Diff for /imach/src/imach.c between versions 1.48 and 1.139

version 1.48, 2002/06/10 13:12:49 version 1.139, 2010/06/14 07:50:17
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.139  2010/06/14 07:50:17  brouard
      After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   This program computes Healthy Life Expectancies from    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a  
   first survey ("cross") where individuals from different ages are    Revision 1.138  2010/04/30 18:19:40  brouard
   interviewed on their health status or degree of disability (in the    *** empty log message ***
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.137  2010/04/29 18:11:38  brouard
   (if any) in individual health status.  Health expectancies are    (Module): Checking covariates for more complex models
   computed from the time spent in each health state according to a    than V1+V2. A lot of change to be done. Unstable.
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.136  2010/04/26 20:30:53  brouard
   simplest model is the multinomial logistic model where pij is the    (Module): merging some libgsl code. Fixing computation
   probability to be observed in state j at the second wave    of likelione (using inter/intrapolation if mle = 0) in order to
   conditional to be observed in state i at the first wave. Therefore    get same likelihood as if mle=1.
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Some cleaning of code and comments added.
   '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 1.135  2009/10/29 15:33:14  brouard
   where the markup *Covariates have to be included here again* invites    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   you to do it.  More covariates you add, slower the  
   convergence.    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.
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.133  2009/07/06 10:21:25  brouard
   identical for each individual. Also, if a individual missed an    just nforces
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.132  2009/07/06 08:22:05  brouard
     Many tings
   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 1.131  2009/06/20 16:22:47  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    Some dimensions resccaled
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.130  2009/05/26 06:44:34  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    (Module): Max Covariate is now set to 20 instead of 8. A
   and the contribution of each individual to the likelihood is simply    lot of cleaning with variables initialized to 0. Trying to make
   hPijx.    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.129  2007/08/31 13:49:27  lievre
   of the life expectancies. It also computes the prevalence limits.    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.128  2006/06/30 13:02:05  brouard
            Institut national d'études démographiques, Paris.    (Module): Clarifications on computing e.j
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.127  2006/04/28 18:11:50  brouard
   It is copyrighted identically to a GNU software product, ie programme and    (Module): Yes the sum of survivors was wrong since
   software can be distributed freely for non commercial use. Latest version    imach-114 because nhstepm was no more computed in the age
   can be accessed at http://euroreves.ined.fr/imach .    loop. Now we define nhstepma in the age loop.
   **********************************************************************/    (Module): In order to speed up (in case of numerous covariates) we
      compute health expectancies (without variances) in a first step
 #include <math.h>    and then all the health expectancies with variances or standard
 #include <stdio.h>    deviation (needs data from the Hessian matrices) which slows the
 #include <stdlib.h>    computation.
 #include <unistd.h>    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
 #define MAXLINE 256  
 #define GNUPLOTPROGRAM "gnuplot"    Revision 1.126  2006/04/28 17:23:28  brouard
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    (Module): Yes the sum of survivors was wrong since
 #define FILENAMELENGTH 80    imach-114 because nhstepm was no more computed in the age
 /*#define DEBUG*/    loop. Now we define nhstepma in the age loop.
 #define windows    Version 0.98h
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */  
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Forecasting file added.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.124  2006/03/22 17:13:53  lievre
 #define NINTERVMAX 8    Parameters are printed with %lf instead of %f (more numbers after the comma).
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    The log-likelihood is printed in the log file
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  
 #define NCOVMAX 8 /* Maximum number of covariates */    Revision 1.123  2006/03/20 10:52:43  brouard
 #define MAXN 20000    * imach.c (Module): <title> changed, corresponds to .htm file
 #define YEARM 12. /* Number of months per year */    name. <head> headers where missing.
 #define AGESUP 130  
 #define AGEBASE 40    * imach.c (Module): Weights can have a decimal point as for
 #ifdef windows    English (a comma might work with a correct LC_NUMERIC environment,
 #define DIRSEPARATOR '\\'    otherwise the weight is truncated).
 #else    Modification of warning when the covariates values are not 0 or
 #define DIRSEPARATOR '/'    1.
 #endif    Version 0.98g
   
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    Revision 1.122  2006/03/20 09:45:41  brouard
 int erreur; /* Error number */    (Module): Weights can have a decimal point as for
 int nvar;    English (a comma might work with a correct LC_NUMERIC environment,
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    otherwise the weight is truncated).
 int npar=NPARMAX;    Modification of warning when the covariates values are not 0 or
 int nlstate=2; /* Number of live states */    1.
 int ndeath=1; /* Number of dead states */    Version 0.98g
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.121  2006/03/16 17:45:01  lievre
     * imach.c (Module): Comments concerning covariates added
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    * imach.c (Module): refinements in the computation of lli if
 int jmin, jmax; /* min, max spacing between 2 waves */    status=-2 in order to have more reliable computation if stepm is
 int mle, weightopt;    not 1 month. Version 0.98f
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Revision 1.120  2006/03/16 15:10:38  lievre
 double jmean; /* Mean space between 2 waves */    (Module): refinements in the computation of lli if
 double **oldm, **newm, **savm; /* Working pointers to matrices */    status=-2 in order to have more reliable computation if stepm is
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    not 1 month. Version 0.98f
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    Revision 1.119  2006/03/15 17:42:26  brouard
 FILE *fichtm; /* Html File */    (Module): Bug if status = -2, the loglikelihood was
 FILE *ficreseij;    computed as likelihood omitting the logarithm. Version O.98e
 char filerese[FILENAMELENGTH];  
 FILE  *ficresvij;    Revision 1.118  2006/03/14 18:20:07  brouard
 char fileresv[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
 FILE  *ficresvpl;    table of variances if popbased=1 .
 char fileresvpl[FILENAMELENGTH];    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 char title[MAXLINE];    (Module): Function pstamp added
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    (Module): Version 0.98d
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];  
     Revision 1.117  2006/03/14 17:16:22  brouard
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 char filerest[FILENAMELENGTH];    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 char fileregp[FILENAMELENGTH];    (Module): Function pstamp added
 char popfile[FILENAMELENGTH];    (Module): Version 0.98d
   
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
 #define NR_END 1    varian-covariance of ej. is needed (Saito).
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
 #define NRANSI  
 #define ITMAX 200    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 #define TOL 2.0e-4    filename with strsep.
   
 #define CGOLD 0.3819660    Revision 1.113  2006/02/24 14:20:24  brouard
 #define ZEPS 1.0e-10    (Module): Memory leaks checks with valgrind and:
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.112  2006/01/30 09:55:26  brouard
 #define TINY 1.0e-20    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   
 static double maxarg1,maxarg2;    Revision 1.111  2006/01/25 20:38:18  brouard
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    (Module): Lots of cleaning and bugs added (Gompertz)
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    (Module): Comments can be added in data file. Missing date values
      can be a simple dot '.'.
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.109  2006/01/24 19:37:15  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): Comments (lines starting with a #) are allowed in data.
   
 int imx;    Revision 1.108  2006/01/19 18:05:42  lievre
 int stepm;    Gnuplot problem appeared...
 /* Stepm, step in month: minimum step interpolation*/    To be fixed
   
 int estepm;    Revision 1.107  2006/01/19 16:20:37  brouard
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    Test existence of gnuplot in imach path
   
 int m,nb;    Revision 1.106  2006/01/19 13:24:36  brouard
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Some cleaning and links added in html output
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.105  2006/01/05 20:23:19  lievre
 double dateintmean=0;    *** empty log message ***
   
 double *weight;    Revision 1.104  2005/09/30 16:11:43  lievre
 int **s; /* Status */    (Module): sump fixed, loop imx fixed, and simplifications.
 double *agedc, **covar, idx;    (Module): If the status is missing at the last wave but we know
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    contributions to the likelihood is 1 - Prob of dying from last
 double ftolhess; /* Tolerance for computing hessian */    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
 /**************** split *************************/  
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    Revision 1.103  2005/09/30 15:54:49  lievre
 {    (Module): sump fixed, loop imx fixed, and simplifications.
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */    Revision 1.102  2004/09/15 17:31:30  brouard
     Add the possibility to read data file including tab characters.
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.101  2004/09/15 10:38:38  brouard
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */    Fix on curr_time
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.100  2004/07/12 18:29:06  brouard
       extern char       *getwd( );    Add version for Mac OS X. Just define UNIX in Makefile
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.99  2004/06/05 08:57:40  brouard
 #else    *** empty log message ***
       extern char       *getcwd( );  
     Revision 1.98  2004/05/16 15:05:56  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    New version 0.97 . First attempt to estimate force of mortality
 #endif    directly from the data i.e. without the need of knowing the health
          return( GLOCK_ERROR_GETCWD );    state at each age, but using a Gompertz model: log u =a + b*age .
       }    This is the basic analysis of mortality and should be done before any
       strcpy( name, path );             /* we've got it */    other analysis, in order to test if the mortality estimated from the
    } else {                             /* strip direcotry from path */    cross-longitudinal survey is different from the mortality estimated
       s++;                              /* after this, the filename */    from other sources like vital statistic data.
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    The same imach parameter file can be used but the option for mle should be -3.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Agnès, who wrote this part of the code, tried to keep most of the
       dirc[l1-l2] = 0;                  /* add zero */    former routines in order to include the new code within the former code.
    }  
    l1 = strlen( dirc );                 /* length of directory */    The output is very simple: only an estimate of the intercept and of
 #ifdef windows    the slope with 95% confident intervals.
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Current limitations:
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    A) Even if you enter covariates, i.e. with the
 #endif    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
    s = strrchr( name, '.' );            /* find last / */    B) There is no computation of Life Expectancy nor Life Table.
    s++;  
    strcpy(ext,s);                       /* save extension */    Revision 1.97  2004/02/20 13:25:42  lievre
    l1= strlen( name);    Version 0.96d. Population forecasting command line is (temporarily)
    l2= strlen( s)+1;    suppressed.
    strncpy( finame, name, l1-l2);  
    finame[l1-l2]= 0;    Revision 1.96  2003/07/15 15:38:55  brouard
    return( 0 );                         /* we're done */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 }    rewritten within the same printf. Workaround: many printfs.
   
     Revision 1.95  2003/07/08 07:54:34  brouard
 /******************************************/    * imach.c (Repository):
     (Repository): Using imachwizard code to output a more meaningful covariance
 void replace(char *s, char*t)    matrix (cov(a12,c31) instead of numbers.
 {  
   int i;    Revision 1.94  2003/06/27 13:00:02  brouard
   int lg=20;    Just cleaning
   i=0;  
   lg=strlen(t);    Revision 1.93  2003/06/25 16:33:55  brouard
   for(i=0; i<= lg; i++) {    (Module): On windows (cygwin) function asctime_r doesn't
     (s[i] = t[i]);    exist so I changed back to asctime which exists.
     if (t[i]== '\\') s[i]='/';    (Module): Version 0.96b
   }  
 }    Revision 1.92  2003/06/25 16:30:45  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 int nbocc(char *s, char occ)    exist so I changed back to asctime which exists.
 {  
   int i,j=0;    Revision 1.91  2003/06/25 15:30:29  brouard
   int lg=20;    * imach.c (Repository): Duplicated warning errors corrected.
   i=0;    (Repository): Elapsed time after each iteration is now output. It
   lg=strlen(s);    helps to forecast when convergence will be reached. Elapsed time
   for(i=0; i<= lg; i++) {    is stamped in powell.  We created a new html file for the graphs
   if  (s[i] == occ ) j++;    concerning matrix of covariance. It has extension -cov.htm.
   }  
   return j;    Revision 1.90  2003/06/24 12:34:15  brouard
 }    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
 void cutv(char *u,char *v, char*t, char occ)    of the covariance matrix to be input.
 {  
   int i,lg,j,p=0;    Revision 1.89  2003/06/24 12:30:52  brouard
   i=0;    (Module): Some bugs corrected for windows. Also, when
   for(j=0; j<=strlen(t)-1; j++) {    mle=-1 a template is output in file "or"mypar.txt with the design
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    of the covariance matrix to be input.
   }  
     Revision 1.88  2003/06/23 17:54:56  brouard
   lg=strlen(t);    * 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.
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);    Revision 1.87  2003/06/18 12:26:01  brouard
   }    Version 0.96
      u[p]='\0';  
     Revision 1.86  2003/06/17 20:04:08  brouard
    for(j=0; j<= lg; j++) {    (Module): Change position of html and gnuplot routines and added
     if (j>=(p+1))(v[j-p-1] = t[j]);    routine fileappend.
   }  
 }    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
 /********************** nrerror ********************/    current date of interview. It may happen when the death was just
     prior to the death. In this case, dh was negative and likelihood
 void nrerror(char error_text[])    was wrong (infinity). We still send an "Error" but patch by
 {    assuming that the date of death was just one stepm after the
   fprintf(stderr,"ERREUR ...\n");    interview.
   fprintf(stderr,"%s\n",error_text);    (Repository): Because some people have very long ID (first column)
   exit(1);    we changed int to long in num[] and we added a new lvector for
 }    memory allocation. But we also truncated to 8 characters (left
 /*********************** vector *******************/    truncation)
 double *vector(int nl, int nh)    (Repository): No more line truncation errors.
 {  
   double *v;    Revision 1.84  2003/06/13 21:44:43  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    * imach.c (Repository): Replace "freqsummary" at a correct
   if (!v) nrerror("allocation failure in vector");    place. It differs from routine "prevalence" which may be called
   return 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)
 /************************ free vector ******************/  
 void free_vector(double*v, int nl, int nh)    Revision 1.83  2003/06/10 13:39:11  lievre
 {    *** empty log message ***
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.82  2003/06/05 15:57:20  brouard
     Add log in  imach.c and  fullversion number is now printed.
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)  */
 {  /*
   int *v;     Interpolated Markov Chain
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Short summary of the programme:
   return v-nl+NR_END;    
 }    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /******************free ivector **************************/    first survey ("cross") where individuals from different ages are
 void free_ivector(int *v, long nl, long nh)    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
   free((FREE_ARG)(v+nl-NR_END));    second wave of interviews ("longitudinal") which measure each change
 }    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
 /******************* imatrix *******************************/    model. More health states you consider, more time is necessary to reach the
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Maximum Likelihood of the parameters involved in the model.  The
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    simplest model is the multinomial logistic model where pij is the
 {    probability to be observed in state j at the second wave
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    conditional to be observed in state i at the first wave. Therefore
   int **m;    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
   /* allocate pointers to rows */    complex model than "constant and age", you should modify the program
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    where the markup *Covariates have to be included here again* invites
   if (!m) nrerror("allocation failure 1 in matrix()");    you to do it.  More covariates you add, slower the
   m += NR_END;    convergence.
   m -= nrl;  
      The advantage of this computer programme, compared to a simple
      multinomial logistic model, is clear when the delay between waves is not
   /* allocate rows and set pointers to them */    identical for each individual. Also, if a individual missed an
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    intermediate interview, the information is lost, but taken into
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    account using an interpolation or extrapolation.  
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    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
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    split into an exact number (nh*stepm) of unobserved intermediate
      states. This elementary transition (by month, quarter,
   /* return pointer to array of pointers to rows */    semester or year) is modelled as a multinomial logistic.  The hPx
   return m;    matrix is simply the matrix product of nh*stepm elementary matrices
 }    and the contribution of each individual to the likelihood is simply
     hPijx.
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Also this programme outputs the covariance matrix of the parameters but also
       int **m;    of the life expectancies. It also computes the period (stable) prevalence. 
       long nch,ncl,nrh,nrl;    
      /* free an int matrix allocated by imatrix() */    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 {             Institut national d'études démographiques, Paris.
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    This software have been partly granted by Euro-REVES, a concerted action
   free((FREE_ARG) (m+nrl-NR_END));    from the European Union.
 }    It is copyrighted identically to a GNU software product, ie programme and
     software can be distributed freely for non commercial use. Latest version
 /******************* matrix *******************************/    can be accessed at http://euroreves.ined.fr/imach .
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   double **m;    
     **********************************************************************/
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  /*
   if (!m) nrerror("allocation failure 1 in matrix()");    main
   m += NR_END;    read parameterfile
   m -= nrl;    read datafile
     concatwav
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    freqsummary
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    if (mle >= 1)
   m[nrl] += NR_END;      mlikeli
   m[nrl] -= ncl;    print results files
     if mle==1 
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;       computes hessian
   return m;    read end of parameter file: agemin, agemax, bage, fage, estepm
 }        begin-prev-date,...
     open gnuplot file
 /*************************free matrix ************************/    open html file
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    period (stable) prevalence
 {     for age prevalim()
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    h Pij x
   free((FREE_ARG)(m+nrl-NR_END));    variance of p varprob
 }    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
 /******************* ma3x *******************************/    Variance-covariance of DFLE
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    prevalence()
 {     movingaverage()
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    varevsij() 
   double ***m;    if popbased==1 varevsij(,popbased)
     total life expectancies
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Variance of period (stable) prevalence
   if (!m) nrerror("allocation failure 1 in matrix()");   end
   m += NR_END;  */
   m -= nrl;  
   
   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;  #include <math.h>
   m[nrl] -= ncl;  #include <stdio.h>
   #include <stdlib.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include <string.h>
   #include <unistd.h>
   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 <limits.h>
   m[nrl][ncl] += NR_END;  #include <sys/types.h>
   m[nrl][ncl] -= nll;  #include <sys/stat.h>
   for (j=ncl+1; j<=nch; j++)  #include <errno.h>
     m[nrl][j]=m[nrl][j-1]+nlay;  extern int errno;
    
   for (i=nrl+1; i<=nrh; i++) {  /* #include <sys/time.h> */
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #include <time.h>
     for (j=ncl+1; j<=nch; j++)  #include "timeval.h"
       m[i][j]=m[i][j-1]+nlay;  
   }  #ifdef GSL
   return m;  #include <gsl/gsl_errno.h>
 }  #include <gsl/gsl_multimin.h>
   #endif
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  /* #include <libintl.h> */
 {  /* #define _(String) gettext (String) */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define MAXLINE 256
   free((FREE_ARG)(m+nrl-NR_END));  
 }  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 /***************** f1dim *************************/  #define FILENAMELENGTH 132
 extern int ncom;  
 extern double *pcom,*xicom;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 extern double (*nrfunc)(double []);  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
    
 double f1dim(double x)  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
 {  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   int j;  
   double f;  #define NINTERVMAX 8
   double *xt;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
    #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   xt=vector(1,ncom);  #define NCOVMAX 20 /* Maximum number of covariates */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define MAXN 20000
   f=(*nrfunc)(xt);  #define YEARM 12. /* Number of months per year */
   free_vector(xt,1,ncom);  #define AGESUP 130
   return f;  #define AGEBASE 40
 }  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   #ifdef UNIX
 /*****************brent *************************/  #define DIRSEPARATOR '/'
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #define CHARSEPARATOR "/"
 {  #define ODIRSEPARATOR '\\'
   int iter;  #else
   double a,b,d,etemp;  #define DIRSEPARATOR '\\'
   double fu,fv,fw,fx;  #define CHARSEPARATOR "\\"
   double ftemp;  #define ODIRSEPARATOR '/'
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #endif
   double e=0.0;  
    /* $Id$ */
   a=(ax < cx ? ax : cx);  /* $State$ */
   b=(ax > cx ? ax : cx);  
   x=w=v=bx;  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
   fw=fv=fx=(*f)(x);  char fullversion[]="$Revision$ $Date$"; 
   for (iter=1;iter<=ITMAX;iter++) {  char strstart[80];
     xm=0.5*(a+b);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  int nvar=0, nforce=0; /* Number of variables, number of forces */
     printf(".");fflush(stdout);  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
 #ifdef DEBUG  int npar=NPARMAX;
     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);  int nlstate=2; /* Number of live states */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int ndeath=1; /* Number of dead states */
 #endif  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int popbased=0;
       *xmin=x;  
       return fx;  int *wav; /* Number of waves for this individuual 0 is possible */
     }  int maxwav=0; /* Maxim number of waves */
     ftemp=fu;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
     if (fabs(e) > tol1) {  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       r=(x-w)*(fx-fv);  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       q=(x-v)*(fx-fw);                     to the likelihood and the sum of weights (done by funcone)*/
       p=(x-v)*q-(x-w)*r;  int mle=1, weightopt=0;
       q=2.0*(q-r);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       if (q > 0.0) p = -p;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       q=fabs(q);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       etemp=e;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       e=d;  double jmean=1; /* Mean space between 2 waves */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  double **oldm, **newm, **savm; /* Working pointers to matrices */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       else {  /*FILE *fic ; */ /* Used in readdata only */
         d=p/q;  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
         u=x+d;  FILE *ficlog, *ficrespow;
         if (u-a < tol2 || b-u < tol2)  int globpr=0; /* Global variable for printing or not */
           d=SIGN(tol1,xm-x);  double fretone; /* Only one call to likelihood */
       }  long ipmx=0; /* Number of contributions */
     } else {  double sw; /* Sum of weights */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  char filerespow[FILENAMELENGTH];
     }  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  FILE *ficresilk;
     fu=(*f)(u);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
     if (fu <= fx) {  FILE *ficresprobmorprev;
       if (u >= x) a=x; else b=x;  FILE *fichtm, *fichtmcov; /* Html File */
       SHFT(v,w,x,u)  FILE *ficreseij;
         SHFT(fv,fw,fx,fu)  char filerese[FILENAMELENGTH];
         } else {  FILE *ficresstdeij;
           if (u < x) a=u; else b=u;  char fileresstde[FILENAMELENGTH];
           if (fu <= fw || w == x) {  FILE *ficrescveij;
             v=w;  char filerescve[FILENAMELENGTH];
             w=u;  FILE  *ficresvij;
             fv=fw;  char fileresv[FILENAMELENGTH];
             fw=fu;  FILE  *ficresvpl;
           } else if (fu <= fv || v == x || v == w) {  char fileresvpl[FILENAMELENGTH];
             v=u;  char title[MAXLINE];
             fv=fu;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
           }  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
         }  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   }  char command[FILENAMELENGTH];
   nrerror("Too many iterations in brent");  int  outcmd=0;
   *xmin=x;  
   return fx;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 }  
   char filelog[FILENAMELENGTH]; /* Log file */
 /****************** mnbrak ***********************/  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  char popfile[FILENAMELENGTH];
             double (*func)(double))  
 {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   double ulim,u,r,q, dum;  
   double fu;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
    struct timezone tzp;
   *fa=(*func)(*ax);  extern int gettimeofday();
   *fb=(*func)(*bx);  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   if (*fb > *fa) {  long time_value;
     SHFT(dum,*ax,*bx,dum)  extern long time();
       SHFT(dum,*fb,*fa,dum)  char strcurr[80], strfor[80];
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);  char *endptr;
   *fc=(*func)(*cx);  long lval;
   while (*fb > *fc) {  double dval;
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  #define NR_END 1
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  #define FREE_ARG char*
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #define FTOL 1.0e-10
     ulim=(*bx)+GLIMIT*(*cx-*bx);  
     if ((*bx-u)*(u-*cx) > 0.0) {  #define NRANSI 
       fu=(*func)(u);  #define ITMAX 200 
     } else if ((*cx-u)*(u-ulim) > 0.0) {  
       fu=(*func)(u);  #define TOL 2.0e-4 
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define CGOLD 0.3819660 
           SHFT(*fb,*fc,fu,(*func)(u))  #define ZEPS 1.0e-10 
           }  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  #define GOLD 1.618034 
       fu=(*func)(u);  #define GLIMIT 100.0 
     } else {  #define TINY 1.0e-20 
       u=(*cx)+GOLD*(*cx-*bx);  
       fu=(*func)(u);  static double maxarg1,maxarg2;
     }  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
     SHFT(*ax,*bx,*cx,u)  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
       SHFT(*fa,*fb,*fc,fu)    
       }  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 }  #define rint(a) floor(a+0.5)
   
 /*************** linmin ************************/  static double sqrarg;
   #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 int ncom;  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 double *pcom,*xicom;  int agegomp= AGEGOMP;
 double (*nrfunc)(double []);  
    int imx; 
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  int stepm=1;
 {  /* Stepm, step in month: minimum step interpolation*/
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  int estepm;
   double f1dim(double x);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  
               double *fc, double (*func)(double));  int m,nb;
   int j;  long *num;
   double xx,xmin,bx,ax;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   double fx,fb,fa;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
    double **pmmij, ***probs;
   ncom=n;  double *ageexmed,*agecens;
   pcom=vector(1,n);  double dateintmean=0;
   xicom=vector(1,n);  
   nrfunc=func;  double *weight;
   for (j=1;j<=n;j++) {  int **s; /* Status */
     pcom[j]=p[j];  double *agedc, **covar, idx;
     xicom[j]=xi[j];  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   }  double *lsurv, *lpop, *tpop;
   ax=0.0;  
   xx=1.0;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  double ftolhess; /* Tolerance for computing hessian */
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  /**************** split *************************/
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 #endif  {
   for (j=1;j<=n;j++) {    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
     xi[j] *= xmin;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
     p[j] += xi[j];    */ 
   }    char  *ss;                            /* pointer */
   free_vector(xicom,1,n);    int   l1, l2;                         /* length counters */
   free_vector(pcom,1,n);  
 }    l1 = strlen(path );                   /* length of path */
     if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 /*************** powell ************************/    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    if ( ss == NULL ) {                   /* no directory, so determine current directory */
             double (*func)(double []))      strcpy( name, path );               /* we got the fullname name because no directory */
 {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   void linmin(double p[], double xi[], int n, double *fret,        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
               double (*func)(double []));      /* get current working directory */
   int i,ibig,j;      /*    extern  char* getcwd ( char *buf , int len);*/
   double del,t,*pt,*ptt,*xit;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   double fp,fptt;        return( GLOCK_ERROR_GETCWD );
   double *xits;      }
   pt=vector(1,n);      /* got dirc from getcwd*/
   ptt=vector(1,n);      printf(" DIRC = %s \n",dirc);
   xit=vector(1,n);    } else {                              /* strip direcotry from path */
   xits=vector(1,n);      ss++;                               /* after this, the filename */
   *fret=(*func)(p);      l2 = strlen( ss );                  /* length of filename */
   for (j=1;j<=n;j++) pt[j]=p[j];      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   for (*iter=1;;++(*iter)) {      strcpy( name, ss );         /* save file name */
     fp=(*fret);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
     ibig=0;      dirc[l1-l2] = 0;                    /* add zero */
     del=0.0;      printf(" DIRC2 = %s \n",dirc);
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    }
     for (i=1;i<=n;i++)    /* We add a separator at the end of dirc if not exists */
       printf(" %d %.12f",i, p[i]);    l1 = strlen( dirc );                  /* length of directory */
     printf("\n");    if( dirc[l1-1] != DIRSEPARATOR ){
     for (i=1;i<=n;i++) {      dirc[l1] =  DIRSEPARATOR;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];      dirc[l1+1] = 0; 
       fptt=(*fret);      printf(" DIRC3 = %s \n",dirc);
 #ifdef DEBUG    }
       printf("fret=%lf \n",*fret);    ss = strrchr( name, '.' );            /* find last / */
 #endif    if (ss >0){
       printf("%d",i);fflush(stdout);      ss++;
       linmin(p,xit,n,fret,func);      strcpy(ext,ss);                     /* save extension */
       if (fabs(fptt-(*fret)) > del) {      l1= strlen( name);
         del=fabs(fptt-(*fret));      l2= strlen(ss)+1;
         ibig=i;      strncpy( finame, name, l1-l2);
       }      finame[l1-l2]= 0;
 #ifdef DEBUG    }
       printf("%d %.12e",i,(*fret));  
       for (j=1;j<=n;j++) {    return( 0 );                          /* we're done */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  }
         printf(" x(%d)=%.12e",j,xit[j]);  
       }  
       for(j=1;j<=n;j++)  /******************************************/
         printf(" p=%.12e",p[j]);  
       printf("\n");  void replace_back_to_slash(char *s, char*t)
 #endif  {
     }    int i;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    int lg=0;
 #ifdef DEBUG    i=0;
       int k[2],l;    lg=strlen(t);
       k[0]=1;    for(i=0; i<= lg; i++) {
       k[1]=-1;      (s[i] = t[i]);
       printf("Max: %.12e",(*func)(p));      if (t[i]== '\\') s[i]='/';
       for (j=1;j<=n;j++)    }
         printf(" %.12e",p[j]);  }
       printf("\n");  
       for(l=0;l<=1;l++) {  char *trimbb(char *out, char *in)
         for (j=1;j<=n;j++) {  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    char *s;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    s=out;
         }    while (*in != '\0'){
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
       }        in++;
 #endif      }
       *out++ = *in++;
     }
       free_vector(xit,1,n);    *out='\0';
       free_vector(xits,1,n);    return s;
       free_vector(ptt,1,n);  }
       free_vector(pt,1,n);  
       return;  char *cutv(char *blocc, char *alocc, char *in, char occ)
     }  {
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
     for (j=1;j<=n;j++) {       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
       ptt[j]=2.0*p[j]-pt[j];       gives blocc="abcdef2ghi" and alocc="j".
       xit[j]=p[j]-pt[j];       If occ is not found blocc is null and alocc is equal to in. Returns alocc
       pt[j]=p[j];    */
     }    char *s, *t;
     fptt=(*func)(ptt);    t=in;s=in;
     if (fptt < fp) {    while (*in != '\0'){
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);      while( *in == occ){
       if (t < 0.0) {        *blocc++ = *in++;
         linmin(p,xit,n,fret,func);        s=in;
         for (j=1;j<=n;j++) {      }
           xi[j][ibig]=xi[j][n];      *blocc++ = *in++;
           xi[j][n]=xit[j];    }
         }    if (s == t) /* occ not found */
 #ifdef DEBUG      *(blocc-(in-s))='\0';
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    else
         for(j=1;j<=n;j++)      *(blocc-(in-s)-1)='\0';
           printf(" %.12e",xit[j]);    in=s;
         printf("\n");    while ( *in != '\0'){
 #endif      *alocc++ = *in++;
       }    }
     }  
   }    *alocc='\0';
 }    return s;
   }
 /**** Prevalence limit ****************/  
   int nbocc(char *s, char occ)
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  {
 {    int i,j=0;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    int lg=20;
      matrix by transitions matrix until convergence is reached */    i=0;
     lg=strlen(s);
   int i, ii,j,k;    for(i=0; i<= lg; i++) {
   double min, max, maxmin, maxmax,sumnew=0.;    if  (s[i] == occ ) j++;
   double **matprod2();    }
   double **out, cov[NCOVMAX], **pmij();    return j;
   double **newm;  }
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /* void cutv(char *u,char *v, char*t, char occ) */
   for (ii=1;ii<=nlstate+ndeath;ii++)  /* { */
     for (j=1;j<=nlstate+ndeath;j++){  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
     }  /*      gives u="abcdef2ghi" and v="j" *\/ */
   /*   int i,lg,j,p=0; */
    cov[1]=1.;  /*   i=0; */
    /*   lg=strlen(t); */
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /*   for(j=0; j<=lg-1; j++) { */
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
     newm=savm;  /*   } */
     /* Covariates have to be included here again */  
      cov[2]=agefin;  /*   for(j=0; j<p; j++) { */
    /*     (u[j] = t[j]); */
       for (k=1; k<=cptcovn;k++) {  /*   } */
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /*      u[p]='\0'; */
         /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/  
       }  /*    for(j=0; j<= lg; j++) { */
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
       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]]];  /* } */
   
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  /********************** nrerror ********************/
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  void nrerror(char error_text[])
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  {
     fprintf(stderr,"ERREUR ...\n");
     savm=oldm;    fprintf(stderr,"%s\n",error_text);
     oldm=newm;    exit(EXIT_FAILURE);
     maxmax=0.;  }
     for(j=1;j<=nlstate;j++){  /*********************** vector *******************/
       min=1.;  double *vector(int nl, int nh)
       max=0.;  {
       for(i=1; i<=nlstate; i++) {    double *v;
         sumnew=0;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    if (!v) nrerror("allocation failure in vector");
         prlim[i][j]= newm[i][j]/(1-sumnew);    return v-nl+NR_END;
         max=FMAX(max,prlim[i][j]);  }
         min=FMIN(min,prlim[i][j]);  
       }  /************************ free vector ******************/
       maxmin=max-min;  void free_vector(double*v, int nl, int nh)
       maxmax=FMAX(maxmax,maxmin);  {
     }    free((FREE_ARG)(v+nl-NR_END));
     if(maxmax < ftolpl){  }
       return prlim;  
     }  /************************ivector *******************************/
   }  int *ivector(long nl,long nh)
 }  {
     int *v;
 /*************** transition probabilities ***************/    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    return v-nl+NR_END;
 {  }
   double s1, s2;  
   /*double t34;*/  /******************free ivector **************************/
   int i,j,j1, nc, ii, jj;  void free_ivector(int *v, long nl, long 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];*/  /************************lvector *******************************/
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  long *lvector(long nl,long nh)
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  {
       }    long *v;
       ps[i][j]=s2;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       /*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 lvector **************************/
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  void free_lvector(long *v, long nl, long nh)
       }  {
       ps[i][j]=s2;    free((FREE_ARG)(v+nl-NR_END));
     }  }
   }  
     /*ps[3][2]=1;*/  /******************* imatrix *******************************/
   int **imatrix(long nrl, long nrh, long ncl, long nch) 
   for(i=1; i<= nlstate; i++){       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
      s1=0;  { 
     for(j=1; j<i; j++)    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       s1+=exp(ps[i][j]);    int **m; 
     for(j=i+1; j<=nlstate+ndeath; j++)    
       s1+=exp(ps[i][j]);    /* allocate pointers to rows */ 
     ps[i][i]=1./(s1+1.);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     for(j=1; j<i; j++)    if (!m) nrerror("allocation failure 1 in matrix()"); 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    m += NR_END; 
     for(j=i+1; j<=nlstate+ndeath; j++)    m -= nrl; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    
   } /* end i */    /* allocate rows and set pointers to them */ 
     m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     for(jj=1; jj<= nlstate+ndeath; jj++){    m[nrl] += NR_END; 
       ps[ii][jj]=0;    m[nrl] -= ncl; 
       ps[ii][ii]=1;    
     }    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   }    
     /* return pointer to array of pointers to rows */ 
     return m; 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  } 
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /****************** free_imatrix *************************/
    }  void free_imatrix(m,nrl,nrh,ncl,nch)
     printf("\n ");        int **m;
     }        long nch,ncl,nrh,nrl; 
     printf("\n ");printf("%lf ",cov[2]);*/       /* free an int matrix allocated by imatrix() */ 
 /*  { 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   goto end;*/    free((FREE_ARG) (m+nrl-NR_END)); 
     return ps;  } 
 }  
   /******************* matrix *******************************/
 /**************** Product of 2 matrices ******************/  double **matrix(long nrl, long nrh, long ncl, long nch)
   {
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
 {    double **m;
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   /* in, b, out are matrice of pointers which should have been initialized    if (!m) nrerror("allocation failure 1 in matrix()");
      before: only the contents of out is modified. The function returns    m += NR_END;
      a pointer to pointers identical to out */    m -= nrl;
   long i, j, k;  
   for(i=nrl; i<= nrh; i++)    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     for(k=ncolol; k<=ncoloh; k++)    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    m[nrl] += NR_END;
         out[i][k] +=in[i][j]*b[j][k];    m[nrl] -= ncl;
   
   return out;    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]) 
      */
 /************* Higher Matrix Product ***************/  }
   
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  /*************************free matrix ************************/
 {  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  {
      duration (i.e. until    free((FREE_ARG)(m[nrl]+ncl-NR_END));
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    free((FREE_ARG)(m+nrl-NR_END));
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  }
      (typically every 2 years instead of every month which is too big).  
      Model is determined by parameters x and covariates have to be  /******************* ma3x *******************************/
      included manually here.  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   {
      */    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     double ***m;
   int i, j, d, h, k;  
   double **out, cov[NCOVMAX];    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double **newm;    if (!m) nrerror("allocation failure 1 in matrix()");
     m += NR_END;
   /* Hstepm could be zero and should return the unit matrix */    m -= nrl;
   for (i=1;i<=nlstate+ndeath;i++)  
     for (j=1;j<=nlstate+ndeath;j++){    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       oldm[i][j]=(i==j ? 1.0 : 0.0);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       po[i][j][0]=(i==j ? 1.0 : 0.0);    m[nrl] += NR_END;
     }    m[nrl] -= ncl;
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(h=1; h <=nhstepm; h++){    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     for(d=1; d <=hstepm; d++){  
       newm=savm;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       /* Covariates have to be included here again */    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       cov[1]=1.;    m[nrl][ncl] += NR_END;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    m[nrl][ncl] -= nll;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    for (j=ncl+1; j<=nch; j++) 
       for (k=1; k<=cptcovage;k++)      m[nrl][j]=m[nrl][j-1]+nlay;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    
       for (k=1; k<=cptcovprod;k++)    for (i=nrl+1; i<=nrh; i++) {
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       for (j=ncl+1; j<=nch; j++) 
         m[i][j]=m[i][j-1]+nlay;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    }
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    return m; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
                    pmij(pmmij,cov,ncovmodel,x,nlstate));             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       savm=oldm;    */
       oldm=newm;  }
     }  
     for(i=1; i<=nlstate+ndeath; i++)  /*************************free ma3x ************************/
       for(j=1;j<=nlstate+ndeath;j++) {  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
         po[i][j][h]=newm[i][j];  {
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
          */    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       }    free((FREE_ARG)(m+nrl-NR_END));
   } /* end h */  }
   return po;  
 }  /*************** function subdirf ***********/
   char *subdirf(char fileres[])
   {
 /*************** log-likelihood *************/    /* Caution optionfilefiname is hidden */
 double func( double *x)    strcpy(tmpout,optionfilefiname);
 {    strcat(tmpout,"/"); /* Add to the right */
   int i, ii, j, k, mi, d, kk;    strcat(tmpout,fileres);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    return tmpout;
   double **out;  }
   double sw; /* Sum of weights */  
   double lli; /* Individual log likelihood */  /*************** function subdirf2 ***********/
   long ipmx;  char *subdirf2(char fileres[], char *preop)
   /*extern weight */  {
   /* We are differentiating ll according to initial status */    
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    /* Caution optionfilefiname is hidden */
   /*for(i=1;i<imx;i++)    strcpy(tmpout,optionfilefiname);
     printf(" %d\n",s[4][i]);    strcat(tmpout,"/");
   */    strcat(tmpout,preop);
   cov[1]=1.;    strcat(tmpout,fileres);
     return tmpout;
   for(k=1; k<=nlstate; k++) ll[k]=0.;  }
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){  
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  /*************** function subdirf3 ***********/
     for(mi=1; mi<= wav[i]-1; mi++){  char *subdirf3(char fileres[], char *preop, char *preop2)
       for (ii=1;ii<=nlstate+ndeath;ii++)  {
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    
       for(d=0; d<dh[mi][i]; d++){    /* Caution optionfilefiname is hidden */
         newm=savm;    strcpy(tmpout,optionfilefiname);
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    strcat(tmpout,"/");
         for (kk=1; kk<=cptcovage;kk++) {    strcat(tmpout,preop);
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    strcat(tmpout,preop2);
         }    strcat(tmpout,fileres);
            return tmpout;
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  }
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  
         savm=oldm;  /***************** f1dim *************************/
         oldm=newm;  extern int ncom; 
          extern double *pcom,*xicom;
          extern double (*nrfunc)(double []); 
       } /* end mult */   
        double f1dim(double x) 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  { 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    int j; 
       ipmx +=1;    double f;
       sw += weight[i];    double *xt; 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;   
     } /* end of wave */    xt=vector(1,ncom); 
   } /* end of individual */    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    free_vector(xt,1,ncom); 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    return f; 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  } 
   return -l;  
 }  /*****************brent *************************/
   double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   { 
 /*********** Maximum Likelihood Estimation ***************/    int iter; 
     double a,b,d,etemp;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    double fu,fv,fw,fx;
 {    double ftemp;
   int i,j, iter;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   double **xi,*delti;    double e=0.0; 
   double fret;   
   xi=matrix(1,npar,1,npar);    a=(ax < cx ? ax : cx); 
   for (i=1;i<=npar;i++)    b=(ax > cx ? ax : cx); 
     for (j=1;j<=npar;j++)    x=w=v=bx; 
       xi[i][j]=(i==j ? 1.0 : 0.0);    fw=fv=fx=(*f)(x); 
   printf("Powell\n");    for (iter=1;iter<=ITMAX;iter++) { 
   powell(p,xi,npar,ftol,&iter,&fret,func);      xm=0.5*(a+b); 
       tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));      printf(".");fflush(stdout);
       fprintf(ficlog,".");fflush(ficlog);
 }  #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);
 /**** Computes Hessian and covariance matrix ***/      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);
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
 {  #endif
   double  **a,**y,*x,pd;      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   double **hess;        *xmin=x; 
   int i, j,jk;        return fx; 
   int *indx;      } 
       ftemp=fu;
   double hessii(double p[], double delta, int theta, double delti[]);      if (fabs(e) > tol1) { 
   double hessij(double p[], double delti[], int i, int j);        r=(x-w)*(fx-fv); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;        q=(x-v)*(fx-fw); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;        p=(x-v)*q-(x-w)*r; 
         q=2.0*(q-r); 
   hess=matrix(1,npar,1,npar);        if (q > 0.0) p = -p; 
         q=fabs(q); 
   printf("\nCalculation of the hessian matrix. Wait...\n");        etemp=e; 
   for (i=1;i<=npar;i++){        e=d; 
     printf("%d",i);fflush(stdout);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     hess[i][i]=hessii(p,ftolhess,i,delti);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     /*printf(" %f ",p[i]);*/        else { 
     /*printf(" %lf ",hess[i][i]);*/          d=p/q; 
   }          u=x+d; 
            if (u-a < tol2 || b-u < tol2) 
   for (i=1;i<=npar;i++) {            d=SIGN(tol1,xm-x); 
     for (j=1;j<=npar;j++)  {        } 
       if (j>i) {      } else { 
         printf(".%d%d",i,j);fflush(stdout);        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         hess[i][j]=hessij(p,delti,i,j);      } 
         hess[j][i]=hess[i][j];          u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
         /*printf(" %lf ",hess[i][j]);*/      fu=(*f)(u); 
       }      if (fu <= fx) { 
     }        if (u >= x) a=x; else b=x; 
   }        SHFT(v,w,x,u) 
   printf("\n");          SHFT(fv,fw,fx,fu) 
           } else { 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");            if (u < x) a=u; else b=u; 
              if (fu <= fw || w == x) { 
   a=matrix(1,npar,1,npar);              v=w; 
   y=matrix(1,npar,1,npar);              w=u; 
   x=vector(1,npar);              fv=fw; 
   indx=ivector(1,npar);              fw=fu; 
   for (i=1;i<=npar;i++)            } else if (fu <= fv || v == x || v == w) { 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];              v=u; 
   ludcmp(a,npar,indx,&pd);              fv=fu; 
             } 
   for (j=1;j<=npar;j++) {          } 
     for (i=1;i<=npar;i++) x[i]=0;    } 
     x[j]=1;    nrerror("Too many iterations in brent"); 
     lubksb(a,npar,indx,x);    *xmin=x; 
     for (i=1;i<=npar;i++){    return fx; 
       matcov[i][j]=x[i];  } 
     }  
   }  /****************** mnbrak ***********************/
   
   printf("\n#Hessian matrix#\n");  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   for (i=1;i<=npar;i++) {              double (*func)(double)) 
     for (j=1;j<=npar;j++) {  { 
       printf("%.3e ",hess[i][j]);    double ulim,u,r,q, dum;
     }    double fu; 
     printf("\n");   
   }    *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
   /* Recompute Inverse */    if (*fb > *fa) { 
   for (i=1;i<=npar;i++)      SHFT(dum,*ax,*bx,dum) 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];        SHFT(dum,*fb,*fa,dum) 
   ludcmp(a,npar,indx,&pd);        } 
     *cx=(*bx)+GOLD*(*bx-*ax); 
   /*  printf("\n#Hessian matrix recomputed#\n");    *fc=(*func)(*cx); 
     while (*fb > *fc) { 
   for (j=1;j<=npar;j++) {      r=(*bx-*ax)*(*fb-*fc); 
     for (i=1;i<=npar;i++) x[i]=0;      q=(*bx-*cx)*(*fb-*fa); 
     x[j]=1;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     lubksb(a,npar,indx,x);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     for (i=1;i<=npar;i++){      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       y[i][j]=x[i];      if ((*bx-u)*(u-*cx) > 0.0) { 
       printf("%.3e ",y[i][j]);        fu=(*func)(u); 
     }      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     printf("\n");        fu=(*func)(u); 
   }        if (fu < *fc) { 
   */          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
   free_matrix(a,1,npar,1,npar);            } 
   free_matrix(y,1,npar,1,npar);      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   free_vector(x,1,npar);        u=ulim; 
   free_ivector(indx,1,npar);        fu=(*func)(u); 
   free_matrix(hess,1,npar,1,npar);      } else { 
         u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
 }      } 
       SHFT(*ax,*bx,*cx,u) 
 /*************** hessian matrix ****************/        SHFT(*fa,*fb,*fc,fu) 
 double hessii( double x[], double delta, int theta, double delti[])        } 
 {  } 
   int i;  
   int l=1, lmax=20;  /*************** linmin ************************/
   double k1,k2;  
   double p2[NPARMAX+1];  int ncom; 
   double res;  double *pcom,*xicom;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  double (*nrfunc)(double []); 
   double fx;   
   int k=0,kmax=10;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   double l1;  { 
     double brent(double ax, double bx, double cx, 
   fx=func(x);                 double (*f)(double), double tol, double *xmin); 
   for (i=1;i<=npar;i++) p2[i]=x[i];    double f1dim(double x); 
   for(l=0 ; l <=lmax; l++){    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     l1=pow(10,l);                double *fc, double (*func)(double)); 
     delts=delt;    int j; 
     for(k=1 ; k <kmax; k=k+1){    double xx,xmin,bx,ax; 
       delt = delta*(l1*k);    double fx,fb,fa;
       p2[theta]=x[theta] +delt;   
       k1=func(p2)-fx;    ncom=n; 
       p2[theta]=x[theta]-delt;    pcom=vector(1,n); 
       k2=func(p2)-fx;    xicom=vector(1,n); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */    nrfunc=func; 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    for (j=1;j<=n;j++) { 
            pcom[j]=p[j]; 
 #ifdef DEBUG      xicom[j]=xi[j]; 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);    } 
 #endif    ax=0.0; 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    xx=1.0; 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
         k=kmax;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       }  #ifdef DEBUG
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         k=kmax; l=lmax*10.;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       }  #endif
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    for (j=1;j<=n;j++) { 
         delts=delt;      xi[j] *= xmin; 
       }      p[j] += xi[j]; 
     }    } 
   }    free_vector(xicom,1,n); 
   delti[theta]=delts;    free_vector(pcom,1,n); 
   return res;  } 
    
 }  char *asc_diff_time(long time_sec, char ascdiff[])
   {
 double hessij( double x[], double delti[], int thetai,int thetaj)    long sec_left, days, hours, minutes;
 {    days = (time_sec) / (60*60*24);
   int i;    sec_left = (time_sec) % (60*60*24);
   int l=1, l1, lmax=20;    hours = (sec_left) / (60*60) ;
   double k1,k2,k3,k4,res,fx;    sec_left = (sec_left) %(60*60);
   double p2[NPARMAX+1];    minutes = (sec_left) /60;
   int k;    sec_left = (sec_left) % (60);
     sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   fx=func(x);    return ascdiff;
   for (k=1; k<=2; k++) {  }
     for (i=1;i<=npar;i++) p2[i]=x[i];  
     p2[thetai]=x[thetai]+delti[thetai]/k;  /*************** powell ************************/
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     k1=func(p2)-fx;              double (*func)(double [])) 
    { 
     p2[thetai]=x[thetai]+delti[thetai]/k;    void linmin(double p[], double xi[], int n, double *fret, 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;                double (*func)(double [])); 
     k2=func(p2)-fx;    int i,ibig,j; 
      double del,t,*pt,*ptt,*xit;
     p2[thetai]=x[thetai]-delti[thetai]/k;    double fp,fptt;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    double *xits;
     k3=func(p2)-fx;    int niterf, itmp;
    
     p2[thetai]=x[thetai]-delti[thetai]/k;    pt=vector(1,n); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    ptt=vector(1,n); 
     k4=func(p2)-fx;    xit=vector(1,n); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    xits=vector(1,n); 
 #ifdef DEBUG    *fret=(*func)(p); 
     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);    for (j=1;j<=n;j++) pt[j]=p[j]; 
 #endif    for (*iter=1;;++(*iter)) { 
   }      fp=(*fret); 
   return res;      ibig=0; 
 }      del=0.0; 
       last_time=curr_time;
 /************** Inverse of matrix **************/      (void) gettimeofday(&curr_time,&tzp);
 void ludcmp(double **a, int n, int *indx, double *d)      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
 {      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
   int i,imax,j,k;  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   double big,dum,sum,temp;     for (i=1;i<=n;i++) {
   double *vv;        printf(" %d %.12f",i, p[i]);
          fprintf(ficlog," %d %.12lf",i, p[i]);
   vv=vector(1,n);        fprintf(ficrespow," %.12lf", p[i]);
   *d=1.0;      }
   for (i=1;i<=n;i++) {      printf("\n");
     big=0.0;      fprintf(ficlog,"\n");
     for (j=1;j<=n;j++)      fprintf(ficrespow,"\n");fflush(ficrespow);
       if ((temp=fabs(a[i][j])) > big) big=temp;      if(*iter <=3){
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");        tm = *localtime(&curr_time.tv_sec);
     vv[i]=1.0/big;        strcpy(strcurr,asctime(&tm));
   }  /*       asctime_r(&tm,strcurr); */
   for (j=1;j<=n;j++) {        forecast_time=curr_time; 
     for (i=1;i<j;i++) {        itmp = strlen(strcurr);
       sum=a[i][j];        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          strcurr[itmp-1]='\0';
       a[i][j]=sum;        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     }        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     big=0.0;        for(niterf=10;niterf<=30;niterf+=10){
     for (i=j;i<=n;i++) {          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
       sum=a[i][j];          tmf = *localtime(&forecast_time.tv_sec);
       for (k=1;k<j;k++)  /*      asctime_r(&tmf,strfor); */
         sum -= a[i][k]*a[k][j];          strcpy(strfor,asctime(&tmf));
       a[i][j]=sum;          itmp = strlen(strfor);
       if ( (dum=vv[i]*fabs(sum)) >= big) {          if(strfor[itmp-1]=='\n')
         big=dum;          strfor[itmp-1]='\0';
         imax=i;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
       }          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
     }        }
     if (j != imax) {      }
       for (k=1;k<=n;k++) {      for (i=1;i<=n;i++) { 
         dum=a[imax][k];        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         a[imax][k]=a[j][k];        fptt=(*fret); 
         a[j][k]=dum;  #ifdef DEBUG
       }        printf("fret=%lf \n",*fret);
       *d = -(*d);        fprintf(ficlog,"fret=%lf \n",*fret);
       vv[imax]=vv[j];  #endif
     }        printf("%d",i);fflush(stdout);
     indx[j]=imax;        fprintf(ficlog,"%d",i);fflush(ficlog);
     if (a[j][j] == 0.0) a[j][j]=TINY;        linmin(p,xit,n,fret,func); 
     if (j != n) {        if (fabs(fptt-(*fret)) > del) { 
       dum=1.0/(a[j][j]);          del=fabs(fptt-(*fret)); 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          ibig=i; 
     }        } 
   }  #ifdef DEBUG
   free_vector(vv,1,n);  /* Doesn't work */        printf("%d %.12e",i,(*fret));
 ;        fprintf(ficlog,"%d %.12e",i,(*fret));
 }        for (j=1;j<=n;j++) {
           xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
 void lubksb(double **a, int n, int *indx, double b[])          printf(" x(%d)=%.12e",j,xit[j]);
 {          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   int i,ii=0,ip,j;        }
   double sum;        for(j=1;j<=n;j++) {
            printf(" p=%.12e",p[j]);
   for (i=1;i<=n;i++) {          fprintf(ficlog," p=%.12e",p[j]);
     ip=indx[i];        }
     sum=b[ip];        printf("\n");
     b[ip]=b[i];        fprintf(ficlog,"\n");
     if (ii)  #endif
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];      } 
     else if (sum) ii=i;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     b[i]=sum;  #ifdef DEBUG
   }        int k[2],l;
   for (i=n;i>=1;i--) {        k[0]=1;
     sum=b[i];        k[1]=-1;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        printf("Max: %.12e",(*func)(p));
     b[i]=sum/a[i][i];        fprintf(ficlog,"Max: %.12e",(*func)(p));
   }        for (j=1;j<=n;j++) {
 }          printf(" %.12e",p[j]);
           fprintf(ficlog," %.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");
          for(l=0;l<=1;l++) {
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;          for (j=1;j<=n;j++) {
   double ***freq; /* Frequencies */            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   double *pp;            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   double pos, k2, dateintsum=0,k2cpt=0;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   FILE *ficresp;          }
   char fileresp[FILENAMELENGTH];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
            fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   pp=vector(1,nlstate);        }
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  #endif
   strcpy(fileresp,"p");  
   strcat(fileresp,fileres);  
   if((ficresp=fopen(fileresp,"w"))==NULL) {        free_vector(xit,1,n); 
     printf("Problem with prevalence resultfile: %s\n", fileresp);        free_vector(xits,1,n); 
     exit(0);        free_vector(ptt,1,n); 
   }        free_vector(pt,1,n); 
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        return; 
   j1=0;      } 
        if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   j=cptcoveff;      for (j=1;j<=n;j++) { 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        ptt[j]=2.0*p[j]-pt[j]; 
          xit[j]=p[j]-pt[j]; 
   for(k1=1; k1<=j;k1++){        pt[j]=p[j]; 
     for(i1=1; i1<=ncodemax[k1];i1++){      } 
       j1++;      fptt=(*func)(ptt); 
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      if (fptt < fp) { 
         scanf("%d", i);*/        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       for (i=-1; i<=nlstate+ndeath; i++)          if (t < 0.0) { 
         for (jk=-1; jk<=nlstate+ndeath; jk++)            linmin(p,xit,n,fret,func); 
           for(m=agemin; m <= agemax+3; m++)          for (j=1;j<=n;j++) { 
             freq[i][jk][m]=0;            xi[j][ibig]=xi[j][n]; 
                  xi[j][n]=xit[j]; 
       dateintsum=0;          }
       k2cpt=0;  #ifdef DEBUG
       for (i=1; i<=imx; i++) {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         bool=1;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         if  (cptcovn>0) {          for(j=1;j<=n;j++){
           for (z1=1; z1<=cptcoveff; z1++)            printf(" %.12e",xit[j]);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])            fprintf(ficlog," %.12e",xit[j]);
               bool=0;          }
         }          printf("\n");
         if (bool==1) {          fprintf(ficlog,"\n");
           for(m=firstpass; m<=lastpass; m++){  #endif
             k2=anint[m][i]+(mint[m][i]/12.);        }
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      } 
               if(agev[m][i]==0) agev[m][i]=agemax+1;    } 
               if(agev[m][i]==1) agev[m][i]=agemax+2;  } 
               if (m<lastpass) {  
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  /**** Prevalence limit (stable or period prevalence)  ****************/
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  
               }  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
                {
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
                 dateintsum=dateintsum+k2;       matrix by transitions matrix until convergence is reached */
                 k2cpt++;  
               }    int i, ii,j,k;
             }    double min, max, maxmin, maxmax,sumnew=0.;
           }    double **matprod2();
         }    double **out, cov[NCOVMAX+1], **pmij();
       }    double **newm;
            double agefin, delaymax=50 ; /* Max number of years to converge */
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
     for (ii=1;ii<=nlstate+ndeath;ii++)
       if  (cptcovn>0) {      for (j=1;j<=nlstate+ndeath;j++){
         fprintf(ficresp, "\n#********** Variable ");        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      }
         fprintf(ficresp, "**********\n#");  
       }     cov[1]=1.;
       for(i=1; i<=nlstate;i++)   
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       fprintf(ficresp, "\n");    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
            newm=savm;
       for(i=(int)agemin; i <= (int)agemax+3; i++){      /* Covariates have to be included here again */
         if(i==(int)agemax+3)      cov[2]=agefin;
           printf("Total");      
         else      for (k=1; k<=cptcovn;k++) {
           printf("Age %d", i);        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         for(jk=1; jk <=nlstate ; jk++){        /*        printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      }
             pp[jk] += freq[jk][m][i];      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         }      for (k=1; k<=cptcovprod;k++)
         for(jk=1; jk <=nlstate ; jk++){        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           for(m=-1, pos=0; m <=0 ; m++)      
             pos += freq[jk][m][i];      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
           if(pp[jk]>=1.e-10)      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
           else      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);      
         }      savm=oldm;
       oldm=newm;
         for(jk=1; jk <=nlstate ; jk++){      maxmax=0.;
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      for(j=1;j<=nlstate;j++){
             pp[jk] += freq[jk][m][i];        min=1.;
         }        max=0.;
         for(i=1; i<=nlstate; i++) {
         for(jk=1,pos=0; jk <=nlstate ; jk++)          sumnew=0;
           pos += pp[jk];          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
         for(jk=1; jk <=nlstate ; jk++){          prlim[i][j]= newm[i][j]/(1-sumnew);
           if(pos>=1.e-5)          max=FMAX(max,prlim[i][j]);
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          min=FMIN(min,prlim[i][j]);
           else        }
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        maxmin=max-min;
           if( i <= (int) agemax){        maxmax=FMAX(maxmax,maxmin);
             if(pos>=1.e-5){      }
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      if(maxmax < ftolpl){
               probs[i][jk][j1]= pp[jk]/pos;        return prlim;
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/      }
             }    }
             else  }
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  
           }  /*************** transition probabilities ***************/ 
         }  
          double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         for(jk=-1; jk <=nlstate+ndeath; jk++)  {
           for(m=-1; m <=nlstate+ndeath; m++)    /* According to parameters values stored in x and the covariate's values stored in cov,
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);       computes the probability to be observed in state j being in state i by appying the
         if(i <= (int) agemax)       model to the ncovmodel covariates (including constant and age).
           fprintf(ficresp,"\n");       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
         printf("\n");       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
       }       ncth covariate in the global vector x is given by the formula:
     }       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   }       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
   dateintmean=dateintsum/k2cpt;       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
         sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
   fclose(ficresp);       Outputs ps[i][j] the probability to be observed in j being in j according to
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
   free_vector(pp,1,nlstate);    */
      double s1, lnpijopii;
   /* End of Freq */    /*double t34;*/
 }    int i,j,j1, nc, ii, jj;
   
 /************ Prevalence ********************/      for(i=1; i<= nlstate; i++){
 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)        for(j=1; j<i;j++){
 {  /* Some frequencies */          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
              /*lnpijopii += param[i][j][nc]*cov[nc];*/
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   double ***freq; /* Frequencies */  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   double *pp;          }
   double pos, k2;          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   pp=vector(1,nlstate);        }
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(j=i+1; j<=nlstate+ndeath;j++){
            for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
   j1=0;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
    /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
   j=cptcoveff;          }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
          }
   for(k1=1; k1<=j;k1++){      }
     for(i1=1; i1<=ncodemax[k1];i1++){      
       j1++;      for(i=1; i<= nlstate; i++){
              s1=0;
       for (i=-1; i<=nlstate+ndeath; i++)          for(j=1; j<i; j++){
         for (jk=-1; jk<=nlstate+ndeath; jk++)            s1+=exp(ps[i][j]); /* In fact sums pij/pii */
           for(m=agemin; m <= agemax+3; m++)          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
             freq[i][jk][m]=0;        }
              for(j=i+1; j<=nlstate+ndeath; j++){
       for (i=1; i<=imx; i++) {          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         bool=1;          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         if  (cptcovn>0) {        }
           for (z1=1; z1<=cptcoveff; z1++)        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        ps[i][i]=1./(s1+1.);
               bool=0;        /* Computing other pijs */
         }        for(j=1; j<i; j++)
         if (bool==1) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
           for(m=firstpass; m<=lastpass; m++){        for(j=i+1; j<=nlstate+ndeath; j++)
             k2=anint[m][i]+(mint[m][i]/12.);          ps[i][j]= exp(ps[i][j])*ps[i][i];
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
               if(agev[m][i]==0) agev[m][i]=agemax+1;      } /* end i */
               if(agev[m][i]==1) agev[m][i]=agemax+2;      
               if (m<lastpass) {      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
                 if (calagedate>0)        for(jj=1; jj<= nlstate+ndeath; jj++){
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          ps[ii][jj]=0;
                 else          ps[ii][ii]=1;
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        }
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];      }
               }      
             }  
           }  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
         }  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       }  /*         printf("ddd %lf ",ps[ii][jj]); */
       for(i=(int)agemin; i <= (int)agemax+3; i++){  /*       } */
         for(jk=1; jk <=nlstate ; jk++){  /*       printf("\n "); */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  /*        } */
             pp[jk] += freq[jk][m][i];  /*        printf("\n ");printf("%lf ",cov[2]); */
         }         /*
         for(jk=1; jk <=nlstate ; jk++){        for(i=1; i<= npar; i++) printf("%f ",x[i]);
           for(m=-1, pos=0; m <=0 ; m++)        goto end;*/
             pos += freq[jk][m][i];      return ps;
         }  }
          
         for(jk=1; jk <=nlstate ; jk++){  /**************** Product of 2 matrices ******************/
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  
             pp[jk] += freq[jk][m][i];  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
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
            /* in, b, out are matrice of pointers which should have been initialized 
         for(jk=1; jk <=nlstate ; jk++){           before: only the contents of out is modified. The function returns
           if( i <= (int) agemax){       a pointer to pointers identical to out */
             if(pos>=1.e-5){    long i, j, k;
               probs[i][jk][j1]= pp[jk]/pos;    for(i=nrl; i<= nrh; i++)
             }      for(k=ncolol; k<=ncoloh; k++)
           }        for(j=ncl,out[i][k]=0.; j<=nch; j++)
         }          out[i][k] +=in[i][j]*b[j][k];
          
       }    return out;
     }  }
   }  
   
    /************* Higher Matrix Product ***************/
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  
   free_vector(pp,1,nlstate);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
    {
 }  /* End of Freq */    /* Computes the transition matrix starting at age 'age' over 
        'nhstepm*hstepm*stepm' months (i.e. until
 /************* Waves Concatenation ***************/       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
 {       (typically every 2 years instead of every month which is too big 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.       for the memory).
      Death is a valid wave (if date is known).       Model is determined by parameters x and covariates have to be 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i       included manually here. 
      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.       */
      */  
     int i, j, d, h, k;
   int i, mi, m;    double **out, cov[NCOVMAX+1];
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    double **newm;
      double sum=0., jmean=0.;*/  
     /* Hstepm could be zero and should return the unit matrix */
   int j, k=0,jk, ju, jl;    for (i=1;i<=nlstate+ndeath;i++)
   double sum=0.;      for (j=1;j<=nlstate+ndeath;j++){
   jmin=1e+5;        oldm[i][j]=(i==j ? 1.0 : 0.0);
   jmax=-1;        po[i][j][0]=(i==j ? 1.0 : 0.0);
   jmean=0.;      }
   for(i=1; i<=imx; i++){    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     mi=0;    for(h=1; h <=nhstepm; h++){
     m=firstpass;      for(d=1; d <=hstepm; d++){
     while(s[m][i] <= nlstate){        newm=savm;
       if(s[m][i]>=1)        /* Covariates have to be included here again */
         mw[++mi][i]=m;        cov[1]=1.;
       if(m >=lastpass)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
         break;        for (k=1; k<=cptcovn;k++) 
       else          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         m++;        for (k=1; k<=cptcovage;k++)
     }/* end while */          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     if (s[m][i] > nlstate){        for (k=1; k<=cptcovprod;k++)
       mi++;     /* Death is another wave */          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */  
       mw[mi][i]=m;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
     }        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     wav[i]=mi;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
     if(mi==0)        savm=oldm;
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        oldm=newm;
   }      }
       for(i=1; i<=nlstate+ndeath; i++)
   for(i=1; i<=imx; i++){        for(j=1;j<=nlstate+ndeath;j++) {
     for(mi=1; mi<wav[i];mi++){          po[i][j][h]=newm[i][j];
       if (stepm <=0)          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
         dh[mi][i]=1;        }
       else{      /*printf("h=%d ",h);*/
         if (s[mw[mi+1][i]][i] > nlstate) {    } /* end h */
           if (agedc[i] < 2*AGESUP) {  /*     printf("\n H=%d \n",h); */
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);    return po;
           if(j==0) j=1;  /* Survives at least one month after exam */  }
           k=k+1;  
           if (j >= jmax) jmax=j;  
           if (j <= jmin) jmin=j;  /*************** log-likelihood *************/
           sum=sum+j;  double func( double *x)
           /*if (j<0) printf("j=%d num=%d \n",j,i); */  {
           }    int i, ii, j, k, mi, d, kk;
         }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
         else{    double **out;
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    double sw; /* Sum of weights */
           k=k+1;    double lli; /* Individual log likelihood */
           if (j >= jmax) jmax=j;    int s1, s2;
           else if (j <= jmin)jmin=j;    double bbh, survp;
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    long ipmx;
           sum=sum+j;    /*extern weight */
         }    /* We are differentiating ll according to initial status */
         jk= j/stepm;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         jl= j -jk*stepm;    /*for(i=1;i<imx;i++) 
         ju= j -(jk+1)*stepm;      printf(" %d\n",s[4][i]);
         if(jl <= -ju)    */
           dh[mi][i]=jk;    cov[1]=1.;
         else  
           dh[mi][i]=jk+1;    for(k=1; k<=nlstate; k++) ll[k]=0.;
         if(dh[mi][i]==0)  
           dh[mi][i]=1; /* At least one step */    if(mle==1){
       }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     }        /* Computes the values of the ncovmodel covariates of the model
   }           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
   jmean=sum/k;           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);           to be observed in j being in i according to the model.
  }         */
 /*********** Tricode ****************************/        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 void tricode(int *Tvar, int **nbcode, int imx)        /* 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] 
   int Ndum[20],ij=1, k, j, i;           has been calculated etc */
   int cptcode=0;        for(mi=1; mi<= wav[i]-1; mi++){
   cptcoveff=0;          for (ii=1;ii<=nlstate+ndeath;ii++)
              for (j=1;j<=nlstate+ndeath;j++){
   for (k=0; k<19; k++) Ndum[k]=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (k=1; k<=7; k++) ncodemax[k]=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          for(d=0; d<dh[mi][i]; d++){
     for (i=1; i<=imx; i++) {            newm=savm;
       ij=(int)(covar[Tvar[j]][i]);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       Ndum[ij]++;            for (kk=1; kk<=cptcovage;kk++) {
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
       if (ij > cptcode) cptcode=ij;            }
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for (i=0; i<=cptcode; i++) {            savm=oldm;
       if(Ndum[i]!=0) ncodemax[j]++;            oldm=newm;
     }          } /* end mult */
     ij=1;        
           /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           /* But now since version 0.9 we anticipate for bias at large stepm.
     for (i=1; i<=ncodemax[j]; i++) {           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       for (k=0; k<=19; k++) {           * (in months) between two waves is not a multiple of stepm, we rounded to 
         if (Ndum[k] != 0) {           * the nearest (and in case of equal distance, to the lowest) interval but now
           nbcode[Tvar[j]][ij]=k;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
                     * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
           ij++;           * probability in order to take into account the bias as a fraction of the way
         }           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
         if (ij > ncodemax[j]) break;           * -stepm/2 to stepm/2 .
       }             * For stepm=1 the results are the same as for previous versions of Imach.
     }           * For stepm > 1 the results are less biased than in previous versions. 
   }             */
           s1=s[mw[mi][i]][i];
  for (k=0; k<19; k++) Ndum[k]=0;          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
  for (i=1; i<=ncovmodel-2; i++) {          /* bias bh is positive if real duration
       ij=Tvar[i];           * is higher than the multiple of stepm and negative otherwise.
       Ndum[ij]++;           */
     }          /* 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){ 
  ij=1;            /* i.e. if s2 is a death state and if the date of death is known 
  for (i=1; i<=10; i++) {               then the contribution to the likelihood is the probability to 
    if((Ndum[i]!=0) && (i<=ncovcol)){               die between last step unit time and current  step unit time, 
      Tvaraff[ij]=i;               which is also equal to probability to die before dh 
      ij++;               minus probability to die before dh-stepm . 
    }               In version up to 0.92 likelihood was computed
  }          as if date of death was unknown. Death was treated as any other
            health state: the date of the interview describes the actual state
     cptcoveff=ij-1;          and not the date of a change in health state. The former idea was
 }          to consider that at each interview the state was recorded
           (healthy, disable or death) and IMaCh was corrected; but when we
 /*********** Health Expectancies ****************/          introduced the exact date of death then we should have modified
           the contribution of an exact death to the likelihood. This new
 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 )          contribution is smaller and very dependent of the step unit
           stepm. It is no more the probability to die between last interview
 {          and month of death but the probability to survive from last
   /* Health expectancies */          interview up to one month before death multiplied by the
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;          probability to die within a month. Thanks to Chris
   double age, agelim, hf;          Jackson for correcting this bug.  Former versions increased
   double ***p3mat,***varhe;          mortality artificially. The bad side is that we add another loop
   double **dnewm,**doldm;          which slows down the processing. The difference can be up to 10%
   double *xp;          lower mortality.
   double **gp, **gm;            */
   double ***gradg, ***trgradg;            lli=log(out[s1][s2] - savm[s1][s2]);
   int theta;  
   
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          } else if  (s2==-2) {
   xp=vector(1,npar);            for (j=1,survp=0. ; j<=nlstate; j++) 
   dnewm=matrix(1,nlstate*2,1,npar);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   doldm=matrix(1,nlstate*2,1,nlstate*2);            /*survp += out[s1][j]; */
              lli= log(survp);
   fprintf(ficreseij,"# Health expectancies\n");          }
   fprintf(ficreseij,"# Age");          
   for(i=1; i<=nlstate;i++)          else if  (s2==-4) { 
     for(j=1; j<=nlstate;j++)            for (j=3,survp=0. ; j<=nlstate; j++)  
       fprintf(ficreseij," %1d-%1d (SE)",i,j);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   fprintf(ficreseij,"\n");            lli= log(survp); 
           } 
   if(estepm < stepm){  
     printf ("Problem %d lower than %d\n",estepm, stepm);          else if  (s2==-5) { 
   }            for (j=1,survp=0. ; j<=2; j++)  
   else  hstepm=estepm;                survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   /* We compute the life expectancy from trapezoids spaced every estepm months            lli= log(survp); 
    * This is mainly to measure the difference between two models: for example          } 
    * if stepm=24 months pijx are given only every 2 years and by summing them          
    * we are calculating an estimate of the Life Expectancy assuming a linear          else{
    * progression inbetween and thus overestimating or underestimating according            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
    * to the curvature of the survival function. If, for the same date, we            /*  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 */
    * estimate the model with stepm=1 month, we can keep estepm to 24 months          } 
    * to compare the new estimate of Life expectancy with the same linear          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
    * hypothesis. A more precise result, taking into account a more precise          /*if(lli ==000.0)*/
    * curvature will be obtained if estepm is as small as stepm. */          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
           ipmx +=1;
   /* For example we decided to compute the life expectancy with the smallest unit */          sw += weight[i];
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      nhstepm is the number of hstepm from age to agelim        } /* end of wave */
      nstepm is the number of stepm from age to agelin.      } /* end of individual */
      Look at hpijx to understand the reason of that which relies in memory size    }  else if(mle==2){
      and note for a fixed period like estepm months */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      survival function given by stepm (the optimization length). Unfortunately it        for(mi=1; mi<= wav[i]-1; mi++){
      means that if the survival funtion is printed only each two years of age and if          for (ii=1;ii<=nlstate+ndeath;ii++)
      you sum them up and add 1 year (area under the trapezoids) you won't get the same            for (j=1;j<=nlstate+ndeath;j++){
      results. So we changed our mind and took the option of the best precision.              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */            }
           for(d=0; d<=dh[mi][i]; d++){
   agelim=AGESUP;            newm=savm;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     /* nhstepm age range expressed in number of stepm */            for (kk=1; kk<=cptcovage;kk++) {
     nstepm=(int) rint((agelim-age)*YEARM/stepm);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */            }
     /* if (stepm >= YEARM) hstepm=1;*/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            savm=oldm;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);            oldm=newm;
     gp=matrix(0,nhstepm,1,nlstate*2);          } /* end mult */
     gm=matrix(0,nhstepm,1,nlstate*2);        
           s1=s[mw[mi][i]][i];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored          s2=s[mw[mi+1][i]][i];
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          bbh=(double)bh[mi][i]/(double)stepm; 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
            ipmx +=1;
           sw += weight[i];
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
     /* Computing Variances of health expectancies */      } /* end of individual */
     }  else if(mle==3){  /* exponential inter-extrapolation */
      for(theta=1; theta <=npar; theta++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(i=1; i<=npar; i++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        for(mi=1; mi<= wav[i]-1; mi++){
       }          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, gp[h][cptj]=0.; h<=nhstepm-1; h++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             gp[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,
                               1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                  savm=oldm;
       for(i=1; i<=npar; i++)            oldm=newm;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          } /* 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]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           cptj=cptj+1;          ipmx +=1;
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){          sw += weight[i];
             gm[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==4){  /* ml=4 no inter-extrapolation */
       for(j=1; j<= nlstate*2; j++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for(h=0; h<=nhstepm-1; h++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        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);
 /* End theta */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
      for(h=0; h<=nhstepm-1; h++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(j=1; j<=nlstate*2;j++)            for (kk=1; kk<=cptcovage;kk++) {
         for(theta=1; theta <=npar; theta++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           trgradg[h][j][theta]=gradg[h][theta][j];            }
                
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      for(i=1;i<=nlstate*2;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1;j<=nlstate*2;j++)            savm=oldm;
         varhe[i][j][(int)age] =0.;            oldm=newm;
           } /* end mult */
      printf("%d|",(int)age);fflush(stdout);        
      for(h=0;h<=nhstepm-1;h++){          s1=s[mw[mi][i]][i];
       for(k=0;k<=nhstepm-1;k++){          s2=s[mw[mi+1][i]][i];
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);          if( s2 > nlstate){ 
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);            lli=log(out[s1][s2] - savm[s1][s2]);
         for(i=1;i<=nlstate*2;i++)          }else{
           for(j=1;j<=nlstate*2;j++)            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;          }
       }          ipmx +=1;
     }          sw += weight[i];
     /* Computing expectancies */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     for(i=1; i<=nlstate;i++)  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
       for(j=1; j<=nlstate;j++)        } /* end of wave */
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){      } /* end of individual */
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
                for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     fprintf(ficreseij,"%3.0f",age );              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     cptj=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i=1; i<=nlstate;i++)            }
       for(j=1; j<=nlstate;j++){          for(d=0; d<dh[mi][i]; d++){
         cptj++;            newm=savm;
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
     fprintf(ficreseij,"\n");              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
                }
     free_matrix(gm,0,nhstepm,1,nlstate*2);          
     free_matrix(gp,0,nhstepm,1,nlstate*2);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);            savm=oldm;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            oldm=newm;
   }          } /* end mult */
   printf("\n");        
           s1=s[mw[mi][i]][i];
   free_vector(xp,1,npar);          s2=s[mw[mi+1][i]][i];
   free_matrix(dnewm,1,nlstate*2,1,npar);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);          ipmx +=1;
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);          sw += weight[i];
 }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
 /************ Variance ******************/        } /* end of wave */
 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)      } /* end of individual */
 {    } /* End of if */
   /* Variance of health expectancies */    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double **newm;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double **dnewm,**doldm;    return -l;
   int i, j, nhstepm, hstepm, h, nstepm ;  }
   int k, cptcode;  
   double *xp;  /*************** log-likelihood *************/
   double **gp, **gm;  double funcone( double *x)
   double ***gradg, ***trgradg;  {
   double ***p3mat;    /* Same as likeli but slower because of a lot of printf and if */
   double age,agelim, hf;    int i, ii, j, k, mi, d, kk;
   int theta;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     double **out;
   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");    double lli; /* Individual log likelihood */
   fprintf(ficresvij,"# Age");    double llt;
   for(i=1; i<=nlstate;i++)    int s1, s2;
     for(j=1; j<=nlstate;j++)    double bbh, survp;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    /*extern weight */
   fprintf(ficresvij,"\n");    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   xp=vector(1,npar);    /*for(i=1;i<imx;i++) 
   dnewm=matrix(1,nlstate,1,npar);      printf(" %d\n",s[4][i]);
   doldm=matrix(1,nlstate,1,nlstate);    */
      cov[1]=1.;
   if(estepm < stepm){  
     printf ("Problem %d lower than %d\n",estepm, stepm);    for(k=1; k<=nlstate; k++) ll[k]=0.;
   }  
   else  hstepm=estepm;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /* For example we decided to compute the life expectancy with the smallest unit */      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.      for(mi=1; mi<= wav[i]-1; mi++){
      nhstepm is the number of hstepm from age to agelim        for (ii=1;ii<=nlstate+ndeath;ii++)
      nstepm is the number of stepm from age to agelin.          for (j=1;j<=nlstate+ndeath;j++){
      Look at hpijx to understand the reason of that which relies in memory size            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      and note for a fixed period like k years */            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* 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        for(d=0; d<dh[mi][i]; d++){
      means that if the survival funtion is printed only each two years of age and if          newm=savm;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      results. So we changed our mind and took the option of the best precision.          for (kk=1; kk<=cptcovage;kk++) {
   */            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          }
   agelim = AGESUP;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          savm=oldm;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          oldm=newm;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        } /* end mult */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        
     gp=matrix(0,nhstepm,1,nlstate);        s1=s[mw[mi][i]][i];
     gm=matrix(0,nhstepm,1,nlstate);        s2=s[mw[mi+1][i]][i];
         bbh=(double)bh[mi][i]/(double)stepm; 
     for(theta=1; theta <=npar; theta++){        /* bias is positive if real duration
       for(i=1; i<=npar; i++){ /* Computes gradient */         * is higher than the multiple of stepm and negative otherwise.
         xp[i] = x[i] + (i==theta ?delti[theta]:0);         */
       }        if( s2 > nlstate && (mle <5) ){  /* Jackson */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            lli=log(out[s1][s2] - savm[s1][s2]);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        } else if  (s2==-2) {
           for (j=1,survp=0. ; j<=nlstate; j++) 
       if (popbased==1) {            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
         for(i=1; i<=nlstate;i++)          lli= log(survp);
           prlim[i][i]=probs[(int)age][i][ij];        }else if (mle==1){
       }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
          } else if(mle==2){
       for(j=1; j<= nlstate; j++){          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         for(h=0; h<=nhstepm; h++){        } else if(mle==3){  /* exponential inter-extrapolation */
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          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 */
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         }          lli=log(out[s1][s2]); /* Original formula */
       }        } else{  /* mle=0 back to 1 */
              lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for(i=1; i<=npar; i++) /* Computes gradient */          /*lli=log(out[s1][s2]); */ /* Original formula */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        } /* End of if */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          ipmx +=1;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        sw += weight[i];
          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       if (popbased==1) {        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         for(i=1; i<=nlstate;i++)        if(globpr){
           prlim[i][i]=probs[(int)age][i][ij];          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
       }   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
       for(j=1; j<= nlstate; j++){                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
         for(h=0; h<=nhstepm; h++){          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)            llt +=ll[k]*gipmx/gsw;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         }          }
       }          fprintf(ficresilk," %10.6f\n", -llt);
         }
       for(j=1; j<= nlstate; j++)      } /* end of wave */
         for(h=0; h<=nhstepm; h++){    } /* end of individual */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     } /* End theta */    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     if(globpr==0){ /* First time we count the contributions and weights */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);      gipmx=ipmx;
       gsw=sw;
     for(h=0; h<=nhstepm; h++)    }
       for(j=1; j<=nlstate;j++)    return -l;
         for(theta=1; theta <=npar; theta++)  }
           trgradg[h][j][theta]=gradg[h][theta][j];  
   
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */  /*************** 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++)  {
         vareij[i][j][(int)age] =0.;    /* This routine should help understanding what is done with 
        the selection of individuals/waves and
     for(h=0;h<=nhstepm;h++){       to check the exact contribution to the likelihood.
       for(k=0;k<=nhstepm;k++){       Plotting could be done.
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);     */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    int k;
         for(i=1;i<=nlstate;i++)  
           for(j=1;j<=nlstate;j++)    if(*globpri !=0){ /* Just counts and sums, no printings */
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;      strcpy(fileresilk,"ilk"); 
       }      strcat(fileresilk,fileres);
     }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", fileresilk);
     fprintf(ficresvij,"%.0f ",age );        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     for(i=1; i<=nlstate;i++)      }
       for(j=1; j<=nlstate;j++){      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(ficresvij," %.4f", vareij[i][j][(int)age]);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       }      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     fprintf(ficresvij,"\n");      for(k=1; k<=nlstate; k++) 
     free_matrix(gp,0,nhstepm,1,nlstate);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     free_matrix(gm,0,nhstepm,1,nlstate);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    }
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);  
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    *fretone=(*funcone)(p);
   } /* End age */    if(*globpri !=0){
        fclose(ficresilk);
   free_vector(xp,1,npar);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   free_matrix(doldm,1,nlstate,1,npar);      fflush(fichtm); 
   free_matrix(dnewm,1,nlstate,1,nlstate);    } 
     return;
 }  }
   
 /************ Variance of prevlim ******************/  
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)  /*********** Maximum Likelihood Estimation ***************/
 {  
   /* Variance of prevalence limit */  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  {
   double **newm;    int i,j, iter;
   double **dnewm,**doldm;    double **xi;
   int i, j, nhstepm, hstepm;    double fret;
   int k, cptcode;    double fretone; /* Only one call to likelihood */
   double *xp;    /*  char filerespow[FILENAMELENGTH];*/
   double *gp, *gm;    xi=matrix(1,npar,1,npar);
   double **gradg, **trgradg;    for (i=1;i<=npar;i++)
   double age,agelim;      for (j=1;j<=npar;j++)
   int theta;        xi[i][j]=(i==j ? 1.0 : 0.0);
        printf("Powell\n");  fprintf(ficlog,"Powell\n");
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");    strcpy(filerespow,"pow"); 
   fprintf(ficresvpl,"# Age");    strcat(filerespow,fileres);
   for(i=1; i<=nlstate;i++)    if((ficrespow=fopen(filerespow,"w"))==NULL) {
       fprintf(ficresvpl," %1d-%1d",i,i);      printf("Problem with resultfile: %s\n", filerespow);
   fprintf(ficresvpl,"\n");      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     }
   xp=vector(1,npar);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   dnewm=matrix(1,nlstate,1,npar);    for (i=1;i<=nlstate;i++)
   doldm=matrix(1,nlstate,1,nlstate);      for(j=1;j<=nlstate+ndeath;j++)
          if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   hstepm=1*YEARM; /* Every year of age */    fprintf(ficrespow,"\n");
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;    powell(p,xi,npar,ftol,&iter,&fret,func);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    free_matrix(xi,1,npar,1,npar);
     if (stepm >= YEARM) hstepm=1;    fclose(ficrespow);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     gradg=matrix(1,npar,1,nlstate);    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     gp=vector(1,nlstate);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     gm=vector(1,nlstate);  
   }
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */  /**** Computes Hessian and covariance matrix ***/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       }  {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double  **a,**y,*x,pd;
       for(i=1;i<=nlstate;i++)    double **hess;
         gp[i] = prlim[i][i];    int i, j,jk;
        int *indx;
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
       for(i=1;i<=nlstate;i++)    void lubksb(double **a, int npar, int *indx, double b[]) ;
         gm[i] = prlim[i][i];    void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
       for(i=1;i<=nlstate;i++)    hess=matrix(1,npar,1,npar);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */    printf("\nCalculation of the hessian matrix. Wait...\n");
     fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     trgradg =matrix(1,nlstate,1,npar);    for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
     for(j=1; j<=nlstate;j++)      fprintf(ficlog,"%d",i);fflush(ficlog);
       for(theta=1; theta <=npar; theta++)     
         trgradg[j][theta]=gradg[theta][j];       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
       
     for(i=1;i<=nlstate;i++)      /*  printf(" %f ",p[i]);
       varpl[i][(int)age] =0.;          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    }
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    
     for(i=1;i<=nlstate;i++)    for (i=1;i<=npar;i++) {
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */      for (j=1;j<=npar;j++)  {
         if (j>i) { 
     fprintf(ficresvpl,"%.0f ",age );          printf(".%d%d",i,j);fflush(stdout);
     for(i=1; i<=nlstate;i++)          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          hess[i][j]=hessij(p,delti,i,j,func,npar);
     fprintf(ficresvpl,"\n");          
     free_vector(gp,1,nlstate);          hess[j][i]=hess[i][j];    
     free_vector(gm,1,nlstate);          /*printf(" %lf ",hess[i][j]);*/
     free_matrix(gradg,1,npar,1,nlstate);        }
     free_matrix(trgradg,1,nlstate,1,npar);      }
   } /* End age */    }
     printf("\n");
   free_vector(xp,1,npar);    fprintf(ficlog,"\n");
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 }    
     a=matrix(1,npar,1,npar);
 /************ Variance of one-step probabilities  ******************/    y=matrix(1,npar,1,npar);
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    x=vector(1,npar);
 {    indx=ivector(1,npar);
   int i, j,  i1, k1, l1;    for (i=1;i<=npar;i++)
   int k2, l2, j1,  z1;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   int k=0,l, cptcode;    ludcmp(a,npar,indx,&pd);
   int first=1;  
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;    for (j=1;j<=npar;j++) {
   double **dnewm,**doldm;      for (i=1;i<=npar;i++) x[i]=0;
   double *xp;      x[j]=1;
   double *gp, *gm;      lubksb(a,npar,indx,x);
   double **gradg, **trgradg;      for (i=1;i<=npar;i++){ 
   double **mu;        matcov[i][j]=x[i];
   double age,agelim, cov[NCOVMAX];      }
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */    }
   int theta;  
   char fileresprob[FILENAMELENGTH];    printf("\n#Hessian matrix#\n");
   char fileresprobcov[FILENAMELENGTH];    fprintf(ficlog,"\n#Hessian matrix#\n");
   char fileresprobcor[FILENAMELENGTH];    for (i=1;i<=npar;i++) { 
       for (j=1;j<=npar;j++) { 
   double ***varpij;        printf("%.3e ",hess[i][j]);
         fprintf(ficlog,"%.3e ",hess[i][j]);
   strcpy(fileresprob,"prob");      }
   strcat(fileresprob,fileres);      printf("\n");
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {      fprintf(ficlog,"\n");
     printf("Problem with resultfile: %s\n", fileresprob);    }
   }  
   strcpy(fileresprobcov,"probcov");    /* Recompute Inverse */
   strcat(fileresprobcov,fileres);    for (i=1;i<=npar;i++)
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     printf("Problem with resultfile: %s\n", fileresprobcov);    ludcmp(a,npar,indx,&pd);
   }  
   strcpy(fileresprobcor,"probcor");    /*  printf("\n#Hessian matrix recomputed#\n");
   strcat(fileresprobcor,fileres);  
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {    for (j=1;j<=npar;j++) {
     printf("Problem with resultfile: %s\n", fileresprobcor);      for (i=1;i<=npar;i++) x[i]=0;
   }      x[j]=1;
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);      lubksb(a,npar,indx,x);
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);      for (i=1;i<=npar;i++){ 
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);        y[i][j]=x[i];
          printf("%.3e ",y[i][j]);
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");        fprintf(ficlog,"%.3e ",y[i][j]);
   fprintf(ficresprob,"# Age");      }
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");      printf("\n");
   fprintf(ficresprobcov,"# Age");      fprintf(ficlog,"\n");
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    }
   fprintf(ficresprobcov,"# Age");    */
   
     free_matrix(a,1,npar,1,npar);
   for(i=1; i<=nlstate;i++)    free_matrix(y,1,npar,1,npar);
     for(j=1; j<=(nlstate+ndeath);j++){    free_vector(x,1,npar);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    free_ivector(indx,1,npar);
       fprintf(ficresprobcov," p%1d-%1d ",i,j);    free_matrix(hess,1,npar,1,npar);
       fprintf(ficresprobcor," p%1d-%1d ",i,j);  
     }    
   fprintf(ficresprob,"\n");  }
   fprintf(ficresprobcov,"\n");  
   fprintf(ficresprobcor,"\n");  /*************** hessian matrix ****************/
   xp=vector(1,npar);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);  {
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));    int i;
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);    int l=1, lmax=20;
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);    double k1,k2;
   first=1;    double p2[MAXPARM+1]; /* identical to x */
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    double res;
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     exit(0);    double fx;
   }    int k=0,kmax=10;
   else{    double l1;
     fprintf(ficgp,"\n# Routine varprob");  
   }    fx=func(x);
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    for (i=1;i<=npar;i++) p2[i]=x[i];
     printf("Problem with html file: %s\n", optionfilehtm);    for(l=0 ; l <=lmax; l++){
     exit(0);      l1=pow(10,l);
   }      delts=delt;
   else{      for(k=1 ; k <kmax; k=k+1){
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");        delt = delta*(l1*k);
     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");        p2[theta]=x[theta] +delt;
     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");        k1=func(p2)-fx;
         p2[theta]=x[theta]-delt;
   }        k2=func(p2)-fx;
   cov[1]=1;        /*res= (k1-2.0*fx+k2)/delt/delt; */
   j=cptcoveff;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        
   j1=0;  #ifdef DEBUGHESS
   for(k1=1; k1<=1;k1++){        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(i1=1; i1<=ncodemax[k1];i1++){        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);
     j1++;  #endif
         /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     if  (cptcovn>0) {        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       fprintf(ficresprob, "\n#********** Variable ");          k=kmax;
       fprintf(ficresprobcov, "\n#********** Variable ");        }
       fprintf(ficgp, "\n#********** Variable ");        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");          k=kmax; l=lmax*10.;
       fprintf(ficresprobcor, "\n#********** Variable ");        }
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       fprintf(ficresprob, "**********\n#");          delts=delt;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        }
       fprintf(ficresprobcov, "**********\n#");      }
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    }
       fprintf(ficgp, "**********\n#");    delti[theta]=delts;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    return res; 
       fprintf(ficgp, "**********\n#");    
       for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  }
       fprintf(fichtm, "**********\n#");  
     }  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
      {
       for (age=bage; age<=fage; age ++){    int i;
         cov[2]=age;    int l=1, l1, lmax=20;
         for (k=1; k<=cptcovn;k++) {    double k1,k2,k3,k4,res,fx;
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];    double p2[MAXPARM+1];
         }    int k;
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  
         for (k=1; k<=cptcovprod;k++)    fx=func(x);
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for (k=1; k<=2; k++) {
              for (i=1;i<=npar;i++) p2[i]=x[i];
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));      p2[thetai]=x[thetai]+delti[thetai]/k;
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
         gp=vector(1,(nlstate)*(nlstate+ndeath));      k1=func(p2)-fx;
         gm=vector(1,(nlstate)*(nlstate+ndeath));    
          p2[thetai]=x[thetai]+delti[thetai]/k;
         for(theta=1; theta <=npar; theta++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           for(i=1; i<=npar; i++)      k2=func(p2)-fx;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    
                p2[thetai]=x[thetai]-delti[thetai]/k;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
                k3=func(p2)-fx;
           k=0;    
           for(i=1; i<= (nlstate); i++){      p2[thetai]=x[thetai]-delti[thetai]/k;
             for(j=1; j<=(nlstate+ndeath);j++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
               k=k+1;      k4=func(p2)-fx;
               gp[k]=pmmij[i][j];      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
             }  #ifdef DEBUG
           }      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
                fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
           for(i=1; i<=npar; i++)  #endif
             xp[i] = x[i] - (i==theta ?delti[theta]:0);    }
        return res;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);  }
           k=0;  
           for(i=1; i<=(nlstate); i++){  /************** Inverse of matrix **************/
             for(j=1; j<=(nlstate+ndeath);j++){  void ludcmp(double **a, int n, int *indx, double *d) 
               k=k+1;  { 
               gm[k]=pmmij[i][j];    int i,imax,j,k; 
             }    double big,dum,sum,temp; 
           }    double *vv; 
         
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)    vv=vector(1,n); 
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      *d=1.0; 
         }    for (i=1;i<=n;i++) { 
       big=0.0; 
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)      for (j=1;j<=n;j++) 
           for(theta=1; theta <=npar; theta++)        if ((temp=fabs(a[i][j])) > big) big=temp; 
             trgradg[j][theta]=gradg[theta][j];      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
              vv[i]=1.0/big; 
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);    } 
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);    for (j=1;j<=n;j++) { 
              for (i=1;i<j;i++) { 
         pmij(pmmij,cov,ncovmodel,x,nlstate);        sum=a[i][j]; 
                for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         k=0;        a[i][j]=sum; 
         for(i=1; i<=(nlstate); i++){      } 
           for(j=1; j<=(nlstate+ndeath);j++){      big=0.0; 
             k=k+1;      for (i=j;i<=n;i++) { 
             mu[k][(int) age]=pmmij[i][j];        sum=a[i][j]; 
           }        for (k=1;k<j;k++) 
         }          sum -= a[i][k]*a[k][j]; 
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)        a[i][j]=sum; 
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)        if ( (dum=vv[i]*fabs(sum)) >= big) { 
             varpij[i][j][(int)age] = doldm[i][j];          big=dum; 
           imax=i; 
         /*printf("\n%d ",(int)age);        } 
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){      } 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      if (j != imax) { 
      }*/        for (k=1;k<=n;k++) { 
           dum=a[imax][k]; 
         fprintf(ficresprob,"\n%d ",(int)age);          a[imax][k]=a[j][k]; 
         fprintf(ficresprobcov,"\n%d ",(int)age);          a[j][k]=dum; 
         fprintf(ficresprobcor,"\n%d ",(int)age);        } 
         *d = -(*d); 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)        vv[imax]=vv[j]; 
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));      } 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){      indx[j]=imax; 
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);      if (a[j][j] == 0.0) a[j][j]=TINY; 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);      if (j != n) { 
         }        dum=1.0/(a[j][j]); 
         i=0;        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         for (k=1; k<=(nlstate);k++){      } 
           for (l=1; l<=(nlstate+ndeath);l++){    } 
             i=i++;    free_vector(vv,1,n);  /* Doesn't work */
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);  ;
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);  } 
             for (j=1; j<=i;j++){  
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);  void lubksb(double **a, int n, int *indx, double b[]) 
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));  { 
             }    int i,ii=0,ip,j; 
           }    double sum; 
         }/* end of loop for state */   
       } /* end of loop for age */    for (i=1;i<=n;i++) { 
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/      ip=indx[i]; 
       for (k1=1; k1<=(nlstate);k1++){      sum=b[ip]; 
         for (l1=1; l1<=(nlstate+ndeath);l1++){      b[ip]=b[i]; 
           if(l1==k1) continue;      if (ii) 
           i=(k1-1)*(nlstate+ndeath)+l1;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
           for (k2=1; k2<=(nlstate);k2++){      else if (sum) ii=i; 
             for (l2=1; l2<=(nlstate+ndeath);l2++){      b[i]=sum; 
               if(l2==k2) continue;    } 
               j=(k2-1)*(nlstate+ndeath)+l2;    for (i=n;i>=1;i--) { 
               if(j<=i) continue;      sum=b[i]; 
               for (age=bage; age<=fage; age ++){      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                 if ((int)age %5==0){      b[i]=sum/a[i][i]; 
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;    } 
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;  } 
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;  
                   mu1=mu[i][(int) age]/stepm*YEARM ;  void pstamp(FILE *fichier)
                   mu2=mu[j][(int) age]/stepm*YEARM;  {
                   /* Computing eigen value of matrix of covariance */    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  }
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);  /************ Frequencies ********************/
                   /* Eigen vectors */  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[])
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));  {  /* Some frequencies */
                   v21=sqrt(1.-v11*v11);    
                   v12=-v21;    int i, m, jk, k1,i1, j1, bool, z1,j;
                   v22=v11;    int first;
                   /*printf(fignu*/    double ***freq; /* Frequencies */
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */    double *pp, **prop;
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */    double pos,posprop, k2, dateintsum=0,k2cpt=0;
                   if(first==1){    char fileresp[FILENAMELENGTH];
                     first=0;    
                     fprintf(ficgp,"\nset parametric;set nolabel");    pp=vector(1,nlstate);
                     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);    prop=matrix(1,nlstate,iagemin,iagemax+3);
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");    strcpy(fileresp,"p");
                     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);    strcat(fileresp,fileres);
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);    if((ficresp=fopen(fileresp,"w"))==NULL) {
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);      printf("Problem with prevalence resultfile: %s\n", fileresp);
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);      exit(0);
                     fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(-%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) t \"%d\"",\    }
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    j1=0;
                   }else{    
                     first=0;    j=cptcoveff;
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
                     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\"",\    first=1;
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \  
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    for(k1=1; k1<=j;k1++){
                   }/* if first */      for(i1=1; i1<=ncodemax[k1];i1++){
                 } /* age mod 5 */        j1++;
               } /* end loop age */        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);          scanf("%d", i);*/
               first=1;        for (i=-5; i<=nlstate+ndeath; i++)  
             } /*l12 */          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           } /* k12 */            for(m=iagemin; m <= iagemax+3; m++)
         } /*l1 */              freq[i][jk][m]=0;
       }/* k1 */  
     } /* loop covariates */      for (i=1; i<=nlstate; i++)  
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);        for(m=iagemin; m <= iagemax+3; m++)
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          prop[i][m]=0;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));        
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);        dateintsum=0;
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        k2cpt=0;
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        for (i=1; i<=imx; i++) {
   }          bool=1;
   free_vector(xp,1,npar);          if  (cptcovn>0) {
   fclose(ficresprob);            for (z1=1; z1<=cptcoveff; z1++) 
   fclose(ficresprobcov);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   fclose(ficresprobcor);                bool=0;
   fclose(ficgp);          }
   fclose(fichtm);          if (bool==1){
 }            for(m=firstpass; m<=lastpass; m++){
               k2=anint[m][i]+(mint[m][i]/12.);
               /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
 /******************* Printing html file ***********/                if(agev[m][i]==0) agev[m][i]=iagemax+1;
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                   int lastpass, int stepm, int weightopt, char model[],\                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\                if (m<lastpass) {
                   int popforecast, int estepm ,\                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   double jprev1, double mprev1,double anprev1, \                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                   double jprev2, double mprev2,double anprev2){                }
   int jj1, k1, i1, cpt;                
   /*char optionfilehtm[FILENAMELENGTH];*/                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {                  dateintsum=dateintsum+k2;
     printf("Problem with %s \n",optionfilehtm), exit(0);                  k2cpt++;
   }                }
                 /*}*/
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n            }
  - 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          }
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n        }
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n         
  - Life expectancies by age and initial health status (estepm=%2d months):        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
    <a href=\"e%s\">e%s</a> <br>\n</li>", \        pstamp(ficresp);
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);        if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          fprintf(ficresp, "**********\n#");
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n        }
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n        for(i=1; i<=nlstate;i++) 
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n        fprintf(ficresp, "\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);        for(i=iagemin; i <= iagemax+3; i++){
           if(i==iagemax+3){
  if(popforecast==1) fprintf(fichtm,"\n            fprintf(ficlog,"Total");
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n          }else{
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n            if(first==1){
         <br>",fileres,fileres,fileres,fileres);              first=0;
  else              printf("See log file for details...\n");
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);            }
 fprintf(fichtm," <li>Graphs</li><p>");            fprintf(ficlog,"Age %d", i);
           }
  m=cptcoveff;          for(jk=1; jk <=nlstate ; jk++){
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               pp[jk] += freq[jk][m][i]; 
  jj1=0;          }
  for(k1=1; k1<=m;k1++){          for(jk=1; jk <=nlstate ; jk++){
    for(i1=1; i1<=ncodemax[k1];i1++){            for(m=-1, pos=0; m <=0 ; m++)
      jj1++;              pos += freq[jk][m][i];
      if (cptcovn > 0) {            if(pp[jk]>=1.e-10){
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");              if(first==1){
        for (cpt=1; cpt<=cptcoveff;cpt++)                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);              }
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
      }            }else{
      /* Pij */              if(first==1)
      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>                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                  fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
      /* Quasi-incidences */            }
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>          }
 <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=0, pp[jk]=0; m <=nlstate+ndeath; m++)
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>              pp[jk] += freq[jk][m][i];
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          }       
        }          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     for(cpt=1; cpt<=nlstate;cpt++) {            pos += pp[jk];
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident            posprop += prop[jk][i];
 interval) in state (%d): v%s%d%d.png <br>          }
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            for(jk=1; jk <=nlstate ; jk++){
      }            if(pos>=1.e-5){
      for(cpt=1; cpt<=nlstate;cpt++) {              if(first==1)
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
      }            }else{
      fprintf(fichtm,"\n<br>- Total life expectancy by age and              if(first==1)
 health expectancies in states (1) and (2): e%s%d.png<br>                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
    }            }
  }            if( i <= iagemax){
 fclose(fichtm);              if(pos>=1.e-5){
 }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                 /*probs[i][jk][j1]= pp[jk]/pos;*/
 /******************* Gnuplot file **************/                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){              }
               else
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   int ng;            }
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {          }
     printf("Problem with file %s",optionfilegnuplot);          
   }          for(jk=-1; jk <=nlstate+ndeath; jk++)
             for(m=-1; m <=nlstate+ndeath; m++)
 #ifdef windows              if(freq[jk][m][i] !=0 ) {
     fprintf(ficgp,"cd \"%s\" \n",pathc);              if(first==1)
 #endif                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
 m=pow(2,cptcoveff);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
                }
  /* 1eme*/          if(i <= iagemax)
   for (cpt=1; cpt<= nlstate ; cpt ++) {            fprintf(ficresp,"\n");
    for (k1=1; k1<= m ; k1 ++) {          if(first==1)
             printf("Others in log...\n");
 #ifdef windows          fprintf(ficlog,"\n");
      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    dateintmean=dateintsum/k2cpt; 
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);   
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);    fclose(ficresp);
 #endif    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     free_vector(pp,1,nlstate);
 for (i=1; i<= nlstate ; i ++) {    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    /* End of Freq */
   else fprintf(ficgp," \%%*lf (\%%*lf)");  }
 }  
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);  /************ Prevalence ********************/
     for (i=1; i<= nlstate ; i ++) {  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)
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  {  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
 }       in each health status at the date of interview (if between dateprev1 and dateprev2).
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);       We still use firstpass and lastpass as another selection.
      for (i=1; i<= nlstate ; i ++) {    */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");   
   else fprintf(ficgp," \%%*lf (\%%*lf)");    int i, m, jk, k1, i1, j1, bool, z1,j;
 }      double ***freq; /* Frequencies */
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    double *pp, **prop;
 #ifdef unix    double pos,posprop; 
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");    double  y2; /* in fractional years */
 #endif    int iagemin, iagemax;
    }  
   }    iagemin= (int) agemin;
   /*2 eme*/    iagemax= (int) agemax;
     /*pp=vector(1,nlstate);*/
   for (k1=1; k1<= m ; k1 ++) {    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    j1=0;
        
     for (i=1; i<= nlstate+1 ; i ++) {    j=cptcoveff;
       k=2*i;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    
       for (j=1; j<= nlstate+1 ; j ++) {    for(k1=1; k1<=j;k1++){
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      for(i1=1; i1<=ncodemax[k1];i1++){
   else fprintf(ficgp," \%%*lf (\%%*lf)");        j1++;
 }          
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");        for (i=1; i<=nlstate; i++)  
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);          for(m=iagemin; m <= iagemax+3; m++)
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);            prop[i][m]=0.0;
       for (j=1; j<= nlstate+1 ; j ++) {       
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        for (i=1; i<=imx; i++) { /* Each individual */
         else fprintf(ficgp," \%%*lf (\%%*lf)");          bool=1;
 }            if  (cptcovn>0) {
       fprintf(ficgp,"\" t\"\" w l 0,");            for (z1=1; z1<=cptcoveff; z1++) 
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       for (j=1; j<= nlstate+1 ; j ++) {                bool=0;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");          if (bool==1) { 
 }              for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       else fprintf(ficgp,"\" t\"\" w l 0,");              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                  if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
   /*3eme*/                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                   /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
   for (k1=1; k1<= m ; k1 ++) {                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     for (cpt=1; cpt<= nlstate ; cpt ++) {                  prop[s[m][i]][iagemax+3] += weight[i]; 
       k=2+nlstate*(2*cpt-2);                } 
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              }
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);            } /* end selection of waves */
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          }
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");        }
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);        for(i=iagemin; i <= iagemax+3; i++){  
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            posprop += prop[jk][i]; 
           } 
 */  
       for (i=1; i< nlstate ; i ++) {          for(jk=1; jk <=nlstate ; jk++){     
         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 <=  iagemax){ 
               if(posprop>=1.e-5){ 
       }                probs[i][jk][j1]= prop[jk][i]/posprop;
     }              } else
   }                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
              } 
   /* CV preval stat */          }/* end jk */ 
     for (k1=1; k1<= m ; k1 ++) {        }/* end i */ 
     for (cpt=1; cpt<nlstate ; cpt ++) {      } /* end i1 */
       k=3;    } /* end k1 */
       fprintf(ficgp,"\nset out \"p%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] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     /*free_vector(pp,1,nlstate);*/
       for (i=1; i< nlstate ; i ++)    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
         fprintf(ficgp,"+$%d",k+i+1);  }  /* End of prevalence */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);  
        /************* Waves Concatenation ***************/
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
       for (i=1; i< nlstate ; i ++) {  {
         l=3+(nlstate+ndeath)*cpt;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
         fprintf(ficgp,"+$%d",l+i+1);       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
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);         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.
   }         */
    
   /* proba elementaires */    int i, mi, m;
    for(i=1,jk=1; i <=nlstate; i++){    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     for(k=1; k <=(nlstate+ndeath); k++){       double sum=0., jmean=0.;*/
       if (k != i) {    int first;
         for(j=1; j <=ncovmodel; j++){    int j, k=0,jk, ju, jl;
            double sum=0.;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    first=0;
           jk++;    jmin=1e+5;
           fprintf(ficgp,"\n");    jmax=-1;
         }    jmean=0.;
       }    for(i=1; i<=imx; i++){
     }      mi=0;
    }      m=firstpass;
       while(s[m][i] <= nlstate){
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
      for(jk=1; jk <=m; jk++) {          mw[++mi][i]=m;
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);        if(m >=lastpass)
        if (ng==2)          break;
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");        else
        else          m++;
          fprintf(ficgp,"\nset title \"Probability\"\n");      }/* end while */
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);      if (s[m][i] > nlstate){
        i=1;        mi++;     /* Death is another wave */
        for(k2=1; k2<=nlstate; k2++) {        /* if(mi==0)  never been interviewed correctly before death */
          k3=i;           /* Only death is a correct wave */
          for(k=1; k<=(nlstate+ndeath); k++) {        mw[mi][i]=m;
            if (k != k2){      }
              if(ng==2)  
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);      wav[i]=mi;
              else      if(mi==0){
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);        nbwarn++;
              ij=1;        if(first==0){
              for(j=3; j <=ncovmodel; j++) {          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          first=1;
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        }
                  ij++;        if(first==1){
                }          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
                else        }
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      } /* end mi==0 */
              }    } /* End individuals */
              fprintf(ficgp,")/(1");  
                  for(i=1; i<=imx; i++){
              for(k1=1; k1 <=nlstate; k1++){        for(mi=1; mi<wav[i];mi++){
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);        if (stepm <=0)
                ij=1;          dh[mi][i]=1;
                for(j=3; j <=ncovmodel; j++){        else{
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);            if (agedc[i] < 2*AGESUP) {
                    ij++;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
                  }              if(j==0) j=1;  /* Survives at least one month after exam */
                  else              else if(j<0){
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);                nberr++;
                }                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                fprintf(ficgp,")");                j=1; /* Temporary Dangerous patch */
              }                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);                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]);
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");                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);
              i=i+ncovmodel;              }
            }              k=k+1;
          }              if (j >= jmax){
        }                jmax=j;
      }                ijmax=i;
    }              }
    fclose(ficgp);              if (j <= jmin){
 }  /* end gnuplot */                jmin=j;
                 ijmin=i;
               }
 /*************** Moving average **************/              sum=sum+j;
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){              /*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);*/
   int i, cpt, cptcod;            }
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)          }
       for (i=1; i<=nlstate;i++)          else{
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
           mobaverage[(int)agedeb][i][cptcod]=0.;  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
      
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){            k=k+1;
       for (i=1; i<=nlstate;i++){            if (j >= jmax) {
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              jmax=j;
           for (cpt=0;cpt<=4;cpt++){              ijmax=i;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];            }
           }            else if (j <= jmin){
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;              jmin=j;
         }              ijmin=i;
       }            }
     }            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
                /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
 }            if(j<0){
               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]);
 /************** Forecasting ******************/              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]);
 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){            }
              sum=sum+j;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;          }
   int *popage;          jk= j/stepm;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;          jl= j -jk*stepm;
   double *popeffectif,*popcount;          ju= j -(jk+1)*stepm;
   double ***p3mat;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   char fileresf[FILENAMELENGTH];            if(jl==0){
               dh[mi][i]=jk;
  agelim=AGESUP;              bh[mi][i]=0;
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;            }else{ /* We want a negative bias in order to only have interpolation ie
                     * to avoid the price of an extra matrix product in likelihood */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              dh[mi][i]=jk+1;
                bh[mi][i]=ju;
              }
   strcpy(fileresf,"f");          }else{
   strcat(fileresf,fileres);            if(jl <= -ju){
   if((ficresf=fopen(fileresf,"w"))==NULL) {              dh[mi][i]=jk;
     printf("Problem with forecast resultfile: %s\n", fileresf);              bh[mi][i]=jl;       /* bias is positive if real duration
   }                                   * is higher than the multiple of stepm and negative otherwise.
   printf("Computing forecasting: result on file '%s' \n", fileresf);                                   */
             }
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            else{
               dh[mi][i]=jk+1;
   if (mobilav==1) {              bh[mi][i]=ju;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            }
     movingaverage(agedeb, fage, ageminpar, mobaverage);            if(dh[mi][i]==0){
   }              dh[mi][i]=1; /* At least one step */
               bh[mi][i]=ju; /* At least one step */
   stepsize=(int) (stepm+YEARM-1)/YEARM;              /*  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);*/
   if (stepm<=12) stepsize=1;            }
            } /* end if mle */
   agelim=AGESUP;        }
        } /* end wave */
   hstepm=1;    }
   hstepm=hstepm/stepm;    jmean=sum/k;
   yp1=modf(dateintmean,&yp);    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);
   anprojmean=yp;    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
   yp2=modf((yp1*12),&yp);   }
   mprojmean=yp;  
   yp1=modf((yp2*30.5),&yp);  /*********** Tricode ****************************/
   jprojmean=yp;  void tricode(int *Tvar, int **nbcode, int imx)
   if(jprojmean==0) jprojmean=1;  {
   if(mprojmean==0) jprojmean=1;    /* Uses cptcovn+2*cptcovprod as the number of covariates */
      /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  
      int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
   for(cptcov=1;cptcov<=i2;cptcov++){    int modmaxcovj=0; /* Modality max of covariates j */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    cptcoveff=0; 
       k=k+1;   
       fprintf(ficresf,"\n#******");    for (k=0; k<maxncov; k++) Ndum[k]=0;
       for(j=1;j<=cptcoveff;j++) {    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       }    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
       fprintf(ficresf,"******\n");      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
       fprintf(ficresf,"# StartingAge FinalAge");                                 modality of this covariate Vj*/ 
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
                                              modality of the nth covariate of individual i. */
              Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         fprintf(ficresf,"\n");        if (ij > modmaxcovj) modmaxcovj=ij; 
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);          /* getting the maximum value of the modality of the covariate
            (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){           female is 1, then modmaxcovj=1.*/
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      }
           nhstepm = nhstepm/hstepm;      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
                for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        if( Ndum[i] != 0 )
           oldm=oldms;savm=savms;          ncodemax[j]++; 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          /* Number of modalities of the j th covariate. In fact
                   ncodemax[j]=2 (dichotom. variables only) but it could be more for
           for (h=0; h<=nhstepm; h++){           historical reasons */
             if (h==(int) (calagedate+YEARM*cpt)) {      } /* Ndum[-1] number of undefined modalities */
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);  
             }      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
             for(j=1; j<=nlstate+ndeath;j++) {      ij=1; 
               kk1=0.;kk2=0;      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
               for(i=1; i<=nlstate;i++) {                      for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
                 if (mobilav==1)          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
                 else {                                       k is a modality. If we have model=V1+V1*sex 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
                 }            ij++;
                          }
               }          if (ij > ncodemax[j]) break; 
               if (h==(int)(calagedate+12*cpt)){        }  /* end of loop on */
                 fprintf(ficresf," %.3f", kk1);      } /* end of loop on modality */ 
                            } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
               }    
             }    for (k=0; k< maxncov; k++) Ndum[k]=0;
           }    
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
         }     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
       }     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
     }     Ndum[ij]++;
   }   }
          
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);   ij=1;
    for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   fclose(ficresf);     if((Ndum[i]!=0) && (i<=ncovcol)){
 }       Tvaraff[ij]=i; /*For printing */
 /************** Forecasting ******************/       ij++;
 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;   ij--;
   int *popage;   cptcoveff=ij; /*Number of simple covariates*/
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  }
   double *popeffectif,*popcount;  
   double ***p3mat,***tabpop,***tabpopprev;  /*********** Health Expectancies ****************/
   char filerespop[FILENAMELENGTH];  
   void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  {
   agelim=AGESUP;    /* Health expectancies, no variances */
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
      int nhstepma, nstepma; /* Decreasing with age */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    double age, agelim, hf;
      double ***p3mat;
      double eip;
   strcpy(filerespop,"pop");  
   strcat(filerespop,fileres);    pstamp(ficreseij);
   if((ficrespop=fopen(filerespop,"w"))==NULL) {    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
     printf("Problem with forecast resultfile: %s\n", filerespop);    fprintf(ficreseij,"# Age");
   }    for(i=1; i<=nlstate;i++){
   printf("Computing forecasting: result on file '%s' \n", filerespop);      for(j=1; j<=nlstate;j++){
         fprintf(ficreseij," e%1d%1d ",i,j);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      }
       fprintf(ficreseij," e%1d. ",i);
   if (mobilav==1) {    }
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    fprintf(ficreseij,"\n");
     movingaverage(agedeb, fage, ageminpar, mobaverage);  
   }    
     if(estepm < stepm){
   stepsize=(int) (stepm+YEARM-1)/YEARM;      printf ("Problem %d lower than %d\n",estepm, stepm);
   if (stepm<=12) stepsize=1;    }
      else  hstepm=estepm;   
   agelim=AGESUP;    /* We compute the life expectancy from trapezoids spaced every estepm months
       * This is mainly to measure the difference between two models: for example
   hstepm=1;     * if stepm=24 months pijx are given only every 2 years and by summing them
   hstepm=hstepm/stepm;     * we are calculating an estimate of the Life Expectancy assuming a linear 
       * progression in between and thus overestimating or underestimating according
   if (popforecast==1) {     * to the curvature of the survival function. If, for the same date, we 
     if((ficpop=fopen(popfile,"r"))==NULL) {     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       printf("Problem with population file : %s\n",popfile);exit(0);     * to compare the new estimate of Life expectancy with the same linear 
     }     * hypothesis. A more precise result, taking into account a more precise
     popage=ivector(0,AGESUP);     * curvature will be obtained if estepm is as small as stepm. */
     popeffectif=vector(0,AGESUP);  
     popcount=vector(0,AGESUP);    /* 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. 
     i=1;         nhstepm is the number of hstepm from age to agelim 
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;       nstepm is the number of stepm from age to agelin. 
           Look at hpijx to understand the reason of that which relies in memory size
     imx=i;       and note for a fixed period like estepm months */
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];    /* 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
        means that if the survival funtion is printed only each two years of age and if
   for(cptcov=1;cptcov<=i2;cptcov++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){       results. So we changed our mind and took the option of the best precision.
       k=k+1;    */
       fprintf(ficrespop,"\n#******");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       for(j=1;j<=cptcoveff;j++) {  
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    agelim=AGESUP;
       }    /* If stepm=6 months */
       fprintf(ficrespop,"******\n");      /* Computed by stepm unit matrices, product of hstepm matrices, stored
       fprintf(ficrespop,"# Age");         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);      
       if (popforecast==1)  fprintf(ficrespop," [Population]");  /* nhstepm age range expressed in number of stepm */
          nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       for (cpt=0; cpt<=0;cpt++) {    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      /* if (stepm >= YEARM) hstepm=1;*/
            nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
           nhstepm = nhstepm/hstepm;    for (age=bage; age<=fage; age ++){ 
                nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           oldm=oldms;savm=savms;      /* if (stepm >= YEARM) hstepm=1;*/
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
          
           for (h=0; h<=nhstepm; h++){      /* If stepm=6 months */
             if (h==(int) (calagedate+YEARM*cpt)) {      /* Computed by stepm unit matrices, product of hstepma matrices, stored
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
             }      
             for(j=1; j<=nlstate+ndeath;j++) {      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
               kk1=0.;kk2=0;      
               for(i=1; i<=nlstate;i++) {                    hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
                 if (mobilav==1)      
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      printf("%d|",(int)age);fflush(stdout);
                 else {      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      
                 }      /* Computing expectancies */
               }      for(i=1; i<=nlstate;i++)
               if (h==(int)(calagedate+12*cpt)){        for(j=1; j<=nlstate;j++)
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
                   /*fprintf(ficrespop," %.3f", kk1);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/            
               }            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
             }  
             for(i=1; i<=nlstate;i++){          }
               kk1=0.;  
                 for(j=1; j<=nlstate;j++){      fprintf(ficreseij,"%3.0f",age );
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];      for(i=1; i<=nlstate;i++){
                 }        eip=0;
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];        for(j=1; j<=nlstate;j++){
             }          eip +=eij[i][j][(int)age];
           fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)        }
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        fprintf(ficreseij,"%9.4f", eip );
           }      }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficreseij,"\n");
         }      
       }    }
      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /******/    printf("\n");
     fprintf(ficlog,"\n");
       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)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  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[] )
           nhstepm = nhstepm/hstepm;  
            {
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* Covariances of health expectancies eij and of total life expectancies according
           oldm=oldms;savm=savms;     to initial status i, ei. .
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      */
           for (h=0; h<=nhstepm; h++){    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
             if (h==(int) (calagedate+YEARM*cpt)) {    int nhstepma, nstepma; /* Decreasing with age */
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    double age, agelim, hf;
             }    double ***p3matp, ***p3matm, ***varhe;
             for(j=1; j<=nlstate+ndeath;j++) {    double **dnewm,**doldm;
               kk1=0.;kk2=0;    double *xp, *xm;
               for(i=1; i<=nlstate;i++) {                  double **gp, **gm;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        double ***gradg, ***trgradg;
               }    int theta;
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);  
             }    double eip, vip;
           }  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    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);
   }    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
      
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   if (popforecast==1) {    fprintf(ficresstdeij,"# Age");
     free_ivector(popage,0,AGESUP);    for(i=1; i<=nlstate;i++){
     free_vector(popeffectif,0,AGESUP);      for(j=1; j<=nlstate;j++)
     free_vector(popcount,0,AGESUP);        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   }      fprintf(ficresstdeij," e%1d. ",i);
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    }
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    fprintf(ficresstdeij,"\n");
   fclose(ficrespop);  
 }    pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
 /***********************************************/    fprintf(ficrescveij,"# Age");
 /**************** Main Program *****************/    for(i=1; i<=nlstate;i++)
 /***********************************************/      for(j=1; j<=nlstate;j++){
         cptj= (j-1)*nlstate+i;
 int main(int argc, char *argv[])        for(i2=1; i2<=nlstate;i2++)
 {          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;            if(cptj2 <= cptj)
   double agedeb, agefin,hf;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          }
       }
   double fret;    fprintf(ficrescveij,"\n");
   double **xi,tmp,delta;    
     if(estepm < stepm){
   double dum; /* Dummy variable */      printf ("Problem %d lower than %d\n",estepm, stepm);
   double ***p3mat;    }
   int *indx;    else  hstepm=estepm;   
   char line[MAXLINE], linepar[MAXLINE];    /* We compute the life expectancy from trapezoids spaced every estepm months
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];     * This is mainly to measure the difference between two models: for example
   int firstobs=1, lastobs=10;     * if stepm=24 months pijx are given only every 2 years and by summing them
   int sdeb, sfin; /* Status at beginning and end */     * we are calculating an estimate of the Life Expectancy assuming a linear 
   int c,  h , cpt,l;     * progression in between and thus overestimating or underestimating according
   int ju,jl, mi;     * to the curvature of the survival function. If, for the same date, we 
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;     * to compare the new estimate of Life expectancy with the same linear 
   int mobilav=0,popforecast=0;     * hypothesis. A more precise result, taking into account a more precise
   int hstepm, nhstepm;     * curvature will be obtained if estepm is as small as stepm. */
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;  
     /* For example we decided to compute the life expectancy with the smallest unit */
   double bage, fage, age, agelim, agebase;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   double ftolpl=FTOL;       nhstepm is the number of hstepm from age to agelim 
   double **prlim;       nstepm is the number of stepm from age to agelin. 
   double *severity;       Look at hpijx to understand the reason of that which relies in memory size
   double ***param; /* Matrix of parameters */       and note for a fixed period like estepm months */
   double  *p;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   double **matcov; /* Matrix of covariance */       survival function given by stepm (the optimization length). Unfortunately it
   double ***delti3; /* Scale */       means that if the survival funtion is printed only each two years of age and if
   double *delti; /* Scale */       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   double ***eij, ***vareij;       results. So we changed our mind and took the option of the best precision.
   double **varpl; /* Variances of prevalence limits by age */    */
   double *epj, vepp;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   double kk1, kk2;  
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    /* If stepm=6 months */
      /* nhstepm age range expressed in number of stepm */
     agelim=AGESUP;
   char *alph[]={"a","a","b","c","d","e"}, str[4];    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
   char z[1]="c", occ;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
 #include <sys/time.h>    
 #include <time.h>    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   /* long total_usecs;    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   struct timeval start_time, end_time;    gp=matrix(0,nhstepm,1,nlstate*nlstate);
      gm=matrix(0,nhstepm,1,nlstate*nlstate);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  
   getcwd(pathcd, size);    for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   printf("\n%s",version);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   if(argc <=1){      /* if (stepm >= YEARM) hstepm=1;*/
     printf("\nEnter the parameter file name: ");      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     scanf("%s",pathtot);  
   }      /* If stepm=6 months */
   else{      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     strcpy(pathtot,argv[1]);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   }      
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   /*cygwin_split_path(pathtot,path,optionfile);  
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      /* Computing  Variances of health expectancies */
   /* cutv(path,optionfile,pathtot,'\\');*/      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          decrease memory allocation */
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);      for(theta=1; theta <=npar; theta++){
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);        for(i=1; i<=npar; i++){ 
   chdir(path);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   replace(pathc,path);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
 /*-------- arguments in the command line --------*/        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   strcpy(fileres,"r");    
   strcat(fileres, optionfilefiname);        for(j=1; j<= nlstate; j++){
   strcat(fileres,".txt");    /* Other files have txt extension */          for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
   /*---------arguments file --------*/              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
               gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {            }
     printf("Problem with optionfile %s\n",optionfile);          }
     goto end;        }
   }       
         for(ij=1; ij<= nlstate*nlstate; ij++)
   strcpy(filereso,"o");          for(h=0; h<=nhstepm-1; h++){
   strcat(filereso,fileres);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   if((ficparo=fopen(filereso,"w"))==NULL) {          }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;      }/* End theta */
   }      
       
   /* Reads comments: lines beginning with '#' */      for(h=0; h<=nhstepm-1; h++)
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate*nlstate;j++)
     ungetc(c,ficpar);          for(theta=1; theta <=npar; theta++)
     fgets(line, MAXLINE, ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
     puts(line);      
     fputs(line,ficparo);  
   }       for(ij=1;ij<=nlstate*nlstate;ij++)
   ungetc(c,ficpar);        for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);  
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);       printf("%d|",(int)age);fflush(stdout);
   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,"%d|",(int)age);fflush(ficlog);
 while((c=getc(ficpar))=='#' && c!= EOF){       for(h=0;h<=nhstepm-1;h++){
     ungetc(c,ficpar);        for(k=0;k<=nhstepm-1;k++){
     fgets(line, MAXLINE, ficpar);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
     puts(line);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
     fputs(line,ficparo);          for(ij=1;ij<=nlstate*nlstate;ij++)
   }            for(ji=1;ji<=nlstate*nlstate;ji++)
   ungetc(c,ficpar);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
          }
          }
   covar=matrix(0,NCOVMAX,1,n);  
   cptcovn=0;      /* Computing expectancies */
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
   ncovmodel=2+cptcovn;        for(j=1; j<=nlstate;j++)
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
              eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
   /* Read guess parameters */            
   /* Reads comments: lines beginning with '#' */            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);          }
     fgets(line, MAXLINE, ficpar);  
     puts(line);      fprintf(ficresstdeij,"%3.0f",age );
     fputs(line,ficparo);      for(i=1; i<=nlstate;i++){
   }        eip=0.;
   ungetc(c,ficpar);        vip=0.;
          for(j=1; j<=nlstate;j++){
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          eip += eij[i][j][(int)age];
     for(i=1; i <=nlstate; i++)          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
     for(j=1; j <=nlstate+ndeath-1; j++){            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
       fscanf(ficpar,"%1d%1d",&i1,&j1);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
       fprintf(ficparo,"%1d%1d",i1,j1);        }
       printf("%1d%1d",i,j);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       for(k=1; k<=ncovmodel;k++){      }
         fscanf(ficpar," %lf",&param[i][j][k]);      fprintf(ficresstdeij,"\n");
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);      fprintf(ficrescveij,"%3.0f",age );
       }      for(i=1; i<=nlstate;i++)
       fscanf(ficpar,"\n");        for(j=1; j<=nlstate;j++){
       printf("\n");          cptj= (j-1)*nlstate+i;
       fprintf(ficparo,"\n");          for(i2=1; i2<=nlstate;i2++)
     }            for(j2=1; j2<=nlstate;j2++){
                cptj2= (j2-1)*nlstate+i2;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;              if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   p=param[1][1];            }
          }
   /* Reads comments: lines beginning with '#' */      fprintf(ficrescveij,"\n");
   while((c=getc(ficpar))=='#' && c!= EOF){     
     ungetc(c,ficpar);    }
     fgets(line, MAXLINE, ficpar);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     puts(line);    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     fputs(line,ficparo);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   }    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   ungetc(c,ficpar);    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    printf("\n");
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    fprintf(ficlog,"\n");
   for(i=1; i <=nlstate; i++){  
     for(j=1; j <=nlstate+ndeath-1; j++){    free_vector(xm,1,npar);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    free_vector(xp,1,npar);
       printf("%1d%1d",i,j);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       fprintf(ficparo,"%1d%1d",i1,j1);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       for(k=1; k<=ncovmodel;k++){    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
         fscanf(ficpar,"%le",&delti3[i][j][k]);  }
         printf(" %le",delti3[i][j][k]);  
         fprintf(ficparo," %le",delti3[i][j][k]);  /************ Variance ******************/
       }  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
       fscanf(ficpar,"\n");  {
       printf("\n");    /* Variance of health expectancies */
       fprintf(ficparo,"\n");    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     }    /* double **newm;*/
   }    double **dnewm,**doldm;
   delti=delti3[1][1];    double **dnewmp,**doldmp;
      int i, j, nhstepm, hstepm, h, nstepm ;
   /* Reads comments: lines beginning with '#' */    int k, cptcode;
   while((c=getc(ficpar))=='#' && c!= EOF){    double *xp;
     ungetc(c,ficpar);    double **gp, **gm;  /* for var eij */
     fgets(line, MAXLINE, ficpar);    double ***gradg, ***trgradg; /*for var eij */
     puts(line);    double **gradgp, **trgradgp; /* for var p point j */
     fputs(line,ficparo);    double *gpp, *gmp; /* for var p point j */
   }    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   ungetc(c,ficpar);    double ***p3mat;
      double age,agelim, hf;
   matcov=matrix(1,npar,1,npar);    double ***mobaverage;
   for(i=1; i <=npar; i++){    int theta;
     fscanf(ficpar,"%s",&str);    char digit[4];
     printf("%s",str);    char digitp[25];
     fprintf(ficparo,"%s",str);  
     for(j=1; j <=i; j++){    char fileresprobmorprev[FILENAMELENGTH];
       fscanf(ficpar," %le",&matcov[i][j]);  
       printf(" %.5le",matcov[i][j]);    if(popbased==1){
       fprintf(ficparo," %.5le",matcov[i][j]);      if(mobilav!=0)
     }        strcpy(digitp,"-populbased-mobilav-");
     fscanf(ficpar,"\n");      else strcpy(digitp,"-populbased-nomobil-");
     printf("\n");    }
     fprintf(ficparo,"\n");    else 
   }      strcpy(digitp,"-stablbased-");
   for(i=1; i <=npar; i++)  
     for(j=i+1;j<=npar;j++)    if (mobilav!=0) {
       matcov[i][j]=matcov[j][i];      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
          if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   printf("\n");        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     /*-------- Rewriting paramater file ----------*/    }
      strcpy(rfileres,"r");    /* "Rparameterfile */  
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/    strcpy(fileresprobmorprev,"prmorprev"); 
      strcat(rfileres,".");    /* */    sprintf(digit,"%-d",ij);
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     if((ficres =fopen(rfileres,"w"))==NULL) {    strcat(fileresprobmorprev,digit); /* Tvar to be done */
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     }    strcat(fileresprobmorprev,fileres);
     fprintf(ficres,"#%s\n",version);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
          printf("Problem with resultfile: %s\n", fileresprobmorprev);
     /*-------- data file ----------*/      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     if((fic=fopen(datafile,"r"))==NULL)    {    }
       printf("Problem with datafile: %s\n", datafile);goto end;    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     }   
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     n= lastobs;    pstamp(ficresprobmorprev);
     severity = vector(1,maxwav);    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);
     outcome=imatrix(1,maxwav+1,1,n);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     num=ivector(1,n);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     moisnais=vector(1,n);      fprintf(ficresprobmorprev," p.%-d SE",j);
     annais=vector(1,n);      for(i=1; i<=nlstate;i++)
     moisdc=vector(1,n);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     andc=vector(1,n);    }  
     agedc=vector(1,n);    fprintf(ficresprobmorprev,"\n");
     cod=ivector(1,n);    fprintf(ficgp,"\n# Routine varevsij");
     weight=vector(1,n);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    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");
     mint=matrix(1,maxwav,1,n);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     anint=matrix(1,maxwav,1,n);  /*   } */
     s=imatrix(1,maxwav+1,1,n);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     adl=imatrix(1,maxwav+1,1,n);        pstamp(ficresvij);
     tab=ivector(1,NCOVMAX);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     ncodemax=ivector(1,8);    if(popbased==1)
       fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
     i=1;    else
     while (fgets(line, MAXLINE, fic) != NULL)    {      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
       if ((i >= firstobs) && (i <=lastobs)) {    fprintf(ficresvij,"# Age");
            for(i=1; i<=nlstate;i++)
         for (j=maxwav;j>=1;j--){      for(j=1; j<=nlstate;j++)
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
           strcpy(line,stra);    fprintf(ficresvij,"\n");
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);  
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    xp=vector(1,npar);
         }    dnewm=matrix(1,nlstate,1,npar);
            doldm=matrix(1,nlstate,1,nlstate);
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
         for (j=ncovcol;j>=1;j--){    
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    if(estepm < stepm){
         }      printf ("Problem %d lower than %d\n",estepm, stepm);
         num[i]=atol(stra);    }
            else  hstepm=estepm;   
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    /* For example we decided to compute the life expectancy with the smallest unit */
           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;}*/    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
         i=i+1;       nstepm is the number of stepm from age to agelin. 
       }       Look at function hpijx to understand why (it is linked to memory size questions) */
     }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     /* printf("ii=%d", ij);       survival function given by stepm (the optimization length). Unfortunately it
        scanf("%d",i);*/       means that if the survival funtion is printed every two years of age and if
   imx=i-1; /* Number of individuals */       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
   /* for (i=1; i<=imx; i++){    */
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    agelim = AGESUP;
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     }*/      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
    /*  for (i=1; i<=imx; i++){      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
      if (s[4][i]==9)  s[4][i]=-1;      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      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]));}*/      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
        gp=matrix(0,nhstepm,1,nlstate);
        gm=matrix(0,nhstepm,1,nlstate);
   /* Calculation of the number of parameter from char model*/  
   Tvar=ivector(1,15);  
   Tprod=ivector(1,15);      for(theta=1; theta <=npar; theta++){
   Tvaraff=ivector(1,15);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   Tvard=imatrix(1,15,1,2);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   Tage=ivector(1,15);              }
            hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   if (strlen(model) >1){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     j=0, j1=0, k1=1, k2=1;  
     j=nbocc(model,'+');        if (popbased==1) {
     j1=nbocc(model,'*');          if(mobilav ==0){
     cptcovn=j+1;            for(i=1; i<=nlstate;i++)
     cptcovprod=j1;              prlim[i][i]=probs[(int)age][i][ij];
              }else{ /* mobilav */ 
     strcpy(modelsav,model);            for(i=1; i<=nlstate;i++)
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){              prlim[i][i]=mobaverage[(int)age][i][ij];
       printf("Error. Non available option model=%s ",model);          }
       goto end;        }
     }    
            for(j=1; j<= nlstate; j++){
     for(i=(j+1); i>=1;i--){          for(h=0; h<=nhstepm; h++){
       cutv(stra,strb,modelsav,'+');            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          }
       /*scanf("%d",i);*/        }
       if (strchr(strb,'*')) {        /* This for computing probability of death (h=1 means
         cutv(strd,strc,strb,'*');           computed over hstepm matrices product = hstepm*stepm months) 
         if (strcmp(strc,"age")==0) {           as a weighted average of prlim.
           cptcovprod--;        */
           cutv(strb,stre,strd,'V');        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           Tvar[i]=atoi(stre);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
           cptcovage++;            gpp[j] += prlim[i][i]*p3mat[i][j][1];
             Tage[cptcovage]=i;        }    
             /*printf("stre=%s ", stre);*/        /* end probability of death */
         }  
         else if (strcmp(strd,"age")==0) {        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           cptcovprod--;          xp[i] = x[i] - (i==theta ?delti[theta]:0);
           cutv(strb,stre,strc,'V');        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
           Tvar[i]=atoi(stre);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           cptcovage++;   
           Tage[cptcovage]=i;        if (popbased==1) {
         }          if(mobilav ==0){
         else {            for(i=1; i<=nlstate;i++)
           cutv(strb,stre,strc,'V');              prlim[i][i]=probs[(int)age][i][ij];
           Tvar[i]=ncovcol+k1;          }else{ /* mobilav */ 
           cutv(strb,strc,strd,'V');            for(i=1; i<=nlstate;i++)
           Tprod[k1]=i;              prlim[i][i]=mobaverage[(int)age][i][ij];
           Tvard[k1][1]=atoi(strc);          }
           Tvard[k1][2]=atoi(stre);        }
           Tvar[cptcovn+k2]=Tvard[k1][1];  
           Tvar[cptcovn+k2+1]=Tvard[k1][2];        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
           for (k=1; k<=lastobs;k++)          for(h=0; h<=nhstepm; h++){
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
           k1++;              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           k2=k2+2;          }
         }        }
       }        /* This for computing probability of death (h=1 means
       else {           computed over hstepm matrices product = hstepm*stepm months) 
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/           as a weighted average of prlim.
        /*  scanf("%d",i);*/        */
       cutv(strd,strc,strb,'V');        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       Tvar[i]=atoi(strc);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
       }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
       strcpy(modelsav,stra);          }    
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        /* end probability of death */
         scanf("%d",i);*/  
     }        for(j=1; j<= nlstate; j++) /* vareij */
 }          for(h=0; h<=nhstepm; h++){
              gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   /* 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);*/        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     fclose(fic);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
     /*  if(mle==1){*/  
     if (weightopt != 1) { /* Maximisation without weights*/      } /* End theta */
       for(i=1;i<=n;i++) weight[i]=1.0;  
     }      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     /*-calculation of age at interview from date of interview and age at death -*/  
     agev=matrix(1,maxwav,1,imx);      for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
     for (i=1; i<=imx; i++) {          for(theta=1; theta <=npar; theta++)
       for(m=2; (m<= maxwav); m++) {            trgradg[h][j][theta]=gradg[h][theta][j];
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){  
          anint[m][i]=9999;      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
          s[m][i]=-1;        for(theta=1; theta <=npar; theta++)
        }          trgradgp[j][theta]=gradgp[theta][j];
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;    
       }  
     }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
     for (i=1; i<=imx; i++)  {        for(j=1;j<=nlstate;j++)
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          vareij[i][j][(int)age] =0.;
       for(m=1; (m<= maxwav); m++){  
         if(s[m][i] >0){      for(h=0;h<=nhstepm;h++){
           if (s[m][i] >= nlstate+1) {        for(k=0;k<=nhstepm;k++){
             if(agedc[i]>0)          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
               if(moisdc[i]!=99 && andc[i]!=9999)          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
                 agev[m][i]=agedc[i];          for(i=1;i<=nlstate;i++)
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/            for(j=1;j<=nlstate;j++)
            else {              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
               if (andc[i]!=9999){        }
               printf("Warning negative age at death: %d line:%d\n",num[i],i);      }
               agev[m][i]=-1;    
               }      /* pptj */
             }      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
           }      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
           else if(s[m][i] !=9){ /* Should no more exist */      for(j=nlstate+1;j<=nlstate+ndeath;j++)
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
             if(mint[m][i]==99 || anint[m][i]==9999)          varppt[j][i]=doldmp[j][i];
               agev[m][i]=1;      /* end ppptj */
             else if(agev[m][i] <agemin){      /*  x centered again */
               agemin=agev[m][i];      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
             }   
             else if(agev[m][i] >agemax){      if (popbased==1) {
               agemax=agev[m][i];        if(mobilav ==0){
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/          for(i=1; i<=nlstate;i++)
             }            prlim[i][i]=probs[(int)age][i][ij];
             /*agev[m][i]=anint[m][i]-annais[i];*/        }else{ /* mobilav */ 
             /*   agev[m][i] = age[i]+2*m;*/          for(i=1; i<=nlstate;i++)
           }            prlim[i][i]=mobaverage[(int)age][i][ij];
           else { /* =9 */        }
             agev[m][i]=1;      }
             s[m][i]=-1;               
           }      /* This for computing probability of death (h=1 means
         }         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
         else /*= 0 Unknown */         as a weighted average of prlim.
           agev[m][i]=1;      */
       }      for(j=nlstate+1;j<=nlstate+ndeath;j++){
            for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     }          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
     for (i=1; i<=imx; i++)  {      }    
       for(m=1; (m<= maxwav); m++){      /* end probability of death */
         if (s[m][i] > (nlstate+ndeath)) {  
           printf("Error: Wrong value in nlstate or ndeath\n");        fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
           goto end;      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         }        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
       }        for(i=1; i<=nlstate;i++){
     }          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      } 
       fprintf(ficresprobmorprev,"\n");
     free_vector(severity,1,maxwav);  
     free_imatrix(outcome,1,maxwav+1,1,n);      fprintf(ficresvij,"%.0f ",age );
     free_vector(moisnais,1,n);      for(i=1; i<=nlstate;i++)
     free_vector(annais,1,n);        for(j=1; j<=nlstate;j++){
     /* free_matrix(mint,1,maxwav,1,n);          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
        free_matrix(anint,1,maxwav,1,n);*/        }
     free_vector(moisdc,1,n);      fprintf(ficresvij,"\n");
     free_vector(andc,1,n);      free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
          free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
     wav=ivector(1,imx);      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    } /* End age */
        free_vector(gpp,nlstate+1,nlstate+ndeath);
     /* Concatenates waves */    free_vector(gmp,nlstate+1,nlstate+ndeath);
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
       Tcode=ivector(1,100);    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
       ncodemax[1]=1;  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);  /*   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); */
    codtab=imatrix(1,100,1,10);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
    h=0;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
    m=pow(2,cptcoveff);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
      fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
    for(k=1;k<=cptcoveff; k++){    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
      for(i=1; i <=(m/pow(2,k));i++){    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
        for(j=1; j <= ncodemax[k]; j++){  */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
            h++;    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
            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 \n",h, k,j,codtab[h][k],Tvar[k]);*/    free_vector(xp,1,npar);
          }    free_matrix(doldm,1,nlstate,1,nlstate);
        }    free_matrix(dnewm,1,nlstate,1,npar);
      }    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
    }    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       codtab[1][2]=1;codtab[2][2]=2; */    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
    /* for(i=1; i <=m ;i++){    fclose(ficresprobmorprev);
       for(k=1; k <=cptcovn; k++){    fflush(ficgp);
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    fflush(fichtm); 
       }  }  /* end varevsij */
       printf("\n");  
       }  /************ Variance of prevlim ******************/
       scanf("%d",i);*/  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[])
      {
    /* Calculates basic frequencies. Computes observed prevalence at single age    /* Variance of prevalence limit */
        and prints on file fileres'p'. */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
        double **dnewm,**doldm;
        int i, j, nhstepm, hstepm;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    int k, cptcode;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double *xp;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double *gp, *gm;
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **gradg, **trgradg;
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    double age,agelim;
          int theta;
     /* 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] */    pstamp(ficresvpl);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     if(mle==1){    for(i=1; i<=nlstate;i++)
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);        fprintf(ficresvpl," %1d-%1d",i,i);
     }    fprintf(ficresvpl,"\n");
      
     /*--------- results files --------------*/    xp=vector(1,npar);
     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);    dnewm=matrix(1,nlstate,1,npar);
      doldm=matrix(1,nlstate,1,nlstate);
     
    jk=1;    hstepm=1*YEARM; /* Every year of age */
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    agelim = AGESUP;
    for(i=1,jk=1; i <=nlstate; i++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      for(k=1; k <=(nlstate+ndeath); k++){      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
        if (k != i)      if (stepm >= YEARM) hstepm=1;
          {      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
            printf("%d%d ",i,k);      gradg=matrix(1,npar,1,nlstate);
            fprintf(ficres,"%1d%1d ",i,k);      gp=vector(1,nlstate);
            for(j=1; j <=ncovmodel; j++){      gm=vector(1,nlstate);
              printf("%f ",p[jk]);  
              fprintf(ficres,"%f ",p[jk]);      for(theta=1; theta <=npar; theta++){
              jk++;        for(i=1; i<=npar; i++){ /* Computes gradient */
            }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
            printf("\n");        }
            fprintf(ficres,"\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
          }        for(i=1;i<=nlstate;i++)
      }          gp[i] = prlim[i][i];
    }      
  if(mle==1){        for(i=1; i<=npar; i++) /* Computes gradient */
     /* Computing hessian and covariance matrix */          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     ftolhess=ftol; /* Usually correct */        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     hesscov(matcov, p, npar, delti, ftolhess, func);        for(i=1;i<=nlstate;i++)
  }          gm[i] = prlim[i][i];
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");  
     printf("# Scales (for hessian or gradient estimation)\n");        for(i=1;i<=nlstate;i++)
      for(i=1,jk=1; i <=nlstate; i++){          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       for(j=1; j <=nlstate+ndeath; j++){      } /* End theta */
         if (j!=i) {  
           fprintf(ficres,"%1d%1d",i,j);      trgradg =matrix(1,nlstate,1,npar);
           printf("%1d%1d",i,j);  
           for(k=1; k<=ncovmodel;k++){      for(j=1; j<=nlstate;j++)
             printf(" %.5e",delti[jk]);        for(theta=1; theta <=npar; theta++)
             fprintf(ficres," %.5e",delti[jk]);          trgradg[j][theta]=gradg[theta][j];
             jk++;  
           }      for(i=1;i<=nlstate;i++)
           printf("\n");        varpl[i][(int)age] =0.;
           fprintf(ficres,"\n");      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
         }      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       }      for(i=1;i<=nlstate;i++)
      }        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
      
     k=1;      fprintf(ficresvpl,"%.0f ",age );
     fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");      for(i=1; i<=nlstate;i++)
     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(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     for(i=1;i<=npar;i++){      fprintf(ficresvpl,"\n");
       /*  if (k>nlstate) k=1;      free_vector(gp,1,nlstate);
       i1=(i-1)/(ncovmodel*nlstate)+1;      free_vector(gm,1,nlstate);
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);      free_matrix(gradg,1,npar,1,nlstate);
       printf("%s%d%d",alph[k],i1,tab[i]);*/      free_matrix(trgradg,1,nlstate,1,npar);
       fprintf(ficres,"%3d",i);    } /* End age */
       printf("%3d",i);  
       for(j=1; j<=i;j++){    free_vector(xp,1,npar);
         fprintf(ficres," %.5e",matcov[i][j]);    free_matrix(doldm,1,nlstate,1,npar);
         printf(" %.5e",matcov[i][j]);    free_matrix(dnewm,1,nlstate,1,nlstate);
       }  
       fprintf(ficres,"\n");  }
       printf("\n");  
       k++;  /************ 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[])
      {
     while((c=getc(ficpar))=='#' && c!= EOF){    int i, j=0,  i1, k1, l1, t, tj;
       ungetc(c,ficpar);    int k2, l2, j1,  z1;
       fgets(line, MAXLINE, ficpar);    int k=0,l, cptcode;
       puts(line);    int first=1, first1;
       fputs(line,ficparo);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     }    double **dnewm,**doldm;
     ungetc(c,ficpar);    double *xp;
     estepm=0;    double *gp, *gm;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    double **gradg, **trgradg;
     if (estepm==0 || estepm < stepm) estepm=stepm;    double **mu;
     if (fage <= 2) {    double age,agelim, cov[NCOVMAX];
       bage = ageminpar;    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
       fage = agemaxpar;    int theta;
     }    char fileresprob[FILENAMELENGTH];
        char fileresprobcov[FILENAMELENGTH];
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    char fileresprobcor[FILENAMELENGTH];
     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);    double ***varpij;
    
     while((c=getc(ficpar))=='#' && c!= EOF){    strcpy(fileresprob,"prob"); 
     ungetc(c,ficpar);    strcat(fileresprob,fileres);
     fgets(line, MAXLINE, ficpar);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     puts(line);      printf("Problem with resultfile: %s\n", fileresprob);
     fputs(line,ficparo);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
   }    }
   ungetc(c,ficpar);    strcpy(fileresprobcov,"probcov"); 
      strcat(fileresprobcov,fileres);
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      printf("Problem with resultfile: %s\n", fileresprobcov);
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
          }
   while((c=getc(ficpar))=='#' && c!= EOF){    strcpy(fileresprobcor,"probcor"); 
     ungetc(c,ficpar);    strcat(fileresprobcor,fileres);
     fgets(line, MAXLINE, ficpar);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
     puts(line);      printf("Problem with resultfile: %s\n", fileresprobcor);
     fputs(line,ficparo);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   }    }
   ungetc(c,ficpar);    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
      fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   fscanf(ficpar,"pop_based=%d\n",&popbased);    pstamp(ficresprob);
   fprintf(ficparo,"pop_based=%d\n",popbased);      fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   fprintf(ficres,"pop_based=%d\n",popbased);      fprintf(ficresprob,"# Age");
      pstamp(ficresprobcov);
   while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     ungetc(c,ficpar);    fprintf(ficresprobcov,"# Age");
     fgets(line, MAXLINE, ficpar);    pstamp(ficresprobcor);
     puts(line);    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fputs(line,ficparo);    fprintf(ficresprobcor,"# Age");
   }  
   ungetc(c,ficpar);  
     for(i=1; i<=nlstate;i++)
   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);      for(j=1; j<=(nlstate+ndeath);j++){
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
 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(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
 while((c=getc(ficpar))=='#' && c!= EOF){   /* fprintf(ficresprob,"\n");
     ungetc(c,ficpar);    fprintf(ficresprobcov,"\n");
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprobcor,"\n");
     puts(line);   */
     fputs(line,ficparo);    xp=vector(1,npar);
   }    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   ungetc(c,ficpar);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    first=1;
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    fprintf(fichtm,"\n");
   
 /*------------ gnuplot -------------*/    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
   strcpy(optionfilegnuplot,optionfilefiname);    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
   strcat(optionfilegnuplot,".gp");    file %s<br>\n",optionfilehtmcov);
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
     printf("Problem with file %s",optionfilegnuplot);  and drawn. It helps understanding how is the covariance between two incidences.\
   }   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
   fclose(ficgp);    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. \
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
 /*--------- index.htm --------*/  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>\
   strcpy(optionfilehtm,optionfile);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
   strcat(optionfilehtm,".htm");   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
     printf("Problem with %s \n",optionfilehtm), exit(0);  
   }    cov[1]=1;
     tj=cptcoveff;
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n    j1=0;
 \n    for(t=1; t<=tj;t++){
 Total number of observations=%d <br>\n      for(i1=1; i1<=ncodemax[t];i1++){ 
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n        j1++;
 <hr  size=\"2\" color=\"#EC5E5E\">        if  (cptcovn>0) {
  <ul><li>Parameter files<br>\n          fprintf(ficresprob, "\n#********** Variable "); 
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  - 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);          fprintf(ficresprob, "**********\n#\n");
   fclose(fichtm);          fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);          fprintf(ficresprobcov, "**********\n#\n");
            
 /*------------ free_vector  -------------*/          fprintf(ficgp, "\n#********** Variable "); 
  chdir(path);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficgp, "**********\n#\n");
  free_ivector(wav,1,imx);          
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);          
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);            fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
  free_ivector(num,1,n);          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  free_vector(agedc,1,n);          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          
  fclose(ficparo);          fprintf(ficresprobcor, "\n#********** Variable ");    
  fclose(ficres);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
   /*--------------- Prevalence limit --------------*/        
          for (age=bage; age<=fage; age ++){ 
   strcpy(filerespl,"pl");          cov[2]=age;
   strcat(filerespl,fileres);          for (k=1; k<=cptcovn;k++) {
   if((ficrespl=fopen(filerespl,"w"))==NULL) {            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;          }
   }          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          for (k=1; k<=cptcovprod;k++)
   fprintf(ficrespl,"#Prevalence limit\n");            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   fprintf(ficrespl,"#Age ");          
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   fprintf(ficrespl,"\n");          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
            gp=vector(1,(nlstate)*(nlstate+ndeath));
   prlim=matrix(1,nlstate,1,nlstate);          gm=vector(1,(nlstate)*(nlstate+ndeath));
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(theta=1; theta <=npar; theta++){
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for(i=1; i<=npar; i++)
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            
   k=0;            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   agebase=ageminpar;            
   agelim=agemaxpar;            k=0;
   ftolpl=1.e-10;            for(i=1; i<= (nlstate); i++){
   i1=cptcoveff;              for(j=1; j<=(nlstate+ndeath);j++){
   if (cptcovn < 1){i1=1;}                k=k+1;
                 gp[k]=pmmij[i][j];
   for(cptcov=1;cptcov<=i1;cptcov++){              }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            }
         k=k+1;            
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/            for(i=1; i<=npar; i++)
         fprintf(ficrespl,"\n#******");              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
         for(j=1;j<=cptcoveff;j++)      
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
         fprintf(ficrespl,"******\n");            k=0;
                    for(i=1; i<=(nlstate); i++){
         for (age=agebase; age<=agelim; age++){              for(j=1; j<=(nlstate+ndeath);j++){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                k=k+1;
           fprintf(ficrespl,"%.0f",age );                gm[k]=pmmij[i][j];
           for(i=1; i<=nlstate;i++)              }
           fprintf(ficrespl," %.5f", prlim[i][i]);            }
           fprintf(ficrespl,"\n");       
         }            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
       }              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
     }          }
   fclose(ficrespl);  
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   /*------------- h Pij x at various ages ------------*/            for(theta=1; theta <=npar; theta++)
                trgradg[j][theta]=gradg[theta][j];
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);          
   if((ficrespij=fopen(filerespij,"w"))==NULL) {          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
   }          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
   printf("Computing pij: result on file '%s' \n", filerespij);          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
            free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   stepsize=(int) (stepm+YEARM-1)/YEARM;          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   /*if (stepm<=24) stepsize=2;*/  
           pmij(pmmij,cov,ncovmodel,x,nlstate);
   agelim=AGESUP;          
   hstepm=stepsize*YEARM; /* Every year of age */          k=0;
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */          for(i=1; i<=(nlstate); i++){
              for(j=1; j<=(nlstate+ndeath);j++){
   k=0;              k=k+1;
   for(cptcov=1;cptcov<=i1;cptcov++){              mu[k][(int) age]=pmmij[i][j];
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            }
       k=k+1;          }
         fprintf(ficrespij,"\n#****** ");          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
         for(j=1;j<=cptcoveff;j++)            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              varpij[i][j][(int)age] = doldm[i][j];
         fprintf(ficrespij,"******\n");  
                  /*printf("\n%d ",(int)age);
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           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(ficresprob,"\n%d ",(int)age);
           fprintf(ficrespij,"# Age");          fprintf(ficresprobcov,"\n%d ",(int)age);
           for(i=1; i<=nlstate;i++)          fprintf(ficresprobcor,"\n%d ",(int)age);
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
           fprintf(ficrespij,"\n");            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
            for (h=0; h<=nhstepm; h++){          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             for(i=1; i<=nlstate;i++)            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
               for(j=1; j<=nlstate+ndeath;j++)          }
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          i=0;
             fprintf(ficrespij,"\n");          for (k=1; k<=(nlstate);k++){
              }            for (l=1; l<=(nlstate+ndeath);l++){ 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              i=i++;
           fprintf(ficrespij,"\n");              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
         }              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
     }              for (j=1; j<=i;j++){
   }                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);              }
             }
   fclose(ficrespij);          }/* end of loop for state */
         } /* end of loop for age */
   
   /*---------- Forecasting ------------------*/        /* Confidence intervalle of pij  */
   if((stepm == 1) && (strcmp(model,".")==0)){        /*
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);          fprintf(ficgp,"\nunset parametric;unset label");
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);          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");
   else{          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);
     erreur=108;          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
     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(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   }          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
          */
   
   /*---------- Health expectancies and variances ------------*/        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
   strcpy(filerest,"t");        for (k2=1; k2<=(nlstate);k2++){
   strcat(filerest,fileres);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
   if((ficrest=fopen(filerest,"w"))==NULL) {            if(l2==k2) continue;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;            j=(k2-1)*(nlstate+ndeath)+l2;
   }            for (k1=1; k1<=(nlstate);k1++){
   printf("Computing Total LEs with variances: file '%s' \n", filerest);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
   strcpy(filerese,"e");                if(i<=j) continue;
   strcat(filerese,fileres);                for (age=bage; age<=fage; age ++){ 
   if((ficreseij=fopen(filerese,"w"))==NULL) {                  if ((int)age %5==0){
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
   }                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
  strcpy(fileresv,"v");                    mu2=mu[j][(int) age]/stepm*YEARM;
   strcat(fileresv,fileres);                    c12=cv12/sqrt(v1*v2);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {                    /* Computing eigen value of matrix of covariance */
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   }                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);                    if ((lc2 <0) || (lc1 <0) ){
   calagedate=-1;                      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);
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);                      fprintf(ficlog,"Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e\n", lc1, lc2, v1, v2, cv12);fflush(ficlog);
                       lc1=fabs(lc1);
   k=0;                      lc2=fabs(lc2);
   for(cptcov=1;cptcov<=i1;cptcov++){                    }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;                    /* Eigen vectors */
       fprintf(ficrest,"\n#****** ");                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       for(j=1;j<=cptcoveff;j++)                    /*v21=sqrt(1.-v11*v11); *//* error */
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    v21=(lc1-v1)/cv12*v11;
       fprintf(ficrest,"******\n");                    v12=-v21;
                     v22=v11;
       fprintf(ficreseij,"\n#****** ");                    tnalp=v21/v11;
       for(j=1;j<=cptcoveff;j++)                    if(first1==1){
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      first1=0;
       fprintf(ficreseij,"******\n");                      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(ficresvij,"\n#****** ");                    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(j=1;j<=cptcoveff;j++)                    /*printf(fignu*/
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
       fprintf(ficresvij,"******\n");                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                      first=0;
       oldm=oldms;savm=savms;                      fprintf(ficgp,"\nset parametric;unset label");
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);                        fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
       oldm=oldms;savm=savms;   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                                  subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                        fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
       fprintf(ficrest,"\n");                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
       epj=vector(1,nlstate+1);                      fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
       for(age=bage; age <=fage ;age++){                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
         if (popbased==1) {                    }else{
           for(i=1; i<=nlstate;i++)                      first=0;
             prlim[i][i]=probs[(int)age][i][k];                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
         }                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                              fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
         fprintf(ficrest," %4.0f",age);                      fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
             epj[j] += prlim[i][i]*eij[i][j][(int)age];                    }/* if first */
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/                  } /* age mod 5 */
           }                } /* end loop age */
           epj[nlstate+1] +=epj[j];                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         }                first=1;
               } /*l12 */
         for(i=1, vepp=0.;i <=nlstate;i++)            } /* k12 */
           for(j=1;j <=nlstate;j++)          } /*l1 */
             vepp += vareij[i][j][(int)age];        }/* k1 */
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));      } /* loop covariates */
         for(j=1;j <=nlstate;j++){    }
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
         }    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
         fprintf(ficrest,"\n");    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
       }    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     }    free_vector(xp,1,npar);
   }    fclose(ficresprob);
 free_matrix(mint,1,maxwav,1,n);    fclose(ficresprobcov);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    fclose(ficresprobcor);
     free_vector(weight,1,n);    fflush(ficgp);
   fclose(ficreseij);    fflush(fichtmcov);
   fclose(ficresvij);  }
   fclose(ficrest);  
   fclose(ficpar);  
   free_vector(epj,1,nlstate+1);  /******************* Printing html file ***********/
    void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
   /*------- Variance limit prevalence------*/                      int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
   strcpy(fileresvpl,"vpl");                    int popforecast, int estepm ,\
   strcat(fileresvpl,fileres);                    double jprev1, double mprev1,double anprev1, \
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {                    double jprev2, double mprev2,double anprev2){
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    int jj1, k1, i1, cpt;
     exit(0);  
   }     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
   k=0;     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
   for(cptcov=1;cptcov<=i1;cptcov++){   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
       k=k+1;     fprintf(fichtm,"\
       fprintf(ficresvpl,"\n#****** ");   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
       for(j=1;j<=cptcoveff;j++)             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     fprintf(fichtm,"\
       fprintf(ficresvpl,"******\n");   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
                   subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
       varpl=matrix(1,nlstate,(int) bage, (int) fage);     fprintf(fichtm,"\
       oldm=oldms;savm=savms;   - (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): \
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);     <a href=\"%s\">%s</a> <br>\n",
     }             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
  }     fprintf(fichtm,"\
    - Population projections by age and states: \
   fclose(ficresvpl);     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   /*---------- End : free ----------------*/  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);  
     m=cptcoveff;
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
     jj1=0;
     for(k1=1; k1<=m;k1++){
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);     for(i1=1; i1<=ncodemax[k1];i1++){
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);       jj1++;
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);       if (cptcovn > 0) {
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
           for (cpt=1; cpt<=cptcoveff;cpt++) 
   free_matrix(matcov,1,npar,1,npar);           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   free_vector(delti,1,npar);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
   free_matrix(agev,1,maxwav,1,imx);       }
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);       /* 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> \
   fprintf(fichtm,"\n</body>");  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
   fclose(fichtm);       /* Quasi-incidences */
   fclose(ficgp);       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
     before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
   if(erreur >0)         /* Period (stable) prevalence in each health state */
     printf("End of Imach with error or warning %d\n",erreur);         for(cpt=1; cpt<nlstate;cpt++){
   else   printf("End of Imach\n");           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
           }
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/       for(cpt=1; cpt<=nlstate;cpt++) {
   /*printf("Total time was %d uSec.\n", total_usecs);*/          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> \
   /*------ End -----------*/  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
  end:   }/* End k1 */
 #ifdef windows   fprintf(fichtm,"</ul>");
   /* chdir(pathcd);*/  
 #endif  
  /*system("wgnuplot graph.plt");*/   fprintf(fichtm,"\
  /*system("../gp37mgw/wgnuplot graph.plt");*/  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
  /*system("cd ../gp37mgw");*/   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/  
  strcpy(plotcmd,GNUPLOTPROGRAM);   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
  strcat(plotcmd," ");           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
  strcat(plotcmd,optionfilegnuplot);   fprintf(fichtm,"\
  system(plotcmd);   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
 #ifdef windows  
   while (z[0] != 'q') {   fprintf(fichtm,"\
     /* chdir(path); */   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
     scanf("%s",z);   fprintf(fichtm,"\
     if (z[0] == 'c') system("./imach");   - 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): \
     else if (z[0] == 'e') system(optionfilehtm);     <a href=\"%s\">%s</a> <br>\n</li>",
     else if (z[0] == 'g') system(plotcmd);             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
     else if (z[0] == 'q') exit(0);   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): \
 #endif     <a href=\"%s\">%s</a> <br>\n</li>",
 }             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else        fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; /* Number of covariates V1+V2*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(k=cptcovn; k>=1;k--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 
                                       */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=2 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1]=atoi(strc); /* m 1 for V1*/
             Tvard[k1][2]=atoi(stre); /* n 4 for V4*/
             Tvar[cptcovn+k2]=Tvard[k1][1]; /* Tvar[(cptcovn=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovn+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovn=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
             k1++;
             k2=k2+2;
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[k]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8); /* hard coded ? */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,15); 
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2); /* For V3*V2 Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,15); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) {
               h=1;
               codtab[h][k]=j;
               codtab[h][Tvar[k]]=j;
             }
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
    endfree:
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.48  
changed lines
  Added in v.1.139


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