Diff for /imach/src/imach.c between versions 1.48 and 1.141

version 1.48, 2002/06/10 13:12:49 version 1.141, 2014/01/26 02:42:01
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.141  2014/01/26 02:42:01  brouard
      * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    Revision 1.140  2011/09/02 10:37:54  brouard
   first survey ("cross") where individuals from different ages are    Summary: times.h is ok with mingw32 now.
   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 1.139  2010/06/14 07:50:17  brouard
   second wave of interviews ("longitudinal") which measure each change    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   (if any) in individual health status.  Health expectancies are    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.138  2010/04/30 18:19:40  brouard
   Maximum Likelihood of the parameters involved in the model.  The    *** empty log message ***
   simplest model is the multinomial logistic model where pij is the  
   probability to be observed in state j at the second wave    Revision 1.137  2010/04/29 18:11:38  brouard
   conditional to be observed in state i at the first wave. Therefore    (Module): Checking covariates for more complex models
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    than V1+V2. A lot of change to be done. Unstable.
   '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 1.136  2010/04/26 20:30:53  brouard
   where the markup *Covariates have to be included here again* invites    (Module): merging some libgsl code. Fixing computation
   you to do it.  More covariates you add, slower the    of likelione (using inter/intrapolation if mle = 0) in order to
   convergence.    get same likelihood as if mle=1.
     Some cleaning of code and comments added.
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.135  2009/10/29 15:33:14  brouard
   identical for each individual. Also, if a individual missed an    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.134  2009/10/29 13:18:53  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   hPijx is the probability to be observed in state i at age x+h  
   conditional to the observed state i at age x. The delay 'h' can be    Revision 1.133  2009/07/06 10:21:25  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    just nforces
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.132  2009/07/06 08:22:05  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    Many tings
   and the contribution of each individual to the likelihood is simply  
   hPijx.    Revision 1.131  2009/06/20 16:22:47  brouard
     Some dimensions resccaled
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Revision 1.130  2009/05/26 06:44:34  brouard
      (Module): Max Covariate is now set to 20 instead of 8. A
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    lot of cleaning with variables initialized to 0. Trying to make
            Institut national d'études démographiques, Paris.    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.129  2007/08/31 13:49:27  lievre
   It is copyrighted identically to a GNU software product, ie programme and    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.128  2006/06/30 13:02:05  brouard
   **********************************************************************/    (Module): Clarifications on computing e.j
    
 #include <math.h>    Revision 1.127  2006/04/28 18:11:50  brouard
 #include <stdio.h>    (Module): Yes the sum of survivors was wrong since
 #include <stdlib.h>    imach-114 because nhstepm was no more computed in the age
 #include <unistd.h>    loop. Now we define nhstepma in the age loop.
     (Module): In order to speed up (in case of numerous covariates) we
 #define MAXLINE 256    compute health expectancies (without variances) in a first step
 #define GNUPLOTPROGRAM "gnuplot"    and then all the health expectancies with variances or standard
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    deviation (needs data from the Hessian matrices) which slows the
 #define FILENAMELENGTH 80    computation.
 /*#define DEBUG*/    In the future we should be able to stop the program is only health
 #define windows    expectancies and graph are needed without standard deviations.
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */  
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    Revision 1.126  2006/04/28 17:23:28  brouard
     (Module): Yes the sum of survivors was wrong since
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    imach-114 because nhstepm was no more computed in the age
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    loop. Now we define nhstepma in the age loop.
     Version 0.98h
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.125  2006/04/04 15:20:31  lievre
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Errors in calculation of health expectancies. Age was not initialized.
 #define NCOVMAX 8 /* Maximum number of covariates */    Forecasting file added.
 #define MAXN 20000  
 #define YEARM 12. /* Number of months per year */    Revision 1.124  2006/03/22 17:13:53  lievre
 #define AGESUP 130    Parameters are printed with %lf instead of %f (more numbers after the comma).
 #define AGEBASE 40    The log-likelihood is printed in the log file
 #ifdef windows  
 #define DIRSEPARATOR '\\'    Revision 1.123  2006/03/20 10:52:43  brouard
 #else    * imach.c (Module): <title> changed, corresponds to .htm file
 #define DIRSEPARATOR '/'    name. <head> headers where missing.
 #endif  
     * imach.c (Module): Weights can have a decimal point as for
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    English (a comma might work with a correct LC_NUMERIC environment,
 int erreur; /* Error number */    otherwise the weight is truncated).
 int nvar;    Modification of warning when the covariates values are not 0 or
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    1.
 int npar=NPARMAX;    Version 0.98g
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.122  2006/03/20 09:45:41  brouard
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    (Module): Weights can have a decimal point as for
 int popbased=0;    English (a comma might work with a correct LC_NUMERIC environment,
     otherwise the weight is truncated).
 int *wav; /* Number of waves for this individuual 0 is possible */    Modification of warning when the covariates values are not 0 or
 int maxwav; /* Maxim number of waves */    1.
 int jmin, jmax; /* min, max spacing between 2 waves */    Version 0.98g
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.121  2006/03/16 17:45:01  lievre
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    * imach.c (Module): Comments concerning covariates added
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    * imach.c (Module): refinements in the computation of lli if
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    status=-2 in order to have more reliable computation if stepm is
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    not 1 month. Version 0.98f
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;  
 FILE *fichtm; /* Html File */    Revision 1.120  2006/03/16 15:10:38  lievre
 FILE *ficreseij;    (Module): refinements in the computation of lli if
 char filerese[FILENAMELENGTH];    status=-2 in order to have more reliable computation if stepm is
 FILE  *ficresvij;    not 1 month. Version 0.98f
 char fileresv[FILENAMELENGTH];  
 FILE  *ficresvpl;    Revision 1.119  2006/03/15 17:42:26  brouard
 char fileresvpl[FILENAMELENGTH];    (Module): Bug if status = -2, the loglikelihood was
 char title[MAXLINE];    computed as likelihood omitting the logarithm. Version O.98e
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];  
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    Revision 1.118  2006/03/14 18:20:07  brouard
     (Module): varevsij Comments added explaining the second
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 char filerest[FILENAMELENGTH];    (Module): Function pstamp added
 char fileregp[FILENAMELENGTH];    (Module): Version 0.98d
 char popfile[FILENAMELENGTH];  
     Revision 1.117  2006/03/14 17:16:22  brouard
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 #define NR_END 1    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define FREE_ARG char*    (Module): Function pstamp added
 #define FTOL 1.0e-10    (Module): Version 0.98d
   
 #define NRANSI    Revision 1.116  2006/03/06 10:29:27  brouard
 #define ITMAX 200    (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 #define TOL 2.0e-4  
     Revision 1.115  2006/02/27 12:17:45  brouard
 #define CGOLD 0.3819660    (Module): One freematrix added in mlikeli! 0.98c
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 #define GOLD 1.618034    filename with strsep.
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.113  2006/02/24 14:20:24  brouard
     (Module): Memory leaks checks with valgrind and:
 static double maxarg1,maxarg2;    datafile was not closed, some imatrix were not freed and on matrix
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    allocation too.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.112  2006/01/30 09:55:26  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define rint(a) floor(a+0.5)  
     Revision 1.111  2006/01/25 20:38:18  brouard
 static double sqrarg;    (Module): Lots of cleaning and bugs added (Gompertz)
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    (Module): Comments can be added in data file. Missing date values
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    can be a simple dot '.'.
   
 int imx;    Revision 1.110  2006/01/25 00:51:50  brouard
 int stepm;    (Module): Lots of cleaning and bugs added (Gompertz)
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.109  2006/01/24 19:37:15  brouard
 int estepm;    (Module): Comments (lines starting with a #) are allowed in data.
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
     Revision 1.108  2006/01/19 18:05:42  lievre
 int m,nb;    Gnuplot problem appeared...
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    To be fixed
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.107  2006/01/19 16:20:37  brouard
 double dateintmean=0;    Test existence of gnuplot in imach path
   
 double *weight;    Revision 1.106  2006/01/19 13:24:36  brouard
 int **s; /* Status */    Some cleaning and links added in html output
 double *agedc, **covar, idx;  
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    Revision 1.105  2006/01/05 20:23:19  lievre
     *** empty log message ***
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 /**************** split *************************/    (Module): If the status is missing at the last wave but we know
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    that the person is alive, then we can code his/her status as -2
 {    (instead of missing=-1 in earlier versions) and his/her
    char *s;                             /* pointer */    contributions to the likelihood is 1 - Prob of dying from last
    int  l1, l2;                         /* length counters */    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( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.103  2005/09/30 15:54:49  lievre
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */    (Module): sump fixed, loop imx fixed, and simplifications.
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.102  2004/09/15 17:31:30  brouard
       extern char       *getwd( );    Add the possibility to read data file including tab characters.
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.101  2004/09/15 10:38:38  brouard
 #else    Fix on curr_time
       extern char       *getcwd( );  
     Revision 1.100  2004/07/12 18:29:06  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Add version for Mac OS X. Just define UNIX in Makefile
 #endif  
          return( GLOCK_ERROR_GETCWD );    Revision 1.99  2004/06/05 08:57:40  brouard
       }    *** empty log message ***
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Revision 1.98  2004/05/16 15:05:56  brouard
       s++;                              /* after this, the filename */    New version 0.97 . First attempt to estimate force of mortality
       l2 = strlen( s );                 /* length of filename */    directly from the data i.e. without the need of knowing the health
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    state at each age, but using a Gompertz model: log u =a + b*age .
       strcpy( name, s );                /* save file name */    This is the basic analysis of mortality and should be done before any
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    other analysis, in order to test if the mortality estimated from the
       dirc[l1-l2] = 0;                  /* add zero */    cross-longitudinal survey is different from the mortality estimated
    }    from other sources like vital statistic data.
    l1 = strlen( dirc );                 /* length of directory */  
 #ifdef windows    The same imach parameter file can be used but the option for mle should be -3.
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Agnès, who wrote this part of the code, tried to keep most of the
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    former routines in order to include the new code within the former code.
 #endif  
    s = strrchr( name, '.' );            /* find last / */    The output is very simple: only an estimate of the intercept and of
    s++;    the slope with 95% confident intervals.
    strcpy(ext,s);                       /* save extension */  
    l1= strlen( name);    Current limitations:
    l2= strlen( s)+1;    A) Even if you enter covariates, i.e. with the
    strncpy( finame, name, l1-l2);    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
    finame[l1-l2]= 0;    B) There is no computation of Life Expectancy nor Life Table.
    return( 0 );                         /* we're done */  
 }    Revision 1.97  2004/02/20 13:25:42  lievre
     Version 0.96d. Population forecasting command line is (temporarily)
     suppressed.
 /******************************************/  
     Revision 1.96  2003/07/15 15:38:55  brouard
 void replace(char *s, char*t)    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 {    rewritten within the same printf. Workaround: many printfs.
   int i;  
   int lg=20;    Revision 1.95  2003/07/08 07:54:34  brouard
   i=0;    * imach.c (Repository):
   lg=strlen(t);    (Repository): Using imachwizard code to output a more meaningful covariance
   for(i=0; i<= lg; i++) {    matrix (cov(a12,c31) instead of numbers.
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.94  2003/06/27 13:00:02  brouard
   }    Just cleaning
 }  
     Revision 1.93  2003/06/25 16:33:55  brouard
 int nbocc(char *s, char occ)    (Module): On windows (cygwin) function asctime_r doesn't
 {    exist so I changed back to asctime which exists.
   int i,j=0;    (Module): Version 0.96b
   int lg=20;  
   i=0;    Revision 1.92  2003/06/25 16:30:45  brouard
   lg=strlen(s);    (Module): On windows (cygwin) function asctime_r doesn't
   for(i=0; i<= lg; i++) {    exist so I changed back to asctime which exists.
   if  (s[i] == occ ) j++;  
   }    Revision 1.91  2003/06/25 15:30:29  brouard
   return j;    * imach.c (Repository): Duplicated warning errors corrected.
 }    (Repository): Elapsed time after each iteration is now output. It
     helps to forecast when convergence will be reached. Elapsed time
 void cutv(char *u,char *v, char*t, char occ)    is stamped in powell.  We created a new html file for the graphs
 {    concerning matrix of covariance. It has extension -cov.htm.
   int i,lg,j,p=0;  
   i=0;    Revision 1.90  2003/06/24 12:34:15  brouard
   for(j=0; j<=strlen(t)-1; j++) {    (Module): Some bugs corrected for windows. Also, when
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    mle=-1 a template is output in file "or"mypar.txt with the design
   }    of the covariance matrix to be input.
   
   lg=strlen(t);    Revision 1.89  2003/06/24 12:30:52  brouard
   for(j=0; j<p; j++) {    (Module): Some bugs corrected for windows. Also, when
     (u[j] = t[j]);    mle=-1 a template is output in file "or"mypar.txt with the design
   }    of the covariance matrix to be input.
      u[p]='\0';  
     Revision 1.88  2003/06/23 17:54:56  brouard
    for(j=0; j<= lg; j++) {    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }    Revision 1.87  2003/06/18 12:26:01  brouard
 }    Version 0.96
   
 /********************** nrerror ********************/    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 void nrerror(char error_text[])    routine fileappend.
 {  
   fprintf(stderr,"ERREUR ...\n");    Revision 1.85  2003/06/17 13:12:43  brouard
   fprintf(stderr,"%s\n",error_text);    * imach.c (Repository): Check when date of death was earlier that
   exit(1);    current date of interview. It may happen when the death was just
 }    prior to the death. In this case, dh was negative and likelihood
 /*********************** vector *******************/    was wrong (infinity). We still send an "Error" but patch by
 double *vector(int nl, int nh)    assuming that the date of death was just one stepm after the
 {    interview.
   double *v;    (Repository): Because some people have very long ID (first column)
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    we changed int to long in num[] and we added a new lvector for
   if (!v) nrerror("allocation failure in vector");    memory allocation. But we also truncated to 8 characters (left
   return v-nl+NR_END;    truncation)
 }    (Repository): No more line truncation errors.
   
 /************************ free vector ******************/    Revision 1.84  2003/06/13 21:44:43  brouard
 void free_vector(double*v, int nl, int nh)    * imach.c (Repository): Replace "freqsummary" at a correct
 {    place. It differs from routine "prevalence" which may be called
   free((FREE_ARG)(v+nl-NR_END));    many times. Probs is memory consuming and must be used with
 }    parcimony.
     Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Revision 1.83  2003/06/10 13:39:11  lievre
 {    *** empty log message ***
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Revision 1.82  2003/06/05 15:57:20  brouard
   if (!v) nrerror("allocation failure in ivector");    Add log in  imach.c and  fullversion number is now printed.
   return v-nl+NR_END;  
 }  */
   /*
 /******************free ivector **************************/     Interpolated Markov Chain
 void free_ivector(int *v, long nl, long nh)  
 {    Short summary of the programme:
   free((FREE_ARG)(v+nl-NR_END));    
 }    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /******************* imatrix *******************************/    first survey ("cross") where individuals from different ages are
 int **imatrix(long nrl, long nrh, long ncl, long nch)    interviewed on their health status or degree of disability (in the
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    case of a health survey which is our main interest) -2- at least a
 {    second wave of interviews ("longitudinal") which measure each change
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    (if any) in individual health status.  Health expectancies are
   int **m;    computed from the time spent in each health state according to a
      model. More health states you consider, more time is necessary to reach the
   /* allocate pointers to rows */    Maximum Likelihood of the parameters involved in the model.  The
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    simplest model is the multinomial logistic model where pij is the
   if (!m) nrerror("allocation failure 1 in matrix()");    probability to be observed in state j at the second wave
   m += NR_END;    conditional to be observed in state i at the first wave. Therefore
   m -= nrl;    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
      '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
   /* allocate rows and set pointers to them */    where the markup *Covariates have to be included here again* invites
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    you to do it.  More covariates you add, slower the
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    convergence.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    The advantage of this computer programme, compared to a simple
      multinomial logistic model, is clear when the delay between waves is not
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    identical for each individual. Also, if a individual missed an
      intermediate interview, the information is lost, but taken into
   /* return pointer to array of pointers to rows */    account using an interpolation or extrapolation.  
   return m;  
 }    hPijx is the probability to be observed in state i at age x+h
     conditional to the observed state i at age x. The delay 'h' can be
 /****************** free_imatrix *************************/    split into an exact number (nh*stepm) of unobserved intermediate
 void free_imatrix(m,nrl,nrh,ncl,nch)    states. This elementary transition (by month, quarter,
       int **m;    semester or year) is modelled as a multinomial logistic.  The hPx
       long nch,ncl,nrh,nrl;    matrix is simply the matrix product of nh*stepm elementary matrices
      /* free an int matrix allocated by imatrix() */    and the contribution of each individual to the likelihood is simply
 {    hPijx.
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));    Also this programme outputs the covariance matrix of the parameters but also
 }    of the life expectancies. It also computes the period (stable) prevalence. 
     
 /******************* matrix *******************************/    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 double **matrix(long nrl, long nrh, long ncl, long nch)             Institut national d'études démographiques, Paris.
 {    This software have been partly granted by Euro-REVES, a concerted action
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    from the European Union.
   double **m;    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    can be accessed at http://euroreves.ined.fr/imach .
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m -= nrl;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    **********************************************************************/
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /*
   m[nrl] += NR_END;    main
   m[nrl] -= ncl;    read parameterfile
     read datafile
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    concatwav
   return m;    freqsummary
 }    if (mle >= 1)
       mlikeli
 /*************************free matrix ************************/    print results files
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    if mle==1 
 {       computes hessian
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    read end of parameter file: agemin, agemax, bage, fage, estepm
   free((FREE_ARG)(m+nrl-NR_END));        begin-prev-date,...
 }    open gnuplot file
     open html file
 /******************* ma3x *******************************/    period (stable) prevalence
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)     for age prevalim()
 {    h Pij x
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    variance of p varprob
   double ***m;    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Variance-covariance of DFLE
   if (!m) nrerror("allocation failure 1 in matrix()");    prevalence()
   m += NR_END;     movingaverage()
   m -= nrl;    varevsij() 
     if popbased==1 varevsij(,popbased)
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    total life expectancies
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Variance of period (stable) prevalence
   m[nrl] += NR_END;   end
   m[nrl] -= ncl;  */
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));   
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #include <math.h>
   m[nrl][ncl] += NR_END;  #include <stdio.h>
   m[nrl][ncl] -= nll;  #include <stdlib.h>
   for (j=ncl+1; j<=nch; j++)  #include <string.h>
     m[nrl][j]=m[nrl][j-1]+nlay;  #include <unistd.h>
    
   for (i=nrl+1; i<=nrh; i++) {  #include <limits.h>
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #include <sys/types.h>
     for (j=ncl+1; j<=nch; j++)  #include <sys/stat.h>
       m[i][j]=m[i][j-1]+nlay;  #include <errno.h>
   }  extern int errno;
   return m;  
 }  #ifdef LINUX
   #include <time.h>
 /*************************free ma3x ************************/  #include "timeval.h"
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #else
 {  #include <sys/time.h>
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #endif
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #ifdef GSL
 }  #include <gsl/gsl_errno.h>
   #include <gsl/gsl_multimin.h>
 /***************** f1dim *************************/  #endif
 extern int ncom;  
 extern double *pcom,*xicom;  /* #include <libintl.h> */
 extern double (*nrfunc)(double []);  /* #define _(String) gettext (String) */
    
 double f1dim(double x)  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
 {  
   int j;  #define GNUPLOTPROGRAM "gnuplot"
   double f;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   double *xt;  #define FILENAMELENGTH 132
    
   xt=vector(1,ncom);  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
   return f;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 }  
   #define NINTERVMAX 8
 /*****************brent *************************/  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 {  #define NCOVMAX 20 /* Maximum number of covariates */
   int iter;  #define MAXN 20000
   double a,b,d,etemp;  #define YEARM 12. /* Number of months per year */
   double fu,fv,fw,fx;  #define AGESUP 130
   double ftemp;  #define AGEBASE 40
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   double e=0.0;  #ifdef UNIX
    #define DIRSEPARATOR '/'
   a=(ax < cx ? ax : cx);  #define CHARSEPARATOR "/"
   b=(ax > cx ? ax : cx);  #define ODIRSEPARATOR '\\'
   x=w=v=bx;  #else
   fw=fv=fx=(*f)(x);  #define DIRSEPARATOR '\\'
   for (iter=1;iter<=ITMAX;iter++) {  #define CHARSEPARATOR "\\"
     xm=0.5*(a+b);  #define ODIRSEPARATOR '/'
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  #endif
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  
     printf(".");fflush(stdout);  /* $Id$ */
 #ifdef DEBUG  /* $State$ */
     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);  
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  char version[]="Imach version 0.98n, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Sicentific Research 25293121)";
 #endif  char fullversion[]="$Revision$ $Date$"; 
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  char strstart[80];
       *xmin=x;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       return fx;  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
     }  int nvar=0, nforce=0; /* Number of variables, number of forces */
     ftemp=fu;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
     if (fabs(e) > tol1) {  int npar=NPARMAX;
       r=(x-w)*(fx-fv);  int nlstate=2; /* Number of live states */
       q=(x-v)*(fx-fw);  int ndeath=1; /* Number of dead states */
       p=(x-v)*q-(x-w)*r;  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       q=2.0*(q-r);  int popbased=0;
       if (q > 0.0) p = -p;  
       q=fabs(q);  int *wav; /* Number of waves for this individuual 0 is possible */
       etemp=e;  int maxwav=0; /* Maxim number of waves */
       e=d;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       else {                     to the likelihood and the sum of weights (done by funcone)*/
         d=p/q;  int mle=1, weightopt=0;
         u=x+d;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
         if (u-a < tol2 || b-u < tol2)  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
           d=SIGN(tol1,xm-x);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       }             * wave mi and wave mi+1 is not an exact multiple of stepm. */
     } else {  double jmean=1; /* Mean space between 2 waves */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  double **oldm, **newm, **savm; /* Working pointers to matrices */
     }  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  /*FILE *fic ; */ /* Used in readdata only */
     fu=(*f)(u);  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     if (fu <= fx) {  FILE *ficlog, *ficrespow;
       if (u >= x) a=x; else b=x;  int globpr=0; /* Global variable for printing or not */
       SHFT(v,w,x,u)  double fretone; /* Only one call to likelihood */
         SHFT(fv,fw,fx,fu)  long ipmx=0; /* Number of contributions */
         } else {  double sw; /* Sum of weights */
           if (u < x) a=u; else b=u;  char filerespow[FILENAMELENGTH];
           if (fu <= fw || w == x) {  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
             v=w;  FILE *ficresilk;
             w=u;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
             fv=fw;  FILE *ficresprobmorprev;
             fw=fu;  FILE *fichtm, *fichtmcov; /* Html File */
           } else if (fu <= fv || v == x || v == w) {  FILE *ficreseij;
             v=u;  char filerese[FILENAMELENGTH];
             fv=fu;  FILE *ficresstdeij;
           }  char fileresstde[FILENAMELENGTH];
         }  FILE *ficrescveij;
   }  char filerescve[FILENAMELENGTH];
   nrerror("Too many iterations in brent");  FILE  *ficresvij;
   *xmin=x;  char fileresv[FILENAMELENGTH];
   return fx;  FILE  *ficresvpl;
 }  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 /****************** mnbrak ***********************/  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
             double (*func)(double))  char command[FILENAMELENGTH];
 {  int  outcmd=0;
   double ulim,u,r,q, dum;  
   double fu;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
    
   *fa=(*func)(*ax);  char filelog[FILENAMELENGTH]; /* Log file */
   *fb=(*func)(*bx);  char filerest[FILENAMELENGTH];
   if (*fb > *fa) {  char fileregp[FILENAMELENGTH];
     SHFT(dum,*ax,*bx,dum)  char popfile[FILENAMELENGTH];
       SHFT(dum,*fb,*fa,dum)  
       }  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   while (*fb > *fc) {  struct timezone tzp;
     r=(*bx-*ax)*(*fb-*fc);  extern int gettimeofday();
     q=(*bx-*cx)*(*fb-*fa);  struct tm tmg, tm, tmf, *gmtime(), *localtime();
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  long time_value;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  extern long time();
     ulim=(*bx)+GLIMIT*(*cx-*bx);  char strcurr[80], strfor[80];
     if ((*bx-u)*(u-*cx) > 0.0) {  
       fu=(*func)(u);  char *endptr;
     } else if ((*cx-u)*(u-ulim) > 0.0) {  long lval;
       fu=(*func)(u);  double dval;
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define NR_END 1
           SHFT(*fb,*fc,fu,(*func)(u))  #define FREE_ARG char*
           }  #define FTOL 1.0e-10
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  #define NRANSI 
       fu=(*func)(u);  #define ITMAX 200 
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);  #define TOL 2.0e-4 
       fu=(*func)(u);  
     }  #define CGOLD 0.3819660 
     SHFT(*ax,*bx,*cx,u)  #define ZEPS 1.0e-10 
       SHFT(*fa,*fb,*fc,fu)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       }  
 }  #define GOLD 1.618034 
   #define GLIMIT 100.0 
 /*************** linmin ************************/  #define TINY 1.0e-20 
   
 int ncom;  static double maxarg1,maxarg2;
 double *pcom,*xicom;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 double (*nrfunc)(double []);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
      
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 {  #define rint(a) floor(a+0.5)
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  static double sqrarg;
   double f1dim(double x);  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
               double *fc, double (*func)(double));  int agegomp= AGEGOMP;
   int j;  
   double xx,xmin,bx,ax;  int imx; 
   double fx,fb,fa;  int stepm=1;
    /* Stepm, step in month: minimum step interpolation*/
   ncom=n;  
   pcom=vector(1,n);  int estepm;
   xicom=vector(1,n);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   nrfunc=func;  
   for (j=1;j<=n;j++) {  int m,nb;
     pcom[j]=p[j];  long *num;
     xicom[j]=xi[j];  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   ax=0.0;  double **pmmij, ***probs;
   xx=1.0;  double *ageexmed,*agecens;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  double dateintmean=0;
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  double *weight;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  int **s; /* Status */
 #endif  double *agedc;
   for (j=1;j<=n;j++) {  double  **covar; /**< covar[i,j], value of jth covariate for individual i,
     xi[j] *= xmin;                    * covar=matrix(0,NCOVMAX,1,n); 
     p[j] += xi[j];                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
   }  double  idx; 
   free_vector(xicom,1,n);  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
   free_vector(pcom,1,n);  int **codtab; /**< codtab=imatrix(1,100,1,10); */
 }  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
   double *lsurv, *lpop, *tpop;
 /*************** powell ************************/  
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
             double (*func)(double []))  double ftolhess; /* Tolerance for computing hessian */
 {  
   void linmin(double p[], double xi[], int n, double *fret,  /**************** split *************************/
               double (*func)(double []));  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   int i,ibig,j;  {
   double del,t,*pt,*ptt,*xit;    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   double fp,fptt;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   double *xits;    */ 
   pt=vector(1,n);    char  *ss;                            /* pointer */
   ptt=vector(1,n);    int   l1, l2;                         /* length counters */
   xit=vector(1,n);  
   xits=vector(1,n);    l1 = strlen(path );                   /* length of path */
   *fret=(*func)(p);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   for (j=1;j<=n;j++) pt[j]=p[j];    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   for (*iter=1;;++(*iter)) {    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     fp=(*fret);      strcpy( name, path );               /* we got the fullname name because no directory */
     ibig=0;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     del=0.0;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      /* get current working directory */
     for (i=1;i<=n;i++)      /*    extern  char* getcwd ( char *buf , int len);*/
       printf(" %d %.12f",i, p[i]);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     printf("\n");        return( GLOCK_ERROR_GETCWD );
     for (i=1;i<=n;i++) {      }
       for (j=1;j<=n;j++) xit[j]=xi[j][i];      /* got dirc from getcwd*/
       fptt=(*fret);      printf(" DIRC = %s \n",dirc);
 #ifdef DEBUG    } else {                              /* strip direcotry from path */
       printf("fret=%lf \n",*fret);      ss++;                               /* after this, the filename */
 #endif      l2 = strlen( ss );                  /* length of filename */
       printf("%d",i);fflush(stdout);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       linmin(p,xit,n,fret,func);      strcpy( name, ss );         /* save file name */
       if (fabs(fptt-(*fret)) > del) {      strncpy( dirc, path, l1 - l2 );     /* now the directory */
         del=fabs(fptt-(*fret));      dirc[l1-l2] = 0;                    /* add zero */
         ibig=i;      printf(" DIRC2 = %s \n",dirc);
       }    }
 #ifdef DEBUG    /* We add a separator at the end of dirc if not exists */
       printf("%d %.12e",i,(*fret));    l1 = strlen( dirc );                  /* length of directory */
       for (j=1;j<=n;j++) {    if( dirc[l1-1] != DIRSEPARATOR ){
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      dirc[l1] =  DIRSEPARATOR;
         printf(" x(%d)=%.12e",j,xit[j]);      dirc[l1+1] = 0; 
       }      printf(" DIRC3 = %s \n",dirc);
       for(j=1;j<=n;j++)    }
         printf(" p=%.12e",p[j]);    ss = strrchr( name, '.' );            /* find last / */
       printf("\n");    if (ss >0){
 #endif      ss++;
     }      strcpy(ext,ss);                     /* save extension */
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      l1= strlen( name);
 #ifdef DEBUG      l2= strlen(ss)+1;
       int k[2],l;      strncpy( finame, name, l1-l2);
       k[0]=1;      finame[l1-l2]= 0;
       k[1]=-1;    }
       printf("Max: %.12e",(*func)(p));  
       for (j=1;j<=n;j++)    return( 0 );                          /* we're done */
         printf(" %.12e",p[j]);  }
       printf("\n");  
       for(l=0;l<=1;l++) {  
         for (j=1;j<=n;j++) {  /******************************************/
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  void replace_back_to_slash(char *s, char*t)
         }  {
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    int i;
       }    int lg=0;
 #endif    i=0;
     lg=strlen(t);
     for(i=0; i<= lg; i++) {
       free_vector(xit,1,n);      (s[i] = t[i]);
       free_vector(xits,1,n);      if (t[i]== '\\') s[i]='/';
       free_vector(ptt,1,n);    }
       free_vector(pt,1,n);  }
       return;  
     }  char *trimbb(char *out, char *in)
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
     for (j=1;j<=n;j++) {    char *s;
       ptt[j]=2.0*p[j]-pt[j];    s=out;
       xit[j]=p[j]-pt[j];    while (*in != '\0'){
       pt[j]=p[j];      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
     }        in++;
     fptt=(*func)(ptt);      }
     if (fptt < fp) {      *out++ = *in++;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    }
       if (t < 0.0) {    *out='\0';
         linmin(p,xit,n,fret,func);    return s;
         for (j=1;j<=n;j++) {  }
           xi[j][ibig]=xi[j][n];  
           xi[j][n]=xit[j];  char *cutv(char *blocc, char *alocc, char *in, char occ)
         }  {
 #ifdef DEBUG    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
         for(j=1;j<=n;j++)       gives blocc="abcdef2ghi" and alocc="j".
           printf(" %.12e",xit[j]);       If occ is not found blocc is null and alocc is equal to in. Returns alocc
         printf("\n");    */
 #endif    char *s, *t;
       }    t=in;s=in;
     }    while (*in != '\0'){
   }      while( *in == occ){
 }        *blocc++ = *in++;
         s=in;
 /**** Prevalence limit ****************/      }
       *blocc++ = *in++;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    }
 {    if (s == t) /* occ not found */
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit      *(blocc-(in-s))='\0';
      matrix by transitions matrix until convergence is reached */    else
       *(blocc-(in-s)-1)='\0';
   int i, ii,j,k;    in=s;
   double min, max, maxmin, maxmax,sumnew=0.;    while ( *in != '\0'){
   double **matprod2();      *alocc++ = *in++;
   double **out, cov[NCOVMAX], **pmij();    }
   double **newm;  
   double agefin, delaymax=50 ; /* Max number of years to converge */    *alocc='\0';
     return s;
   for (ii=1;ii<=nlstate+ndeath;ii++)  }
     for (j=1;j<=nlstate+ndeath;j++){  
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  int nbocc(char *s, char occ)
     }  {
     int i,j=0;
    cov[1]=1.;    int lg=20;
      i=0;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    lg=strlen(s);
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    for(i=0; i<= lg; i++) {
     newm=savm;    if  (s[i] == occ ) j++;
     /* Covariates have to be included here again */    }
      cov[2]=agefin;    return j;
    }
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /* void cutv(char *u,char *v, char*t, char occ) */
         /*      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]]);*/  /* { */
       }  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       for (k=1; k<=cptcovprod;k++)  /*      gives u="abcdef2ghi" and v="j" *\/ */
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /*   int i,lg,j,p=0; */
   /*   i=0; */
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  /*   lg=strlen(t); */
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /*   for(j=0; j<=lg-1; j++) { */
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  /*   } */
   
     savm=oldm;  /*   for(j=0; j<p; j++) { */
     oldm=newm;  /*     (u[j] = t[j]); */
     maxmax=0.;  /*   } */
     for(j=1;j<=nlstate;j++){  /*      u[p]='\0'; */
       min=1.;  
       max=0.;  /*    for(j=0; j<= lg; j++) { */
       for(i=1; i<=nlstate; i++) {  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
         sumnew=0;  /*   } */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /* } */
         prlim[i][j]= newm[i][j]/(1-sumnew);  
         max=FMAX(max,prlim[i][j]);  /********************** nrerror ********************/
         min=FMIN(min,prlim[i][j]);  
       }  void nrerror(char error_text[])
       maxmin=max-min;  {
       maxmax=FMAX(maxmax,maxmin);    fprintf(stderr,"ERREUR ...\n");
     }    fprintf(stderr,"%s\n",error_text);
     if(maxmax < ftolpl){    exit(EXIT_FAILURE);
       return prlim;  }
     }  /*********************** vector *******************/
   }  double *vector(int nl, int nh)
 }  {
     double *v;
 /*************** transition probabilities ***************/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     if (!v) nrerror("allocation failure in vector");
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    return v-nl+NR_END;
 {  }
   double s1, s2;  
   /*double t34;*/  /************************ free vector ******************/
   int i,j,j1, nc, ii, jj;  void free_vector(double*v, int nl, int nh)
   {
     for(i=1; i<= nlstate; i++){    free((FREE_ARG)(v+nl-NR_END));
     for(j=1; j<i;j++){  }
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  
         /*s2 += param[i][j][nc]*cov[nc];*/  /************************ivector *******************************/
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  int *ivector(long nl,long nh)
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  {
       }    int *v;
       ps[i][j]=s2;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    if (!v) nrerror("allocation failure in ivector");
     }    return v-nl+NR_END;
     for(j=i+1; j<=nlstate+ndeath;j++){  }
       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];  /******************free ivector **************************/
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  void free_ivector(int *v, long nl, long nh)
       }  {
       ps[i][j]=s2;    free((FREE_ARG)(v+nl-NR_END));
     }  }
   }  
     /*ps[3][2]=1;*/  /************************lvector *******************************/
   long *lvector(long nl,long nh)
   for(i=1; i<= nlstate; i++){  {
      s1=0;    long *v;
     for(j=1; j<i; j++)    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       s1+=exp(ps[i][j]);    if (!v) nrerror("allocation failure in ivector");
     for(j=i+1; j<=nlstate+ndeath; j++)    return v-nl+NR_END;
       s1+=exp(ps[i][j]);  }
     ps[i][i]=1./(s1+1.);  
     for(j=1; j<i; j++)  /******************free lvector **************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  void free_lvector(long *v, long nl, long nh)
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    free((FREE_ARG)(v+nl-NR_END));
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  }
   } /* end i */  
   /******************* imatrix *******************************/
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     for(jj=1; jj<= nlstate+ndeath; jj++){       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       ps[ii][jj]=0;  { 
       ps[ii][ii]=1;    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     }    int **m; 
   }    
     /* allocate pointers to rows */ 
     m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    if (!m) nrerror("allocation failure 1 in matrix()"); 
     for(jj=1; jj<= nlstate+ndeath; jj++){    m += NR_END; 
      printf("%lf ",ps[ii][jj]);    m -= nrl; 
    }    
     printf("\n ");    
     }    /* allocate rows and set pointers to them */ 
     printf("\n ");printf("%lf ",cov[2]);*/    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
 /*    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    m[nrl] += NR_END; 
   goto end;*/    m[nrl] -= ncl; 
     return ps;    
 }    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     
 /**************** Product of 2 matrices ******************/    /* return pointer to array of pointers to rows */ 
     return m; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  } 
 {  
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  /****************** free_imatrix *************************/
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  void free_imatrix(m,nrl,nrh,ncl,nch)
   /* in, b, out are matrice of pointers which should have been initialized        int **m;
      before: only the contents of out is modified. The function returns        long nch,ncl,nrh,nrl; 
      a pointer to pointers identical to out */       /* free an int matrix allocated by imatrix() */ 
   long i, j, k;  { 
   for(i=nrl; i<= nrh; i++)    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     for(k=ncolol; k<=ncoloh; k++)    free((FREE_ARG) (m+nrl-NR_END)); 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  } 
         out[i][k] +=in[i][j]*b[j][k];  
   /******************* matrix *******************************/
   return out;  double **matrix(long nrl, long nrh, long ncl, long nch)
 }  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     double **m;
 /************* Higher Matrix Product ***************/  
     m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    if (!m) nrerror("allocation failure 1 in matrix()");
 {    m += NR_END;
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    m -= nrl;
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
      (typically every 2 years instead of every month which is too big).    m[nrl] += NR_END;
      Model is determined by parameters x and covariates have to be    m[nrl] -= ncl;
      included manually here.  
     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]) 
   int i, j, d, h, k;     */
   double **out, cov[NCOVMAX];  }
   double **newm;  
   /*************************free matrix ************************/
   /* Hstepm could be zero and should return the unit matrix */  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   for (i=1;i<=nlstate+ndeath;i++)  {
     for (j=1;j<=nlstate+ndeath;j++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       oldm[i][j]=(i==j ? 1.0 : 0.0);    free((FREE_ARG)(m+nrl-NR_END));
       po[i][j][0]=(i==j ? 1.0 : 0.0);  }
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /******************* ma3x *******************************/
   for(h=1; h <=nhstepm; h++){  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     for(d=1; d <=hstepm; d++){  {
       newm=savm;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       /* Covariates have to be included here again */    double ***m;
       cov[1]=1.;  
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if (!m) nrerror("allocation failure 1 in matrix()");
       for (k=1; k<=cptcovage;k++)    m += NR_END;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m -= nrl;
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    m[nrl] -= ncl;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  
       savm=oldm;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       oldm=newm;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     }    m[nrl][ncl] += NR_END;
     for(i=1; i<=nlstate+ndeath; i++)    m[nrl][ncl] -= nll;
       for(j=1;j<=nlstate+ndeath;j++) {    for (j=ncl+1; j<=nch; j++) 
         po[i][j][h]=newm[i][j];      m[nrl][j]=m[nrl][j-1]+nlay;
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    
          */    for (i=nrl+1; i<=nrh; i++) {
       }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   } /* end h */      for (j=ncl+1; j<=nch; j++) 
   return po;        m[i][j]=m[i][j-1]+nlay;
 }    }
     return m; 
     /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 /*************** log-likelihood *************/             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
 double func( double *x)    */
 {  }
   int i, ii, j, k, mi, d, kk;  
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  /*************************free ma3x ************************/
   double **out;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   double sw; /* Sum of weights */  {
   double lli; /* Individual log likelihood */    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   long ipmx;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   /*extern weight */    free((FREE_ARG)(m+nrl-NR_END));
   /* We are differentiating ll according to initial status */  }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  
   /*for(i=1;i<imx;i++)  /*************** function subdirf ***********/
     printf(" %d\n",s[4][i]);  char *subdirf(char fileres[])
   */  {
   cov[1]=1.;    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   for(k=1; k<=nlstate; k++) ll[k]=0.;    strcat(tmpout,"/"); /* Add to the right */
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    strcat(tmpout,fileres);
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    return tmpout;
     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);  /*************** function subdirf2 ***********/
       for(d=0; d<dh[mi][i]; d++){  char *subdirf2(char fileres[], char *preop)
         newm=savm;  {
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    
         for (kk=1; kk<=cptcovage;kk++) {    /* Caution optionfilefiname is hidden */
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    strcpy(tmpout,optionfilefiname);
         }    strcat(tmpout,"/");
            strcat(tmpout,preop);
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    strcat(tmpout,fileres);
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    return tmpout;
         savm=oldm;  }
         oldm=newm;  
          /*************** function subdirf3 ***********/
          char *subdirf3(char fileres[], char *preop, char *preop2)
       } /* end mult */  {
          
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    /* Caution optionfilefiname is hidden */
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    strcpy(tmpout,optionfilefiname);
       ipmx +=1;    strcat(tmpout,"/");
       sw += weight[i];    strcat(tmpout,preop);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    strcat(tmpout,preop2);
     } /* end of wave */    strcat(tmpout,fileres);
   } /* end of individual */    return tmpout;
   }
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  /***************** f1dim *************************/
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  extern int ncom; 
   return -l;  extern double *pcom,*xicom;
 }  extern double (*nrfunc)(double []); 
    
   double f1dim(double x) 
 /*********** Maximum Likelihood Estimation ***************/  { 
     int j; 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    double f;
 {    double *xt; 
   int i,j, iter;   
   double **xi,*delti;    xt=vector(1,ncom); 
   double fret;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   xi=matrix(1,npar,1,npar);    f=(*nrfunc)(xt); 
   for (i=1;i<=npar;i++)    free_vector(xt,1,ncom); 
     for (j=1;j<=npar;j++)    return f; 
       xi[i][j]=(i==j ? 1.0 : 0.0);  } 
   printf("Powell\n");  
   powell(p,xi,npar,ftol,&iter,&fret,func);  /*****************brent *************************/
   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  { 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    int iter; 
     double a,b,d,etemp;
 }    double fu,fv,fw,fx;
     double ftemp;
 /**** Computes Hessian and covariance matrix ***/    double p,q,r,tol1,tol2,u,v,w,x,xm; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    double e=0.0; 
 {   
   double  **a,**y,*x,pd;    a=(ax < cx ? ax : cx); 
   double **hess;    b=(ax > cx ? ax : cx); 
   int i, j,jk;    x=w=v=bx; 
   int *indx;    fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
   double hessii(double p[], double delta, int theta, double delti[]);      xm=0.5*(a+b); 
   double hessij(double p[], double delti[], int i, int j);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   void ludcmp(double **a, int npar, int *indx, double *d) ;      printf(".");fflush(stdout);
       fprintf(ficlog,".");fflush(ficlog);
   hess=matrix(1,npar,1,npar);  #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);
   printf("\nCalculation of the hessian matrix. Wait...\n");      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   for (i=1;i<=npar;i++){      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     printf("%d",i);fflush(stdout);  #endif
     hess[i][i]=hessii(p,ftolhess,i,delti);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     /*printf(" %f ",p[i]);*/        *xmin=x; 
     /*printf(" %lf ",hess[i][i]);*/        return fx; 
   }      } 
        ftemp=fu;
   for (i=1;i<=npar;i++) {      if (fabs(e) > tol1) { 
     for (j=1;j<=npar;j++)  {        r=(x-w)*(fx-fv); 
       if (j>i) {        q=(x-v)*(fx-fw); 
         printf(".%d%d",i,j);fflush(stdout);        p=(x-v)*q-(x-w)*r; 
         hess[i][j]=hessij(p,delti,i,j);        q=2.0*(q-r); 
         hess[j][i]=hess[i][j];            if (q > 0.0) p = -p; 
         /*printf(" %lf ",hess[i][j]);*/        q=fabs(q); 
       }        etemp=e; 
     }        e=d; 
   }        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   printf("\n");          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         else { 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");          d=p/q; 
            u=x+d; 
   a=matrix(1,npar,1,npar);          if (u-a < tol2 || b-u < tol2) 
   y=matrix(1,npar,1,npar);            d=SIGN(tol1,xm-x); 
   x=vector(1,npar);        } 
   indx=ivector(1,npar);      } else { 
   for (i=1;i<=npar;i++)        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      } 
   ludcmp(a,npar,indx,&pd);      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 { 
       matcov[i][j]=x[i];            if (u < x) a=u; else b=u; 
     }            if (fu <= fw || w == x) { 
   }              v=w; 
               w=u; 
   printf("\n#Hessian matrix#\n");              fv=fw; 
   for (i=1;i<=npar;i++) {              fw=fu; 
     for (j=1;j<=npar;j++) {            } else if (fu <= fv || v == x || v == w) { 
       printf("%.3e ",hess[i][j]);              v=u; 
     }              fv=fu; 
     printf("\n");            } 
   }          } 
     } 
   /* Recompute Inverse */    nrerror("Too many iterations in brent"); 
   for (i=1;i<=npar;i++)    *xmin=x; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    return fx; 
   ludcmp(a,npar,indx,&pd);  } 
   
   /*  printf("\n#Hessian matrix recomputed#\n");  /****************** mnbrak ***********************/
   
   for (j=1;j<=npar;j++) {  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
     for (i=1;i<=npar;i++) x[i]=0;              double (*func)(double)) 
     x[j]=1;  { 
     lubksb(a,npar,indx,x);    double ulim,u,r,q, dum;
     for (i=1;i<=npar;i++){    double fu; 
       y[i][j]=x[i];   
       printf("%.3e ",y[i][j]);    *fa=(*func)(*ax); 
     }    *fb=(*func)(*bx); 
     printf("\n");    if (*fb > *fa) { 
   }      SHFT(dum,*ax,*bx,dum) 
   */        SHFT(dum,*fb,*fa,dum) 
         } 
   free_matrix(a,1,npar,1,npar);    *cx=(*bx)+GOLD*(*bx-*ax); 
   free_matrix(y,1,npar,1,npar);    *fc=(*func)(*cx); 
   free_vector(x,1,npar);    while (*fb > *fc) { 
   free_ivector(indx,1,npar);      r=(*bx-*ax)*(*fb-*fc); 
   free_matrix(hess,1,npar,1,npar);      q=(*bx-*cx)*(*fb-*fa); 
       u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
         (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
 }      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if ((*bx-u)*(u-*cx) > 0.0) { 
 /*************** hessian matrix ****************/        fu=(*func)(u); 
 double hessii( double x[], double delta, int theta, double delti[])      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 {        fu=(*func)(u); 
   int i;        if (fu < *fc) { 
   int l=1, lmax=20;          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   double k1,k2;            SHFT(*fb,*fc,fu,(*func)(u)) 
   double p2[NPARMAX+1];            } 
   double res;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        u=ulim; 
   double fx;        fu=(*func)(u); 
   int k=0,kmax=10;      } else { 
   double l1;        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
   fx=func(x);      } 
   for (i=1;i<=npar;i++) p2[i]=x[i];      SHFT(*ax,*bx,*cx,u) 
   for(l=0 ; l <=lmax; l++){        SHFT(*fa,*fb,*fc,fu) 
     l1=pow(10,l);        } 
     delts=delt;  } 
     for(k=1 ; k <kmax; k=k+1){  
       delt = delta*(l1*k);  /*************** linmin ************************/
       p2[theta]=x[theta] +delt;  
       k1=func(p2)-fx;  int ncom; 
       p2[theta]=x[theta]-delt;  double *pcom,*xicom;
       k2=func(p2)-fx;  double (*nrfunc)(double []); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */   
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
        { 
 #ifdef DEBUG    double brent(double ax, double bx, double cx, 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);                 double (*f)(double), double tol, double *xmin); 
 #endif    double f1dim(double x); 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){                double *fc, double (*func)(double)); 
         k=kmax;    int j; 
       }    double xx,xmin,bx,ax; 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    double fx,fb,fa;
         k=kmax; l=lmax*10.;   
       }    ncom=n; 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    pcom=vector(1,n); 
         delts=delt;    xicom=vector(1,n); 
       }    nrfunc=func; 
     }    for (j=1;j<=n;j++) { 
   }      pcom[j]=p[j]; 
   delti[theta]=delts;      xicom[j]=xi[j]; 
   return res;    } 
      ax=0.0; 
 }    xx=1.0; 
     mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
 double hessij( double x[], double delti[], int thetai,int thetaj)    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
 {  #ifdef DEBUG
   int i;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   int l=1, l1, lmax=20;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   double k1,k2,k3,k4,res,fx;  #endif
   double p2[NPARMAX+1];    for (j=1;j<=n;j++) { 
   int k;      xi[j] *= xmin; 
       p[j] += xi[j]; 
   fx=func(x);    } 
   for (k=1; k<=2; k++) {    free_vector(xicom,1,n); 
     for (i=1;i<=npar;i++) p2[i]=x[i];    free_vector(pcom,1,n); 
     p2[thetai]=x[thetai]+delti[thetai]/k;  } 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  
     k1=func(p2)-fx;  char *asc_diff_time(long time_sec, char ascdiff[])
    {
     p2[thetai]=x[thetai]+delti[thetai]/k;    long sec_left, days, hours, minutes;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    days = (time_sec) / (60*60*24);
     k2=func(p2)-fx;    sec_left = (time_sec) % (60*60*24);
      hours = (sec_left) / (60*60) ;
     p2[thetai]=x[thetai]-delti[thetai]/k;    sec_left = (sec_left) %(60*60);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    minutes = (sec_left) /60;
     k3=func(p2)-fx;    sec_left = (sec_left) % (60);
      sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     p2[thetai]=x[thetai]-delti[thetai]/k;    return ascdiff;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  }
     k4=func(p2)-fx;  
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  /*************** powell ************************/
 #ifdef DEBUG  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);              double (*func)(double [])) 
 #endif  { 
   }    void linmin(double p[], double xi[], int n, double *fret, 
   return res;                double (*func)(double [])); 
 }    int i,ibig,j; 
     double del,t,*pt,*ptt,*xit;
 /************** Inverse of matrix **************/    double fp,fptt;
 void ludcmp(double **a, int n, int *indx, double *d)    double *xits;
 {    int niterf, itmp;
   int i,imax,j,k;  
   double big,dum,sum,temp;    pt=vector(1,n); 
   double *vv;    ptt=vector(1,n); 
      xit=vector(1,n); 
   vv=vector(1,n);    xits=vector(1,n); 
   *d=1.0;    *fret=(*func)(p); 
   for (i=1;i<=n;i++) {    for (j=1;j<=n;j++) pt[j]=p[j]; 
     big=0.0;    for (*iter=1;;++(*iter)) { 
     for (j=1;j<=n;j++)      fp=(*fret); 
       if ((temp=fabs(a[i][j])) > big) big=temp;      ibig=0; 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");      del=0.0; 
     vv[i]=1.0/big;      last_time=curr_time;
   }      (void) gettimeofday(&curr_time,&tzp);
   for (j=1;j<=n;j++) {      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
     for (i=1;i<j;i++) {      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);
       sum=a[i][j];  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];     for (i=1;i<=n;i++) {
       a[i][j]=sum;        printf(" %d %.12f",i, p[i]);
     }        fprintf(ficlog," %d %.12lf",i, p[i]);
     big=0.0;        fprintf(ficrespow," %.12lf", p[i]);
     for (i=j;i<=n;i++) {      }
       sum=a[i][j];      printf("\n");
       for (k=1;k<j;k++)      fprintf(ficlog,"\n");
         sum -= a[i][k]*a[k][j];      fprintf(ficrespow,"\n");fflush(ficrespow);
       a[i][j]=sum;      if(*iter <=3){
       if ( (dum=vv[i]*fabs(sum)) >= big) {        tm = *localtime(&curr_time.tv_sec);
         big=dum;        strcpy(strcurr,asctime(&tm));
         imax=i;  /*       asctime_r(&tm,strcurr); */
       }        forecast_time=curr_time; 
     }        itmp = strlen(strcurr);
     if (j != imax) {        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       for (k=1;k<=n;k++) {          strcurr[itmp-1]='\0';
         dum=a[imax][k];        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         a[imax][k]=a[j][k];        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         a[j][k]=dum;        for(niterf=10;niterf<=30;niterf+=10){
       }          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
       *d = -(*d);          tmf = *localtime(&forecast_time.tv_sec);
       vv[imax]=vv[j];  /*      asctime_r(&tmf,strfor); */
     }          strcpy(strfor,asctime(&tmf));
     indx[j]=imax;          itmp = strlen(strfor);
     if (a[j][j] == 0.0) a[j][j]=TINY;          if(strfor[itmp-1]=='\n')
     if (j != n) {          strfor[itmp-1]='\0';
       dum=1.0/(a[j][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);
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          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);
     }        }
   }      }
   free_vector(vv,1,n);  /* Doesn't work */      for (i=1;i<=n;i++) { 
 ;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
 }        fptt=(*fret); 
   #ifdef DEBUG
 void lubksb(double **a, int n, int *indx, double b[])        printf("fret=%lf \n",*fret);
 {        fprintf(ficlog,"fret=%lf \n",*fret);
   int i,ii=0,ip,j;  #endif
   double sum;        printf("%d",i);fflush(stdout);
          fprintf(ficlog,"%d",i);fflush(ficlog);
   for (i=1;i<=n;i++) {        linmin(p,xit,n,fret,func); 
     ip=indx[i];        if (fabs(fptt-(*fret)) > del) { 
     sum=b[ip];          del=fabs(fptt-(*fret)); 
     b[ip]=b[i];          ibig=i; 
     if (ii)        } 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  #ifdef DEBUG
     else if (sum) ii=i;        printf("%d %.12e",i,(*fret));
     b[i]=sum;        fprintf(ficlog,"%d %.12e",i,(*fret));
   }        for (j=1;j<=n;j++) {
   for (i=n;i>=1;i--) {          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     sum=b[i];          printf(" x(%d)=%.12e",j,xit[j]);
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     b[i]=sum/a[i][i];        }
   }        for(j=1;j<=n;j++) {
 }          printf(" p=%.12e",p[j]);
           fprintf(ficlog," p=%.12e",p[j]);
 /************ Frequencies ********************/        }
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)        printf("\n");
 {  /* Some frequencies */        fprintf(ficlog,"\n");
    #endif
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;      } 
   double ***freq; /* Frequencies */      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   double *pp;  #ifdef DEBUG
   double pos, k2, dateintsum=0,k2cpt=0;        int k[2],l;
   FILE *ficresp;        k[0]=1;
   char fileresp[FILENAMELENGTH];        k[1]=-1;
          printf("Max: %.12e",(*func)(p));
   pp=vector(1,nlstate);        fprintf(ficlog,"Max: %.12e",(*func)(p));
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        for (j=1;j<=n;j++) {
   strcpy(fileresp,"p");          printf(" %.12e",p[j]);
   strcat(fileresp,fileres);          fprintf(ficlog," %.12e",p[j]);
   if((ficresp=fopen(fileresp,"w"))==NULL) {        }
     printf("Problem with prevalence resultfile: %s\n", fileresp);        printf("\n");
     exit(0);        fprintf(ficlog,"\n");
   }        for(l=0;l<=1;l++) {
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          for (j=1;j<=n;j++) {
   j1=0;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
              printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   j=cptcoveff;            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 (cptcovn<1) {j=1;ncodemax[1]=1;}          }
            printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   for(k1=1; k1<=j;k1++){          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     for(i1=1; i1<=ncodemax[k1];i1++){        }
       j1++;  #endif
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);  
         scanf("%d", i);*/  
       for (i=-1; i<=nlstate+ndeath; i++)          free_vector(xit,1,n); 
         for (jk=-1; jk<=nlstate+ndeath; jk++)          free_vector(xits,1,n); 
           for(m=agemin; m <= agemax+3; m++)        free_vector(ptt,1,n); 
             freq[i][jk][m]=0;        free_vector(pt,1,n); 
              return; 
       dateintsum=0;      } 
       k2cpt=0;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       for (i=1; i<=imx; i++) {      for (j=1;j<=n;j++) { 
         bool=1;        ptt[j]=2.0*p[j]-pt[j]; 
         if  (cptcovn>0) {        xit[j]=p[j]-pt[j]; 
           for (z1=1; z1<=cptcoveff; z1++)        pt[j]=p[j]; 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      } 
               bool=0;      fptt=(*func)(ptt); 
         }      if (fptt < fp) { 
         if (bool==1) {        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
           for(m=firstpass; m<=lastpass; m++){        if (t < 0.0) { 
             k2=anint[m][i]+(mint[m][i]/12.);          linmin(p,xit,n,fret,func); 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          for (j=1;j<=n;j++) { 
               if(agev[m][i]==0) agev[m][i]=agemax+1;            xi[j][ibig]=xi[j][n]; 
               if(agev[m][i]==1) agev[m][i]=agemax+2;            xi[j][n]=xit[j]; 
               if (m<lastpass) {          }
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  #ifdef DEBUG
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
               }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
                        for(j=1;j<=n;j++){
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {            printf(" %.12e",xit[j]);
                 dateintsum=dateintsum+k2;            fprintf(ficlog," %.12e",xit[j]);
                 k2cpt++;          }
               }          printf("\n");
             }          fprintf(ficlog,"\n");
           }  #endif
         }        }
       }      } 
            } 
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  } 
   
       if  (cptcovn>0) {  /**** Prevalence limit (stable or period prevalence)  ****************/
         fprintf(ficresp, "\n#********** Variable ");  
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
         fprintf(ficresp, "**********\n#");  {
       }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       for(i=1; i<=nlstate;i++)       matrix by transitions matrix until convergence is reached */
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  
       fprintf(ficresp, "\n");    int i, ii,j,k;
          double min, max, maxmin, maxmax,sumnew=0.;
       for(i=(int)agemin; i <= (int)agemax+3; i++){    double **matprod2();
         if(i==(int)agemax+3)    double **out, cov[NCOVMAX+1], **pmij();
           printf("Total");    double **newm;
         else    double agefin, delaymax=50 ; /* Max number of years to converge */
           printf("Age %d", i);  
         for(jk=1; jk <=nlstate ; jk++){    for (ii=1;ii<=nlstate+ndeath;ii++)
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for (j=1;j<=nlstate+ndeath;j++){
             pp[jk] += freq[jk][m][i];        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }      }
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pos=0; m <=0 ; m++)     cov[1]=1.;
             pos += freq[jk][m][i];   
           if(pp[jk]>=1.e-10)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           else      newm=savm;
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);      /* Covariates have to be included here again */
         }      cov[2]=agefin;
       
         for(jk=1; jk <=nlstate ; jk++){      for (k=1; k<=cptcovn;k++) {
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
             pp[jk] += freq[jk][m][i];        /*        printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
         }      }
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         for(jk=1,pos=0; jk <=nlstate ; jk++)      for (k=1; k<=cptcovprod;k++)
           pos += pp[jk];        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         for(jk=1; jk <=nlstate ; jk++){      
           if(pos>=1.e-5)      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
           else      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
           if( i <= (int) agemax){      
             if(pos>=1.e-5){      savm=oldm;
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      oldm=newm;
               probs[i][jk][j1]= pp[jk]/pos;      maxmax=0.;
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/      for(j=1;j<=nlstate;j++){
             }        min=1.;
             else        max=0.;
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        for(i=1; i<=nlstate; i++) {
           }          sumnew=0;
         }          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
                  prlim[i][j]= newm[i][j]/(1-sumnew);
         for(jk=-1; jk <=nlstate+ndeath; jk++)          max=FMAX(max,prlim[i][j]);
           for(m=-1; m <=nlstate+ndeath; m++)          min=FMIN(min,prlim[i][j]);
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);        }
         if(i <= (int) agemax)        maxmin=max-min;
           fprintf(ficresp,"\n");        maxmax=FMAX(maxmax,maxmin);
         printf("\n");      }
       }      if(maxmax < ftolpl){
     }        return prlim;
   }      }
   dateintmean=dateintsum/k2cpt;    }
    }
   fclose(ficresp);  
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  /*************** transition probabilities ***************/ 
   free_vector(pp,1,nlstate);  
    double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   /* End of Freq */  {
 }    /* According to parameters values stored in x and the covariate's values stored in cov,
        computes the probability to be observed in state j being in state i by appying the
 /************ Prevalence ********************/       model to the ncovmodel covariates (including constant and age).
 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)       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
 {  /* Some frequencies */       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
         ncth covariate in the global vector x is given by the formula:
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   double ***freq; /* Frequencies */       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
   double *pp;       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
   double pos, k2;       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
        Outputs ps[i][j] the probability to be observed in j being in j according to
   pp=vector(1,nlstate);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    */
      double s1, lnpijopii;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    /*double t34;*/
   j1=0;    int i,j,j1, nc, ii, jj;
    
   j=cptcoveff;      for(i=1; i<= nlstate; i++){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for(j=1; j<i;j++){
            for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   for(k1=1; k1<=j;k1++){            /*lnpijopii += param[i][j][nc]*cov[nc];*/
     for(i1=1; i1<=ncodemax[k1];i1++){            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
       j1++;  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
                }
       for (i=-1; i<=nlstate+ndeath; i++)            ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         for (jk=-1; jk<=nlstate+ndeath; jk++)    /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
           for(m=agemin; m <= agemax+3; m++)        }
             freq[i][jk][m]=0;        for(j=i+1; j<=nlstate+ndeath;j++){
                for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
       for (i=1; i<=imx; i++) {            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
         bool=1;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
         if  (cptcovn>0) {  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
           for (z1=1; z1<=cptcoveff; z1++)          }
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
               bool=0;        }
         }      }
         if (bool==1) {      
           for(m=firstpass; m<=lastpass; m++){      for(i=1; i<= nlstate; i++){
             k2=anint[m][i]+(mint[m][i]/12.);        s1=0;
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        for(j=1; j<i; j++){
               if(agev[m][i]==0) agev[m][i]=agemax+1;          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
               if(agev[m][i]==1) agev[m][i]=agemax+2;          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
               if (m<lastpass) {        }
                 if (calagedate>0)        for(j=i+1; j<=nlstate+ndeath; j++){
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
                 else          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        }
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];        /* 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++)
       for(i=(int)agemin; i <= (int)agemax+3; i++){          ps[i][j]= exp(ps[i][j])*ps[i][i];
         for(jk=1; jk <=nlstate ; jk++){        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      } /* end i */
             pp[jk] += freq[jk][m][i];      
         }      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         for(jk=1; jk <=nlstate ; jk++){        for(jj=1; jj<= nlstate+ndeath; jj++){
           for(m=-1, pos=0; m <=0 ; m++)          ps[ii][jj]=0;
             pos += freq[jk][m][i];          ps[ii][ii]=1;
         }        }
              }
         for(jk=1; jk <=nlstate ; jk++){      
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  
             pp[jk] += freq[jk][m][i];  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
         }  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
          /*         printf("ddd %lf ",ps[ii][jj]); */
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];  /*       } */
          /*       printf("\n "); */
         for(jk=1; jk <=nlstate ; jk++){      /*        } */
           if( i <= (int) agemax){  /*        printf("\n ");printf("%lf ",cov[2]); */
             if(pos>=1.e-5){         /*
               probs[i][jk][j1]= pp[jk]/pos;        for(i=1; i<= npar; i++) printf("%f ",x[i]);
             }        goto end;*/
           }      return ps;
         }  }
          
       }  /**************** Product of 2 matrices ******************/
     }  
   }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   {
      /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   free_vector(pp,1,nlstate);    /* in, b, out are matrice of pointers which should have been initialized 
         before: only the contents of out is modified. The function returns
 }  /* End of Freq */       a pointer to pointers identical to out */
     long i, j, k;
 /************* Waves Concatenation ***************/    for(i=nrl; i<= nrh; i++)
       for(k=ncolol; k<=ncoloh; k++)
 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(j=ncl,out[i][k]=0.; j<=nch; j++)
 {          out[i][k] +=in[i][j]*b[j][k];
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.  
      Death is a valid wave (if date is known).    return out;
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i  }
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]  
      and mw[mi+1][i]. dh depends on stepm.  
      */  /************* Higher Matrix Product ***************/
   
   int i, mi, m;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  {
      double sum=0., jmean=0.;*/    /* Computes the transition matrix starting at age 'age' over 
        'nhstepm*hstepm*stepm' months (i.e. until
   int j, k=0,jk, ju, jl;       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   double sum=0.;       nhstepm*hstepm matrices. 
   jmin=1e+5;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   jmax=-1;       (typically every 2 years instead of every month which is too big 
   jmean=0.;       for the memory).
   for(i=1; i<=imx; i++){       Model is determined by parameters x and covariates have to be 
     mi=0;       included manually here. 
     m=firstpass;  
     while(s[m][i] <= nlstate){       */
       if(s[m][i]>=1)  
         mw[++mi][i]=m;    int i, j, d, h, k;
       if(m >=lastpass)    double **out, cov[NCOVMAX+1];
         break;    double **newm;
       else  
         m++;    /* Hstepm could be zero and should return the unit matrix */
     }/* end while */    for (i=1;i<=nlstate+ndeath;i++)
     if (s[m][i] > nlstate){      for (j=1;j<=nlstate+ndeath;j++){
       mi++;     /* Death is another wave */        oldm[i][j]=(i==j ? 1.0 : 0.0);
       /* if(mi==0)  never been interviewed correctly before death */        po[i][j][0]=(i==j ? 1.0 : 0.0);
          /* Only death is a correct wave */      }
       mw[mi][i]=m;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     }    for(h=1; h <=nhstepm; h++){
       for(d=1; d <=hstepm; d++){
     wav[i]=mi;        newm=savm;
     if(mi==0)        /* Covariates have to be included here again */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        cov[1]=1.;
   }        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         for (k=1; k<=cptcovn;k++) 
   for(i=1; i<=imx; i++){          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
     for(mi=1; mi<wav[i];mi++){        for (k=1; k<=cptcovage;k++)
       if (stepm <=0)          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         dh[mi][i]=1;        for (k=1; k<=cptcovprod;k++)
       else{          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         if (s[mw[mi+1][i]][i] > nlstate) {  
           if (agedc[i] < 2*AGESUP) {  
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
           if(j==0) j=1;  /* Survives at least one month after exam */        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           k=k+1;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           if (j >= jmax) jmax=j;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
           if (j <= jmin) jmin=j;        savm=oldm;
           sum=sum+j;        oldm=newm;
           /*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++) {
         else{          po[i][j][h]=newm[i][j];
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
           k=k+1;        }
           if (j >= jmax) jmax=j;      /*printf("h=%d ",h);*/
           else if (j <= jmin)jmin=j;    } /* end h */
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */  /*     printf("\n H=%d \n",h); */
           sum=sum+j;    return po;
         }  }
         jk= j/stepm;  
         jl= j -jk*stepm;  
         ju= j -(jk+1)*stepm;  /*************** log-likelihood *************/
         if(jl <= -ju)  double func( double *x)
           dh[mi][i]=jk;  {
         else    int i, ii, j, k, mi, d, kk;
           dh[mi][i]=jk+1;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
         if(dh[mi][i]==0)    double **out;
           dh[mi][i]=1; /* At least one step */    double sw; /* Sum of weights */
       }    double lli; /* Individual log likelihood */
     }    int s1, s2;
   }    double bbh, survp;
   jmean=sum/k;    long ipmx;
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);    /*extern weight */
  }    /* We are differentiating ll according to initial status */
 /*********** Tricode ****************************/    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
 void tricode(int *Tvar, int **nbcode, int imx)    /*for(i=1;i<imx;i++) 
 {      printf(" %d\n",s[4][i]);
   int Ndum[20],ij=1, k, j, i;    */
   int cptcode=0;    cov[1]=1.;
   cptcoveff=0;  
      for(k=1; k<=nlstate; k++) ll[k]=0.;
   for (k=0; k<19; k++) Ndum[k]=0;  
   for (k=1; k<=7; k++) ncodemax[k]=0;    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {        /* Computes the values of the ncovmodel covariates of the model
     for (i=1; i<=imx; i++) {           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
       ij=(int)(covar[Tvar[j]][i]);           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
       Ndum[ij]++;           to be observed in j being in i according to the model.
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/         */
       if (ij > cptcode) cptcode=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] 
            is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
     for (i=0; i<=cptcode; i++) {           has been calculated etc */
       if(Ndum[i]!=0) ncodemax[j]++;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
     ij=1;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=1; i<=ncodemax[j]; i++) {            }
       for (k=0; k<=19; k++) {          for(d=0; d<dh[mi][i]; d++){
         if (Ndum[k] != 0) {            newm=savm;
           nbcode[Tvar[j]][ij]=k;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                      for (kk=1; kk<=cptcovage;kk++) {
           ij++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
         }            }
         if (ij > ncodemax[j]) break;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       }                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     }            savm=oldm;
   }              oldm=newm;
           } /* end mult */
  for (k=0; k<19; k++) Ndum[k]=0;        
           /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
  for (i=1; i<=ncovmodel-2; i++) {          /* But now since version 0.9 we anticipate for bias at large stepm.
       ij=Tvar[i];           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       Ndum[ij]++;           * (in months) between two waves is not a multiple of stepm, we rounded to 
     }           * the nearest (and in case of equal distance, to the lowest) interval but now
            * we keep into memory the bias bh[mi][i] and also the previous matrix product
  ij=1;           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
  for (i=1; i<=10; i++) {           * probability in order to take into account the bias as a fraction of the way
    if((Ndum[i]!=0) && (i<=ncovcol)){           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
      Tvaraff[ij]=i;           * -stepm/2 to stepm/2 .
      ij++;           * For stepm=1 the results are the same as for previous versions of Imach.
    }           * For stepm > 1 the results are less biased than in previous versions. 
  }           */
            s1=s[mw[mi][i]][i];
     cptcoveff=ij-1;          s2=s[mw[mi+1][i]][i];
 }          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias bh is positive if real duration
 /*********** Health Expectancies ****************/           * is higher than the multiple of stepm and negative otherwise.
            */
 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 )          /* 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){ 
 {            /* i.e. if s2 is a death state and if the date of death is known 
   /* Health expectancies */               then the contribution to the likelihood is the probability to 
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;               die between last step unit time and current  step unit time, 
   double age, agelim, hf;               which is also equal to probability to die before dh 
   double ***p3mat,***varhe;               minus probability to die before dh-stepm . 
   double **dnewm,**doldm;               In version up to 0.92 likelihood was computed
   double *xp;          as if date of death was unknown. Death was treated as any other
   double **gp, **gm;          health state: the date of the interview describes the actual state
   double ***gradg, ***trgradg;          and not the date of a change in health state. The former idea was
   int theta;          to consider that at each interview the state was recorded
           (healthy, disable or death) and IMaCh was corrected; but when we
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          introduced the exact date of death then we should have modified
   xp=vector(1,npar);          the contribution of an exact death to the likelihood. This new
   dnewm=matrix(1,nlstate*2,1,npar);          contribution is smaller and very dependent of the step unit
   doldm=matrix(1,nlstate*2,1,nlstate*2);          stepm. It is no more the probability to die between last interview
            and month of death but the probability to survive from last
   fprintf(ficreseij,"# Health expectancies\n");          interview up to one month before death multiplied by the
   fprintf(ficreseij,"# Age");          probability to die within a month. Thanks to Chris
   for(i=1; i<=nlstate;i++)          Jackson for correcting this bug.  Former versions increased
     for(j=1; j<=nlstate;j++)          mortality artificially. The bad side is that we add another loop
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          which slows down the processing. The difference can be up to 10%
   fprintf(ficreseij,"\n");          lower mortality.
             */
   if(estepm < stepm){            lli=log(out[s1][s2] - savm[s1][s2]);
     printf ("Problem %d lower than %d\n",estepm, stepm);  
   }  
   else  hstepm=estepm;            } else if  (s2==-2) {
   /* We compute the life expectancy from trapezoids spaced every estepm months            for (j=1,survp=0. ; j<=nlstate; j++) 
    * This is mainly to measure the difference between two models: for example              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
    * if stepm=24 months pijx are given only every 2 years and by summing them            /*survp += out[s1][j]; */
    * we are calculating an estimate of the Life Expectancy assuming a linear            lli= log(survp);
    * progression inbetween and thus overestimating or underestimating according          }
    * 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          else if  (s2==-4) { 
    * to compare the new estimate of Life expectancy with the same linear            for (j=3,survp=0. ; j<=nlstate; j++)  
    * hypothesis. A more precise result, taking into account a more precise              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
    * curvature will be obtained if estepm is as small as stepm. */            lli= log(survp); 
           } 
   /* 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.          else if  (s2==-5) { 
      nhstepm is the number of hstepm from age to agelim            for (j=1,survp=0. ; j<=2; j++)  
      nstepm is the number of stepm from age to agelin.              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
      Look at hpijx to understand the reason of that which relies in memory size            lli= log(survp); 
      and note for a fixed period like estepm months */          } 
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          
      survival function given by stepm (the optimization length). Unfortunately it          else{
      means that if the survival funtion is printed only each two years of age and if            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same            /*  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 */
      results. So we changed our mind and took the option of the best precision.          } 
   */          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          /*if(lli ==000.0)*/
           /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
   agelim=AGESUP;          ipmx +=1;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          sw += weight[i];
     /* nhstepm age range expressed in number of stepm */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     nstepm=(int) rint((agelim-age)*YEARM/stepm);        } /* end of wave */
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */      } /* end of individual */
     /* if (stepm >= YEARM) hstepm=1;*/    }  else if(mle==2){
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);        for(mi=1; mi<= wav[i]-1; mi++){
     gp=matrix(0,nhstepm,1,nlstate*2);          for (ii=1;ii<=nlstate+ndeath;ii++)
     gm=matrix(0,nhstepm,1,nlstate*2);            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* Computed by stepm unit matrices, product of hstepm matrices, stored              savm[ii][j]=(ii==j ? 1.0 : 0.0);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            }
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            for(d=0; d<=dh[mi][i]; d++){
              newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     /* Computing Variances of health expectancies */            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      for(theta=1; theta <=npar; theta++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(i=1; i<=npar; i++){            savm=oldm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            oldm=newm;
       }          } /* end mult */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          
            s1=s[mw[mi][i]][i];
       cptj=0;          s2=s[mw[mi+1][i]][i];
       for(j=1; j<= nlstate; j++){          bbh=(double)bh[mi][i]/(double)stepm; 
         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 */
           cptj=cptj+1;          ipmx +=1;
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          sw += weight[i];
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           }        } /* end of wave */
         }      } /* end of individual */
       }    }  else if(mle==3){  /* exponential inter-extrapolation */
            for (i=1,ipmx=0, sw=0.; i<=imx; i++){
              for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(i=1; i<=npar; i++)        for(mi=1; mi<= wav[i]-1; mi++){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          for (ii=1;ii<=nlstate+ndeath;ii++)
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              for (j=1;j<=nlstate+ndeath;j++){
                    oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       cptj=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<= nlstate; j++){            }
         for(i=1;i<=nlstate;i++){          for(d=0; d<dh[mi][i]; d++){
           cptj=cptj+1;            newm=savm;
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            for (kk=1; kk<=cptcovage;kk++) {
           }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         }            }
       }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       for(j=1; j<= nlstate*2; j++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(h=0; h<=nhstepm-1; h++){            savm=oldm;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];            oldm=newm;
         }          } /* end mult */
      }        
              s1=s[mw[mi][i]][i];
 /* End theta */          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           ipmx +=1;
      for(h=0; h<=nhstepm-1; h++)          sw += weight[i];
       for(j=1; j<=nlstate*2;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(theta=1; theta <=npar; theta++)        } /* end of wave */
           trgradg[h][j][theta]=gradg[h][theta][j];      } /* end of individual */
          }else if (mle==4){  /* ml=4 no inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      for(i=1;i<=nlstate*2;i++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1;j<=nlstate*2;j++)        for(mi=1; mi<= wav[i]-1; mi++){
         varhe[i][j][(int)age] =0.;          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
      printf("%d|",(int)age);fflush(stdout);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      for(h=0;h<=nhstepm-1;h++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(k=0;k<=nhstepm-1;k++){            }
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);          for(d=0; d<dh[mi][i]; d++){
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);            newm=savm;
         for(i=1;i<=nlstate*2;i++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           for(j=1;j<=nlstate*2;j++)            for (kk=1; kk<=cptcovage;kk++) {
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
     }          
     /* Computing expectancies */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1; j<=nlstate;j++)            savm=oldm;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){            oldm=newm;
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          } /* end mult */
                  
 /* 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]);*/          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
         }          if( s2 > nlstate){ 
             lli=log(out[s1][s2] - savm[s1][s2]);
     fprintf(ficreseij,"%3.0f",age );          }else{
     cptj=0;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     for(i=1; i<=nlstate;i++)          }
       for(j=1; j<=nlstate;j++){          ipmx +=1;
         cptj++;          sw += weight[i];
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          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]); */
     fprintf(ficreseij,"\n");        } /* end of wave */
          } /* end of individual */
     free_matrix(gm,0,nhstepm,1,nlstate*2);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     free_matrix(gp,0,nhstepm,1,nlstate*2);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
   }            for (j=1;j<=nlstate+ndeath;j++){
   printf("\n");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_vector(xp,1,npar);            }
   free_matrix(dnewm,1,nlstate*2,1,npar);          for(d=0; d<dh[mi][i]; d++){
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);            newm=savm;
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);            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];
 /************ Variance ******************/            }
 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)          
 {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   /* Variance of health expectancies */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/            savm=oldm;
   double **newm;            oldm=newm;
   double **dnewm,**doldm;          } /* end mult */
   int i, j, nhstepm, hstepm, h, nstepm ;        
   int k, cptcode;          s1=s[mw[mi][i]][i];
   double *xp;          s2=s[mw[mi+1][i]][i];
   double **gp, **gm;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   double ***gradg, ***trgradg;          ipmx +=1;
   double ***p3mat;          sw += weight[i];
   double age,agelim, hf;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int theta;          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
         } /* end of wave */
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");      } /* end of individual */
   fprintf(ficresvij,"# Age");    } /* End of if */
   for(i=1; i<=nlstate;i++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     for(j=1; j<=nlstate;j++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   fprintf(ficresvij,"\n");    return -l;
   }
   xp=vector(1,npar);  
   dnewm=matrix(1,nlstate,1,npar);  /*************** log-likelihood *************/
   doldm=matrix(1,nlstate,1,nlstate);  double funcone( double *x)
    {
   if(estepm < stepm){    /* Same as likeli but slower because of a lot of printf and if */
     printf ("Problem %d lower than %d\n",estepm, stepm);    int i, ii, j, k, mi, d, kk;
   }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   else  hstepm=estepm;      double **out;
   /* For example we decided to compute the life expectancy with the smallest unit */    double lli; /* Individual log likelihood */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.    double llt;
      nhstepm is the number of hstepm from age to agelim    int s1, s2;
      nstepm is the number of stepm from age to agelin.    double bbh, survp;
      Look at hpijx to understand the reason of that which relies in memory size    /*extern weight */
      and note for a fixed period like k years */    /* We are differentiating ll according to initial status */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
      survival function given by stepm (the optimization length). Unfortunately it    /*for(i=1;i<imx;i++) 
      means that if the survival funtion is printed only each two years of age and if      printf(" %d\n",s[4][i]);
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    */
      results. So we changed our mind and took the option of the best precision.    cov[1]=1.;
   */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    for(k=1; k<=nlstate; k++) ll[k]=0.;
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */      for(mi=1; mi<= wav[i]-1; mi++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for (ii=1;ii<=nlstate+ndeath;ii++)
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);          for (j=1;j<=nlstate+ndeath;j++){
     gp=matrix(0,nhstepm,1,nlstate);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     gm=matrix(0,nhstepm,1,nlstate);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }
     for(theta=1; theta <=npar; theta++){        for(d=0; d<dh[mi][i]; d++){
       for(i=1; i<=npar; i++){ /* Computes gradient */          newm=savm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }          for (kk=1; kk<=cptcovage;kk++) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          }
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       if (popbased==1) {                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(i=1; i<=nlstate;i++)          savm=oldm;
           prlim[i][i]=probs[(int)age][i][ij];          oldm=newm;
       }        } /* end mult */
          
       for(j=1; j<= nlstate; j++){        s1=s[mw[mi][i]][i];
         for(h=0; h<=nhstepm; h++){        s2=s[mw[mi+1][i]][i];
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        bbh=(double)bh[mi][i]/(double)stepm; 
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        /* bias is positive if real duration
         }         * is higher than the multiple of stepm and negative otherwise.
       }         */
            if( s2 > nlstate && (mle <5) ){  /* Jackson */
       for(i=1; i<=npar; i++) /* Computes gradient */          lli=log(out[s1][s2] - savm[s1][s2]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        } else if  (s2==-2) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for (j=1,survp=0. ; j<=nlstate; j++) 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
            lli= log(survp);
       if (popbased==1) {        }else if (mle==1){
         for(i=1; i<=nlstate;i++)          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           prlim[i][i]=probs[(int)age][i][ij];        } else if(mle==2){
       }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         } else if(mle==3){  /* exponential inter-extrapolation */
       for(j=1; j<= nlstate; j++){          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 */
         for(h=0; h<=nhstepm; h++){        } else if (mle==4){  /* mle=4 no inter-extrapolation */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          lli=log(out[s1][s2]); /* Original formula */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        } else{  /* mle=0 back to 1 */
         }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       }          /*lli=log(out[s1][s2]); */ /* Original formula */
         } /* End of if */
       for(j=1; j<= nlstate; j++)        ipmx +=1;
         for(h=0; h<=nhstepm; h++){        sw += weight[i];
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
     } /* End theta */        if(globpr){
           fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     for(h=0; h<=nhstepm; h++)                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       for(j=1; j<=nlstate;j++)          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
         for(theta=1; theta <=npar; theta++)            llt +=ll[k]*gipmx/gsw;
           trgradg[h][j][theta]=gradg[h][theta][j];            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           }
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          fprintf(ficresilk," %10.6f\n", -llt);
     for(i=1;i<=nlstate;i++)        }
       for(j=1;j<=nlstate;j++)      } /* end of wave */
         vareij[i][j][(int)age] =0.;    } /* end of individual */
     for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     for(h=0;h<=nhstepm;h++){    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       for(k=0;k<=nhstepm;k++){    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    if(globpr==0){ /* First time we count the contributions and weights */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      gipmx=ipmx;
         for(i=1;i<=nlstate;i++)      gsw=sw;
           for(j=1;j<=nlstate;j++)    }
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    return -l;
       }  }
     }  
   
     fprintf(ficresvij,"%.0f ",age );  /*************** function likelione ***********/
     for(i=1; i<=nlstate;i++)  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       for(j=1; j<=nlstate;j++){  {
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    /* This routine should help understanding what is done with 
       }       the selection of individuals/waves and
     fprintf(ficresvij,"\n");       to check the exact contribution to the likelihood.
     free_matrix(gp,0,nhstepm,1,nlstate);       Plotting could be done.
     free_matrix(gm,0,nhstepm,1,nlstate);     */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    int k;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);  
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    if(*globpri !=0){ /* Just counts and sums, no printings */
   } /* End age */      strcpy(fileresilk,"ilk"); 
        strcat(fileresilk,fileres);
   free_vector(xp,1,npar);      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   free_matrix(doldm,1,nlstate,1,npar);        printf("Problem with resultfile: %s\n", fileresilk);
   free_matrix(dnewm,1,nlstate,1,nlstate);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
 }      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");
       fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
 /************ Variance of prevlim ******************/      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
 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)      for(k=1; k<=nlstate; k++) 
 {        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   /* Variance of prevalence limit */      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;  
   double **dnewm,**doldm;    *fretone=(*funcone)(p);
   int i, j, nhstepm, hstepm;    if(*globpri !=0){
   int k, cptcode;      fclose(ficresilk);
   double *xp;      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   double *gp, *gm;      fflush(fichtm); 
   double **gradg, **trgradg;    } 
   double age,agelim;    return;
   int theta;  }
      
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");  
   fprintf(ficresvpl,"# Age");  /*********** Maximum Likelihood Estimation ***************/
   for(i=1; i<=nlstate;i++)  
       fprintf(ficresvpl," %1d-%1d",i,i);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   fprintf(ficresvpl,"\n");  {
     int i,j, iter;
   xp=vector(1,npar);    double **xi;
   dnewm=matrix(1,nlstate,1,npar);    double fret;
   doldm=matrix(1,nlstate,1,nlstate);    double fretone; /* Only one call to likelihood */
      /*  char filerespow[FILENAMELENGTH];*/
   hstepm=1*YEARM; /* Every year of age */    xi=matrix(1,npar,1,npar);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for (i=1;i<=npar;i++)
   agelim = AGESUP;      for (j=1;j<=npar;j++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        xi[i][j]=(i==j ? 1.0 : 0.0);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     if (stepm >= YEARM) hstepm=1;    strcpy(filerespow,"pow"); 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    strcat(filerespow,fileres);
     gradg=matrix(1,npar,1,nlstate);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     gp=vector(1,nlstate);      printf("Problem with resultfile: %s\n", filerespow);
     gm=vector(1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     }
     for(theta=1; theta <=npar; theta++){    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       for(i=1; i<=npar; i++){ /* Computes gradient */    for (i=1;i<=nlstate;i++)
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for(j=1;j<=nlstate+ndeath;j++)
       }        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fprintf(ficrespow,"\n");
       for(i=1;i<=nlstate;i++)  
         gp[i] = prlim[i][i];    powell(p,xi,npar,ftol,&iter,&fret,func);
      
       for(i=1; i<=npar; i++) /* Computes gradient */    free_matrix(xi,1,npar,1,npar);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    fclose(ficrespow);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
       for(i=1;i<=nlstate;i++)    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         gm[i] = prlim[i][i];    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   
       for(i=1;i<=nlstate;i++)  }
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */  /**** Computes Hessian and covariance matrix ***/
   void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     trgradg =matrix(1,nlstate,1,npar);  {
     double  **a,**y,*x,pd;
     for(j=1; j<=nlstate;j++)    double **hess;
       for(theta=1; theta <=npar; theta++)    int i, j,jk;
         trgradg[j][theta]=gradg[theta][j];    int *indx;
   
     for(i=1;i<=nlstate;i++)    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       varpl[i][(int)age] =0.;    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    void lubksb(double **a, int npar, int *indx, double b[]) ;
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    void ludcmp(double **a, int npar, int *indx, double *d) ;
     for(i=1;i<=nlstate;i++)    double gompertz(double p[]);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    hess=matrix(1,npar,1,npar);
   
     fprintf(ficresvpl,"%.0f ",age );    printf("\nCalculation of the hessian matrix. Wait...\n");
     for(i=1; i<=nlstate;i++)    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    for (i=1;i<=npar;i++){
     fprintf(ficresvpl,"\n");      printf("%d",i);fflush(stdout);
     free_vector(gp,1,nlstate);      fprintf(ficlog,"%d",i);fflush(ficlog);
     free_vector(gm,1,nlstate);     
     free_matrix(gradg,1,npar,1,nlstate);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     free_matrix(trgradg,1,nlstate,1,npar);      
   } /* End age */      /*  printf(" %f ",p[i]);
           printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   free_vector(xp,1,npar);    }
   free_matrix(doldm,1,nlstate,1,npar);    
   free_matrix(dnewm,1,nlstate,1,nlstate);    for (i=1;i<=npar;i++) {
       for (j=1;j<=npar;j++)  {
 }        if (j>i) { 
           printf(".%d%d",i,j);fflush(stdout);
 /************ Variance of one-step probabilities  ******************/          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)          hess[i][j]=hessij(p,delti,i,j,func,npar);
 {          
   int i, j,  i1, k1, l1;          hess[j][i]=hess[i][j];    
   int k2, l2, j1,  z1;          /*printf(" %lf ",hess[i][j]);*/
   int k=0,l, cptcode;        }
   int first=1;      }
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;    }
   double **dnewm,**doldm;    printf("\n");
   double *xp;    fprintf(ficlog,"\n");
   double *gp, *gm;  
   double **gradg, **trgradg;    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   double **mu;    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   double age,agelim, cov[NCOVMAX];    
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */    a=matrix(1,npar,1,npar);
   int theta;    y=matrix(1,npar,1,npar);
   char fileresprob[FILENAMELENGTH];    x=vector(1,npar);
   char fileresprobcov[FILENAMELENGTH];    indx=ivector(1,npar);
   char fileresprobcor[FILENAMELENGTH];    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   double ***varpij;    ludcmp(a,npar,indx,&pd);
   
   strcpy(fileresprob,"prob");    for (j=1;j<=npar;j++) {
   strcat(fileresprob,fileres);      for (i=1;i<=npar;i++) x[i]=0;
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {      x[j]=1;
     printf("Problem with resultfile: %s\n", fileresprob);      lubksb(a,npar,indx,x);
   }      for (i=1;i<=npar;i++){ 
   strcpy(fileresprobcov,"probcov");        matcov[i][j]=x[i];
   strcat(fileresprobcov,fileres);      }
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    }
     printf("Problem with resultfile: %s\n", fileresprobcov);  
   }    printf("\n#Hessian matrix#\n");
   strcpy(fileresprobcor,"probcor");    fprintf(ficlog,"\n#Hessian matrix#\n");
   strcat(fileresprobcor,fileres);    for (i=1;i<=npar;i++) { 
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {      for (j=1;j<=npar;j++) { 
     printf("Problem with resultfile: %s\n", fileresprobcor);        printf("%.3e ",hess[i][j]);
   }        fprintf(ficlog,"%.3e ",hess[i][j]);
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);      }
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);      printf("\n");
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      fprintf(ficlog,"\n");
      }
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");  
   fprintf(ficresprob,"# Age");    /* Recompute Inverse */
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");    for (i=1;i<=npar;i++)
   fprintf(ficresprobcov,"# Age");      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    ludcmp(a,npar,indx,&pd);
   fprintf(ficresprobcov,"# Age");  
     /*  printf("\n#Hessian matrix recomputed#\n");
   
   for(i=1; i<=nlstate;i++)    for (j=1;j<=npar;j++) {
     for(j=1; j<=(nlstate+ndeath);j++){      for (i=1;i<=npar;i++) x[i]=0;
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);      x[j]=1;
       fprintf(ficresprobcov," p%1d-%1d ",i,j);      lubksb(a,npar,indx,x);
       fprintf(ficresprobcor," p%1d-%1d ",i,j);      for (i=1;i<=npar;i++){ 
     }          y[i][j]=x[i];
   fprintf(ficresprob,"\n");        printf("%.3e ",y[i][j]);
   fprintf(ficresprobcov,"\n");        fprintf(ficlog,"%.3e ",y[i][j]);
   fprintf(ficresprobcor,"\n");      }
   xp=vector(1,npar);      printf("\n");
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);      fprintf(ficlog,"\n");
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));    }
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);    */
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);  
   first=1;    free_matrix(a,1,npar,1,npar);
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    free_matrix(y,1,npar,1,npar);
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    free_vector(x,1,npar);
     exit(0);    free_ivector(indx,1,npar);
   }    free_matrix(hess,1,npar,1,npar);
   else{  
     fprintf(ficgp,"\n# Routine varprob");  
   }  }
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {  
     printf("Problem with html file: %s\n", optionfilehtm);  /*************** hessian matrix ****************/
     exit(0);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   }  {
   else{    int i;
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");    int l=1, lmax=20;
     fprintf(fichtm,"\n<br> We have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");    double k1,k2;
     fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");    double p2[MAXPARM+1]; /* identical to x */
     double res;
   }    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   cov[1]=1;    double fx;
   j=cptcoveff;    int k=0,kmax=10;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    double l1;
   j1=0;  
   for(k1=1; k1<=1;k1++){    fx=func(x);
     for(i1=1; i1<=ncodemax[k1];i1++){    for (i=1;i<=npar;i++) p2[i]=x[i];
     j1++;    for(l=0 ; l <=lmax; l++){
       l1=pow(10,l);
     if  (cptcovn>0) {      delts=delt;
       fprintf(ficresprob, "\n#********** Variable ");      for(k=1 ; k <kmax; k=k+1){
       fprintf(ficresprobcov, "\n#********** Variable ");        delt = delta*(l1*k);
       fprintf(ficgp, "\n#********** Variable ");        p2[theta]=x[theta] +delt;
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");        k1=func(p2)-fx;
       fprintf(ficresprobcor, "\n#********** Variable ");        p2[theta]=x[theta]-delt;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        k2=func(p2)-fx;
       fprintf(ficresprob, "**********\n#");        /*res= (k1-2.0*fx+k2)/delt/delt; */
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
       fprintf(ficresprobcov, "**********\n#");        
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  #ifdef DEBUGHESS
       fprintf(ficgp, "**********\n#");        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        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);
       fprintf(ficgp, "**********\n#");  #endif
       for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       fprintf(fichtm, "**********\n#");        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     }          k=kmax;
            }
       for (age=bage; age<=fage; age ++){        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
         cov[2]=age;          k=kmax; l=lmax*10.;
         for (k=1; k<=cptcovn;k++) {        }
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
         }          delts=delt;
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];        }
         for (k=1; k<=cptcovprod;k++)      }
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    }
            delti[theta]=delts;
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));    return res; 
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);    
         gp=vector(1,(nlstate)*(nlstate+ndeath));  }
         gm=vector(1,(nlstate)*(nlstate+ndeath));  
      double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
         for(theta=1; theta <=npar; theta++){  {
           for(i=1; i<=npar; i++)    int i;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    int l=1, l1, lmax=20;
              double k1,k2,k3,k4,res,fx;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    double p2[MAXPARM+1];
              int k;
           k=0;  
           for(i=1; i<= (nlstate); i++){    fx=func(x);
             for(j=1; j<=(nlstate+ndeath);j++){    for (k=1; k<=2; k++) {
               k=k+1;      for (i=1;i<=npar;i++) p2[i]=x[i];
               gp[k]=pmmij[i][j];      p2[thetai]=x[thetai]+delti[thetai]/k;
             }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           }      k1=func(p2)-fx;
              
           for(i=1; i<=npar; i++)      p2[thetai]=x[thetai]+delti[thetai]/k;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
          k2=func(p2)-fx;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    
           k=0;      p2[thetai]=x[thetai]-delti[thetai]/k;
           for(i=1; i<=(nlstate); i++){      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
             for(j=1; j<=(nlstate+ndeath);j++){      k3=func(p2)-fx;
               k=k+1;    
               gm[k]=pmmij[i][j];      p2[thetai]=x[thetai]-delti[thetai]/k;
             }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           }      k4=func(p2)-fx;
            res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)  #ifdef DEBUG
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         }      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   #endif
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)    }
           for(theta=1; theta <=npar; theta++)    return res;
             trgradg[j][theta]=gradg[theta][j];  }
          
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);  /************** Inverse of matrix **************/
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);  void ludcmp(double **a, int n, int *indx, double *d) 
          { 
         pmij(pmmij,cov,ncovmodel,x,nlstate);    int i,imax,j,k; 
            double big,dum,sum,temp; 
         k=0;    double *vv; 
         for(i=1; i<=(nlstate); i++){   
           for(j=1; j<=(nlstate+ndeath);j++){    vv=vector(1,n); 
             k=k+1;    *d=1.0; 
             mu[k][(int) age]=pmmij[i][j];    for (i=1;i<=n;i++) { 
           }      big=0.0; 
         }      for (j=1;j<=n;j++) 
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)        if ((temp=fabs(a[i][j])) > big) big=temp; 
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
             varpij[i][j][(int)age] = doldm[i][j];      vv[i]=1.0/big; 
     } 
         /*printf("\n%d ",(int)age);    for (j=1;j<=n;j++) { 
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){      for (i=1;i<j;i++) { 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));        sum=a[i][j]; 
      }*/        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
         fprintf(ficresprob,"\n%d ",(int)age);      } 
         fprintf(ficresprobcov,"\n%d ",(int)age);      big=0.0; 
         fprintf(ficresprobcor,"\n%d ",(int)age);      for (i=j;i<=n;i++) { 
         sum=a[i][j]; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)        for (k=1;k<j;k++) 
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));          sum -= a[i][k]*a[k][j]; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){        a[i][j]=sum; 
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);          big=dum; 
         }          imax=i; 
         i=0;        } 
         for (k=1; k<=(nlstate);k++){      } 
           for (l=1; l<=(nlstate+ndeath);l++){      if (j != imax) { 
             i=i++;        for (k=1;k<=n;k++) { 
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);          dum=a[imax][k]; 
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);          a[imax][k]=a[j][k]; 
             for (j=1; j<=i;j++){          a[j][k]=dum; 
               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]));        *d = -(*d); 
             }        vv[imax]=vv[j]; 
           }      } 
         }/* end of loop for state */      indx[j]=imax; 
       } /* end of loop for age */      if (a[j][j] == 0.0) a[j][j]=TINY; 
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/      if (j != n) { 
       for (k1=1; k1<=(nlstate);k1++){        dum=1.0/(a[j][j]); 
         for (l1=1; l1<=(nlstate+ndeath);l1++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
           if(l1==k1) continue;      } 
           i=(k1-1)*(nlstate+ndeath)+l1;    } 
           for (k2=1; k2<=(nlstate);k2++){    free_vector(vv,1,n);  /* Doesn't work */
             for (l2=1; l2<=(nlstate+ndeath);l2++){  ;
               if(l2==k2) continue;  } 
               j=(k2-1)*(nlstate+ndeath)+l2;  
               if(j<=i) continue;  void lubksb(double **a, int n, int *indx, double b[]) 
               for (age=bage; age<=fage; age ++){  { 
                 if ((int)age %5==0){    int i,ii=0,ip,j; 
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;    double sum; 
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;   
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;    for (i=1;i<=n;i++) { 
                   mu1=mu[i][(int) age]/stepm*YEARM ;      ip=indx[i]; 
                   mu2=mu[j][(int) age]/stepm*YEARM;      sum=b[ip]; 
                   /* Computing eigen value of matrix of covariance */      b[ip]=b[i]; 
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));      if (ii) 
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);      else if (sum) ii=i; 
                   /* Eigen vectors */      b[i]=sum; 
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));    } 
                   v21=sqrt(1.-v11*v11);    for (i=n;i>=1;i--) { 
                   v12=-v21;      sum=b[i]; 
                   v22=v11;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                   /*printf(fignu*/      b[i]=sum/a[i][i]; 
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */    } 
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */  } 
                   if(first==1){  
                     first=0;  void pstamp(FILE *fichier)
                     fprintf(ficgp,"\nset parametric;set nolabel");  {
                     fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1);    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");  }
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%1d%1d-%1d%1d.png\">varpijgr%s%1d%1d-%1d%1d.png</A>, ",k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1);  
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);  /************ Frequencies ********************/
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);  {  /* Some frequencies */
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    
                     fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(-%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) t \"%d\"",\    int i, m, jk, k1,i1, j1, bool, z1,j;
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    int first;
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    double ***freq; /* Frequencies */
                   }else{    double *pp, **prop;
                     first=0;    double pos,posprop, k2, dateintsum=0,k2cpt=0;
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    char fileresp[FILENAMELENGTH];
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);    
                     fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(-%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) t \"%d\"",\    pp=vector(1,nlstate);
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    prop=matrix(1,nlstate,iagemin,iagemax+3);
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    strcpy(fileresp,"p");
                   }/* if first */    strcat(fileresp,fileres);
                 } /* age mod 5 */    if((ficresp=fopen(fileresp,"w"))==NULL) {
               } /* end loop age */      printf("Problem with prevalence resultfile: %s\n", fileresp);
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
               first=1;      exit(0);
             } /*l12 */    }
           } /* k12 */    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
         } /*l1 */    j1=0;
       }/* k1 */    
     } /* loop covariates */    j=cptcoveff;
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));  
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    first=1;
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);  
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    for(k1=1; k1<=j;k1++){
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      for(i1=1; i1<=ncodemax[k1];i1++){
   }        j1++;
   free_vector(xp,1,npar);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   fclose(ficresprob);          scanf("%d", i);*/
   fclose(ficresprobcov);        for (i=-5; i<=nlstate+ndeath; i++)  
   fclose(ficresprobcor);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
   fclose(ficgp);            for(m=iagemin; m <= iagemax+3; m++)
   fclose(fichtm);              freq[i][jk][m]=0;
 }  
       for (i=1; i<=nlstate; i++)  
         for(m=iagemin; m <= iagemax+3; m++)
 /******************* Printing html file ***********/          prop[i][m]=0;
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        
                   int lastpass, int stepm, int weightopt, char model[],\        dateintsum=0;
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\        k2cpt=0;
                   int popforecast, int estepm ,\        for (i=1; i<=imx; i++) {
                   double jprev1, double mprev1,double anprev1, \          bool=1;
                   double jprev2, double mprev2,double anprev2){          if  (cptcovn>0) {
   int jj1, k1, i1, cpt;            for (z1=1; z1<=cptcoveff; z1++) 
   /*char optionfilehtm[FILENAMELENGTH];*/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {                bool=0;
     printf("Problem with %s \n",optionfilehtm), exit(0);          }
   }          if (bool==1){
             for(m=firstpass; m<=lastpass; m++){
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n              k2=anint[m][i]+(mint[m][i]/12.);
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n                if(agev[m][i]==0) agev[m][i]=iagemax+1;
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n                if(agev[m][i]==1) agev[m][i]=iagemax+2;
  - Life expectancies by age and initial health status (estepm=%2d months):                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
    <a href=\"e%s\">e%s</a> <br>\n</li>", \                if (m<lastpass) {
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n                }
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n                
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n                  dateintsum=dateintsum+k2;
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n                  k2cpt++;
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n                }
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n                /*}*/
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);            }
           }
  if(popforecast==1) fprintf(fichtm,"\n        }
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n         
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
         <br>",fileres,fileres,fileres,fileres);        pstamp(ficresp);
  else        if  (cptcovn>0) {
    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(ficresp, "\n#********** Variable "); 
 fprintf(fichtm," <li>Graphs</li><p>");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresp, "**********\n#");
  m=cptcoveff;        }
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}        for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
  jj1=0;        fprintf(ficresp, "\n");
  for(k1=1; k1<=m;k1++){        
    for(i1=1; i1<=ncodemax[k1];i1++){        for(i=iagemin; i <= iagemax+3; i++){
      jj1++;          if(i==iagemax+3){
      if (cptcovn > 0) {            fprintf(ficlog,"Total");
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");          }else{
        for (cpt=1; cpt<=cptcoveff;cpt++)            if(first==1){
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);              first=0;
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");              printf("See log file for details...\n");
      }            }
      /* Pij */            fprintf(ficlog,"Age %d", i);
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>          }
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              for(jk=1; jk <=nlstate ; jk++){
      /* Quasi-incidences */            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>              pp[jk] += freq[jk][m][i]; 
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          }
        /* Stable prevalence in each health state */          for(jk=1; jk <=nlstate ; jk++){
        for(cpt=1; cpt<nlstate;cpt++){            for(m=-1, pos=0; m <=0 ; m++)
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>              pos += freq[jk][m][i];
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            if(pp[jk]>=1.e-10){
        }              if(first==1){
     for(cpt=1; cpt<=nlstate;cpt++) {                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              }
 interval) in state (%d): v%s%d%d.png <br>              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              }else{
      }              if(first==1)
      for(cpt=1; cpt<=nlstate;cpt++) {                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            }
      }          }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and  
 health expectancies in states (1) and (2): e%s%d.png<br>          for(jk=1; jk <=nlstate ; jk++){
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
    }              pp[jk] += freq[jk][m][i];
  }          }       
 fclose(fichtm);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
 }            pos += pp[jk];
             posprop += prop[jk][i];
 /******************* Gnuplot file **************/          }
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){          for(jk=1; jk <=nlstate ; jk++){
             if(pos>=1.e-5){
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;              if(first==1)
   int ng;                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     printf("Problem with file %s",optionfilegnuplot);            }else{
   }              if(first==1)
                 printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 #ifdef windows              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     fprintf(ficgp,"cd \"%s\" \n",pathc);            }
 #endif            if( i <= iagemax){
 m=pow(2,cptcoveff);              if(pos>=1.e-5){
                  fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
  /* 1eme*/                /*probs[i][jk][j1]= pp[jk]/pos;*/
   for (cpt=1; cpt<= nlstate ; cpt ++) {                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
    for (k1=1; k1<= m ; k1 ++) {              }
               else
 #ifdef windows                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            }
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);          }
 #endif          
 #ifdef unix          for(jk=-1; jk <=nlstate+ndeath; jk++)
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            for(m=-1; m <=nlstate+ndeath; m++)
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);              if(freq[jk][m][i] !=0 ) {
 #endif              if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
 for (i=1; i<= nlstate ; i ++) {                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          if(i <= iagemax)
 }            fprintf(ficresp,"\n");
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);          if(first==1)
     for (i=1; i<= nlstate ; i ++) {            printf("Others in log...\n");
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          fprintf(ficlog,"\n");
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }      }
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    }
      for (i=1; i<= nlstate ; i ++) {    dateintmean=dateintsum/k2cpt; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");   
   else fprintf(ficgp," \%%*lf (\%%*lf)");    fclose(ficresp);
 }      free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    free_vector(pp,1,nlstate);
 #ifdef unix    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");    /* End of Freq */
 #endif  }
    }  
   }  /************ Prevalence ********************/
   /*2 eme*/  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)
   {  
   for (k1=1; k1<= m ; k1 ++) {    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);       in each health status at the date of interview (if between dateprev1 and dateprev2).
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);       We still use firstpass and lastpass as another selection.
        */
     for (i=1; i<= nlstate+1 ; i ++) {   
       k=2*i;    int i, m, jk, k1, i1, j1, bool, z1,j;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    double ***freq; /* Frequencies */
       for (j=1; j<= nlstate+1 ; j ++) {    double *pp, **prop;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    double pos,posprop; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double  y2; /* in fractional years */
 }      int iagemin, iagemax;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    iagemin= (int) agemin;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    iagemax= (int) agemax;
       for (j=1; j<= nlstate+1 ; j ++) {    /*pp=vector(1,nlstate);*/
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    prop=matrix(1,nlstate,iagemin,iagemax+3); 
         else fprintf(ficgp," \%%*lf (\%%*lf)");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
 }      j1=0;
       fprintf(ficgp,"\" t\"\" w l 0,");    
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    j=cptcoveff;
       for (j=1; j<= nlstate+1 ; j ++) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for(k1=1; k1<=j;k1++){
 }        for(i1=1; i1<=ncodemax[k1];i1++){
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        j1++;
       else fprintf(ficgp,"\" t\"\" w l 0,");        
     }        for (i=1; i<=nlstate; i++)  
   }          for(m=iagemin; m <= iagemax+3; m++)
              prop[i][m]=0.0;
   /*3eme*/       
         for (i=1; i<=imx; i++) { /* Each individual */
   for (k1=1; k1<= m ; k1 ++) {          bool=1;
     for (cpt=1; cpt<= nlstate ; cpt ++) {          if  (cptcovn>0) {
       k=2+nlstate*(2*cpt-2);            for (z1=1; z1<=cptcoveff; z1++) 
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);                bool=0;
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          } 
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          if (bool==1) { 
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
 */                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
       for (i=1; i< nlstate ; i ++) {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
         fprintf(ficgp," ,\"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(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]]);*/
                   prop[s[m][i]][(int)agev[m][i]] += weight[i];
       }                  prop[s[m][i]][iagemax+3] += weight[i]; 
     }                } 
   }              }
              } /* end selection of waves */
   /* CV preval stat */          }
     for (k1=1; k1<= m ; k1 ++) {        }
     for (cpt=1; cpt<nlstate ; cpt ++) {        for(i=iagemin; i <= iagemax+3; i++){  
       k=3;          
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);            posprop += prop[jk][i]; 
           } 
       for (i=1; i< nlstate ; i ++)  
         fprintf(ficgp,"+$%d",k+i+1);          for(jk=1; jk <=nlstate ; jk++){     
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);            if( i <=  iagemax){ 
                    if(posprop>=1.e-5){ 
       l=3+(nlstate+ndeath)*cpt;                probs[i][jk][j1]= prop[jk][i]/posprop;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);              } else
       for (i=1; i< nlstate ; i ++) {                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
         l=3+(nlstate+ndeath)*cpt;            } 
         fprintf(ficgp,"+$%d",l+i+1);          }/* end jk */ 
       }        }/* end i */ 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);        } /* end i1 */
     }    } /* end k1 */
   }      
      /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
   /* proba elementaires */    /*free_vector(pp,1,nlstate);*/
    for(i=1,jk=1; i <=nlstate; i++){    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     for(k=1; k <=(nlstate+ndeath); k++){  }  /* End of prevalence */
       if (k != i) {  
         for(j=1; j <=ncovmodel; j++){  /************* Waves Concatenation ***************/
          
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);  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)
           jk++;  {
           fprintf(ficgp,"\n");    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
         }       Death is a valid wave (if date is known).
       }       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
    }       and mw[mi+1][i]. dh depends on stepm.
        */
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/  
      for(jk=1; jk <=m; jk++) {    int i, mi, m;
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        if (ng==2)       double sum=0., jmean=0.;*/
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");    int first;
        else    int j, k=0,jk, ju, jl;
          fprintf(ficgp,"\nset title \"Probability\"\n");    double sum=0.;
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);    first=0;
        i=1;    jmin=1e+5;
        for(k2=1; k2<=nlstate; k2++) {    jmax=-1;
          k3=i;    jmean=0.;
          for(k=1; k<=(nlstate+ndeath); k++) {    for(i=1; i<=imx; i++){
            if (k != k2){      mi=0;
              if(ng==2)      m=firstpass;
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);      while(s[m][i] <= nlstate){
              else        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          mw[++mi][i]=m;
              ij=1;        if(m >=lastpass)
              for(j=3; j <=ncovmodel; j++) {          break;
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        else
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          m++;
                  ij++;      }/* end while */
                }      if (s[m][i] > nlstate){
                else        mi++;     /* Death is another wave */
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        /* if(mi==0)  never been interviewed correctly before death */
              }           /* Only death is a correct wave */
              fprintf(ficgp,")/(1");        mw[mi][i]=m;
                    }
              for(k1=1; k1 <=nlstate; k1++){    
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);      wav[i]=mi;
                ij=1;      if(mi==0){
                for(j=3; j <=ncovmodel; j++){        nbwarn++;
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        if(first==0){
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
                    ij++;          first=1;
                  }        }
                  else        if(first==1){
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
                }        }
                fprintf(ficgp,")");      } /* end mi==0 */
              }    } /* End individuals */
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);  
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    for(i=1; i<=imx; i++){
              i=i+ncovmodel;      for(mi=1; mi<wav[i];mi++){
            }        if (stepm <=0)
          }          dh[mi][i]=1;
        }        else{
      }          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
    }            if (agedc[i] < 2*AGESUP) {
    fclose(ficgp);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
 }  /* end gnuplot */              if(j==0) j=1;  /* Survives at least one month after exam */
               else if(j<0){
                 nberr++;
 /*************** Moving average **************/                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]);
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){                j=1; /* Temporary Dangerous patch */
                 printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
   int i, cpt, cptcod;                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]);
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)                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<=nlstate;i++)              }
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)              k=k+1;
           mobaverage[(int)agedeb][i][cptcod]=0.;              if (j >= jmax){
                    jmax=j;
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){                ijmax=i;
       for (i=1; i<=nlstate;i++){              }
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              if (j <= jmin){
           for (cpt=0;cpt<=4;cpt++){                jmin=j;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];                ijmin=i;
           }              }
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;              sum=sum+j;
         }              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       }              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     }            }
              }
 }          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
 /************** Forecasting ******************/  
 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){            k=k+1;
              if (j >= jmax) {
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;              jmax=j;
   int *popage;              ijmax=i;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;            }
   double *popeffectif,*popcount;            else if (j <= jmin){
   double ***p3mat;              jmin=j;
   char fileresf[FILENAMELENGTH];              ijmin=i;
             }
  agelim=AGESUP;            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;            /*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]);*/
             if(j<0){
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              nberr++;
                printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
   strcpy(fileresf,"f");            }
   strcat(fileresf,fileres);            sum=sum+j;
   if((ficresf=fopen(fileresf,"w"))==NULL) {          }
     printf("Problem with forecast resultfile: %s\n", fileresf);          jk= j/stepm;
   }          jl= j -jk*stepm;
   printf("Computing forecasting: result on file '%s' \n", fileresf);          ju= j -(jk+1)*stepm;
           if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            if(jl==0){
               dh[mi][i]=jk;
   if (mobilav==1) {              bh[mi][i]=0;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            }else{ /* We want a negative bias in order to only have interpolation ie
     movingaverage(agedeb, fage, ageminpar, mobaverage);                    * to avoid the price of an extra matrix product in likelihood */
   }              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
   stepsize=(int) (stepm+YEARM-1)/YEARM;            }
   if (stepm<=12) stepsize=1;          }else{
              if(jl <= -ju){
   agelim=AGESUP;              dh[mi][i]=jk;
                bh[mi][i]=jl;       /* bias is positive if real duration
   hstepm=1;                                   * is higher than the multiple of stepm and negative otherwise.
   hstepm=hstepm/stepm;                                   */
   yp1=modf(dateintmean,&yp);            }
   anprojmean=yp;            else{
   yp2=modf((yp1*12),&yp);              dh[mi][i]=jk+1;
   mprojmean=yp;              bh[mi][i]=ju;
   yp1=modf((yp2*30.5),&yp);            }
   jprojmean=yp;            if(dh[mi][i]==0){
   if(jprojmean==0) jprojmean=1;              dh[mi][i]=1; /* At least one step */
   if(mprojmean==0) jprojmean=1;              bh[mi][i]=ju; /* At least one step */
                /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);            }
            } /* end if mle */
   for(cptcov=1;cptcov<=i2;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      } /* end wave */
       k=k+1;    }
       fprintf(ficresf,"\n#******");    jmean=sum/k;
       for(j=1;j<=cptcoveff;j++) {    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %d) Max=%d (%d) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
       }   }
       fprintf(ficresf,"******\n");  
       fprintf(ficresf,"# StartingAge FinalAge");  /*********** Tricode ****************************/
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  void tricode(int *Tvar, int **nbcode, int imx)
        {
          /* Uses cptcovn+2*cptcovprod as the number of covariates */
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
         fprintf(ficresf,"\n");  
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
     int modmaxcovj=0; /* Modality max of covariates j */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    cptcoveff=0; 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);   
           nhstepm = nhstepm/hstepm;    for (k=0; k<maxncov; k++) Ndum[k]=0;
              for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
                                         modality of this covariate Vj*/ 
           for (h=0; h<=nhstepm; h++){        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 (h==(int) (calagedate+YEARM*cpt)) {                                        modality of the nth covariate of individual i. */
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
             }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
             for(j=1; j<=nlstate+ndeath;j++) {        if (ij > modmaxcovj) modmaxcovj=ij; 
               kk1=0.;kk2=0;        /* getting the maximum value of the modality of the covariate
               for(i=1; i<=nlstate;i++) {                         (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
                 if (mobilav==1)           female is 1, then modmaxcovj=1.*/
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      }
                 else {      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
                 }        if( Ndum[i] != 0 )
                          ncodemax[j]++; 
               }        /* Number of modalities of the j th covariate. In fact
               if (h==(int)(calagedate+12*cpt)){           ncodemax[j]=2 (dichotom. variables only) but it could be more for
                 fprintf(ficresf," %.3f", kk1);           historical reasons */
                              } /* Ndum[-1] number of undefined modalities */
               }  
             }      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
           }      ij=1; 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      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 */
       }          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
     }            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
   }                                       k is a modality. If we have model=V1+V1*sex 
                                               then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            ij++;
           }
   fclose(ficresf);          if (ij > ncodemax[j]) break; 
 }        }  /* end of loop on */
 /************** Forecasting ******************/      } /* end of loop on modality */ 
 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){    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
      
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    for (k=0; k< maxncov; k++) Ndum[k]=0;
   int *popage;    
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
   double *popeffectif,*popcount;     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   double ***p3mat,***tabpop,***tabpopprev;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
   char filerespop[FILENAMELENGTH];     Ndum[ij]++;
    }
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);   ij=1;
   agelim=AGESUP;   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;     if((Ndum[i]!=0) && (i<=ncovcol)){
         Tvaraff[ij]=i; /*For printing */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);       ij++;
       }
     }
   strcpy(filerespop,"pop");   ij--;
   strcat(filerespop,fileres);   cptcoveff=ij; /*Number of simple covariates*/
   if((ficrespop=fopen(filerespop,"w"))==NULL) {  }
     printf("Problem with forecast resultfile: %s\n", filerespop);  
   }  /*********** Health Expectancies ****************/
   printf("Computing forecasting: result on file '%s' \n", filerespop);  
   void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   if (cptcoveff==0) ncodemax[cptcoveff]=1;  
   {
   if (mobilav==1) {    /* Health expectancies, no variances */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
     movingaverage(agedeb, fage, ageminpar, mobaverage);    int nhstepma, nstepma; /* Decreasing with age */
   }    double age, agelim, hf;
     double ***p3mat;
   stepsize=(int) (stepm+YEARM-1)/YEARM;    double eip;
   if (stepm<=12) stepsize=1;  
      pstamp(ficreseij);
   agelim=AGESUP;    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
      fprintf(ficreseij,"# Age");
   hstepm=1;    for(i=1; i<=nlstate;i++){
   hstepm=hstepm/stepm;      for(j=1; j<=nlstate;j++){
          fprintf(ficreseij," e%1d%1d ",i,j);
   if (popforecast==1) {      }
     if((ficpop=fopen(popfile,"r"))==NULL) {      fprintf(ficreseij," e%1d. ",i);
       printf("Problem with population file : %s\n",popfile);exit(0);    }
     }    fprintf(ficreseij,"\n");
     popage=ivector(0,AGESUP);  
     popeffectif=vector(0,AGESUP);    
     popcount=vector(0,AGESUP);    if(estepm < stepm){
          printf ("Problem %d lower than %d\n",estepm, stepm);
     i=1;      }
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    else  hstepm=estepm;   
        /* We compute the life expectancy from trapezoids spaced every estepm months
     imx=i;     * This is mainly to measure the difference between two models: for example
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];     * if stepm=24 months pijx are given only every 2 years and by summing them
   }     * we are calculating an estimate of the Life Expectancy assuming a linear 
      * progression in between and thus overestimating or underestimating according
   for(cptcov=1;cptcov<=i2;cptcov++){     * to the curvature of the survival function. If, for the same date, we 
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       k=k+1;     * to compare the new estimate of Life expectancy with the same linear 
       fprintf(ficrespop,"\n#******");     * hypothesis. A more precise result, taking into account a more precise
       for(j=1;j<=cptcoveff;j++) {     * curvature will be obtained if estepm is as small as stepm. */
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       }    /* For example we decided to compute the life expectancy with the smallest unit */
       fprintf(ficrespop,"******\n");    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       fprintf(ficrespop,"# Age");       nhstepm is the number of hstepm from age to agelim 
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);       nstepm is the number of stepm from age to agelin. 
       if (popforecast==1)  fprintf(ficrespop," [Population]");       Look at hpijx to understand the reason of that which relies in memory size
             and note for a fixed period like estepm months */
       for (cpt=0; cpt<=0;cpt++) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);         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
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);       results. So we changed our mind and took the option of the best precision.
           nhstepm = nhstepm/hstepm;    */
              hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;    agelim=AGESUP;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      /* If stepm=6 months */
              /* Computed by stepm unit matrices, product of hstepm matrices, stored
           for (h=0; h<=nhstepm; h++){         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
             if (h==(int) (calagedate+YEARM*cpt)) {      
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);  /* nhstepm age range expressed in number of stepm */
             }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             for(j=1; j<=nlstate+ndeath;j++) {    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
               kk1=0.;kk2=0;    /* if (stepm >= YEARM) hstepm=1;*/
               for(i=1; i<=nlstate;i++) {                  nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
                 if (mobilav==1)    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];  
                 else {    for (age=bage; age<=fage; age ++){ 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
                 }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
               }      /* if (stepm >= YEARM) hstepm=1;*/
               if (h==(int)(calagedate+12*cpt)){      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;  
                   /*fprintf(ficrespop," %.3f", kk1);      /* If stepm=6 months */
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/      /* Computed by stepm unit matrices, product of hstepma matrices, stored
               }         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
             }      
             for(i=1; i<=nlstate;i++){      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
               kk1=0.;      
                 for(j=1; j<=nlstate;j++){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];      
                 }      printf("%d|",(int)age);fflush(stdout);
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
             }      
       /* Computing expectancies */
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)      for(i=1; i<=nlstate;i++)
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        for(j=1; j<=nlstate;j++)
           }          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
         }            
       }            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
    
   /******/          }
   
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {      fprintf(ficreseij,"%3.0f",age );
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        for(i=1; i<=nlstate;i++){
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        eip=0;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        for(j=1; j<=nlstate;j++){
           nhstepm = nhstepm/hstepm;          eip +=eij[i][j][(int)age];
                    fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        }
           oldm=oldms;savm=savms;        fprintf(ficreseij,"%9.4f", eip );
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        }
           for (h=0; h<=nhstepm; h++){      fprintf(ficreseij,"\n");
             if (h==(int) (calagedate+YEARM*cpt)) {      
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    }
             }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             for(j=1; j<=nlstate+ndeath;j++) {    printf("\n");
               kk1=0.;kk2=0;    fprintf(ficlog,"\n");
               for(i=1; i<=nlstate;i++) {                  
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];      }
               }  
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
             }  
           }  {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* Covariances of health expectancies eij and of total life expectancies according
         }     to initial status i, ei. .
       }    */
    }    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   }    int nhstepma, nstepma; /* Decreasing with age */
      double age, agelim, hf;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    double ***p3matp, ***p3matm, ***varhe;
     double **dnewm,**doldm;
   if (popforecast==1) {    double *xp, *xm;
     free_ivector(popage,0,AGESUP);    double **gp, **gm;
     free_vector(popeffectif,0,AGESUP);    double ***gradg, ***trgradg;
     free_vector(popcount,0,AGESUP);    int theta;
   }  
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    double eip, vip;
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   fclose(ficrespop);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
 }    xp=vector(1,npar);
     xm=vector(1,npar);
 /***********************************************/    dnewm=matrix(1,nlstate*nlstate,1,npar);
 /**************** Main Program *****************/    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
 /***********************************************/    
     pstamp(ficresstdeij);
 int main(int argc, char *argv[])    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
 {    fprintf(ficresstdeij,"# Age");
     for(i=1; i<=nlstate;i++){
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      for(j=1; j<=nlstate;j++)
   double agedeb, agefin,hf;        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;      fprintf(ficresstdeij," e%1d. ",i);
     }
   double fret;    fprintf(ficresstdeij,"\n");
   double **xi,tmp,delta;  
     pstamp(ficrescveij);
   double dum; /* Dummy variable */    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   double ***p3mat;    fprintf(ficrescveij,"# Age");
   int *indx;    for(i=1; i<=nlstate;i++)
   char line[MAXLINE], linepar[MAXLINE];      for(j=1; j<=nlstate;j++){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        cptj= (j-1)*nlstate+i;
   int firstobs=1, lastobs=10;        for(i2=1; i2<=nlstate;i2++)
   int sdeb, sfin; /* Status at beginning and end */          for(j2=1; j2<=nlstate;j2++){
   int c,  h , cpt,l;            cptj2= (j2-1)*nlstate+i2;
   int ju,jl, mi;            if(cptj2 <= cptj)
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          }
   int mobilav=0,popforecast=0;      }
   int hstepm, nhstepm;    fprintf(ficrescveij,"\n");
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;    
     if(estepm < stepm){
   double bage, fage, age, agelim, agebase;      printf ("Problem %d lower than %d\n",estepm, stepm);
   double ftolpl=FTOL;    }
   double **prlim;    else  hstepm=estepm;   
   double *severity;    /* We compute the life expectancy from trapezoids spaced every estepm months
   double ***param; /* Matrix of parameters */     * This is mainly to measure the difference between two models: for example
   double  *p;     * if stepm=24 months pijx are given only every 2 years and by summing them
   double **matcov; /* Matrix of covariance */     * we are calculating an estimate of the Life Expectancy assuming a linear 
   double ***delti3; /* Scale */     * progression in between and thus overestimating or underestimating according
   double *delti; /* Scale */     * to the curvature of the survival function. If, for the same date, we 
   double ***eij, ***vareij;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   double **varpl; /* Variances of prevalence limits by age */     * to compare the new estimate of Life expectancy with the same linear 
   double *epj, vepp;     * hypothesis. A more precise result, taking into account a more precise
   double kk1, kk2;     * curvature will be obtained if estepm is as small as stepm. */
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;  
      /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   char *alph[]={"a","a","b","c","d","e"}, str[4];       nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   char z[1]="c", occ;       and note for a fixed period like estepm months */
 #include <sys/time.h>    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
 #include <time.h>       survival function given by stepm (the optimization length). Unfortunately it
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];       means that if the survival funtion is printed only each two years of age and if
         you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   /* long total_usecs;       results. So we changed our mind and took the option of the best precision.
   struct timeval start_time, end_time;    */
      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   getcwd(pathcd, size);    /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
   printf("\n%s",version);    agelim=AGESUP;
   if(argc <=1){    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     printf("\nEnter the parameter file name: ");    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     scanf("%s",pathtot);    /* if (stepm >= YEARM) hstepm=1;*/
   }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   else{    
     strcpy(pathtot,argv[1]);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   /*cygwin_split_path(pathtot,path,optionfile);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    gp=matrix(0,nhstepm,1,nlstate*nlstate);
   /* cutv(path,optionfile,pathtot,'\\');*/    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    for (age=bage; age<=fage; age ++){ 
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   chdir(path);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   replace(pathc,path);      /* if (stepm >= YEARM) hstepm=1;*/
       nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
 /*-------- arguments in the command line --------*/  
       /* If stepm=6 months */
   strcpy(fileres,"r");      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   strcat(fileres, optionfilefiname);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   strcat(fileres,".txt");    /* Other files have txt extension */      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   /*---------arguments file --------*/  
       /* Computing  Variances of health expectancies */
   if((ficpar=fopen(optionfile,"r"))==NULL)    {      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
     printf("Problem with optionfile %s\n",optionfile);         decrease memory allocation */
     goto end;      for(theta=1; theta <=npar; theta++){
   }        for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
   strcpy(filereso,"o");          xm[i] = x[i] - (i==theta ?delti[theta]:0);
   strcat(filereso,fileres);        }
   if((ficparo=fopen(filereso,"w"))==NULL) {        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   }    
         for(j=1; j<= nlstate; j++){
   /* Reads comments: lines beginning with '#' */          for(i=1; i<=nlstate; i++){
   while((c=getc(ficpar))=='#' && c!= EOF){            for(h=0; h<=nhstepm-1; h++){
     ungetc(c,ficpar);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
     fgets(line, MAXLINE, ficpar);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
     puts(line);            }
     fputs(line,ficparo);          }
   }        }
   ungetc(c,ficpar);       
         for(ij=1; ij<= nlstate*nlstate; ij++)
   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);          for(h=0; h<=nhstepm-1; h++){
   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);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   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){      }/* End theta */
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      
     puts(line);      for(h=0; h<=nhstepm-1; h++)
     fputs(line,ficparo);        for(j=1; j<=nlstate*nlstate;j++)
   }          for(theta=1; theta <=npar; theta++)
   ungetc(c,ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
        
      
   covar=matrix(0,NCOVMAX,1,n);       for(ij=1;ij<=nlstate*nlstate;ij++)
   cptcovn=0;        for(ji=1;ji<=nlstate*nlstate;ji++)
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;          varhe[ij][ji][(int)age] =0.;
   
   ncovmodel=2+cptcovn;       printf("%d|",(int)age);fflush(stdout);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         for(h=0;h<=nhstepm-1;h++){
   /* Read guess parameters */        for(k=0;k<=nhstepm-1;k++){
   /* Reads comments: lines beginning with '#' */          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   while((c=getc(ficpar))=='#' && c!= EOF){          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
     ungetc(c,ficpar);          for(ij=1;ij<=nlstate*nlstate;ij++)
     fgets(line, MAXLINE, ficpar);            for(ji=1;ji<=nlstate*nlstate;ji++)
     puts(line);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     fputs(line,ficparo);        }
   }      }
   ungetc(c,ficpar);  
        /* Computing expectancies */
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     for(i=1; i <=nlstate; i++)      for(i=1; i<=nlstate;i++)
     for(j=1; j <=nlstate+ndeath-1; j++){        for(j=1; j<=nlstate;j++)
       fscanf(ficpar,"%1d%1d",&i1,&j1);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       fprintf(ficparo,"%1d%1d",i1,j1);            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
       printf("%1d%1d",i,j);            
       for(k=1; k<=ncovmodel;k++){            /* 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]);*/
         fscanf(ficpar," %lf",&param[i][j][k]);  
         printf(" %lf",param[i][j][k]);          }
         fprintf(ficparo," %lf",param[i][j][k]);  
       }      fprintf(ficresstdeij,"%3.0f",age );
       fscanf(ficpar,"\n");      for(i=1; i<=nlstate;i++){
       printf("\n");        eip=0.;
       fprintf(ficparo,"\n");        vip=0.;
     }        for(j=1; j<=nlstate;j++){
            eip += eij[i][j][(int)age];
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
             vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
   p=param[1][1];          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
          }
   /* Reads comments: lines beginning with '#' */        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
   while((c=getc(ficpar))=='#' && c!= EOF){      }
     ungetc(c,ficpar);      fprintf(ficresstdeij,"\n");
     fgets(line, MAXLINE, ficpar);  
     puts(line);      fprintf(ficrescveij,"%3.0f",age );
     fputs(line,ficparo);      for(i=1; i<=nlstate;i++)
   }        for(j=1; j<=nlstate;j++){
   ungetc(c,ficpar);          cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);            for(j2=1; j2<=nlstate;j2++){
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */              cptj2= (j2-1)*nlstate+i2;
   for(i=1; i <=nlstate; i++){              if(cptj2 <= cptj)
     for(j=1; j <=nlstate+ndeath-1; j++){                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
       fscanf(ficpar,"%1d%1d",&i1,&j1);            }
       printf("%1d%1d",i,j);        }
       fprintf(ficparo,"%1d%1d",i1,j1);      fprintf(ficrescveij,"\n");
       for(k=1; k<=ncovmodel;k++){     
         fscanf(ficpar,"%le",&delti3[i][j][k]);    }
         printf(" %le",delti3[i][j][k]);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         fprintf(ficparo," %le",delti3[i][j][k]);    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
       }    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
       fscanf(ficpar,"\n");    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
       printf("\n");    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficparo,"\n");    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }    printf("\n");
   }    fprintf(ficlog,"\n");
   delti=delti3[1][1];  
      free_vector(xm,1,npar);
   /* Reads comments: lines beginning with '#' */    free_vector(xp,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     ungetc(c,ficpar);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     fgets(line, MAXLINE, ficpar);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     puts(line);  }
     fputs(line,ficparo);  
   }  /************ Variance ******************/
   ungetc(c,ficpar);  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[])
    {
   matcov=matrix(1,npar,1,npar);    /* Variance of health expectancies */
   for(i=1; i <=npar; i++){    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     fscanf(ficpar,"%s",&str);    /* double **newm;*/
     printf("%s",str);    double **dnewm,**doldm;
     fprintf(ficparo,"%s",str);    double **dnewmp,**doldmp;
     for(j=1; j <=i; j++){    int i, j, nhstepm, hstepm, h, nstepm ;
       fscanf(ficpar," %le",&matcov[i][j]);    int k, cptcode;
       printf(" %.5le",matcov[i][j]);    double *xp;
       fprintf(ficparo," %.5le",matcov[i][j]);    double **gp, **gm;  /* for var eij */
     }    double ***gradg, ***trgradg; /*for var eij */
     fscanf(ficpar,"\n");    double **gradgp, **trgradgp; /* for var p point j */
     printf("\n");    double *gpp, *gmp; /* for var p point j */
     fprintf(ficparo,"\n");    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   }    double ***p3mat;
   for(i=1; i <=npar; i++)    double age,agelim, hf;
     for(j=i+1;j<=npar;j++)    double ***mobaverage;
       matcov[i][j]=matcov[j][i];    int theta;
        char digit[4];
   printf("\n");    char digitp[25];
   
     char fileresprobmorprev[FILENAMELENGTH];
     /*-------- Rewriting paramater file ----------*/  
      strcpy(rfileres,"r");    /* "Rparameterfile */    if(popbased==1){
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/      if(mobilav!=0)
      strcat(rfileres,".");    /* */        strcpy(digitp,"-populbased-mobilav-");
      strcat(rfileres,optionfilext);    /* Other files have txt extension */      else strcpy(digitp,"-populbased-nomobil-");
     if((ficres =fopen(rfileres,"w"))==NULL) {    }
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    else 
     }      strcpy(digitp,"-stablbased-");
     fprintf(ficres,"#%s\n",version);  
        if (mobilav!=0) {
     /*-------- data file ----------*/      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     if((fic=fopen(datafile,"r"))==NULL)    {      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
       printf("Problem with datafile: %s\n", datafile);goto end;        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
     }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     n= lastobs;    }
     severity = vector(1,maxwav);  
     outcome=imatrix(1,maxwav+1,1,n);    strcpy(fileresprobmorprev,"prmorprev"); 
     num=ivector(1,n);    sprintf(digit,"%-d",ij);
     moisnais=vector(1,n);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     annais=vector(1,n);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     moisdc=vector(1,n);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     andc=vector(1,n);    strcat(fileresprobmorprev,fileres);
     agedc=vector(1,n);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     cod=ivector(1,n);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     weight=vector(1,n);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    }
     mint=matrix(1,maxwav,1,n);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     anint=matrix(1,maxwav,1,n);   
     s=imatrix(1,maxwav+1,1,n);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     adl=imatrix(1,maxwav+1,1,n);        pstamp(ficresprobmorprev);
     tab=ivector(1,NCOVMAX);    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);
     ncodemax=ivector(1,8);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     i=1;      fprintf(ficresprobmorprev," p.%-d SE",j);
     while (fgets(line, MAXLINE, fic) != NULL)    {      for(i=1; i<=nlstate;i++)
       if ((i >= firstobs) && (i <=lastobs)) {        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
            }  
         for (j=maxwav;j>=1;j--){    fprintf(ficresprobmorprev,"\n");
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    fprintf(ficgp,"\n# Routine varevsij");
           strcpy(line,stra);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
         }  /*   } */
            varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    pstamp(ficresvij);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     if(popbased==1)
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    else
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    fprintf(ficresvij,"# Age");
         for (j=ncovcol;j>=1;j--){    for(i=1; i<=nlstate;i++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      for(j=1; j<=nlstate;j++)
         }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
         num[i]=atol(stra);    fprintf(ficresvij,"\n");
          
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    xp=vector(1,npar);
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/    dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
         i=i+1;    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       }    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     }  
     /* printf("ii=%d", ij);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
        scanf("%d",i);*/    gpp=vector(nlstate+1,nlstate+ndeath);
   imx=i-1; /* Number of individuals */    gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   /* for (i=1; i<=imx; i++){    
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    if(estepm < stepm){
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;      printf ("Problem %d lower than %d\n",estepm, stepm);
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    }
     }*/    else  hstepm=estepm;   
    /*  for (i=1; i<=imx; i++){    /* For example we decided to compute the life expectancy with the smallest unit */
      if (s[4][i]==9)  s[4][i]=-1;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
      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]));}*/       nhstepm is the number of hstepm from age to agelim 
         nstepm is the number of stepm from age to agelin. 
         Look at function hpijx to understand why (it is linked to memory size questions) */
   /* Calculation of the number of parameter from char model*/    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   Tvar=ivector(1,15);       survival function given by stepm (the optimization length). Unfortunately it
   Tprod=ivector(1,15);       means that if the survival funtion is printed every two years of age and if
   Tvaraff=ivector(1,15);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   Tvard=imatrix(1,15,1,2);       results. So we changed our mind and took the option of the best precision.
   Tage=ivector(1,15);          */
        hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   if (strlen(model) >1){    agelim = AGESUP;
     j=0, j1=0, k1=1, k2=1;    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     j=nbocc(model,'+');      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     j1=nbocc(model,'*');      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     cptcovn=j+1;      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     cptcovprod=j1;      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
          gp=matrix(0,nhstepm,1,nlstate);
     strcpy(modelsav,model);      gm=matrix(0,nhstepm,1,nlstate);
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);  
       goto end;      for(theta=1; theta <=npar; theta++){
     }        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
              xp[i] = x[i] + (i==theta ?delti[theta]:0);
     for(i=(j+1); i>=1;i--){        }
       cutv(stra,strb,modelsav,'+');        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/  
       /*scanf("%d",i);*/        if (popbased==1) {
       if (strchr(strb,'*')) {          if(mobilav ==0){
         cutv(strd,strc,strb,'*');            for(i=1; i<=nlstate;i++)
         if (strcmp(strc,"age")==0) {              prlim[i][i]=probs[(int)age][i][ij];
           cptcovprod--;          }else{ /* mobilav */ 
           cutv(strb,stre,strd,'V');            for(i=1; i<=nlstate;i++)
           Tvar[i]=atoi(stre);              prlim[i][i]=mobaverage[(int)age][i][ij];
           cptcovage++;          }
             Tage[cptcovage]=i;        }
             /*printf("stre=%s ", stre);*/    
         }        for(j=1; j<= nlstate; j++){
         else if (strcmp(strd,"age")==0) {          for(h=0; h<=nhstepm; h++){
           cptcovprod--;            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
           cutv(strb,stre,strc,'V');              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           Tvar[i]=atoi(stre);          }
           cptcovage++;        }
           Tage[cptcovage]=i;        /* This for computing probability of death (h=1 means
         }           computed over hstepm matrices product = hstepm*stepm months) 
         else {           as a weighted average of prlim.
           cutv(strb,stre,strc,'V');        */
           Tvar[i]=ncovcol+k1;        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           cutv(strb,strc,strd,'V');          for(i=1,gpp[j]=0.; i<= nlstate; i++)
           Tprod[k1]=i;            gpp[j] += prlim[i][i]*p3mat[i][j][1];
           Tvard[k1][1]=atoi(strc);        }    
           Tvard[k1][2]=atoi(stre);        /* end probability of death */
           Tvar[cptcovn+k2]=Tvard[k1][1];  
           Tvar[cptcovn+k2+1]=Tvard[k1][2];        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           for (k=1; k<=lastobs;k++)          xp[i] = x[i] - (i==theta ?delti[theta]:0);
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           k1++;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           k2=k2+2;   
         }        if (popbased==1) {
       }          if(mobilav ==0){
       else {            for(i=1; i<=nlstate;i++)
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/              prlim[i][i]=probs[(int)age][i][ij];
        /*  scanf("%d",i);*/          }else{ /* mobilav */ 
       cutv(strd,strc,strb,'V');            for(i=1; i<=nlstate;i++)
       Tvar[i]=atoi(strc);              prlim[i][i]=mobaverage[(int)age][i][ij];
       }          }
       strcpy(modelsav,stra);          }
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);  
         scanf("%d",i);*/        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
     }          for(h=0; h<=nhstepm; h++){
 }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
                gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);          }
   printf("cptcovprod=%d ", cptcovprod);        }
   scanf("%d ",i);*/        /* This for computing probability of death (h=1 means
     fclose(fic);           computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
     /*  if(mle==1){*/        */
     if (weightopt != 1) { /* Maximisation without weights*/        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       for(i=1;i<=n;i++) weight[i]=1.0;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     /*-calculation of age at interview from date of interview and age at death -*/        }    
     agev=matrix(1,maxwav,1,imx);        /* end probability of death */
   
     for (i=1; i<=imx; i++) {        for(j=1; j<= nlstate; j++) /* vareij */
       for(m=2; (m<= maxwav); m++) {          for(h=0; h<=nhstepm; h++){
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
          anint[m][i]=9999;          }
          s[m][i]=-1;  
        }        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
       }        }
     }  
       } /* End theta */
     for (i=1; i<=imx; i++)  {  
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
       for(m=1; (m<= maxwav); m++){  
         if(s[m][i] >0){      for(h=0; h<=nhstepm; h++) /* veij */
           if (s[m][i] >= nlstate+1) {        for(j=1; j<=nlstate;j++)
             if(agedc[i]>0)          for(theta=1; theta <=npar; theta++)
               if(moisdc[i]!=99 && andc[i]!=9999)            trgradg[h][j][theta]=gradg[h][theta][j];
                 agev[m][i]=agedc[i];  
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
            else {        for(theta=1; theta <=npar; theta++)
               if (andc[i]!=9999){          trgradgp[j][theta]=gradgp[theta][j];
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    
               agev[m][i]=-1;  
               }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
             }      for(i=1;i<=nlstate;i++)
           }        for(j=1;j<=nlstate;j++)
           else if(s[m][i] !=9){ /* Should no more exist */          vareij[i][j][(int)age] =0.;
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);  
             if(mint[m][i]==99 || anint[m][i]==9999)      for(h=0;h<=nhstepm;h++){
               agev[m][i]=1;        for(k=0;k<=nhstepm;k++){
             else if(agev[m][i] <agemin){          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
               agemin=agev[m][i];          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/          for(i=1;i<=nlstate;i++)
             }            for(j=1;j<=nlstate;j++)
             else if(agev[m][i] >agemax){              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
               agemax=agev[m][i];        }
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/      }
             }    
             /*agev[m][i]=anint[m][i]-annais[i];*/      /* pptj */
             /*   agev[m][i] = age[i]+2*m;*/      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
           }      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
           else { /* =9 */      for(j=nlstate+1;j<=nlstate+ndeath;j++)
             agev[m][i]=1;        for(i=nlstate+1;i<=nlstate+ndeath;i++)
             s[m][i]=-1;          varppt[j][i]=doldmp[j][i];
           }      /* end ppptj */
         }      /*  x centered again */
         else /*= 0 Unknown */      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
           agev[m][i]=1;      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
       }   
          if (popbased==1) {
     }        if(mobilav ==0){
     for (i=1; i<=imx; i++)  {          for(i=1; i<=nlstate;i++)
       for(m=1; (m<= maxwav); m++){            prlim[i][i]=probs[(int)age][i][ij];
         if (s[m][i] > (nlstate+ndeath)) {        }else{ /* mobilav */ 
           printf("Error: Wrong value in nlstate or ndeath\n");            for(i=1; i<=nlstate;i++)
           goto end;            prlim[i][i]=mobaverage[(int)age][i][ij];
         }        }
       }      }
     }               
       /* This for computing probability of death (h=1 means
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
     free_vector(severity,1,maxwav);      */
     free_imatrix(outcome,1,maxwav+1,1,n);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
     free_vector(moisnais,1,n);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     free_vector(annais,1,n);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     /* free_matrix(mint,1,maxwav,1,n);      }    
        free_matrix(anint,1,maxwav,1,n);*/      /* end probability of death */
     free_vector(moisdc,1,n);  
     free_vector(andc,1,n);      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]));
     wav=ivector(1,imx);        for(i=1; i<=nlstate;i++){
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);        }
          } 
     /* Concatenates waves */      fprintf(ficresprobmorprev,"\n");
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
       Tcode=ivector(1,100);        for(j=1; j<=nlstate;j++){
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
       ncodemax[1]=1;        }
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      fprintf(ficresvij,"\n");
            free_matrix(gp,0,nhstepm,1,nlstate);
    codtab=imatrix(1,100,1,10);      free_matrix(gm,0,nhstepm,1,nlstate);
    h=0;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
    m=pow(2,cptcoveff);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
        free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
    for(k=1;k<=cptcoveff; k++){    } /* End age */
      for(i=1; i <=(m/pow(2,k));i++){    free_vector(gpp,nlstate+1,nlstate+ndeath);
        for(j=1; j <= ncodemax[k]; j++){    free_vector(gmp,nlstate+1,nlstate+ndeath);
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
            h++;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
          }    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
        }  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
      }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
    }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
       codtab[1][2]=1;codtab[2][2]=2; */    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
    /* for(i=1; i <=m ;i++){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
       for(k=1; k <=cptcovn; k++){    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    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);
       printf("\n");  */
       }  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
       scanf("%d",i);*/    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
      
    /* Calculates basic frequencies. Computes observed prevalence at single age    free_vector(xp,1,npar);
        and prints on file fileres'p'. */    free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
        free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
        free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fclose(ficresprobmorprev);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fflush(ficgp);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fflush(fichtm); 
        }  /* end varevsij */
     /* 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] */  /************ Variance of prevlim ******************/
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     if(mle==1){    /* Variance of prevalence limit */
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     }    double **newm;
        double **dnewm,**doldm;
     /*--------- results files --------------*/    int i, j, nhstepm, hstepm;
     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);    int k, cptcode;
      double *xp;
     double *gp, *gm;
    jk=1;    double **gradg, **trgradg;
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    double age,agelim;
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    int theta;
    for(i=1,jk=1; i <=nlstate; i++){    
      for(k=1; k <=(nlstate+ndeath); k++){    pstamp(ficresvpl);
        if (k != i)    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
          {    fprintf(ficresvpl,"# Age");
            printf("%d%d ",i,k);    for(i=1; i<=nlstate;i++)
            fprintf(ficres,"%1d%1d ",i,k);        fprintf(ficresvpl," %1d-%1d",i,i);
            for(j=1; j <=ncovmodel; j++){    fprintf(ficresvpl,"\n");
              printf("%f ",p[jk]);  
              fprintf(ficres,"%f ",p[jk]);    xp=vector(1,npar);
              jk++;    dnewm=matrix(1,nlstate,1,npar);
            }    doldm=matrix(1,nlstate,1,nlstate);
            printf("\n");    
            fprintf(ficres,"\n");    hstepm=1*YEARM; /* Every year of age */
          }    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
      }    agelim = AGESUP;
    }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
  if(mle==1){      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     /* Computing hessian and covariance matrix */      if (stepm >= YEARM) hstepm=1;
     ftolhess=ftol; /* Usually correct */      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
     hesscov(matcov, p, npar, delti, ftolhess, func);      gradg=matrix(1,npar,1,nlstate);
  }      gp=vector(1,nlstate);
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");      gm=vector(1,nlstate);
     printf("# Scales (for hessian or gradient estimation)\n");  
      for(i=1,jk=1; i <=nlstate; i++){      for(theta=1; theta <=npar; theta++){
       for(j=1; j <=nlstate+ndeath; j++){        for(i=1; i<=npar; i++){ /* Computes gradient */
         if (j!=i) {          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           fprintf(ficres,"%1d%1d",i,j);        }
           printf("%1d%1d",i,j);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           for(k=1; k<=ncovmodel;k++){        for(i=1;i<=nlstate;i++)
             printf(" %.5e",delti[jk]);          gp[i] = prlim[i][i];
             fprintf(ficres," %.5e",delti[jk]);      
             jk++;        for(i=1; i<=npar; i++) /* Computes gradient */
           }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           printf("\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           fprintf(ficres,"\n");        for(i=1;i<=nlstate;i++)
         }          gm[i] = prlim[i][i];
       }  
      }        for(i=1;i<=nlstate;i++)
              gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
     k=1;      } /* End theta */
     fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");  
     printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");      trgradg =matrix(1,nlstate,1,npar);
     for(i=1;i<=npar;i++){  
       /*  if (k>nlstate) k=1;      for(j=1; j<=nlstate;j++)
       i1=(i-1)/(ncovmodel*nlstate)+1;        for(theta=1; theta <=npar; theta++)
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          trgradg[j][theta]=gradg[theta][j];
       printf("%s%d%d",alph[k],i1,tab[i]);*/  
       fprintf(ficres,"%3d",i);      for(i=1;i<=nlstate;i++)
       printf("%3d",i);        varpl[i][(int)age] =0.;
       for(j=1; j<=i;j++){      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
         fprintf(ficres," %.5e",matcov[i][j]);      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
         printf(" %.5e",matcov[i][j]);      for(i=1;i<=nlstate;i++)
       }        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
       fprintf(ficres,"\n");  
       printf("\n");      fprintf(ficresvpl,"%.0f ",age );
       k++;      for(i=1; i<=nlstate;i++)
     }        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
          fprintf(ficresvpl,"\n");
     while((c=getc(ficpar))=='#' && c!= EOF){      free_vector(gp,1,nlstate);
       ungetc(c,ficpar);      free_vector(gm,1,nlstate);
       fgets(line, MAXLINE, ficpar);      free_matrix(gradg,1,npar,1,nlstate);
       puts(line);      free_matrix(trgradg,1,nlstate,1,npar);
       fputs(line,ficparo);    } /* End age */
     }  
     ungetc(c,ficpar);    free_vector(xp,1,npar);
     estepm=0;    free_matrix(doldm,1,nlstate,1,npar);
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    free_matrix(dnewm,1,nlstate,1,nlstate);
     if (estepm==0 || estepm < stepm) estepm=stepm;  
     if (fage <= 2) {  }
       bage = ageminpar;  
       fage = agemaxpar;  /************ Variance of one-step probabilities  ******************/
     }  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
      {
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    int i, j=0,  i1, k1, l1, t, tj;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    int k2, l2, j1,  z1;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    int k=0,l, cptcode;
      int first=1, first1;
     while((c=getc(ficpar))=='#' && c!= EOF){    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     ungetc(c,ficpar);    double **dnewm,**doldm;
     fgets(line, MAXLINE, ficpar);    double *xp;
     puts(line);    double *gp, *gm;
     fputs(line,ficparo);    double **gradg, **trgradg;
   }    double **mu;
   ungetc(c,ficpar);    double age,agelim, cov[NCOVMAX];
      double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    int theta;
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    char fileresprob[FILENAMELENGTH];
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    char fileresprobcov[FILENAMELENGTH];
          char fileresprobcor[FILENAMELENGTH];
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    double ***varpij;
     fgets(line, MAXLINE, ficpar);  
     puts(line);    strcpy(fileresprob,"prob"); 
     fputs(line,ficparo);    strcat(fileresprob,fileres);
   }    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   ungetc(c,ficpar);      printf("Problem with resultfile: %s\n", fileresprob);
        fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    strcpy(fileresprobcov,"probcov"); 
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
   fscanf(ficpar,"pop_based=%d\n",&popbased);      printf("Problem with resultfile: %s\n", fileresprobcov);
   fprintf(ficparo,"pop_based=%d\n",popbased);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
   fprintf(ficres,"pop_based=%d\n",popbased);      }
      strcpy(fileresprobcor,"probcor"); 
   while((c=getc(ficpar))=='#' && c!= EOF){    strcat(fileresprobcor,fileres);
     ungetc(c,ficpar);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
     fgets(line, MAXLINE, ficpar);      printf("Problem with resultfile: %s\n", fileresprobcor);
     puts(line);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     fputs(line,ficparo);    }
   }    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   ungetc(c,ficpar);    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   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);    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
 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);    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
 while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficresprob,"# Age");
     ungetc(c,ficpar);    pstamp(ficresprobcov);
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     puts(line);    fprintf(ficresprobcov,"# Age");
     fputs(line,ficparo);    pstamp(ficresprobcor);
   }    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   ungetc(c,ficpar);    fprintf(ficresprobcor,"# Age");
   
   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(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    for(i=1; i<=nlstate;i++)
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
 /*------------ gnuplot -------------*/      }  
   strcpy(optionfilegnuplot,optionfilefiname);   /* fprintf(ficresprob,"\n");
   strcat(optionfilegnuplot,".gp");    fprintf(ficresprobcov,"\n");
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {    fprintf(ficresprobcor,"\n");
     printf("Problem with file %s",optionfilegnuplot);   */
   }    xp=vector(1,npar);
   fclose(ficgp);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
 /*--------- index.htm --------*/    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
   strcpy(optionfilehtm,optionfile);    first=1;
   strcat(optionfilehtm,".htm");    fprintf(ficgp,"\n# Routine varprob");
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     printf("Problem with %s \n",optionfilehtm), exit(0);    fprintf(fichtm,"\n");
   }  
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n    file %s<br>\n",optionfilehtmcov);
 \n    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
 Total number of observations=%d <br>\n  and drawn. It helps understanding how is the covariance between two incidences.\
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
 <hr  size=\"2\" color=\"#EC5E5E\">    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. \
  <ul><li>Parameter files<br>\n  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
  - Gnuplot file name: <a href=\"%s\">%s</a><br></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);  standard deviations wide on each axis. <br>\
   fclose(fichtm);   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>\
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
    
 /*------------ free_vector  -------------*/    cov[1]=1;
  chdir(path);    tj=cptcoveff;
      if (cptcovn<1) {tj=1;ncodemax[1]=1;}
  free_ivector(wav,1,imx);    j1=0;
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    for(t=1; t<=tj;t++){
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);        for(i1=1; i1<=ncodemax[t];i1++){ 
  free_ivector(num,1,n);        j1++;
  free_vector(agedc,1,n);        if  (cptcovn>0) {
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          fprintf(ficresprob, "\n#********** Variable "); 
  fclose(ficparo);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  fclose(ficres);          fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   /*--------------- Prevalence limit --------------*/          fprintf(ficresprobcov, "**********\n#\n");
            
   strcpy(filerespl,"pl");          fprintf(ficgp, "\n#********** Variable "); 
   strcat(filerespl,fileres);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {          fprintf(ficgp, "**********\n#\n");
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;          
   }          
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
   fprintf(ficrespl,"#Prevalence limit\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   fprintf(ficrespl,"#Age ");          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          
   fprintf(ficrespl,"\n");          fprintf(ficresprobcor, "\n#********** Variable ");    
            for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   prlim=matrix(1,nlstate,1,nlstate);          fprintf(ficresprobcor, "**********\n#");    
   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 */        for (age=bage; age<=fage; age ++){ 
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          cov[2]=age;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          for (k=1; k<=cptcovn;k++) {
   k=0;            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   agebase=ageminpar;          }
   agelim=agemaxpar;          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   ftolpl=1.e-10;          for (k=1; k<=cptcovprod;k++)
   i1=cptcoveff;            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   if (cptcovn < 1){i1=1;}          
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   for(cptcov=1;cptcov<=i1;cptcov++){          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          gp=vector(1,(nlstate)*(nlstate+ndeath));
         k=k+1;          gm=vector(1,(nlstate)*(nlstate+ndeath));
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/      
         fprintf(ficrespl,"\n#******");          for(theta=1; theta <=npar; theta++){
         for(j=1;j<=cptcoveff;j++)            for(i=1; i<=npar; i++)
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
         fprintf(ficrespl,"******\n");            
                    pmij(pmmij,cov,ncovmodel,xp,nlstate);
         for (age=agebase; age<=agelim; age++){            
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            k=0;
           fprintf(ficrespl,"%.0f",age );            for(i=1; i<= (nlstate); i++){
           for(i=1; i<=nlstate;i++)              for(j=1; j<=(nlstate+ndeath);j++){
           fprintf(ficrespl," %.5f", prlim[i][i]);                k=k+1;
           fprintf(ficrespl,"\n");                gp[k]=pmmij[i][j];
         }              }
       }            }
     }            
   fclose(ficrespl);            for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
   /*------------- h Pij x at various ages ------------*/      
              pmij(pmmij,cov,ncovmodel,xp,nlstate);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);            k=0;
   if((ficrespij=fopen(filerespij,"w"))==NULL) {            for(i=1; i<=(nlstate); i++){
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;              for(j=1; j<=(nlstate+ndeath);j++){
   }                k=k+1;
   printf("Computing pij: result on file '%s' \n", filerespij);                gm[k]=pmmij[i][j];
                }
   stepsize=(int) (stepm+YEARM-1)/YEARM;            }
   /*if (stepm<=24) stepsize=2;*/       
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
   agelim=AGESUP;              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
   hstepm=stepsize*YEARM; /* Every year of age */          }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
            for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   k=0;            for(theta=1; theta <=npar; theta++)
   for(cptcov=1;cptcov<=i1;cptcov++){              trgradg[j][theta]=gradg[theta][j];
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          
       k=k+1;          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
         fprintf(ficrespij,"\n#****** ");          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
         for(j=1;j<=cptcoveff;j++)          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
         fprintf(ficrespij,"******\n");          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
                  free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          pmij(pmmij,cov,ncovmodel,x,nlstate);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          k=0;
           oldm=oldms;savm=savms;          for(i=1; i<=(nlstate); i++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              for(j=1; j<=(nlstate+ndeath);j++){
           fprintf(ficrespij,"# Age");              k=k+1;
           for(i=1; i<=nlstate;i++)              mu[k][(int) age]=pmmij[i][j];
             for(j=1; j<=nlstate+ndeath;j++)            }
               fprintf(ficrespij," %1d-%1d",i,j);          }
           fprintf(ficrespij,"\n");          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
            for (h=0; h<=nhstepm; h++){            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );              varpij[i][j][(int)age] = doldm[i][j];
             for(i=1; i<=nlstate;i++)  
               for(j=1; j<=nlstate+ndeath;j++)          /*printf("\n%d ",(int)age);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficrespij,"\n");            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
              }            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            }*/
           fprintf(ficrespij,"\n");  
         }          fprintf(ficresprob,"\n%d ",(int)age);
     }          fprintf(ficresprobcov,"\n%d ",(int)age);
   }          fprintf(ficresprobcor,"\n%d ",(int)age);
   
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
   fclose(ficrespij);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   /*---------- Forecasting ------------------*/          }
   if((stepm == 1) && (strcmp(model,".")==0)){          i=0;
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);          for (k=1; k<=(nlstate);k++){
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);            for (l=1; l<=(nlstate+ndeath);l++){ 
   }              i=i++;
   else{              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
     erreur=108;              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
     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);              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]));
               }
   /*---------- Health expectancies and variances ------------*/            }
           }/* end of loop for state */
   strcpy(filerest,"t");        } /* end of loop for age */
   strcat(filerest,fileres);  
   if((ficrest=fopen(filerest,"w"))==NULL) {        /* Confidence intervalle of pij  */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;        /*
   }          fprintf(ficgp,"\nunset parametric;unset label");
   printf("Computing Total LEs with variances: file '%s' \n", filerest);          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);
   strcpy(filerese,"e");          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
   strcat(filerese,fileres);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   if((ficreseij=fopen(filerese,"w"))==NULL) {          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);        */
   }  
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
  strcpy(fileresv,"v");        for (k2=1; k2<=(nlstate);k2++){
   strcat(fileresv,fileres);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
   if((ficresvij=fopen(fileresv,"w"))==NULL) {            if(l2==k2) continue;
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);            j=(k2-1)*(nlstate+ndeath)+l2;
   }            for (k1=1; k1<=(nlstate);k1++){
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   calagedate=-1;                if(l1==k1) continue;
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);                i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
   k=0;                for (age=bage; age<=fage; age ++){ 
   for(cptcov=1;cptcov<=i1;cptcov++){                  if ((int)age %5==0){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
       k=k+1;                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
       fprintf(ficrest,"\n#****** ");                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
       for(j=1;j<=cptcoveff;j++)                    mu1=mu[i][(int) age]/stepm*YEARM ;
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    mu2=mu[j][(int) age]/stepm*YEARM;
       fprintf(ficrest,"******\n");                    c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
       fprintf(ficreseij,"\n#****** ");                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       for(j=1;j<=cptcoveff;j++)                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    if ((lc2 <0) || (lc1 <0) ){
       fprintf(ficreseij,"******\n");                      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);
       fprintf(ficresvij,"\n#****** ");                      lc1=fabs(lc1);
       for(j=1;j<=cptcoveff;j++)                      lc2=fabs(lc2);
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    }
       fprintf(ficresvij,"******\n");  
                     /* Eigen vectors */
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       oldm=oldms;savm=savms;                    /*v21=sqrt(1.-v11*v11); *//* error */
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);                      v21=(lc1-v1)/cv12*v11;
                      v12=-v21;
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    v22=v11;
       oldm=oldms;savm=savms;                    tnalp=v21/v11;
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);                    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(ficrest,"#Total LEs with variances: e.. (std) ");                    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);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);                    /*printf(fignu*/
       fprintf(ficrest,"\n");                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
       epj=vector(1,nlstate+1);                    if(first==1){
       for(age=bage; age <=fage ;age++){                      first=0;
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                      fprintf(ficgp,"\nset parametric;unset label");
         if (popbased==1) {                      fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
           for(i=1; i<=nlstate;i++)                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
             prlim[i][i]=probs[(int)age][i][k];                      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,\
         fprintf(ficrest," %4.0f",age);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
             epj[j] += prlim[i][i]*eij[i][j][(int)age];                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/                      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);
           epj[nlstate+1] +=epj[j];                      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),\
         for(i=1, vepp=0.;i <=nlstate;i++)                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
           for(j=1;j <=nlstate;j++)                    }else{
             vepp += vareij[i][j][(int)age];                      first=0;
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
         for(j=1;j <=nlstate;j++){                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));                      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",\
         fprintf(ficrest,"\n");                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
       }                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
     }                    }/* if first */
   }                  } /* age mod 5 */
 free_matrix(mint,1,maxwav,1,n);                } /* end loop age */
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
     free_vector(weight,1,n);                first=1;
   fclose(ficreseij);              } /*l12 */
   fclose(ficresvij);            } /* k12 */
   fclose(ficrest);          } /*l1 */
   fclose(ficpar);        }/* k1 */
   free_vector(epj,1,nlstate+1);      } /* loop covariates */
      }
   /*------- Variance limit prevalence------*/      free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
   strcpy(fileresvpl,"vpl");    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   strcat(fileresvpl,fileres);    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    free_vector(xp,1,npar);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    fclose(ficresprob);
     exit(0);    fclose(ficresprobcov);
   }    fclose(ficresprobcor);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    fflush(ficgp);
     fflush(fichtmcov);
   k=0;  }
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;  /******************* Printing html file ***********/
       fprintf(ficresvpl,"\n#****** ");  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
       for(j=1;j<=cptcoveff;j++)                    int lastpass, int stepm, int weightopt, char model[],\
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
       fprintf(ficresvpl,"******\n");                    int popforecast, int estepm ,\
                          double jprev1, double mprev1,double anprev1, \
       varpl=matrix(1,nlstate,(int) bage, (int) fage);                    double jprev2, double mprev2,double anprev2){
       oldm=oldms;savm=savms;    int jj1, k1, i1, cpt;
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  
     }     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>");
   fclose(ficresvpl);     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 ",
   /*---------- End : free ----------------*/             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);     fprintf(fichtm,"\
     - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);     fprintf(fichtm,"\
     - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
               subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);     fprintf(fichtm,"\
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);   - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);     <a href=\"%s\">%s</a> <br>\n",
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
       fprintf(fichtm,"\
   free_matrix(matcov,1,npar,1,npar);   - Population projections by age and states: \
   free_vector(delti,1,npar);     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   free_matrix(agev,1,maxwav,1,imx);  
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
   fprintf(fichtm,"\n</body>");   m=cptcoveff;
   fclose(fichtm);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   fclose(ficgp);  
     jj1=0;
    for(k1=1; k1<=m;k1++){
   if(erreur >0)     for(i1=1; i1<=ncodemax[k1];i1++){
     printf("End of Imach with error or warning %d\n",erreur);       jj1++;
   else   printf("End of Imach\n");       if (cptcovn > 0) {
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
           for (cpt=1; cpt<=cptcoveff;cpt++) 
   /* 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);*/           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   /*printf("Total time was %d uSec.\n", total_usecs);*/         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
   /*------ End -----------*/       }
        /* 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> \
  end:  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
 #ifdef windows       /* Quasi-incidences */
   /* chdir(pathcd);*/       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
 #endif   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> \
  /*system("wgnuplot graph.plt");*/  <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
  /*system("../gp37mgw/wgnuplot graph.plt");*/         /* Period (stable) prevalence in each health state */
  /*system("cd ../gp37mgw");*/         for(cpt=1; cpt<nlstate;cpt++){
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
  strcpy(plotcmd,GNUPLOTPROGRAM);  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
  strcat(plotcmd," ");         }
  strcat(plotcmd,optionfilegnuplot);       for(cpt=1; cpt<=nlstate;cpt++) {
  system(plotcmd);          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);
 #ifdef windows       }
   while (z[0] != 'q') {     } /* end i1 */
     /* chdir(path); */   }/* End k1 */
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");   fprintf(fichtm,"</ul>");
     scanf("%s",z);  
     if (z[0] == 'c') system("./imach");  
     else if (z[0] == 'e') system(optionfilehtm);   fprintf(fichtm,"\
     else if (z[0] == 'g') system(plotcmd);  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
     else if (z[0] == 'q') exit(0);   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   }  
 #endif   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
 }           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else        fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; /* Number of covariates V1+V2*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(k=cptcovn; k>=1;k--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 
                                       */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=2 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1]=atoi(strc); /* m 1 for V1*/
             Tvard[k1][2]=atoi(stre); /* n 4 for V4*/
             Tvar[cptcovn+k2]=Tvard[k1][1]; /* Tvar[(cptcovn=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovn+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovn=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
             k1++;
             k2=k2+2;
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[k]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line,stdout);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8); /* hard coded ? */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,15); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,15); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             codtab[h][k]=j;
             codtab[h][Tvar[k]]=j;
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       fprintf(ficgp,"set datafile missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*here or after loop ? */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.48  
changed lines
  Added in v.1.141


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