevalence limit\n");    double age,agelim;
   fprintf(ficrespl,"#Age ");    int theta;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    
   fprintf(ficrespl,"\n");    pstamp(ficresvpl);
      fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
   prlim=matrix(1,nlstate,1,nlstate);    fprintf(ficresvpl,"# Age");
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    for(i=1; i<=nlstate;i++)
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresvpl," %1d-%1d",i,i);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresvpl,"\n");
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    xp=vector(1,npar);
   k=0;    dnewm=matrix(1,nlstate,1,npar);
   agebase=ageminpar;    doldm=matrix(1,nlstate,1,nlstate);
   agelim=agemaxpar;    
   ftolpl=1.e-10;    hstepm=1*YEARM; /* Every year of age */
   i1=cptcoveff;    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
   if (cptcovn < 1){i1=1;}    agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   for(cptcov=1;cptcov<=i1;cptcov++){      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      if (stepm >= YEARM) hstepm=1;
         k=k+1;      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/      gradg=matrix(1,npar,1,nlstate);
         fprintf(ficrespl,"\n#******");      gp=vector(1,nlstate);
         for(j=1;j<=cptcoveff;j++)      gm=vector(1,nlstate);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
         fprintf(ficrespl,"******\n");      for(theta=1; theta <=npar; theta++){
                for(i=1; i<=npar; i++){ /* Computes gradient */
         for (age=agebase; age<=agelim; age++){          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        }
           fprintf(ficrespl,"%.0f",age );        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           for(i=1; i<=nlstate;i++)        for(i=1;i<=nlstate;i++)
           fprintf(ficrespl," %.5f", prlim[i][i]);          gp[i] = prlim[i][i];
           fprintf(ficrespl,"\n");      
         }        for(i=1; i<=npar; i++) /* Computes gradient */
       }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   fclose(ficrespl);        for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   /*------------- h Pij x at various ages ------------*/  
          for(i=1;i<=nlstate;i++)
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      } /* End theta */
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  
   }      trgradg =matrix(1,nlstate,1,npar);
   printf("Computing pij: result on file '%s' \n", filerespij);  
        for(j=1; j<=nlstate;j++)
   stepsize=(int) (stepm+YEARM-1)/YEARM;        for(theta=1; theta <=npar; theta++)
   /*if (stepm<=24) stepsize=2;*/          trgradg[j][theta]=gradg[theta][j];
   
   agelim=AGESUP;      for(i=1;i<=nlstate;i++)
   hstepm=stepsize*YEARM; /* Every year of age */        varpl[i][(int)age] =0.;
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
        matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
   k=0;      for(i=1;i<=nlstate;i++)
   for(cptcov=1;cptcov<=i1;cptcov++){        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;      fprintf(ficresvpl,"%.0f ",age );
         fprintf(ficrespij,"\n#****** ");      for(i=1; i<=nlstate;i++)
         for(j=1;j<=cptcoveff;j++)        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      fprintf(ficresvpl,"\n");
         fprintf(ficrespij,"******\n");      free_vector(gp,1,nlstate);
              free_vector(gm,1,nlstate);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      free_matrix(gradg,1,npar,1,nlstate);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      free_matrix(trgradg,1,nlstate,1,npar);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    } /* End age */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;    free_vector(xp,1,npar);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      free_matrix(doldm,1,nlstate,1,npar);
           fprintf(ficrespij,"# Age");    free_matrix(dnewm,1,nlstate,1,nlstate);
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)  }
               fprintf(ficrespij," %1d-%1d",i,j);  
           fprintf(ficrespij,"\n");  /************ Variance of one-step probabilities  ******************/
            for (h=0; h<=nhstepm; h++){  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );  {
             for(i=1; i<=nlstate;i++)    int i, j=0,  i1, k1, l1, t, tj;
               for(j=1; j<=nlstate+ndeath;j++)    int k2, l2, j1,  z1;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    int k=0,l, cptcode;
             fprintf(ficrespij,"\n");    int first=1, first1;
              }    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double **dnewm,**doldm;
           fprintf(ficrespij,"\n");    double *xp;
         }    double *gp, *gm;
     }    double **gradg, **trgradg;
   }    double **mu;
     double age,agelim, cov[NCOVMAX];
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
   fclose(ficrespij);    char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   /*---------- Forecasting ------------------*/  
   if((stepm == 1) && (strcmp(model,".")==0)){    double ***varpij;
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);  
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    strcpy(fileresprob,"prob"); 
   }    strcat(fileresprob,fileres);
   else{    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     erreur=108;      printf("Problem with resultfile: %s\n", fileresprob);
     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,"Problem with resultfile: %s\n", fileresprob);
   }    }
      strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
   /*---------- Health expectancies and variances ------------*/    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
   strcpy(filerest,"t");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   strcat(filerest,fileres);    }
   if((ficrest=fopen(filerest,"w"))==NULL) {    strcpy(fileresprobcor,"probcor"); 
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    strcat(fileresprobcor,fileres);
   }    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
   strcpy(filerese,"e");    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   strcat(filerese,fileres);    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   if((ficreseij=fopen(filerese,"w"))==NULL) {    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   }    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
  strcpy(fileresv,"v");    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   strcat(fileresv,fileres);    fprintf(ficresprob,"# Age");
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    pstamp(ficresprobcov);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   }    fprintf(ficresprobcov,"# Age");
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    pstamp(ficresprobcor);
   calagedate=-1;    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    fprintf(ficresprobcor,"# Age");
   
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){    for(i=1; i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      for(j=1; j<=(nlstate+ndeath);j++){
       k=k+1;        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
       fprintf(ficrest,"\n#****** ");        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       for(j=1;j<=cptcoveff;j++)        fprintf(ficresprobcor," p%1d-%1d ",i,j);
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      }  
       fprintf(ficrest,"******\n");   /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
       fprintf(ficreseij,"\n#****** ");    fprintf(ficresprobcor,"\n");
       for(j=1;j<=cptcoveff;j++)   */
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    xp=vector(1,npar);
       fprintf(ficreseij,"******\n");    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
       fprintf(ficresvij,"\n#****** ");    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
       for(j=1;j<=cptcoveff;j++)    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    first=1;
       fprintf(ficresvij,"******\n");    fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    fprintf(fichtm,"\n");
       oldm=oldms;savm=savms;  
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);      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\
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    file %s<br>\n",optionfilehtmcov);
       oldm=oldms;savm=savms;    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);  and drawn. It helps understanding how is the covariance between two incidences.\
       They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
    It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);  standard deviations wide on each axis. <br>\
       fprintf(ficrest,"\n");   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
       epj=vector(1,nlstate+1);  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
       for(age=bage; age <=fage ;age++){  
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    cov[1]=1;
         if (popbased==1) {    tj=cptcoveff;
           for(i=1; i<=nlstate;i++)    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
             prlim[i][i]=probs[(int)age][i][k];    j1=0;
         }    for(t=1; t<=tj;t++){
              for(i1=1; i1<=ncodemax[t];i1++){ 
         fprintf(ficrest," %4.0f",age);        j1++;
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){        if  (cptcovn>0) {
           for(i=1, epj[j]=0.;i <=nlstate;i++) {          fprintf(ficresprob, "\n#********** Variable "); 
             epj[j] += prlim[i][i]*eij[i][j][(int)age];          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/          fprintf(ficresprob, "**********\n#\n");
           }          fprintf(ficresprobcov, "\n#********** Variable "); 
           epj[nlstate+1] +=epj[j];          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         }          fprintf(ficresprobcov, "**********\n#\n");
           
         for(i=1, vepp=0.;i <=nlstate;i++)          fprintf(ficgp, "\n#********** Variable "); 
           for(j=1;j <=nlstate;j++)          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             vepp += vareij[i][j][(int)age];          fprintf(ficgp, "**********\n#\n");
         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(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
         }          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         fprintf(ficrest,"\n");          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
       }          
     }          fprintf(ficresprobcor, "\n#********** Variable ");    
   }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 free_matrix(mint,1,maxwav,1,n);          fprintf(ficresprobcor, "**********\n#");    
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);        }
     free_vector(weight,1,n);        
   fclose(ficreseij);        for (age=bage; age<=fage; age ++){ 
   fclose(ficresvij);          cov[2]=age;
   fclose(ficrest);          for (k=1; k<=cptcovn;k++) {
   fclose(ficpar);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   free_vector(epj,1,nlstate+1);          }
            for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   /*------- Variance limit prevalence------*/            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]]];
   strcpy(fileresvpl,"vpl");          
   strcat(fileresvpl,fileres);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);          gp=vector(1,(nlstate)*(nlstate+ndeath));
     exit(0);          gm=vector(1,(nlstate)*(nlstate+ndeath));
   }      
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
   k=0;              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
   for(cptcov=1;cptcov<=i1;cptcov++){            
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            pmij(pmmij,cov,ncovmodel,xp,nlstate);
       k=k+1;            
       fprintf(ficresvpl,"\n#****** ");            k=0;
       for(j=1;j<=cptcoveff;j++)            for(i=1; i<= (nlstate); i++){
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              for(j=1; j<=(nlstate+ndeath);j++){
       fprintf(ficresvpl,"******\n");                k=k+1;
                      gp[k]=pmmij[i][j];
       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);            
     }            for(i=1; i<=npar; i++)
  }              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
   fclose(ficresvpl);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
   /*---------- End : free ----------------*/            for(i=1; i<=(nlstate); i++){
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);              for(j=1; j<=(nlstate+ndeath);j++){
                  k=k+1;
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                gm[k]=pmmij[i][j];
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);              }
              }
         
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          }
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);  
            for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   free_matrix(matcov,1,npar,1,npar);            for(theta=1; theta <=npar; theta++)
   free_vector(delti,1,npar);              trgradg[j][theta]=gradg[theta][j];
   free_matrix(agev,1,maxwav,1,imx);          
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
   if(erreur >0)          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
     printf("End of Imach with error or warning %d\n",erreur);          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
   else   printf("End of Imach\n");          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
    
   /* 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);*/          pmij(pmmij,cov,ncovmodel,x,nlstate);
   /*printf("Total time was %d uSec.\n", total_usecs);*/          
   /*------ End -----------*/          k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
  end:              k=k+1;
 #ifdef windows              mu[k][(int) age]=pmmij[i][j];
   /* chdir(pathcd);*/            }
 #endif          }
  /*system("wgnuplot graph.plt");*/          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
  /*system("../gp37mgw/wgnuplot graph.plt");*/            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
  /*system("cd ../gp37mgw");*/              varpij[i][j][(int)age] = doldm[i][j];
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/  
  strcpy(plotcmd,GNUPLOTPROGRAM);          /*printf("\n%d ",(int)age);
  strcat(plotcmd," ");            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
  strcat(plotcmd,optionfilegnuplot);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
  system(plotcmd);            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
 #ifdef windows  
   while (z[0] != 'q') {          fprintf(ficresprob,"\n%d ",(int)age);
     /* chdir(path); */          fprintf(ficresprobcov,"\n%d ",(int)age);
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");          fprintf(ficresprobcor,"\n%d ",(int)age);
     scanf("%s",z);  
     if (z[0] == 'c') system("./imach");          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
     else if (z[0] == 'e') system(optionfilehtm);            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
     else if (z[0] == 'g') system(plotcmd);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     else if (z[0] == 'q') exit(0);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
   }            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
 #endif          }
 }          i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     if ((lc2 <0) || (lc1 <0) ){
                       printf("Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Continuing by making them positive: WRONG RESULTS.\n", lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
                       fprintf(ficlog,"Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e\n", lc1, lc2, v1, v2, cv12);fflush(ficlog);
                       lc1=fabs(lc1);
                       lc2=fabs(lc2);
                     }
   
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
       } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else        fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l lt 1,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l lt 2,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l lt 2,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 3",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l lt 1,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l lt 1");
         else fprintf(ficgp,"\" t\"\" w l lt 1,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /* Bug valgrind */
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; /* Number of covariates V1+V2*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(k=cptcovn; k>=1;k--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 
                                       */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=2 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1]=atoi(strc); /* m 1 for V1*/
             Tvard[k1][2]=atoi(stre); /* n 4 for V4*/
             Tvar[cptcovn+k2]=Tvard[k1][1]; /* Tvar[(cptcovn=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovn+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovn=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
             k1++;
             k2=k2+2;
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[k]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line,stdout);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8); /* hard coded ? */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,15); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,15); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=pow(2,cptcoveff-k);i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             /**< codtab(h,k)  k
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     1
              */
             codtab[h][k]=j;
             codtab[h][Tvar[k]]=j;
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       fprintf(ficgp,"set datafile missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=pow(2,cptcoveff);
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         //for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           //printf("cptcov=%d cptcod=%d codtab=%d\n",cptcov, cptcod,codtab[cptcod][cptcov]);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           } /* Age */
           /* was end of cptcod */
       } /* cptcov */
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*here or after loop ? */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.41  
changed lines
  Added in v.1.143


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